TSTP Solution File: LCL109-6 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:49:36 EDT 2022
% Result : Unsatisfiable 194.10s 194.28s
% Output : CNFRefutation 194.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 91
% Number of leaves : 255
% Syntax : Number of clauses : 1037 ( 524 unt; 0 nHn; 526 RR)
% Number of literals : 1781 (1780 equ; 747 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 2148 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
not(X) = xor(X,truth) ).
cnf(axiom_2,axiom,
xor(X,falsehood) = X ).
cnf(axiom_4,axiom,
and_star(X,truth) = X ).
cnf(axiom_5,axiom,
and_star(X,falsehood) = falsehood ).
cnf(axiom_6,axiom,
and_star(xor(truth,X),X) = falsehood ).
cnf(axiom_7,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ).
cnf(axiom_8,axiom,
and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ).
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(and_star_associativity,axiom,
and_star(and_star(X,Y),Z) = and_star(X,and_star(Y,Z)) ).
cnf(and_star_commutativity,axiom,
and_star(X,Y) = and_star(Y,X) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(implies_definition,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != 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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( not(X) != xor(X,truth)
| xor(X,truth) = not(X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X))),bind(Y0,$fot(xor(X,truth)))]]) ).
cnf(refute_0_4,plain,
xor(X,truth) = not(X),
inference(resolve,[$cnf( $equal(not(X),xor(X,truth)) )],[axiom_1,refute_0_3]) ).
cnf(refute_0_5,plain,
xor(xor(X,truth),Y) = xor(xor(X,truth),Y),
introduced(tautology,[refl,[$fot(xor(xor(X,truth),Y))]]) ).
cnf(refute_0_6,plain,
( xor(X,truth) != not(X)
| xor(xor(X,truth),Y) != xor(xor(X,truth),Y)
| xor(xor(X,truth),Y) = xor(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_7,plain,
( xor(X,truth) != not(X)
| xor(xor(X,truth),Y) = xor(not(X),Y) ),
inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
xor(xor(X,truth),Y) = xor(not(X),Y),
inference(resolve,[$cnf( $equal(xor(X,truth),not(X)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
| xor(xor(X,truth),Y) != xor(not(X),Y)
| xor(X,xor(truth,Y)) = xor(not(X),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X,xor(truth,Y)),xor(not(X),Y)) ),[0],$fot(xor(xor(X,truth),Y))]]) ).
cnf(refute_0_10,plain,
( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
| xor(X,xor(truth,Y)) = xor(not(X),Y) ),
inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(not(X),Y)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
xor(X,xor(truth,Y)) = xor(not(X),Y),
inference(resolve,[$cnf( $equal(xor(X,xor(truth,Y)),xor(xor(X,truth),Y)) )],[axiom_7,refute_0_10]) ).
cnf(refute_0_12,plain,
xor(X_6,xor(truth,truth)) = xor(not(X_6),truth),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_6)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_13,plain,
not(not(X_6)) = xor(not(X_6),truth),
inference(subst,[],[axiom_1:[bind(X,$fot(not(X_6)))]]) ).
cnf(refute_0_14,plain,
( not(not(X_6)) != xor(not(X_6),truth)
| xor(not(X_6),truth) = not(not(X_6)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(not(X_6)))),bind(Y0,$fot(xor(not(X_6),truth)))]]) ).
cnf(refute_0_15,plain,
xor(not(X_6),truth) = not(not(X_6)),
inference(resolve,[$cnf( $equal(not(not(X_6)),xor(not(X_6),truth)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(not(X_6),truth) != not(not(X_6))
| xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).
cnf(refute_0_17,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),not(not(X_6))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
xor(X_6,xor(truth,truth)) = not(not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
not(truth) = xor(truth,truth),
inference(subst,[],[axiom_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_20,plain,
( not(truth) != xor(truth,truth)
| xor(truth,truth) = not(truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(truth))),bind(Y0,$fot(xor(truth,truth)))]]) ).
cnf(refute_0_21,plain,
xor(truth,truth) = not(truth),
inference(resolve,[$cnf( $equal(not(truth),xor(truth,truth)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(truth,truth) != not(truth)
| xor(X_6,not(truth)) = xor(not(X_6),truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) ),[0,1],$fot(not(truth))]]) ).
cnf(refute_0_23,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(X_6,not(truth)) = xor(not(X_6),truth) ),
inference(resolve,[$cnf( $equal(xor(truth,truth),not(truth)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
xor(X_6,not(truth)) = xor(not(X_6),truth),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_23]) ).
cnf(refute_0_25,plain,
xor(X_6,falsehood) = X_6,
inference(subst,[],[axiom_2:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_26,plain,
xor(X_6,not(truth)) = xor(X_6,not(truth)),
introduced(tautology,[refl,[$fot(xor(X_6,not(truth)))]]) ).
cnf(refute_0_27,plain,
( not(truth) != falsehood
| xor(X_6,not(truth)) != xor(X_6,not(truth))
| xor(X_6,not(truth)) = xor(X_6,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_28,plain,
( not(truth) != falsehood
| xor(X_6,not(truth)) = xor(X_6,falsehood) ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
xor(X_6,not(truth)) = xor(X_6,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_28]) ).
cnf(refute_0_30,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_31,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_30]) ).
cnf(refute_0_32,plain,
( xor(X_6,falsehood) != X_6
| xor(X_6,not(truth)) != xor(X_6,falsehood)
| xor(X_6,not(truth)) = X_6 ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(X_6,not(truth)))),bind(Y0,$fot(xor(X_6,falsehood))),bind(Z0,$fot(X_6))]]) ).
cnf(refute_0_33,plain,
( xor(X_6,falsehood) != X_6
| xor(X_6,not(truth)) = X_6 ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,falsehood)) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
xor(X_6,not(truth)) = X_6,
inference(resolve,[$cnf( $equal(xor(X_6,falsehood),X_6) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
( xor(X_6,not(truth)) != X_6
| xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(not(X_6),truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) ),[0],$fot(X_6)]]) ).
cnf(refute_0_36,plain,
( xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(not(X_6),truth) ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),X_6) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( xor(X,Y) != xor(Y,X)
| xor(Y,X) = xor(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).
cnf(refute_0_38,plain,
xor(Y,X) = xor(X,Y),
inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_37]) ).
cnf(refute_0_39,plain,
xor(not(X_6),truth) = xor(truth,not(X_6)),
inference(subst,[],[refute_0_38:[bind(X,$fot(truth)),bind(Y,$fot(not(X_6)))]]) ).
cnf(refute_0_40,plain,
( X_6 != xor(not(X_6),truth)
| xor(not(X_6),truth) != xor(truth,not(X_6))
| X_6 = xor(truth,not(X_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_6,xor(truth,not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).
cnf(refute_0_41,plain,
( X_6 != xor(not(X_6),truth)
| X_6 = xor(truth,not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(truth,not(X_6)) ),
inference(resolve,[$cnf( $equal(X_6,xor(not(X_6),truth)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
X_6 = xor(truth,not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) )],[refute_0_24,refute_0_42]) ).
cnf(refute_0_44,plain,
( X_6 != xor(truth,not(X_6))
| xor(truth,not(X_6)) = X_6 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(xor(truth,not(X_6))))]]) ).
cnf(refute_0_45,plain,
xor(truth,not(X_6)) = X_6,
inference(resolve,[$cnf( $equal(X_6,xor(truth,not(X_6))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( xor(not(X_6),truth) != xor(truth,not(X_6))
| xor(truth,not(X_6)) != X_6
| xor(not(X_6),truth) = X_6 ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(not(X_6),truth))),bind(Y0,$fot(xor(truth,not(X_6)))),bind(Z0,$fot(X_6))]]) ).
cnf(refute_0_47,plain,
( xor(truth,not(X_6)) != X_6
| xor(not(X_6),truth) = X_6 ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
xor(not(X_6),truth) = X_6,
inference(resolve,[$cnf( $equal(xor(truth,not(X_6)),X_6) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(not(X_6),truth) != X_6
| xor(X_6,xor(truth,truth)) = X_6 ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(X_6,xor(truth,truth)))),bind(Y0,$fot(xor(not(X_6),truth))),bind(Z0,$fot(X_6))]]) ).
cnf(refute_0_50,plain,
( xor(not(X_6),truth) != X_6
| xor(X_6,xor(truth,truth)) = X_6 ),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_49]) ).
cnf(refute_0_51,plain,
xor(X_6,xor(truth,truth)) = X_6,
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),X_6) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
( xor(X_6,xor(truth,truth)) != X_6
| xor(X_6,xor(truth,truth)) != not(not(X_6))
| X_6 = not(not(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(X_6)]]) ).
cnf(refute_0_53,plain,
( xor(X_6,xor(truth,truth)) != not(not(X_6))
| X_6 = not(not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),X_6) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
X_6 = not(not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) )],[refute_0_18,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(X_73,implies(X_72,X_71)) = not(not(implies(X_73,implies(X_72,X_71)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_73,implies(X_72,X_71))))]]) ).
cnf(refute_0_56,plain,
and_star(and_star(not(X_28),X_40),X_41) = and_star(not(X_28),and_star(X_40,X_41)),
inference(subst,[],[and_star_associativity:[bind(X,$fot(not(X_28))),bind(Y,$fot(X_40)),bind(Z,$fot(X_41))]]) ).
cnf(refute_0_57,plain,
and_star(not(X_28),Y) = and_star(Y,not(X_28)),
inference(subst,[],[and_star_commutativity:[bind(X,$fot(not(X_28)))]]) ).
cnf(refute_0_58,plain,
and_star(X_17,not(X_18)) = not(not(and_star(X_17,not(X_18)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(and_star(X_17,not(X_18))))]]) ).
cnf(refute_0_59,plain,
not(X_6) = xor(truth,not(not(X_6))),
inference(subst,[],[refute_0_43:[bind(X_6,$fot(not(X_6)))]]) ).
cnf(refute_0_60,plain,
( X_6 != not(not(X_6))
| not(not(X_6)) = X_6 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(not(not(X_6))))]]) ).
cnf(refute_0_61,plain,
not(not(X_6)) = X_6,
inference(resolve,[$cnf( $equal(X_6,not(not(X_6))) )],[refute_0_54,refute_0_60]) ).
cnf(refute_0_62,plain,
( not(X_6) != xor(truth,not(not(X_6)))
| not(not(X_6)) != X_6
| not(X_6) = xor(truth,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(not(X_6),xor(truth,not(not(X_6)))) ),[1,1],$fot(X_6)]]) ).
cnf(refute_0_63,plain,
( not(X_6) != xor(truth,not(not(X_6)))
| not(X_6) = xor(truth,X_6) ),
inference(resolve,[$cnf( $equal(not(not(X_6)),X_6) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
not(X_6) = xor(truth,X_6),
inference(resolve,[$cnf( $equal(not(X_6),xor(truth,not(not(X_6)))) )],[refute_0_59,refute_0_63]) ).
cnf(refute_0_65,plain,
( not(X_6) != xor(truth,X_6)
| xor(truth,X_6) = not(X_6) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X_6))),bind(Y0,$fot(xor(truth,X_6)))]]) ).
cnf(refute_0_66,plain,
xor(truth,X_6) = not(X_6),
inference(resolve,[$cnf( $equal(not(X_6),xor(truth,X_6)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
xor(truth,Y) = not(Y),
inference(subst,[],[refute_0_66:[bind(X_6,$fot(Y))]]) ).
cnf(refute_0_68,plain,
and_star(X,xor(truth,Y)) = and_star(X,xor(truth,Y)),
introduced(tautology,[refl,[$fot(and_star(X,xor(truth,Y)))]]) ).
cnf(refute_0_69,plain,
( and_star(X,xor(truth,Y)) != and_star(X,xor(truth,Y))
| xor(truth,Y) != not(Y)
| and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) ),[1,1],$fot(not(Y))]]) ).
cnf(refute_0_70,plain,
( xor(truth,Y) != not(Y)
| and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
and_star(X,xor(truth,Y)) = and_star(X,not(Y)),
inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
not(and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
introduced(tautology,[refl,[$fot(not(and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_73,plain,
( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
| not(and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
| not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) ),[1,0],$fot(and_star(X,not(Y)))]]) ).
cnf(refute_0_74,plain,
( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
| not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,not(Y))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
inference(subst,[],[refute_0_66:[bind(X_6,$fot(and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_77,plain,
( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
| xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(xor(truth,and_star(X,xor(truth,Y))))),bind(Y0,$fot(not(and_star(X,xor(truth,Y))))),bind(Z0,$fot(not(and_star(X,not(Y)))))]]) ).
cnf(refute_0_78,plain,
( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
| xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| implies(X,Y) = not(and_star(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),not(and_star(X,not(Y)))) ),[0],$fot(xor(truth,and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_81,plain,
( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
| implies(X,Y) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(X,Y) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(implies(X,Y),xor(truth,and_star(X,xor(truth,Y)))) )],[implies_definition,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(X_17,X_18) = not(and_star(X_17,not(X_18))),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_17)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_84,plain,
( implies(X_17,X_18) != not(and_star(X_17,not(X_18)))
| not(and_star(X_17,not(X_18))) = implies(X_17,X_18) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_17,X_18))),bind(Y0,$fot(not(and_star(X_17,not(X_18)))))]]) ).
cnf(refute_0_85,plain,
not(and_star(X_17,not(X_18))) = implies(X_17,X_18),
inference(resolve,[$cnf( $equal(implies(X_17,X_18),not(and_star(X_17,not(X_18)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( and_star(X_17,not(X_18)) != not(not(and_star(X_17,not(X_18))))
| not(and_star(X_17,not(X_18))) != implies(X_17,X_18)
| and_star(X_17,not(X_18)) = not(implies(X_17,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_17,not(X_18)),not(not(and_star(X_17,not(X_18))))) ),[1,0],$fot(implies(X_17,X_18))]]) ).
cnf(refute_0_87,plain,
( and_star(X_17,not(X_18)) != not(not(and_star(X_17,not(X_18))))
| and_star(X_17,not(X_18)) = not(implies(X_17,X_18)) ),
inference(resolve,[$cnf( $equal(not(and_star(X_17,not(X_18))),implies(X_17,X_18)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
and_star(X_17,not(X_18)) = not(implies(X_17,X_18)),
inference(resolve,[$cnf( $equal(and_star(X_17,not(X_18)),not(not(and_star(X_17,not(X_18))))) )],[refute_0_58,refute_0_87]) ).
cnf(refute_0_89,plain,
and_star(Y,not(X_28)) = not(implies(Y,X_28)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(Y)),bind(X_18,$fot(X_28))]]) ).
cnf(refute_0_90,plain,
( and_star(Y,not(X_28)) != not(implies(Y,X_28))
| and_star(not(X_28),Y) != and_star(Y,not(X_28))
| and_star(not(X_28),Y) = not(implies(Y,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_28),Y),and_star(Y,not(X_28))) ),[1],$fot(not(implies(Y,X_28)))]]) ).
cnf(refute_0_91,plain,
( and_star(not(X_28),Y) != and_star(Y,not(X_28))
| and_star(not(X_28),Y) = not(implies(Y,X_28)) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(X_28)),not(implies(Y,X_28))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
and_star(not(X_28),Y) = not(implies(Y,X_28)),
inference(resolve,[$cnf( $equal(and_star(not(X_28),Y),and_star(Y,not(X_28))) )],[refute_0_57,refute_0_91]) ).
cnf(refute_0_93,plain,
and_star(not(X_28),X_40) = not(implies(X_40,X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_40))]]) ).
cnf(refute_0_94,plain,
( and_star(and_star(not(X_28),X_40),X_41) != and_star(not(X_28),and_star(X_40,X_41))
| and_star(not(X_28),X_40) != not(implies(X_40,X_28))
| and_star(not(implies(X_40,X_28)),X_41) = and_star(not(X_28),and_star(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(and_star(not(X_28),X_40),X_41),and_star(not(X_28),and_star(X_40,X_41))) ),[0,0],$fot(not(implies(X_40,X_28)))]]) ).
cnf(refute_0_95,plain,
( and_star(and_star(not(X_28),X_40),X_41) != and_star(not(X_28),and_star(X_40,X_41))
| and_star(not(implies(X_40,X_28)),X_41) = and_star(not(X_28),and_star(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),X_40),not(implies(X_40,X_28))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
and_star(not(implies(X_40,X_28)),X_41) = and_star(not(X_28),and_star(X_40,X_41)),
inference(resolve,[$cnf( $equal(and_star(and_star(not(X_28),X_40),X_41),and_star(not(X_28),and_star(X_40,X_41))) )],[refute_0_56,refute_0_95]) ).
cnf(refute_0_97,plain,
and_star(not(implies(X_40,X_28)),X_41) = not(implies(X_41,implies(X_40,X_28))),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_41)),bind(X_28,$fot(implies(X_40,X_28)))]]) ).
cnf(refute_0_98,plain,
( and_star(not(implies(X_40,X_28)),X_41) != and_star(not(X_28),and_star(X_40,X_41))
| and_star(not(implies(X_40,X_28)),X_41) != not(implies(X_41,implies(X_40,X_28)))
| not(implies(X_41,implies(X_40,X_28))) = and_star(not(X_28),and_star(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(implies(X_40,X_28)),X_41),and_star(not(X_28),and_star(X_40,X_41))) ),[0],$fot(not(implies(X_41,implies(X_40,X_28))))]]) ).
cnf(refute_0_99,plain,
( and_star(not(implies(X_40,X_28)),X_41) != and_star(not(X_28),and_star(X_40,X_41))
| not(implies(X_41,implies(X_40,X_28))) = and_star(not(X_28),and_star(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(and_star(not(implies(X_40,X_28)),X_41),not(implies(X_41,implies(X_40,X_28)))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
and_star(and_star(X_39,X_40),not(X_18)) = not(implies(and_star(X_39,X_40),X_18)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(and_star(X_39,X_40)))]]) ).
cnf(refute_0_101,plain,
and_star(and_star(X_39,X_40),not(X_18)) = and_star(X_39,and_star(X_40,not(X_18))),
inference(subst,[],[and_star_associativity:[bind(X,$fot(X_39)),bind(Y,$fot(X_40)),bind(Z,$fot(not(X_18)))]]) ).
cnf(refute_0_102,plain,
( and_star(and_star(X_39,X_40),not(X_18)) != and_star(X_39,and_star(X_40,not(X_18)))
| and_star(and_star(X_39,X_40),not(X_18)) != not(implies(and_star(X_39,X_40),X_18))
| and_star(X_39,and_star(X_40,not(X_18))) = not(implies(and_star(X_39,X_40),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(and_star(X_39,X_40),not(X_18)),not(implies(and_star(X_39,X_40),X_18))) ),[0],$fot(and_star(X_39,and_star(X_40,not(X_18))))]]) ).
cnf(refute_0_103,plain,
( and_star(and_star(X_39,X_40),not(X_18)) != not(implies(and_star(X_39,X_40),X_18))
| and_star(X_39,and_star(X_40,not(X_18))) = not(implies(and_star(X_39,X_40),X_18)) ),
inference(resolve,[$cnf( $equal(and_star(and_star(X_39,X_40),not(X_18)),and_star(X_39,and_star(X_40,not(X_18)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
and_star(X_39,and_star(X_40,not(X_18))) = not(implies(and_star(X_39,X_40),X_18)),
inference(resolve,[$cnf( $equal(and_star(and_star(X_39,X_40),not(X_18)),not(implies(and_star(X_39,X_40),X_18))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
and_star(X_39,not(implies(X_40,X_18))) = not(implies(X_39,implies(X_40,X_18))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_39)),bind(X_18,$fot(implies(X_40,X_18)))]]) ).
cnf(refute_0_106,plain,
and_star(X_40,not(X_18)) = not(implies(X_40,X_18)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_40))]]) ).
cnf(refute_0_107,plain,
and_star(X_39,and_star(X_40,not(X_18))) = and_star(X_39,and_star(X_40,not(X_18))),
introduced(tautology,[refl,[$fot(and_star(X_39,and_star(X_40,not(X_18))))]]) ).
cnf(refute_0_108,plain,
( and_star(X_39,and_star(X_40,not(X_18))) != and_star(X_39,and_star(X_40,not(X_18)))
| and_star(X_40,not(X_18)) != not(implies(X_40,X_18))
| and_star(X_39,and_star(X_40,not(X_18))) = and_star(X_39,not(implies(X_40,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),and_star(X_39,and_star(X_40,not(X_18)))) ),[1,1],$fot(not(implies(X_40,X_18)))]]) ).
cnf(refute_0_109,plain,
( and_star(X_40,not(X_18)) != not(implies(X_40,X_18))
| and_star(X_39,and_star(X_40,not(X_18))) = and_star(X_39,not(implies(X_40,X_18))) ),
inference(resolve,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),and_star(X_39,and_star(X_40,not(X_18)))) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
and_star(X_39,and_star(X_40,not(X_18))) = and_star(X_39,not(implies(X_40,X_18))),
inference(resolve,[$cnf( $equal(and_star(X_40,not(X_18)),not(implies(X_40,X_18))) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
( and_star(X_39,and_star(X_40,not(X_18))) != and_star(X_39,not(implies(X_40,X_18)))
| and_star(X_39,not(implies(X_40,X_18))) != not(implies(X_39,implies(X_40,X_18)))
| and_star(X_39,and_star(X_40,not(X_18))) = not(implies(X_39,implies(X_40,X_18))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(and_star(X_39,and_star(X_40,not(X_18))))),bind(Y0,$fot(and_star(X_39,not(implies(X_40,X_18))))),bind(Z0,$fot(not(implies(X_39,implies(X_40,X_18)))))]]) ).
cnf(refute_0_112,plain,
( and_star(X_39,not(implies(X_40,X_18))) != not(implies(X_39,implies(X_40,X_18)))
| and_star(X_39,and_star(X_40,not(X_18))) = not(implies(X_39,implies(X_40,X_18))) ),
inference(resolve,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),and_star(X_39,not(implies(X_40,X_18)))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
and_star(X_39,and_star(X_40,not(X_18))) = not(implies(X_39,implies(X_40,X_18))),
inference(resolve,[$cnf( $equal(and_star(X_39,not(implies(X_40,X_18))),not(implies(X_39,implies(X_40,X_18)))) )],[refute_0_105,refute_0_112]) ).
cnf(refute_0_114,plain,
( and_star(X_39,and_star(X_40,not(X_18))) != not(implies(X_39,implies(X_40,X_18)))
| and_star(X_39,and_star(X_40,not(X_18))) != not(implies(and_star(X_39,X_40),X_18))
| not(implies(X_39,implies(X_40,X_18))) = not(implies(and_star(X_39,X_40),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),not(implies(and_star(X_39,X_40),X_18))) ),[0],$fot(not(implies(X_39,implies(X_40,X_18))))]]) ).
cnf(refute_0_115,plain,
( and_star(X_39,and_star(X_40,not(X_18))) != not(implies(and_star(X_39,X_40),X_18))
| not(implies(X_39,implies(X_40,X_18))) = not(implies(and_star(X_39,X_40),X_18)) ),
inference(resolve,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),not(implies(X_39,implies(X_40,X_18)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
not(implies(X_39,implies(X_40,X_18))) = not(implies(and_star(X_39,X_40),X_18)),
inference(resolve,[$cnf( $equal(and_star(X_39,and_star(X_40,not(X_18))),not(implies(and_star(X_39,X_40),X_18))) )],[refute_0_104,refute_0_115]) ).
cnf(refute_0_117,plain,
( not(implies(X_39,implies(X_40,X_18))) != not(implies(and_star(X_39,X_40),X_18))
| not(implies(and_star(X_39,X_40),X_18)) = not(implies(X_39,implies(X_40,X_18))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(implies(X_39,implies(X_40,X_18))))),bind(Y0,$fot(not(implies(and_star(X_39,X_40),X_18))))]]) ).
cnf(refute_0_118,plain,
not(implies(and_star(X_39,X_40),X_18)) = not(implies(X_39,implies(X_40,X_18))),
inference(resolve,[$cnf( $equal(not(implies(X_39,implies(X_40,X_18))),not(implies(and_star(X_39,X_40),X_18))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
not(implies(and_star(X_40,X_41),X_28)) = not(implies(X_40,implies(X_41,X_28))),
inference(subst,[],[refute_0_118:[bind(X_18,$fot(X_28)),bind(X_39,$fot(X_40)),bind(X_40,$fot(X_41))]]) ).
cnf(refute_0_120,plain,
and_star(not(X_28),and_star(X_40,X_41)) = not(implies(and_star(X_40,X_41),X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(and_star(X_40,X_41)))]]) ).
cnf(refute_0_121,plain,
( and_star(not(X_28),and_star(X_40,X_41)) != not(implies(and_star(X_40,X_41),X_28))
| not(implies(and_star(X_40,X_41),X_28)) != not(implies(X_40,implies(X_41,X_28)))
| and_star(not(X_28),and_star(X_40,X_41)) = not(implies(X_40,implies(X_41,X_28))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(and_star(not(X_28),and_star(X_40,X_41)))),bind(Y0,$fot(not(implies(and_star(X_40,X_41),X_28)))),bind(Z0,$fot(not(implies(X_40,implies(X_41,X_28)))))]]) ).
cnf(refute_0_122,plain,
( not(implies(and_star(X_40,X_41),X_28)) != not(implies(X_40,implies(X_41,X_28)))
| and_star(not(X_28),and_star(X_40,X_41)) = not(implies(X_40,implies(X_41,X_28))) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),and_star(X_40,X_41)),not(implies(and_star(X_40,X_41),X_28))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
and_star(not(X_28),and_star(X_40,X_41)) = not(implies(X_40,implies(X_41,X_28))),
inference(resolve,[$cnf( $equal(not(implies(and_star(X_40,X_41),X_28)),not(implies(X_40,implies(X_41,X_28)))) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( and_star(not(X_28),and_star(X_40,X_41)) != not(implies(X_40,implies(X_41,X_28)))
| not(implies(X_41,implies(X_40,X_28))) != and_star(not(X_28),and_star(X_40,X_41))
| not(implies(X_41,implies(X_40,X_28))) = not(implies(X_40,implies(X_41,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_41,implies(X_40,X_28))),and_star(not(X_28),and_star(X_40,X_41))) ),[1],$fot(not(implies(X_40,implies(X_41,X_28))))]]) ).
cnf(refute_0_125,plain,
( not(implies(X_41,implies(X_40,X_28))) != and_star(not(X_28),and_star(X_40,X_41))
| not(implies(X_41,implies(X_40,X_28))) = not(implies(X_40,implies(X_41,X_28))) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),and_star(X_40,X_41)),not(implies(X_40,implies(X_41,X_28)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( and_star(not(implies(X_40,X_28)),X_41) != and_star(not(X_28),and_star(X_40,X_41))
| not(implies(X_41,implies(X_40,X_28))) = not(implies(X_40,implies(X_41,X_28))) ),
inference(resolve,[$cnf( $equal(not(implies(X_41,implies(X_40,X_28))),and_star(not(X_28),and_star(X_40,X_41))) )],[refute_0_99,refute_0_125]) ).
cnf(refute_0_127,plain,
not(implies(X_41,implies(X_40,X_28))) = not(implies(X_40,implies(X_41,X_28))),
inference(resolve,[$cnf( $equal(and_star(not(implies(X_40,X_28)),X_41),and_star(not(X_28),and_star(X_40,X_41))) )],[refute_0_96,refute_0_126]) ).
cnf(refute_0_128,plain,
not(implies(X_73,implies(X_72,X_71))) = not(implies(X_72,implies(X_73,X_71))),
inference(subst,[],[refute_0_127:[bind(X_28,$fot(X_71)),bind(X_40,$fot(X_72)),bind(X_41,$fot(X_73))]]) ).
cnf(refute_0_129,plain,
( implies(X_73,implies(X_72,X_71)) != not(not(implies(X_73,implies(X_72,X_71))))
| not(implies(X_73,implies(X_72,X_71))) != not(implies(X_72,implies(X_73,X_71)))
| implies(X_73,implies(X_72,X_71)) = not(not(implies(X_72,implies(X_73,X_71)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_73,implies(X_72,X_71)),not(not(implies(X_73,implies(X_72,X_71))))) ),[1,0],$fot(not(implies(X_72,implies(X_73,X_71))))]]) ).
cnf(refute_0_130,plain,
( implies(X_73,implies(X_72,X_71)) != not(not(implies(X_73,implies(X_72,X_71))))
| implies(X_73,implies(X_72,X_71)) = not(not(implies(X_72,implies(X_73,X_71)))) ),
inference(resolve,[$cnf( $equal(not(implies(X_73,implies(X_72,X_71))),not(implies(X_72,implies(X_73,X_71)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(X_73,implies(X_72,X_71)) = not(not(implies(X_72,implies(X_73,X_71)))),
inference(resolve,[$cnf( $equal(implies(X_73,implies(X_72,X_71)),not(not(implies(X_73,implies(X_72,X_71))))) )],[refute_0_55,refute_0_130]) ).
cnf(refute_0_132,plain,
not(not(implies(X_72,implies(X_73,X_71)))) = implies(X_72,implies(X_73,X_71)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_72,implies(X_73,X_71))))]]) ).
cnf(refute_0_133,plain,
( implies(X_73,implies(X_72,X_71)) != not(not(implies(X_72,implies(X_73,X_71))))
| not(not(implies(X_72,implies(X_73,X_71)))) != implies(X_72,implies(X_73,X_71))
| implies(X_73,implies(X_72,X_71)) = implies(X_72,implies(X_73,X_71)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_73,implies(X_72,X_71)),implies(X_72,implies(X_73,X_71))) ),[0],$fot(not(not(implies(X_72,implies(X_73,X_71)))))]]) ).
cnf(refute_0_134,plain,
( implies(X_73,implies(X_72,X_71)) != not(not(implies(X_72,implies(X_73,X_71))))
| implies(X_73,implies(X_72,X_71)) = implies(X_72,implies(X_73,X_71)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_72,implies(X_73,X_71)))),implies(X_72,implies(X_73,X_71))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(X_73,implies(X_72,X_71)) = implies(X_72,implies(X_73,X_71)),
inference(resolve,[$cnf( $equal(implies(X_73,implies(X_72,X_71)),not(not(implies(X_72,implies(X_73,X_71))))) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
( implies(X_73,implies(X_72,X_71)) != implies(X_72,implies(X_73,X_71))
| implies(X_72,implies(X_73,X_71)) = implies(X_73,implies(X_72,X_71)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_73,implies(X_72,X_71)))),bind(Y0,$fot(implies(X_72,implies(X_73,X_71))))]]) ).
cnf(refute_0_137,plain,
implies(X_72,implies(X_73,X_71)) = implies(X_73,implies(X_72,X_71)),
inference(resolve,[$cnf( $equal(implies(X_73,implies(X_72,X_71)),implies(X_72,implies(X_73,X_71))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
implies(implies(a,b),implies(b,a)) = implies(b,implies(implies(a,b),a)),
inference(subst,[],[refute_0_137:[bind(X_71,$fot(a)),bind(X_72,$fot(implies(a,b))),bind(X_73,$fot(b))]]) ).
cnf(refute_0_139,plain,
implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(implies(a,b),implies(b,a)),a),
introduced(tautology,[refl,[$fot(implies(implies(implies(a,b),implies(b,a)),a))]]) ).
cnf(refute_0_140,plain,
( implies(implies(a,b),implies(b,a)) != implies(b,implies(implies(a,b),a))
| implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(implies(a,b),implies(b,a)),a)
| implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(implies(a,b),implies(b,a)),a)) ),[1,0],$fot(implies(b,implies(implies(a,b),a)))]]) ).
cnf(refute_0_141,plain,
( implies(implies(a,b),implies(b,a)) != implies(b,implies(implies(a,b),a))
| implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(implies(a,b),implies(b,a)),a)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a),
inference(resolve,[$cnf( $equal(implies(implies(a,b),implies(b,a)),implies(b,implies(implies(a,b),a))) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(implies(a,b),implies(b,a)),a)),
introduced(tautology,[refl,[$fot(implies(b,implies(implies(implies(a,b),implies(b,a)),a)))]]) ).
cnf(refute_0_144,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(implies(a,b),implies(b,a)),a))
| implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(b,implies(implies(a,b),a)),a)
| implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) ),[1,1],$fot(implies(implies(b,implies(implies(a,b),a)),a))]]) ).
cnf(refute_0_145,plain,
( implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(b,implies(implies(a,b),a)),a)
| implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(b,implies(implies(a,b),a)),a)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(implies(a,b),implies(b,a)),a)),
inference(subst,[],[refute_0_137:[bind(X_71,$fot(a)),bind(X_72,$fot(implies(implies(a,b),implies(b,a)))),bind(X_73,$fot(b))]]) ).
cnf(refute_0_148,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != implies(b,implies(implies(implies(a,b),implies(b,a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(implies(a,b),implies(b,a)),implies(b,a)))),bind(Y0,$fot(implies(b,implies(implies(implies(a,b),implies(b,a)),a)))),bind(Z0,$fot(implies(b,implies(implies(b,implies(implies(a,b),a)),a))))]]) ).
cnf(refute_0_149,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) ),[1],$fot(truth)]]) ).
cnf(refute_0_152,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),truth) )],[refute_0_152,prove_wajsberg_mv_4]) ).
cnf(refute_0_154,plain,
implies(X_74,implies(X_75,X_74)) = not(not(implies(X_74,implies(X_75,X_74)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_74,implies(X_75,X_74))))]]) ).
cnf(refute_0_155,plain,
not(implies(X_73,implies(X_71,X_71))) = not(implies(X_71,implies(X_73,X_71))),
inference(subst,[],[refute_0_127:[bind(X_28,$fot(X_71)),bind(X_40,$fot(X_71)),bind(X_41,$fot(X_73))]]) ).
cnf(refute_0_156,plain,
implies(X_23,X_23) = not(not(implies(X_23,X_23))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_23,X_23)))]]) ).
cnf(refute_0_157,plain,
( and_star(X,Y) != and_star(Y,X)
| and_star(Y,X) = and_star(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and_star(X,Y))),bind(Y0,$fot(and_star(Y,X)))]]) ).
cnf(refute_0_158,plain,
and_star(Y,X) = and_star(X,Y),
inference(resolve,[$cnf( $equal(and_star(X,Y),and_star(Y,X)) )],[and_star_commutativity,refute_0_157]) ).
cnf(refute_0_159,plain,
and_star(xor(truth,X),X) = and_star(X,xor(truth,X)),
inference(subst,[],[refute_0_158:[bind(Y,$fot(xor(truth,X)))]]) ).
cnf(refute_0_160,plain,
( and_star(xor(truth,X),X) != and_star(X,xor(truth,X))
| and_star(xor(truth,X),X) != falsehood
| and_star(X,xor(truth,X)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,X),X),falsehood) ),[0],$fot(and_star(X,xor(truth,X)))]]) ).
cnf(refute_0_161,plain,
( and_star(xor(truth,X),X) != falsehood
| and_star(X,xor(truth,X)) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),X),and_star(X,xor(truth,X))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
and_star(X,xor(truth,X)) = falsehood,
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),X),falsehood) )],[axiom_6,refute_0_161]) ).
cnf(refute_0_163,plain,
and_star(not(X_9),xor(truth,not(X_9))) = falsehood,
inference(subst,[],[refute_0_162:[bind(X,$fot(not(X_9)))]]) ).
cnf(refute_0_164,plain,
X_9 = xor(truth,not(X_9)),
inference(subst,[],[refute_0_43:[bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_165,plain,
( X_9 != xor(truth,not(X_9))
| xor(truth,not(X_9)) = X_9 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_9)),bind(Y0,$fot(xor(truth,not(X_9))))]]) ).
cnf(refute_0_166,plain,
xor(truth,not(X_9)) = X_9,
inference(resolve,[$cnf( $equal(X_9,xor(truth,not(X_9))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( and_star(not(X_9),xor(truth,not(X_9))) != falsehood
| xor(truth,not(X_9)) != X_9
| and_star(not(X_9),X_9) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_9),xor(truth,not(X_9))),falsehood) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_168,plain,
( and_star(not(X_9),xor(truth,not(X_9))) != falsehood
| and_star(not(X_9),X_9) = falsehood ),
inference(resolve,[$cnf( $equal(xor(truth,not(X_9)),X_9) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
and_star(not(X_9),X_9) = falsehood,
inference(resolve,[$cnf( $equal(and_star(not(X_9),xor(truth,not(X_9))),falsehood) )],[refute_0_163,refute_0_168]) ).
cnf(refute_0_170,plain,
and_star(not(X_9),X_9) = and_star(X_9,not(X_9)),
inference(subst,[],[refute_0_158:[bind(X,$fot(X_9)),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_171,plain,
( and_star(not(X_9),X_9) != and_star(X_9,not(X_9))
| and_star(not(X_9),X_9) != falsehood
| and_star(X_9,not(X_9)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_9),X_9),falsehood) ),[0],$fot(and_star(X_9,not(X_9)))]]) ).
cnf(refute_0_172,plain,
( and_star(not(X_9),X_9) != falsehood
| and_star(X_9,not(X_9)) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(not(X_9),X_9),and_star(X_9,not(X_9))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
and_star(X_9,not(X_9)) = falsehood,
inference(resolve,[$cnf( $equal(and_star(not(X_9),X_9),falsehood) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
and_star(X_9,not(X_9)) = not(implies(X_9,X_9)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_9)),bind(X_18,$fot(X_9))]]) ).
cnf(refute_0_175,plain,
( and_star(X_9,not(X_9)) != falsehood
| and_star(X_9,not(X_9)) != not(implies(X_9,X_9))
| not(implies(X_9,X_9)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_9,not(X_9)),falsehood) ),[0],$fot(not(implies(X_9,X_9)))]]) ).
cnf(refute_0_176,plain,
( and_star(X_9,not(X_9)) != falsehood
| not(implies(X_9,X_9)) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(X_9,not(X_9)),not(implies(X_9,X_9))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
not(implies(X_9,X_9)) = falsehood,
inference(resolve,[$cnf( $equal(and_star(X_9,not(X_9)),falsehood) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
not(implies(X_23,X_23)) = falsehood,
inference(subst,[],[refute_0_177:[bind(X_9,$fot(X_23))]]) ).
cnf(refute_0_179,plain,
( implies(X_23,X_23) != not(not(implies(X_23,X_23)))
| not(implies(X_23,X_23)) != falsehood
| implies(X_23,X_23) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_23,X_23),not(not(implies(X_23,X_23)))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_180,plain,
( implies(X_23,X_23) != not(not(implies(X_23,X_23)))
| implies(X_23,X_23) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(implies(X_23,X_23)),falsehood) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(X_23,X_23) = not(falsehood),
inference(resolve,[$cnf( $equal(implies(X_23,X_23),not(not(implies(X_23,X_23)))) )],[refute_0_156,refute_0_180]) ).
cnf(refute_0_182,plain,
truth = not(not(truth)),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(truth))]]) ).
cnf(refute_0_183,plain,
( not(truth) != falsehood
| truth != not(not(truth))
| truth = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(truth,not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_184,plain,
( truth != not(not(truth))
| truth = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_183]) ).
cnf(refute_0_185,plain,
truth = not(falsehood),
inference(resolve,[$cnf( $equal(truth,not(not(truth))) )],[refute_0_182,refute_0_184]) ).
cnf(refute_0_186,plain,
( truth != not(falsehood)
| not(falsehood) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(not(falsehood)))]]) ).
cnf(refute_0_187,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(truth,not(falsehood)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( implies(X_23,X_23) != not(falsehood)
| not(falsehood) != truth
| implies(X_23,X_23) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_23,X_23),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_189,plain,
( implies(X_23,X_23) != not(falsehood)
| implies(X_23,X_23) = truth ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(X_23,X_23) = truth,
inference(resolve,[$cnf( $equal(implies(X_23,X_23),not(falsehood)) )],[refute_0_181,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(X_71,X_71) = truth,
inference(subst,[],[refute_0_190:[bind(X_23,$fot(X_71))]]) ).
cnf(refute_0_192,plain,
( implies(X_71,X_71) != truth
| not(implies(X_73,implies(X_71,X_71))) != not(implies(X_71,implies(X_73,X_71)))
| not(implies(X_73,truth)) = not(implies(X_71,implies(X_73,X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_73,implies(X_71,X_71))),not(implies(X_71,implies(X_73,X_71)))) ),[0,0,1],$fot(truth)]]) ).
cnf(refute_0_193,plain,
( not(implies(X_73,implies(X_71,X_71))) != not(implies(X_71,implies(X_73,X_71)))
| not(implies(X_73,truth)) = not(implies(X_71,implies(X_73,X_71))) ),
inference(resolve,[$cnf( $equal(implies(X_71,X_71),truth) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
not(implies(X_73,truth)) = not(implies(X_71,implies(X_73,X_71))),
inference(resolve,[$cnf( $equal(not(implies(X_73,implies(X_71,X_71))),not(implies(X_71,implies(X_73,X_71)))) )],[refute_0_155,refute_0_193]) ).
cnf(refute_0_195,plain,
implies(X_17,truth) = not(and_star(X_17,not(truth))),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_17)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_196,plain,
( implies(X_17,truth) != not(and_star(X_17,not(truth)))
| not(truth) != falsehood
| implies(X_17,truth) = not(and_star(X_17,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,truth),not(and_star(X_17,not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_197,plain,
( implies(X_17,truth) != not(and_star(X_17,not(truth)))
| implies(X_17,truth) = not(and_star(X_17,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(X_17,truth) = not(and_star(X_17,falsehood)),
inference(resolve,[$cnf( $equal(implies(X_17,truth),not(and_star(X_17,not(truth)))) )],[refute_0_195,refute_0_197]) ).
cnf(refute_0_199,plain,
and_star(X_17,falsehood) = falsehood,
inference(subst,[],[axiom_5:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_200,plain,
not(and_star(X_17,falsehood)) = not(and_star(X_17,falsehood)),
introduced(tautology,[refl,[$fot(not(and_star(X_17,falsehood)))]]) ).
cnf(refute_0_201,plain,
( and_star(X_17,falsehood) != falsehood
| not(and_star(X_17,falsehood)) != not(and_star(X_17,falsehood))
| not(and_star(X_17,falsehood)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X_17,falsehood)),not(and_star(X_17,falsehood))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_202,plain,
( and_star(X_17,falsehood) != falsehood
| not(and_star(X_17,falsehood)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(and_star(X_17,falsehood)),not(and_star(X_17,falsehood))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
not(and_star(X_17,falsehood)) = not(falsehood),
inference(resolve,[$cnf( $equal(and_star(X_17,falsehood),falsehood) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( not(and_star(X_17,falsehood)) != not(falsehood)
| not(falsehood) != truth
| not(and_star(X_17,falsehood)) = truth ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(X_17,falsehood)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_205,plain,
( not(falsehood) != truth
| not(and_star(X_17,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(not(and_star(X_17,falsehood)),not(falsehood)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
not(and_star(X_17,falsehood)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_205]) ).
cnf(refute_0_207,plain,
( implies(X_17,truth) != not(and_star(X_17,falsehood))
| not(and_star(X_17,falsehood)) != truth
| implies(X_17,truth) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_17,truth),truth) ),[0],$fot(not(and_star(X_17,falsehood)))]]) ).
cnf(refute_0_208,plain,
( implies(X_17,truth) != not(and_star(X_17,falsehood))
| implies(X_17,truth) = truth ),
inference(resolve,[$cnf( $equal(not(and_star(X_17,falsehood)),truth) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(X_17,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_17,truth),not(and_star(X_17,falsehood))) )],[refute_0_198,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(X_73,truth) = truth,
inference(subst,[],[refute_0_209:[bind(X_17,$fot(X_73))]]) ).
cnf(refute_0_211,plain,
not(implies(X_73,truth)) = not(implies(X_73,truth)),
introduced(tautology,[refl,[$fot(not(implies(X_73,truth)))]]) ).
cnf(refute_0_212,plain,
( implies(X_73,truth) != truth
| not(implies(X_73,truth)) != not(implies(X_73,truth))
| not(implies(X_73,truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_73,truth)),not(implies(X_73,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_213,plain,
( implies(X_73,truth) != truth
| not(implies(X_73,truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_73,truth)),not(implies(X_73,truth))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
not(implies(X_73,truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_73,truth),truth) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( not(implies(X_73,truth)) != not(truth)
| not(truth) != falsehood
| not(implies(X_73,truth)) = falsehood ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(implies(X_73,truth)))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_216,plain,
( not(truth) != falsehood
| not(implies(X_73,truth)) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(X_73,truth)),not(truth)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
not(implies(X_73,truth)) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_216]) ).
cnf(refute_0_218,plain,
( not(implies(X_73,truth)) != falsehood
| not(implies(X_73,truth)) != not(implies(X_71,implies(X_73,X_71)))
| falsehood = not(implies(X_71,implies(X_73,X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_73,truth)),not(implies(X_71,implies(X_73,X_71)))) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_219,plain,
( not(implies(X_73,truth)) != not(implies(X_71,implies(X_73,X_71)))
| falsehood = not(implies(X_71,implies(X_73,X_71))) ),
inference(resolve,[$cnf( $equal(not(implies(X_73,truth)),falsehood) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
falsehood = not(implies(X_71,implies(X_73,X_71))),
inference(resolve,[$cnf( $equal(not(implies(X_73,truth)),not(implies(X_71,implies(X_73,X_71)))) )],[refute_0_194,refute_0_219]) ).
cnf(refute_0_221,plain,
falsehood = not(implies(X_74,implies(X_75,X_74))),
inference(subst,[],[refute_0_220:[bind(X_71,$fot(X_74)),bind(X_73,$fot(X_75))]]) ).
cnf(refute_0_222,plain,
( falsehood != not(implies(X_74,implies(X_75,X_74)))
| not(implies(X_74,implies(X_75,X_74))) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(not(implies(X_74,implies(X_75,X_74)))))]]) ).
cnf(refute_0_223,plain,
not(implies(X_74,implies(X_75,X_74))) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,not(implies(X_74,implies(X_75,X_74)))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( implies(X_74,implies(X_75,X_74)) != not(not(implies(X_74,implies(X_75,X_74))))
| not(implies(X_74,implies(X_75,X_74))) != falsehood
| implies(X_74,implies(X_75,X_74)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_74,implies(X_75,X_74)),not(not(implies(X_74,implies(X_75,X_74))))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_225,plain,
( implies(X_74,implies(X_75,X_74)) != not(not(implies(X_74,implies(X_75,X_74))))
| implies(X_74,implies(X_75,X_74)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(implies(X_74,implies(X_75,X_74))),falsehood) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(X_74,implies(X_75,X_74)) = not(falsehood),
inference(resolve,[$cnf( $equal(implies(X_74,implies(X_75,X_74)),not(not(implies(X_74,implies(X_75,X_74))))) )],[refute_0_154,refute_0_225]) ).
cnf(refute_0_227,plain,
( implies(X_74,implies(X_75,X_74)) != not(falsehood)
| not(falsehood) != truth
| implies(X_74,implies(X_75,X_74)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_74,implies(X_75,X_74)),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_228,plain,
( implies(X_74,implies(X_75,X_74)) != not(falsehood)
| implies(X_74,implies(X_75,X_74)) = truth ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_227]) ).
cnf(refute_0_229,plain,
implies(X_74,implies(X_75,X_74)) = truth,
inference(resolve,[$cnf( $equal(implies(X_74,implies(X_75,X_74)),not(falsehood)) )],[refute_0_226,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(b,implies(implies(a,b),b)) = truth,
inference(subst,[],[refute_0_229:[bind(X_74,$fot(b)),bind(X_75,$fot(implies(a,b)))]]) ).
cnf(refute_0_231,plain,
implies(implies(X_51,X_50),X_50) = not(not(implies(implies(X_51,X_50),X_50))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(implies(X_51,X_50),X_50)))]]) ).
cnf(refute_0_232,plain,
and_star(not(X_28),implies(not(X_28),X_33)) = not(implies(implies(not(X_28),X_33),X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(not(X_28),X_33)))]]) ).
cnf(refute_0_233,plain,
xor(and_star(xor(truth,X),Y),truth) = not(and_star(xor(truth,X),Y)),
inference(subst,[],[refute_0_4:[bind(X,$fot(and_star(xor(truth,X),Y)))]]) ).
cnf(refute_0_234,plain,
and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(xor(and_star(xor(truth,X),Y),truth),Y),
introduced(tautology,[refl,[$fot(and_star(xor(and_star(xor(truth,X),Y),truth),Y))]]) ).
cnf(refute_0_235,plain,
( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,X),Y),truth),Y)
| xor(and_star(xor(truth,X),Y),truth) != not(and_star(xor(truth,X),Y))
| and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,X),Y),truth),Y)) ),[1,0],$fot(not(and_star(xor(truth,X),Y)))]]) ).
cnf(refute_0_236,plain,
( xor(and_star(xor(truth,X),Y),truth) != not(and_star(xor(truth,X),Y))
| and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y) ),
inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,X),Y),truth),Y)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
and_star(xor(and_star(xor(truth,X),Y),truth),Y) = and_star(not(and_star(xor(truth,X),Y)),Y),
inference(resolve,[$cnf( $equal(xor(and_star(xor(truth,X),Y),truth),not(and_star(xor(truth,X),Y))) )],[refute_0_233,refute_0_236]) ).
cnf(refute_0_238,plain,
( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(not(and_star(xor(truth,X),Y)),Y)
| and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) ),[0],$fot(and_star(not(and_star(xor(truth,X),Y)),Y))]]) ).
cnf(refute_0_239,plain,
( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(xor(and_star(xor(truth,Y),X),truth),X) ),
inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(not(and_star(xor(truth,X),Y)),Y)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
xor(and_star(xor(truth,Y),X),truth) = not(and_star(xor(truth,Y),X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(and_star(xor(truth,Y),X)))]]) ).
cnf(refute_0_241,plain,
and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(xor(and_star(xor(truth,Y),X),truth),X),
introduced(tautology,[refl,[$fot(and_star(xor(and_star(xor(truth,Y),X),truth),X))]]) ).
cnf(refute_0_242,plain,
( and_star(xor(and_star(xor(truth,Y),X),truth),X) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| xor(and_star(xor(truth,Y),X),truth) != not(and_star(xor(truth,Y),X))
| and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(not(and_star(xor(truth,Y),X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(and_star(xor(truth,Y),X),truth),X),and_star(xor(and_star(xor(truth,Y),X),truth),X)) ),[1,0],$fot(not(and_star(xor(truth,Y),X)))]]) ).
cnf(refute_0_243,plain,
( xor(and_star(xor(truth,Y),X),truth) != not(and_star(xor(truth,Y),X))
| and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(not(and_star(xor(truth,Y),X)),X) ),
inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,Y),X),truth),X),and_star(xor(and_star(xor(truth,Y),X),truth),X)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
and_star(xor(and_star(xor(truth,Y),X),truth),X) = and_star(not(and_star(xor(truth,Y),X)),X),
inference(resolve,[$cnf( $equal(xor(and_star(xor(truth,Y),X),truth),not(and_star(xor(truth,Y),X))) )],[refute_0_240,refute_0_243]) ).
cnf(refute_0_245,plain,
( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| and_star(xor(and_star(xor(truth,Y),X),truth),X) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) ),[0],$fot(and_star(xor(and_star(xor(truth,Y),X),truth),X))]]) ).
cnf(refute_0_246,plain,
( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,Y),X),truth),X),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( and_star(xor(and_star(xor(truth,X),Y),truth),Y) != and_star(xor(and_star(xor(truth,Y),X),truth),X)
| and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X) ),
inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) )],[refute_0_239,refute_0_246]) ).
cnf(refute_0_248,plain,
and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(not(and_star(xor(truth,Y),X)),X),
inference(resolve,[$cnf( $equal(and_star(xor(and_star(xor(truth,X),Y),truth),Y),and_star(xor(and_star(xor(truth,Y),X),truth),X)) )],[axiom_8,refute_0_247]) ).
cnf(refute_0_249,plain,
and_star(not(and_star(xor(truth,X),Y)),Y) = and_star(Y,not(and_star(xor(truth,X),Y))),
inference(subst,[],[refute_0_158:[bind(X,$fot(Y)),bind(Y,$fot(not(and_star(xor(truth,X),Y))))]]) ).
cnf(refute_0_250,plain,
( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(Y,not(and_star(xor(truth,X),Y)))
| and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(not(and_star(xor(truth,Y),X)),X) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) ),[0],$fot(and_star(Y,not(and_star(xor(truth,X),Y))))]]) ).
cnf(refute_0_251,plain,
( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(not(and_star(xor(truth,Y),X)),X) ),
inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(Y,not(and_star(xor(truth,X),Y)))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
and_star(not(and_star(xor(truth,Y),X)),X) = and_star(X,not(and_star(xor(truth,Y),X))),
inference(subst,[],[refute_0_158:[bind(Y,$fot(not(and_star(xor(truth,Y),X))))]]) ).
cnf(refute_0_253,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(not(and_star(xor(truth,Y),X)),X) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[0],$fot(and_star(not(and_star(xor(truth,Y),X)),X))]]) ).
cnf(refute_0_254,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,Y),X)),X),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
( and_star(not(and_star(xor(truth,X),Y)),Y) != and_star(not(and_star(xor(truth,Y),X)),X)
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))),
inference(resolve,[$cnf( $equal(and_star(not(and_star(xor(truth,X),Y)),Y),and_star(not(and_star(xor(truth,Y),X)),X)) )],[refute_0_248,refute_0_255]) ).
cnf(refute_0_257,plain,
xor(truth,X) = not(X),
inference(subst,[],[refute_0_66:[bind(X_6,$fot(X))]]) ).
cnf(refute_0_258,plain,
and_star(xor(truth,X),Y) = and_star(xor(truth,X),Y),
introduced(tautology,[refl,[$fot(and_star(xor(truth,X),Y))]]) ).
cnf(refute_0_259,plain,
( and_star(xor(truth,X),Y) != and_star(xor(truth,X),Y)
| xor(truth,X) != not(X)
| and_star(xor(truth,X),Y) = and_star(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(xor(truth,X),Y)) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_260,plain,
( xor(truth,X) != not(X)
| and_star(xor(truth,X),Y) = and_star(not(X),Y) ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(xor(truth,X),Y)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
and_star(xor(truth,X),Y) = and_star(not(X),Y),
inference(resolve,[$cnf( $equal(xor(truth,X),not(X)) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
not(and_star(xor(truth,X),Y)) = not(and_star(xor(truth,X),Y)),
introduced(tautology,[refl,[$fot(not(and_star(xor(truth,X),Y)))]]) ).
cnf(refute_0_263,plain,
( and_star(xor(truth,X),Y) != and_star(not(X),Y)
| not(and_star(xor(truth,X),Y)) != not(and_star(xor(truth,X),Y))
| not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(xor(truth,X),Y))) ),[1,0],$fot(and_star(not(X),Y))]]) ).
cnf(refute_0_264,plain,
( and_star(xor(truth,X),Y) != and_star(not(X),Y)
| not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)) ),
inference(resolve,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(xor(truth,X),Y))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
not(and_star(xor(truth,X),Y)) = not(and_star(not(X),Y)),
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),Y),and_star(not(X),Y)) )],[refute_0_261,refute_0_264]) ).
cnf(refute_0_266,plain,
and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(xor(truth,X),Y))),
introduced(tautology,[refl,[$fot(and_star(Y,not(and_star(xor(truth,X),Y))))]]) ).
cnf(refute_0_267,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(Y,not(and_star(xor(truth,X),Y)))
| not(and_star(xor(truth,X),Y)) != not(and_star(not(X),Y))
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(xor(truth,X),Y)))) ),[1,1],$fot(not(and_star(not(X),Y)))]]) ).
cnf(refute_0_268,plain,
( not(and_star(xor(truth,X),Y)) != not(and_star(not(X),Y))
| and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(xor(truth,X),Y)))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
and_star(Y,not(and_star(xor(truth,X),Y))) = and_star(Y,not(and_star(not(X),Y))),
inference(resolve,[$cnf( $equal(not(and_star(xor(truth,X),Y)),not(and_star(not(X),Y))) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(Y,not(and_star(not(X),Y)))
| and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[0],$fot(and_star(Y,not(and_star(not(X),Y))))]]) ).
cnf(refute_0_271,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(xor(truth,Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(Y,not(and_star(not(X),Y)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
and_star(xor(truth,Y),X) = and_star(xor(truth,Y),X),
introduced(tautology,[refl,[$fot(and_star(xor(truth,Y),X))]]) ).
cnf(refute_0_273,plain,
( and_star(xor(truth,Y),X) != and_star(xor(truth,Y),X)
| xor(truth,Y) != not(Y)
| and_star(xor(truth,Y),X) = and_star(not(Y),X) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(xor(truth,Y),X)) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_274,plain,
( xor(truth,Y) != not(Y)
| and_star(xor(truth,Y),X) = and_star(not(Y),X) ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(xor(truth,Y),X)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
and_star(xor(truth,Y),X) = and_star(not(Y),X),
inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_67,refute_0_274]) ).
cnf(refute_0_276,plain,
not(and_star(xor(truth,Y),X)) = not(and_star(xor(truth,Y),X)),
introduced(tautology,[refl,[$fot(not(and_star(xor(truth,Y),X)))]]) ).
cnf(refute_0_277,plain,
( and_star(xor(truth,Y),X) != and_star(not(Y),X)
| not(and_star(xor(truth,Y),X)) != not(and_star(xor(truth,Y),X))
| not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(xor(truth,Y),X))) ),[1,0],$fot(and_star(not(Y),X))]]) ).
cnf(refute_0_278,plain,
( and_star(xor(truth,Y),X) != and_star(not(Y),X)
| not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)) ),
inference(resolve,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(xor(truth,Y),X))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
not(and_star(xor(truth,Y),X)) = not(and_star(not(Y),X)),
inference(resolve,[$cnf( $equal(and_star(xor(truth,Y),X),and_star(not(Y),X)) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(xor(truth,Y),X))),
introduced(tautology,[refl,[$fot(and_star(X,not(and_star(xor(truth,Y),X))))]]) ).
cnf(refute_0_281,plain,
( and_star(X,not(and_star(xor(truth,Y),X))) != and_star(X,not(and_star(xor(truth,Y),X)))
| not(and_star(xor(truth,Y),X)) != not(and_star(not(Y),X))
| and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X,not(and_star(xor(truth,Y),X))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[1,1],$fot(not(and_star(not(Y),X)))]]) ).
cnf(refute_0_282,plain,
( not(and_star(xor(truth,Y),X)) != not(and_star(not(Y),X))
| and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(X,not(and_star(xor(truth,Y),X))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
and_star(X,not(and_star(xor(truth,Y),X))) = and_star(X,not(and_star(not(Y),X))),
inference(resolve,[$cnf( $equal(not(and_star(xor(truth,Y),X)),not(and_star(not(Y),X))) )],[refute_0_279,refute_0_282]) ).
cnf(refute_0_284,plain,
( and_star(X,not(and_star(xor(truth,Y),X))) != and_star(X,not(and_star(not(Y),X)))
| and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) ),[1],$fot(and_star(X,not(and_star(not(Y),X))))]]) ).
cnf(refute_0_285,plain,
( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(X,not(and_star(xor(truth,Y),X))),and_star(X,not(and_star(not(Y),X)))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
( and_star(Y,not(and_star(xor(truth,X),Y))) != and_star(X,not(and_star(xor(truth,Y),X)))
| and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_271,refute_0_285]) ).
cnf(refute_0_287,plain,
and_star(Y,not(and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(xor(truth,X),Y))),and_star(X,not(and_star(xor(truth,Y),X)))) )],[refute_0_256,refute_0_286]) ).
cnf(refute_0_288,plain,
and_star(Y,not(and_star(not(X),Y))) = not(implies(Y,and_star(not(X),Y))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(Y)),bind(X_18,$fot(and_star(not(X),Y)))]]) ).
cnf(refute_0_289,plain,
( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
| and_star(Y,not(and_star(not(X),Y))) != not(implies(Y,and_star(not(X),Y)))
| not(implies(Y,and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) ),[0],$fot(not(implies(Y,and_star(not(X),Y))))]]) ).
cnf(refute_0_290,plain,
( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
| not(implies(Y,and_star(not(X),Y))) = and_star(X,not(and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),not(implies(Y,and_star(not(X),Y)))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
and_star(X,not(and_star(not(Y),X))) = not(implies(X,and_star(not(Y),X))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X)),bind(X_18,$fot(and_star(not(Y),X)))]]) ).
cnf(refute_0_292,plain,
( and_star(X,not(and_star(not(Y),X))) != not(implies(X,and_star(not(Y),X)))
| not(implies(Y,and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
| not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) ),[1],$fot(not(implies(X,and_star(not(Y),X))))]]) ).
cnf(refute_0_293,plain,
( not(implies(Y,and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
| not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(and_star(X,not(and_star(not(Y),X))),not(implies(X,and_star(not(Y),X)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( and_star(Y,not(and_star(not(X),Y))) != and_star(X,not(and_star(not(Y),X)))
| not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
not(implies(Y,and_star(not(X),Y))) = not(implies(X,and_star(not(Y),X))),
inference(resolve,[$cnf( $equal(and_star(Y,not(and_star(not(X),Y))),and_star(X,not(and_star(not(Y),X)))) )],[refute_0_287,refute_0_294]) ).
cnf(refute_0_296,plain,
not(not(and_star(Y,implies(Y,X)))) = and_star(Y,implies(Y,X)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(and_star(Y,implies(Y,X))))]]) ).
cnf(refute_0_297,plain,
implies(X_17,not(X_6)) = not(and_star(X_17,not(not(X_6)))),
inference(subst,[],[refute_0_82:[bind(X,$fot(X_17)),bind(Y,$fot(not(X_6)))]]) ).
cnf(refute_0_298,plain,
( implies(X_17,not(X_6)) != not(and_star(X_17,not(not(X_6))))
| not(not(X_6)) != X_6
| implies(X_17,not(X_6)) = not(and_star(X_17,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,not(X_6)),not(and_star(X_17,not(not(X_6))))) ),[1,0,1],$fot(X_6)]]) ).
cnf(refute_0_299,plain,
( implies(X_17,not(X_6)) != not(and_star(X_17,not(not(X_6))))
| implies(X_17,not(X_6)) = not(and_star(X_17,X_6)) ),
inference(resolve,[$cnf( $equal(not(not(X_6)),X_6) )],[refute_0_61,refute_0_298]) ).
cnf(refute_0_300,plain,
implies(X_17,not(X_6)) = not(and_star(X_17,X_6)),
inference(resolve,[$cnf( $equal(implies(X_17,not(X_6)),not(and_star(X_17,not(not(X_6))))) )],[refute_0_297,refute_0_299]) ).
cnf(refute_0_301,plain,
implies(Y,not(implies(Y,X))) = not(and_star(Y,implies(Y,X))),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(Y)),bind(X_6,$fot(implies(Y,X)))]]) ).
cnf(refute_0_302,plain,
and_star(not(X),Y) = not(implies(Y,X)),
inference(subst,[],[refute_0_92:[bind(X_28,$fot(X))]]) ).
cnf(refute_0_303,plain,
implies(Y,and_star(not(X),Y)) = implies(Y,and_star(not(X),Y)),
introduced(tautology,[refl,[$fot(implies(Y,and_star(not(X),Y)))]]) ).
cnf(refute_0_304,plain,
( and_star(not(X),Y) != not(implies(Y,X))
| implies(Y,and_star(not(X),Y)) != implies(Y,and_star(not(X),Y))
| implies(Y,and_star(not(X),Y)) = implies(Y,not(implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,and_star(not(X),Y)),implies(Y,and_star(not(X),Y))) ),[1,1],$fot(not(implies(Y,X)))]]) ).
cnf(refute_0_305,plain,
( and_star(not(X),Y) != not(implies(Y,X))
| implies(Y,and_star(not(X),Y)) = implies(Y,not(implies(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(Y,and_star(not(X),Y)),implies(Y,and_star(not(X),Y))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(Y,and_star(not(X),Y)) = implies(Y,not(implies(Y,X))),
inference(resolve,[$cnf( $equal(and_star(not(X),Y),not(implies(Y,X))) )],[refute_0_302,refute_0_305]) ).
cnf(refute_0_307,plain,
( implies(Y,and_star(not(X),Y)) != implies(Y,not(implies(Y,X)))
| implies(Y,not(implies(Y,X))) != not(and_star(Y,implies(Y,X)))
| implies(Y,and_star(not(X),Y)) = not(and_star(Y,implies(Y,X))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(Y,and_star(not(X),Y)))),bind(Y0,$fot(implies(Y,not(implies(Y,X))))),bind(Z0,$fot(not(and_star(Y,implies(Y,X)))))]]) ).
cnf(refute_0_308,plain,
( implies(Y,not(implies(Y,X))) != not(and_star(Y,implies(Y,X)))
| implies(Y,and_star(not(X),Y)) = not(and_star(Y,implies(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(Y,and_star(not(X),Y)),implies(Y,not(implies(Y,X)))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(Y,and_star(not(X),Y)) = not(and_star(Y,implies(Y,X))),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,X))),not(and_star(Y,implies(Y,X)))) )],[refute_0_301,refute_0_308]) ).
cnf(refute_0_310,plain,
not(implies(Y,and_star(not(X),Y))) = not(implies(Y,and_star(not(X),Y))),
introduced(tautology,[refl,[$fot(not(implies(Y,and_star(not(X),Y))))]]) ).
cnf(refute_0_311,plain,
( implies(Y,and_star(not(X),Y)) != not(and_star(Y,implies(Y,X)))
| not(implies(Y,and_star(not(X),Y))) != not(implies(Y,and_star(not(X),Y)))
| not(implies(Y,and_star(not(X),Y))) = not(not(and_star(Y,implies(Y,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),not(implies(Y,and_star(not(X),Y)))) ),[1,0],$fot(not(and_star(Y,implies(Y,X))))]]) ).
cnf(refute_0_312,plain,
( implies(Y,and_star(not(X),Y)) != not(and_star(Y,implies(Y,X)))
| not(implies(Y,and_star(not(X),Y))) = not(not(and_star(Y,implies(Y,X)))) ),
inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),not(implies(Y,and_star(not(X),Y)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
not(implies(Y,and_star(not(X),Y))) = not(not(and_star(Y,implies(Y,X)))),
inference(resolve,[$cnf( $equal(implies(Y,and_star(not(X),Y)),not(and_star(Y,implies(Y,X)))) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( not(implies(Y,and_star(not(X),Y))) != not(not(and_star(Y,implies(Y,X))))
| not(not(and_star(Y,implies(Y,X)))) != and_star(Y,implies(Y,X))
| not(implies(Y,and_star(not(X),Y))) = and_star(Y,implies(Y,X)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(implies(Y,and_star(not(X),Y))))),bind(Y0,$fot(not(not(and_star(Y,implies(Y,X)))))),bind(Z0,$fot(and_star(Y,implies(Y,X))))]]) ).
cnf(refute_0_315,plain,
( not(not(and_star(Y,implies(Y,X)))) != and_star(Y,implies(Y,X))
| not(implies(Y,and_star(not(X),Y))) = and_star(Y,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),not(not(and_star(Y,implies(Y,X))))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
not(implies(Y,and_star(not(X),Y))) = and_star(Y,implies(Y,X)),
inference(resolve,[$cnf( $equal(not(not(and_star(Y,implies(Y,X)))),and_star(Y,implies(Y,X))) )],[refute_0_296,refute_0_315]) ).
cnf(refute_0_317,plain,
( not(implies(Y,and_star(not(X),Y))) != and_star(Y,implies(Y,X))
| not(implies(Y,and_star(not(X),Y))) != not(implies(X,and_star(not(Y),X)))
| and_star(Y,implies(Y,X)) = not(implies(X,and_star(not(Y),X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),not(implies(X,and_star(not(Y),X)))) ),[0],$fot(and_star(Y,implies(Y,X)))]]) ).
cnf(refute_0_318,plain,
( not(implies(Y,and_star(not(X),Y))) != not(implies(X,and_star(not(Y),X)))
| and_star(Y,implies(Y,X)) = not(implies(X,and_star(not(Y),X))) ),
inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),and_star(Y,implies(Y,X))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
not(not(and_star(X,implies(X,Y)))) = and_star(X,implies(X,Y)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(and_star(X,implies(X,Y))))]]) ).
cnf(refute_0_320,plain,
implies(X,not(implies(X,Y))) = not(and_star(X,implies(X,Y))),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(X)),bind(X_6,$fot(implies(X,Y)))]]) ).
cnf(refute_0_321,plain,
and_star(not(Y),X) = not(implies(X,Y)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X)),bind(X_28,$fot(Y))]]) ).
cnf(refute_0_322,plain,
implies(X,and_star(not(Y),X)) = implies(X,and_star(not(Y),X)),
introduced(tautology,[refl,[$fot(implies(X,and_star(not(Y),X)))]]) ).
cnf(refute_0_323,plain,
( and_star(not(Y),X) != not(implies(X,Y))
| implies(X,and_star(not(Y),X)) != implies(X,and_star(not(Y),X))
| implies(X,and_star(not(Y),X)) = implies(X,not(implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,and_star(not(Y),X)),implies(X,and_star(not(Y),X))) ),[1,1],$fot(not(implies(X,Y)))]]) ).
cnf(refute_0_324,plain,
( and_star(not(Y),X) != not(implies(X,Y))
| implies(X,and_star(not(Y),X)) = implies(X,not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(X,and_star(not(Y),X)),implies(X,and_star(not(Y),X))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
implies(X,and_star(not(Y),X)) = implies(X,not(implies(X,Y))),
inference(resolve,[$cnf( $equal(and_star(not(Y),X),not(implies(X,Y))) )],[refute_0_321,refute_0_324]) ).
cnf(refute_0_326,plain,
( implies(X,and_star(not(Y),X)) != implies(X,not(implies(X,Y)))
| implies(X,not(implies(X,Y))) != not(and_star(X,implies(X,Y)))
| implies(X,and_star(not(Y),X)) = not(and_star(X,implies(X,Y))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(X,and_star(not(Y),X)))),bind(Y0,$fot(implies(X,not(implies(X,Y))))),bind(Z0,$fot(not(and_star(X,implies(X,Y)))))]]) ).
cnf(refute_0_327,plain,
( implies(X,not(implies(X,Y))) != not(and_star(X,implies(X,Y)))
| implies(X,and_star(not(Y),X)) = not(and_star(X,implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(X,and_star(not(Y),X)),implies(X,not(implies(X,Y)))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(X,and_star(not(Y),X)) = not(and_star(X,implies(X,Y))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,Y))),not(and_star(X,implies(X,Y)))) )],[refute_0_320,refute_0_327]) ).
cnf(refute_0_329,plain,
not(implies(X,and_star(not(Y),X))) = not(implies(X,and_star(not(Y),X))),
introduced(tautology,[refl,[$fot(not(implies(X,and_star(not(Y),X))))]]) ).
cnf(refute_0_330,plain,
( implies(X,and_star(not(Y),X)) != not(and_star(X,implies(X,Y)))
| not(implies(X,and_star(not(Y),X))) != not(implies(X,and_star(not(Y),X)))
| not(implies(X,and_star(not(Y),X))) = not(not(and_star(X,implies(X,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,and_star(not(Y),X))),not(implies(X,and_star(not(Y),X)))) ),[1,0],$fot(not(and_star(X,implies(X,Y))))]]) ).
cnf(refute_0_331,plain,
( implies(X,and_star(not(Y),X)) != not(and_star(X,implies(X,Y)))
| not(implies(X,and_star(not(Y),X))) = not(not(and_star(X,implies(X,Y)))) ),
inference(resolve,[$cnf( $equal(not(implies(X,and_star(not(Y),X))),not(implies(X,and_star(not(Y),X)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
not(implies(X,and_star(not(Y),X))) = not(not(and_star(X,implies(X,Y)))),
inference(resolve,[$cnf( $equal(implies(X,and_star(not(Y),X)),not(and_star(X,implies(X,Y)))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
( not(implies(X,and_star(not(Y),X))) != not(not(and_star(X,implies(X,Y))))
| not(not(and_star(X,implies(X,Y)))) != and_star(X,implies(X,Y))
| not(implies(X,and_star(not(Y),X))) = and_star(X,implies(X,Y)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(implies(X,and_star(not(Y),X))))),bind(Y0,$fot(not(not(and_star(X,implies(X,Y)))))),bind(Z0,$fot(and_star(X,implies(X,Y))))]]) ).
cnf(refute_0_334,plain,
( not(not(and_star(X,implies(X,Y)))) != and_star(X,implies(X,Y))
| not(implies(X,and_star(not(Y),X))) = and_star(X,implies(X,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(X,and_star(not(Y),X))),not(not(and_star(X,implies(X,Y))))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
not(implies(X,and_star(not(Y),X))) = and_star(X,implies(X,Y)),
inference(resolve,[$cnf( $equal(not(not(and_star(X,implies(X,Y)))),and_star(X,implies(X,Y))) )],[refute_0_319,refute_0_334]) ).
cnf(refute_0_336,plain,
( and_star(Y,implies(Y,X)) != not(implies(X,and_star(not(Y),X)))
| not(implies(X,and_star(not(Y),X))) != and_star(X,implies(X,Y))
| and_star(Y,implies(Y,X)) = and_star(X,implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and_star(Y,implies(Y,X)),and_star(X,implies(X,Y))) ),[0],$fot(not(implies(X,and_star(not(Y),X))))]]) ).
cnf(refute_0_337,plain,
( and_star(Y,implies(Y,X)) != not(implies(X,and_star(not(Y),X)))
| and_star(Y,implies(Y,X)) = and_star(X,implies(X,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(X,and_star(not(Y),X))),and_star(X,implies(X,Y))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
( not(implies(Y,and_star(not(X),Y))) != not(implies(X,and_star(not(Y),X)))
| and_star(Y,implies(Y,X)) = and_star(X,implies(X,Y)) ),
inference(resolve,[$cnf( $equal(and_star(Y,implies(Y,X)),not(implies(X,and_star(not(Y),X)))) )],[refute_0_318,refute_0_337]) ).
cnf(refute_0_339,plain,
and_star(Y,implies(Y,X)) = and_star(X,implies(X,Y)),
inference(resolve,[$cnf( $equal(not(implies(Y,and_star(not(X),Y))),not(implies(X,and_star(not(Y),X)))) )],[refute_0_295,refute_0_338]) ).
cnf(refute_0_340,plain,
and_star(not(X_28),implies(not(X_28),X_33)) = and_star(X_33,implies(X_33,not(X_28))),
inference(subst,[],[refute_0_339:[bind(X,$fot(X_33)),bind(Y,$fot(not(X_28)))]]) ).
cnf(refute_0_341,plain,
( and_star(not(X_28),implies(not(X_28),X_33)) != and_star(X_33,implies(X_33,not(X_28)))
| and_star(not(X_28),implies(not(X_28),X_33)) != not(implies(implies(not(X_28),X_33),X_28))
| and_star(X_33,implies(X_33,not(X_28))) = not(implies(implies(not(X_28),X_33),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_28),implies(not(X_28),X_33)),not(implies(implies(not(X_28),X_33),X_28))) ),[0],$fot(and_star(X_33,implies(X_33,not(X_28))))]]) ).
cnf(refute_0_342,plain,
( and_star(not(X_28),implies(not(X_28),X_33)) != not(implies(implies(not(X_28),X_33),X_28))
| and_star(X_33,implies(X_33,not(X_28))) = not(implies(implies(not(X_28),X_33),X_28)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),implies(not(X_28),X_33)),and_star(X_33,implies(X_33,not(X_28)))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
and_star(X_33,implies(X_33,not(X_28))) = not(implies(implies(not(X_28),X_33),X_28)),
inference(resolve,[$cnf( $equal(and_star(not(X_28),implies(not(X_28),X_33)),not(implies(implies(not(X_28),X_33),X_28))) )],[refute_0_232,refute_0_342]) ).
cnf(refute_0_344,plain,
and_star(X_33,not(and_star(X_33,X_28))) = not(implies(X_33,and_star(X_33,X_28))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_33)),bind(X_18,$fot(and_star(X_33,X_28)))]]) ).
cnf(refute_0_345,plain,
implies(X_33,not(X_28)) = not(and_star(X_33,X_28)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(X_33)),bind(X_6,$fot(X_28))]]) ).
cnf(refute_0_346,plain,
and_star(X_33,implies(X_33,not(X_28))) = and_star(X_33,implies(X_33,not(X_28))),
introduced(tautology,[refl,[$fot(and_star(X_33,implies(X_33,not(X_28))))]]) ).
cnf(refute_0_347,plain,
( and_star(X_33,implies(X_33,not(X_28))) != and_star(X_33,implies(X_33,not(X_28)))
| implies(X_33,not(X_28)) != not(and_star(X_33,X_28))
| and_star(X_33,implies(X_33,not(X_28))) = and_star(X_33,not(and_star(X_33,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),and_star(X_33,implies(X_33,not(X_28)))) ),[1,1],$fot(not(and_star(X_33,X_28)))]]) ).
cnf(refute_0_348,plain,
( implies(X_33,not(X_28)) != not(and_star(X_33,X_28))
| and_star(X_33,implies(X_33,not(X_28))) = and_star(X_33,not(and_star(X_33,X_28))) ),
inference(resolve,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),and_star(X_33,implies(X_33,not(X_28)))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
and_star(X_33,implies(X_33,not(X_28))) = and_star(X_33,not(and_star(X_33,X_28))),
inference(resolve,[$cnf( $equal(implies(X_33,not(X_28)),not(and_star(X_33,X_28))) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
( and_star(X_33,implies(X_33,not(X_28))) != and_star(X_33,not(and_star(X_33,X_28)))
| and_star(X_33,not(and_star(X_33,X_28))) != not(implies(X_33,and_star(X_33,X_28)))
| and_star(X_33,implies(X_33,not(X_28))) = not(implies(X_33,and_star(X_33,X_28))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(and_star(X_33,implies(X_33,not(X_28))))),bind(Y0,$fot(and_star(X_33,not(and_star(X_33,X_28))))),bind(Z0,$fot(not(implies(X_33,and_star(X_33,X_28)))))]]) ).
cnf(refute_0_351,plain,
( and_star(X_33,not(and_star(X_33,X_28))) != not(implies(X_33,and_star(X_33,X_28)))
| and_star(X_33,implies(X_33,not(X_28))) = not(implies(X_33,and_star(X_33,X_28))) ),
inference(resolve,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),and_star(X_33,not(and_star(X_33,X_28)))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
and_star(X_33,implies(X_33,not(X_28))) = not(implies(X_33,and_star(X_33,X_28))),
inference(resolve,[$cnf( $equal(and_star(X_33,not(and_star(X_33,X_28))),not(implies(X_33,and_star(X_33,X_28)))) )],[refute_0_344,refute_0_351]) ).
cnf(refute_0_353,plain,
( and_star(X_33,implies(X_33,not(X_28))) != not(implies(X_33,and_star(X_33,X_28)))
| and_star(X_33,implies(X_33,not(X_28))) != not(implies(implies(not(X_28),X_33),X_28))
| not(implies(X_33,and_star(X_33,X_28))) = not(implies(implies(not(X_28),X_33),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),not(implies(implies(not(X_28),X_33),X_28))) ),[0],$fot(not(implies(X_33,and_star(X_33,X_28))))]]) ).
cnf(refute_0_354,plain,
( and_star(X_33,implies(X_33,not(X_28))) != not(implies(implies(not(X_28),X_33),X_28))
| not(implies(X_33,and_star(X_33,X_28))) = not(implies(implies(not(X_28),X_33),X_28)) ),
inference(resolve,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),not(implies(X_33,and_star(X_33,X_28)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
not(implies(X_33,and_star(X_33,X_28))) = not(implies(implies(not(X_28),X_33),X_28)),
inference(resolve,[$cnf( $equal(and_star(X_33,implies(X_33,not(X_28))),not(implies(implies(not(X_28),X_33),X_28))) )],[refute_0_343,refute_0_354]) ).
cnf(refute_0_356,plain,
not(implies(not(X_28),and_star(not(X_28),X_35))) = not(implies(implies(not(X_35),not(X_28)),X_35)),
inference(subst,[],[refute_0_355:[bind(X_28,$fot(X_35)),bind(X_33,$fot(not(X_28)))]]) ).
cnf(refute_0_357,plain,
and_star(not(X_28),X_35) = not(implies(X_35,X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_35))]]) ).
cnf(refute_0_358,plain,
( and_star(not(X_28),X_35) != not(implies(X_35,X_28))
| not(implies(not(X_28),and_star(not(X_28),X_35))) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(not(X_35),not(X_28)),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_28),and_star(not(X_28),X_35))),not(implies(implies(not(X_35),not(X_28)),X_35))) ),[0,0,1],$fot(not(implies(X_35,X_28)))]]) ).
cnf(refute_0_359,plain,
( not(implies(not(X_28),and_star(not(X_28),X_35))) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(not(X_35),not(X_28)),X_35)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),X_35),not(implies(X_35,X_28))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(not(X_35),not(X_28)),X_35)),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),and_star(not(X_28),X_35))),not(implies(implies(not(X_35),not(X_28)),X_35))) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
not(not(implies(implies(X_35,X_28),X_28))) = implies(implies(X_35,X_28),X_28),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(X_35,X_28),X_28)))]]) ).
cnf(refute_0_362,plain,
and_star(not(X_28),implies(X_35,X_28)) = not(implies(implies(X_35,X_28),X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(X_35,X_28)))]]) ).
cnf(refute_0_363,plain,
not(and_star(not(X_28),implies(X_35,X_28))) = not(and_star(not(X_28),implies(X_35,X_28))),
introduced(tautology,[refl,[$fot(not(and_star(not(X_28),implies(X_35,X_28))))]]) ).
cnf(refute_0_364,plain,
( and_star(not(X_28),implies(X_35,X_28)) != not(implies(implies(X_35,X_28),X_28))
| not(and_star(not(X_28),implies(X_35,X_28))) != not(and_star(not(X_28),implies(X_35,X_28)))
| not(and_star(not(X_28),implies(X_35,X_28))) = not(not(implies(implies(X_35,X_28),X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_28),implies(X_35,X_28))),not(and_star(not(X_28),implies(X_35,X_28)))) ),[1,0],$fot(not(implies(implies(X_35,X_28),X_28)))]]) ).
cnf(refute_0_365,plain,
( and_star(not(X_28),implies(X_35,X_28)) != not(implies(implies(X_35,X_28),X_28))
| not(and_star(not(X_28),implies(X_35,X_28))) = not(not(implies(implies(X_35,X_28),X_28))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_28),implies(X_35,X_28))),not(and_star(not(X_28),implies(X_35,X_28)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
not(and_star(not(X_28),implies(X_35,X_28))) = not(not(implies(implies(X_35,X_28),X_28))),
inference(resolve,[$cnf( $equal(and_star(not(X_28),implies(X_35,X_28)),not(implies(implies(X_35,X_28),X_28))) )],[refute_0_362,refute_0_365]) ).
cnf(refute_0_367,plain,
( not(and_star(not(X_28),implies(X_35,X_28))) != not(not(implies(implies(X_35,X_28),X_28)))
| not(not(implies(implies(X_35,X_28),X_28))) != implies(implies(X_35,X_28),X_28)
| not(and_star(not(X_28),implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_28),implies(X_35,X_28))))),bind(Y0,$fot(not(not(implies(implies(X_35,X_28),X_28))))),bind(Z0,$fot(implies(implies(X_35,X_28),X_28)))]]) ).
cnf(refute_0_368,plain,
( not(not(implies(implies(X_35,X_28),X_28))) != implies(implies(X_35,X_28),X_28)
| not(and_star(not(X_28),implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_28),implies(X_35,X_28))),not(not(implies(implies(X_35,X_28),X_28)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
not(and_star(not(X_28),implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28),
inference(resolve,[$cnf( $equal(not(not(implies(implies(X_35,X_28),X_28))),implies(implies(X_35,X_28),X_28)) )],[refute_0_361,refute_0_368]) ).
cnf(refute_0_370,plain,
implies(not(X_28),not(implies(X_35,X_28))) = not(and_star(not(X_28),implies(X_35,X_28))),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(not(X_28))),bind(X_6,$fot(implies(X_35,X_28)))]]) ).
cnf(refute_0_371,plain,
( implies(not(X_28),not(implies(X_35,X_28))) != not(and_star(not(X_28),implies(X_35,X_28)))
| not(and_star(not(X_28),implies(X_35,X_28))) != implies(implies(X_35,X_28),X_28)
| implies(not(X_28),not(implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_28),not(implies(X_35,X_28))))),bind(Y0,$fot(not(and_star(not(X_28),implies(X_35,X_28))))),bind(Z0,$fot(implies(implies(X_35,X_28),X_28)))]]) ).
cnf(refute_0_372,plain,
( not(and_star(not(X_28),implies(X_35,X_28))) != implies(implies(X_35,X_28),X_28)
| implies(not(X_28),not(implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28) ),
inference(resolve,[$cnf( $equal(implies(not(X_28),not(implies(X_35,X_28))),not(and_star(not(X_28),implies(X_35,X_28)))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
implies(not(X_28),not(implies(X_35,X_28))) = implies(implies(X_35,X_28),X_28),
inference(resolve,[$cnf( $equal(not(and_star(not(X_28),implies(X_35,X_28))),implies(implies(X_35,X_28),X_28)) )],[refute_0_369,refute_0_372]) ).
cnf(refute_0_374,plain,
not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(not(X_28),not(implies(X_35,X_28)))),
introduced(tautology,[refl,[$fot(not(implies(not(X_28),not(implies(X_35,X_28)))))]]) ).
cnf(refute_0_375,plain,
( implies(not(X_28),not(implies(X_35,X_28))) != implies(implies(X_35,X_28),X_28)
| not(implies(not(X_28),not(implies(X_35,X_28)))) != not(implies(not(X_28),not(implies(X_35,X_28))))
| not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(X_35,X_28),X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_28),not(implies(X_35,X_28)))),not(implies(not(X_28),not(implies(X_35,X_28))))) ),[1,0],$fot(implies(implies(X_35,X_28),X_28))]]) ).
cnf(refute_0_376,plain,
( implies(not(X_28),not(implies(X_35,X_28))) != implies(implies(X_35,X_28),X_28)
| not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(X_35,X_28),X_28)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),not(implies(X_35,X_28)))),not(implies(not(X_28),not(implies(X_35,X_28))))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
not(implies(not(X_28),not(implies(X_35,X_28)))) = not(implies(implies(X_35,X_28),X_28)),
inference(resolve,[$cnf( $equal(implies(not(X_28),not(implies(X_35,X_28))),implies(implies(X_35,X_28),X_28)) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
( not(implies(not(X_28),not(implies(X_35,X_28)))) != not(implies(implies(X_35,X_28),X_28))
| not(implies(not(X_28),not(implies(X_35,X_28)))) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(not(X_35),not(X_28)),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_28),not(implies(X_35,X_28)))),not(implies(implies(not(X_35),not(X_28)),X_35))) ),[0],$fot(not(implies(implies(X_35,X_28),X_28)))]]) ).
cnf(refute_0_379,plain,
( not(implies(not(X_28),not(implies(X_35,X_28)))) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(not(X_35),not(X_28)),X_35)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),not(implies(X_35,X_28)))),not(implies(implies(X_35,X_28),X_28))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
not(not(implies(X_28,X_35))) = implies(X_28,X_35),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_28,X_35)))]]) ).
cnf(refute_0_381,plain,
and_star(not(X_35),X_28) = not(implies(X_28,X_35)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_28)),bind(X_28,$fot(X_35))]]) ).
cnf(refute_0_382,plain,
not(and_star(not(X_35),X_28)) = not(and_star(not(X_35),X_28)),
introduced(tautology,[refl,[$fot(not(and_star(not(X_35),X_28)))]]) ).
cnf(refute_0_383,plain,
( and_star(not(X_35),X_28) != not(implies(X_28,X_35))
| not(and_star(not(X_35),X_28)) != not(and_star(not(X_35),X_28))
| not(and_star(not(X_35),X_28)) = not(not(implies(X_28,X_35))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_35),X_28)),not(and_star(not(X_35),X_28))) ),[1,0],$fot(not(implies(X_28,X_35)))]]) ).
cnf(refute_0_384,plain,
( and_star(not(X_35),X_28) != not(implies(X_28,X_35))
| not(and_star(not(X_35),X_28)) = not(not(implies(X_28,X_35))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_35),X_28)),not(and_star(not(X_35),X_28))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
not(and_star(not(X_35),X_28)) = not(not(implies(X_28,X_35))),
inference(resolve,[$cnf( $equal(and_star(not(X_35),X_28),not(implies(X_28,X_35))) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
( not(and_star(not(X_35),X_28)) != not(not(implies(X_28,X_35)))
| not(not(implies(X_28,X_35))) != implies(X_28,X_35)
| not(and_star(not(X_35),X_28)) = implies(X_28,X_35) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_35),X_28)))),bind(Y0,$fot(not(not(implies(X_28,X_35))))),bind(Z0,$fot(implies(X_28,X_35)))]]) ).
cnf(refute_0_387,plain,
( not(not(implies(X_28,X_35))) != implies(X_28,X_35)
| not(and_star(not(X_35),X_28)) = implies(X_28,X_35) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_35),X_28)),not(not(implies(X_28,X_35)))) )],[refute_0_385,refute_0_386]) ).
cnf(refute_0_388,plain,
not(and_star(not(X_35),X_28)) = implies(X_28,X_35),
inference(resolve,[$cnf( $equal(not(not(implies(X_28,X_35))),implies(X_28,X_35)) )],[refute_0_380,refute_0_387]) ).
cnf(refute_0_389,plain,
implies(not(X_35),not(X_28)) = not(and_star(not(X_35),X_28)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(not(X_35))),bind(X_6,$fot(X_28))]]) ).
cnf(refute_0_390,plain,
( implies(not(X_35),not(X_28)) != not(and_star(not(X_35),X_28))
| not(and_star(not(X_35),X_28)) != implies(X_28,X_35)
| implies(not(X_35),not(X_28)) = implies(X_28,X_35) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_35),not(X_28)))),bind(Y0,$fot(not(and_star(not(X_35),X_28)))),bind(Z0,$fot(implies(X_28,X_35)))]]) ).
cnf(refute_0_391,plain,
( not(and_star(not(X_35),X_28)) != implies(X_28,X_35)
| implies(not(X_35),not(X_28)) = implies(X_28,X_35) ),
inference(resolve,[$cnf( $equal(implies(not(X_35),not(X_28)),not(and_star(not(X_35),X_28))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
implies(not(X_35),not(X_28)) = implies(X_28,X_35),
inference(resolve,[$cnf( $equal(not(and_star(not(X_35),X_28)),implies(X_28,X_35)) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
implies(implies(not(X_35),not(X_28)),X_35) = implies(implies(not(X_35),not(X_28)),X_35),
introduced(tautology,[refl,[$fot(implies(implies(not(X_35),not(X_28)),X_35))]]) ).
cnf(refute_0_394,plain,
( implies(implies(not(X_35),not(X_28)),X_35) != implies(implies(not(X_35),not(X_28)),X_35)
| implies(not(X_35),not(X_28)) != implies(X_28,X_35)
| implies(implies(not(X_35),not(X_28)),X_35) = implies(implies(X_28,X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_35),not(X_28)),X_35),implies(implies(not(X_35),not(X_28)),X_35)) ),[1,0],$fot(implies(X_28,X_35))]]) ).
cnf(refute_0_395,plain,
( implies(not(X_35),not(X_28)) != implies(X_28,X_35)
| implies(implies(not(X_35),not(X_28)),X_35) = implies(implies(X_28,X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_35),not(X_28)),X_35),implies(implies(not(X_35),not(X_28)),X_35)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
implies(implies(not(X_35),not(X_28)),X_35) = implies(implies(X_28,X_35),X_35),
inference(resolve,[$cnf( $equal(implies(not(X_35),not(X_28)),implies(X_28,X_35)) )],[refute_0_392,refute_0_395]) ).
cnf(refute_0_397,plain,
not(implies(implies(not(X_35),not(X_28)),X_35)) = not(implies(implies(not(X_35),not(X_28)),X_35)),
introduced(tautology,[refl,[$fot(not(implies(implies(not(X_35),not(X_28)),X_35)))]]) ).
cnf(refute_0_398,plain,
( implies(implies(not(X_35),not(X_28)),X_35) != implies(implies(X_28,X_35),X_35)
| not(implies(implies(not(X_35),not(X_28)),X_35)) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(not(X_35),not(X_28)),X_35)) = not(implies(implies(X_28,X_35),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(X_35),not(X_28)),X_35)),not(implies(implies(not(X_35),not(X_28)),X_35))) ),[1,0],$fot(implies(implies(X_28,X_35),X_35))]]) ).
cnf(refute_0_399,plain,
( implies(implies(not(X_35),not(X_28)),X_35) != implies(implies(X_28,X_35),X_35)
| not(implies(implies(not(X_35),not(X_28)),X_35)) = not(implies(implies(X_28,X_35),X_35)) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(X_35),not(X_28)),X_35)),not(implies(implies(not(X_35),not(X_28)),X_35))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
not(implies(implies(not(X_35),not(X_28)),X_35)) = not(implies(implies(X_28,X_35),X_35)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_35),not(X_28)),X_35),implies(implies(X_28,X_35),X_35)) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
( not(implies(implies(X_35,X_28),X_28)) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(not(X_35),not(X_28)),X_35)) != not(implies(implies(X_28,X_35),X_35))
| not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(X_28,X_35),X_35)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(implies(implies(X_35,X_28),X_28)),not(implies(implies(X_28,X_35),X_35))) ),[0],$fot(not(implies(implies(not(X_35),not(X_28)),X_35)))]]) ).
cnf(refute_0_402,plain,
( not(implies(implies(X_35,X_28),X_28)) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(X_28,X_35),X_35)) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(X_35),not(X_28)),X_35)),not(implies(implies(X_28,X_35),X_35))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
( not(implies(not(X_28),not(implies(X_35,X_28)))) != not(implies(implies(not(X_35),not(X_28)),X_35))
| not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(X_28,X_35),X_35)) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X_35,X_28),X_28)),not(implies(implies(not(X_35),not(X_28)),X_35))) )],[refute_0_379,refute_0_402]) ).
cnf(refute_0_404,plain,
not(implies(implies(X_35,X_28),X_28)) = not(implies(implies(X_28,X_35),X_35)),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),not(implies(X_35,X_28)))),not(implies(implies(not(X_35),not(X_28)),X_35))) )],[refute_0_360,refute_0_403]) ).
cnf(refute_0_405,plain,
not(implies(implies(X_51,X_50),X_50)) = not(implies(implies(X_50,X_51),X_51)),
inference(subst,[],[refute_0_404:[bind(X_28,$fot(X_50)),bind(X_35,$fot(X_51))]]) ).
cnf(refute_0_406,plain,
( implies(implies(X_51,X_50),X_50) != not(not(implies(implies(X_51,X_50),X_50)))
| not(implies(implies(X_51,X_50),X_50)) != not(implies(implies(X_50,X_51),X_51))
| implies(implies(X_51,X_50),X_50) = not(not(implies(implies(X_50,X_51),X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_51,X_50),X_50),not(not(implies(implies(X_51,X_50),X_50)))) ),[1,0],$fot(not(implies(implies(X_50,X_51),X_51)))]]) ).
cnf(refute_0_407,plain,
( implies(implies(X_51,X_50),X_50) != not(not(implies(implies(X_51,X_50),X_50)))
| implies(implies(X_51,X_50),X_50) = not(not(implies(implies(X_50,X_51),X_51))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X_51,X_50),X_50)),not(implies(implies(X_50,X_51),X_51))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
implies(implies(X_51,X_50),X_50) = not(not(implies(implies(X_50,X_51),X_51))),
inference(resolve,[$cnf( $equal(implies(implies(X_51,X_50),X_50),not(not(implies(implies(X_51,X_50),X_50)))) )],[refute_0_231,refute_0_407]) ).
cnf(refute_0_409,plain,
not(not(implies(implies(X_50,X_51),X_51))) = implies(implies(X_50,X_51),X_51),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(X_50,X_51),X_51)))]]) ).
cnf(refute_0_410,plain,
( implies(implies(X_51,X_50),X_50) != not(not(implies(implies(X_50,X_51),X_51)))
| not(not(implies(implies(X_50,X_51),X_51))) != implies(implies(X_50,X_51),X_51)
| implies(implies(X_51,X_50),X_50) = implies(implies(X_50,X_51),X_51) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_51,X_50),X_50),implies(implies(X_50,X_51),X_51)) ),[0],$fot(not(not(implies(implies(X_50,X_51),X_51))))]]) ).
cnf(refute_0_411,plain,
( implies(implies(X_51,X_50),X_50) != not(not(implies(implies(X_50,X_51),X_51)))
| implies(implies(X_51,X_50),X_50) = implies(implies(X_50,X_51),X_51) ),
inference(resolve,[$cnf( $equal(not(not(implies(implies(X_50,X_51),X_51))),implies(implies(X_50,X_51),X_51)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
implies(implies(X_51,X_50),X_50) = implies(implies(X_50,X_51),X_51),
inference(resolve,[$cnf( $equal(implies(implies(X_51,X_50),X_50),not(not(implies(implies(X_50,X_51),X_51)))) )],[refute_0_408,refute_0_411]) ).
cnf(refute_0_413,plain,
implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_50,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67)),
inference(subst,[],[refute_0_412:[bind(X_51,$fot(implies(implies(X_50,X_67),X_67)))]]) ).
cnf(refute_0_414,plain,
implies(X_58,implies(implies(X_58,X_57),X_57)) = not(not(implies(X_58,implies(implies(X_58,X_57),X_57)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_58,implies(implies(X_58,X_57),X_57))))]]) ).
cnf(refute_0_415,plain,
not(implies(implies(X_56,X_54),implies(X_56,X_54))) = not(implies(and_star(implies(X_56,X_54),X_56),X_54)),
inference(subst,[],[refute_0_116:[bind(X_18,$fot(X_54)),bind(X_39,$fot(implies(X_56,X_54))),bind(X_40,$fot(X_56))]]) ).
cnf(refute_0_416,plain,
implies(implies(X_56,X_54),implies(X_56,X_54)) = truth,
inference(subst,[],[refute_0_190:[bind(X_23,$fot(implies(X_56,X_54)))]]) ).
cnf(refute_0_417,plain,
( implies(implies(X_56,X_54),implies(X_56,X_54)) != truth
| not(implies(implies(X_56,X_54),implies(X_56,X_54))) != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| not(truth) = not(implies(and_star(implies(X_56,X_54),X_56),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(X_56,X_54),implies(X_56,X_54))),not(implies(and_star(implies(X_56,X_54),X_56),X_54))) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_418,plain,
( not(implies(implies(X_56,X_54),implies(X_56,X_54))) != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| not(truth) = not(implies(and_star(implies(X_56,X_54),X_56),X_54)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_56,X_54),implies(X_56,X_54)),truth) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
not(truth) = not(implies(and_star(implies(X_56,X_54),X_56),X_54)),
inference(resolve,[$cnf( $equal(not(implies(implies(X_56,X_54),implies(X_56,X_54))),not(implies(and_star(implies(X_56,X_54),X_56),X_54))) )],[refute_0_415,refute_0_418]) ).
cnf(refute_0_420,plain,
( not(truth) != falsehood
| not(truth) != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| falsehood = not(implies(and_star(implies(X_56,X_54),X_56),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(not(truth),not(implies(and_star(implies(X_56,X_54),X_56),X_54))) ),[0],$fot(falsehood)]]) ).
cnf(refute_0_421,plain,
( not(truth) != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| falsehood = not(implies(and_star(implies(X_56,X_54),X_56),X_54)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_420]) ).
cnf(refute_0_422,plain,
( not(implies(X_41,implies(X_40,X_28))) != not(implies(X_40,implies(X_41,X_28)))
| not(implies(X_40,implies(X_41,X_28))) = not(implies(X_41,implies(X_40,X_28))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(implies(X_41,implies(X_40,X_28))))),bind(Y0,$fot(not(implies(X_40,implies(X_41,X_28)))))]]) ).
cnf(refute_0_423,plain,
not(implies(X_40,implies(X_41,X_28))) = not(implies(X_41,implies(X_40,X_28))),
inference(resolve,[$cnf( $equal(not(implies(X_41,implies(X_40,X_28))),not(implies(X_40,implies(X_41,X_28)))) )],[refute_0_127,refute_0_422]) ).
cnf(refute_0_424,plain,
not(implies(implies(X_56,X_54),implies(X_56,X_54))) = not(implies(X_56,implies(implies(X_56,X_54),X_54))),
inference(subst,[],[refute_0_423:[bind(X_28,$fot(X_54)),bind(X_40,$fot(implies(X_56,X_54))),bind(X_41,$fot(X_56))]]) ).
cnf(refute_0_425,plain,
not(implies(and_star(implies(X_56,X_54),X_56),X_54)) = not(implies(implies(X_56,X_54),implies(X_56,X_54))),
inference(subst,[],[refute_0_118:[bind(X_18,$fot(X_54)),bind(X_39,$fot(implies(X_56,X_54))),bind(X_40,$fot(X_56))]]) ).
cnf(refute_0_426,plain,
( not(implies(and_star(implies(X_56,X_54),X_56),X_54)) != not(implies(implies(X_56,X_54),implies(X_56,X_54)))
| not(implies(implies(X_56,X_54),implies(X_56,X_54))) != not(implies(X_56,implies(implies(X_56,X_54),X_54)))
| not(implies(and_star(implies(X_56,X_54),X_56),X_54)) = not(implies(X_56,implies(implies(X_56,X_54),X_54))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(implies(and_star(implies(X_56,X_54),X_56),X_54)))),bind(Y0,$fot(not(implies(implies(X_56,X_54),implies(X_56,X_54))))),bind(Z0,$fot(not(implies(X_56,implies(implies(X_56,X_54),X_54)))))]]) ).
cnf(refute_0_427,plain,
( not(implies(implies(X_56,X_54),implies(X_56,X_54))) != not(implies(X_56,implies(implies(X_56,X_54),X_54)))
| not(implies(and_star(implies(X_56,X_54),X_56),X_54)) = not(implies(X_56,implies(implies(X_56,X_54),X_54))) ),
inference(resolve,[$cnf( $equal(not(implies(and_star(implies(X_56,X_54),X_56),X_54)),not(implies(implies(X_56,X_54),implies(X_56,X_54)))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
not(implies(and_star(implies(X_56,X_54),X_56),X_54)) = not(implies(X_56,implies(implies(X_56,X_54),X_54))),
inference(resolve,[$cnf( $equal(not(implies(implies(X_56,X_54),implies(X_56,X_54))),not(implies(X_56,implies(implies(X_56,X_54),X_54)))) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
( falsehood != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| not(implies(and_star(implies(X_56,X_54),X_56),X_54)) != not(implies(X_56,implies(implies(X_56,X_54),X_54)))
| falsehood = not(implies(X_56,implies(implies(X_56,X_54),X_54))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(falsehood,not(implies(X_56,implies(implies(X_56,X_54),X_54)))) ),[0],$fot(not(implies(and_star(implies(X_56,X_54),X_56),X_54)))]]) ).
cnf(refute_0_430,plain,
( falsehood != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| falsehood = not(implies(X_56,implies(implies(X_56,X_54),X_54))) ),
inference(resolve,[$cnf( $equal(not(implies(and_star(implies(X_56,X_54),X_56),X_54)),not(implies(X_56,implies(implies(X_56,X_54),X_54)))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
( not(truth) != not(implies(and_star(implies(X_56,X_54),X_56),X_54))
| falsehood = not(implies(X_56,implies(implies(X_56,X_54),X_54))) ),
inference(resolve,[$cnf( $equal(falsehood,not(implies(and_star(implies(X_56,X_54),X_56),X_54))) )],[refute_0_421,refute_0_430]) ).
cnf(refute_0_432,plain,
falsehood = not(implies(X_56,implies(implies(X_56,X_54),X_54))),
inference(resolve,[$cnf( $equal(not(truth),not(implies(and_star(implies(X_56,X_54),X_56),X_54))) )],[refute_0_419,refute_0_431]) ).
cnf(refute_0_433,plain,
falsehood = not(implies(X_58,implies(implies(X_58,X_57),X_57))),
inference(subst,[],[refute_0_432:[bind(X_54,$fot(X_57)),bind(X_56,$fot(X_58))]]) ).
cnf(refute_0_434,plain,
( falsehood != not(implies(X_58,implies(implies(X_58,X_57),X_57)))
| not(implies(X_58,implies(implies(X_58,X_57),X_57))) = falsehood ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(falsehood)),bind(Y0,$fot(not(implies(X_58,implies(implies(X_58,X_57),X_57)))))]]) ).
cnf(refute_0_435,plain,
not(implies(X_58,implies(implies(X_58,X_57),X_57))) = falsehood,
inference(resolve,[$cnf( $equal(falsehood,not(implies(X_58,implies(implies(X_58,X_57),X_57)))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
( implies(X_58,implies(implies(X_58,X_57),X_57)) != not(not(implies(X_58,implies(implies(X_58,X_57),X_57))))
| not(implies(X_58,implies(implies(X_58,X_57),X_57))) != falsehood
| implies(X_58,implies(implies(X_58,X_57),X_57)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_58,implies(implies(X_58,X_57),X_57)),not(not(implies(X_58,implies(implies(X_58,X_57),X_57))))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_437,plain,
( implies(X_58,implies(implies(X_58,X_57),X_57)) != not(not(implies(X_58,implies(implies(X_58,X_57),X_57))))
| implies(X_58,implies(implies(X_58,X_57),X_57)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(implies(X_58,implies(implies(X_58,X_57),X_57))),falsehood) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
implies(X_58,implies(implies(X_58,X_57),X_57)) = not(falsehood),
inference(resolve,[$cnf( $equal(implies(X_58,implies(implies(X_58,X_57),X_57)),not(not(implies(X_58,implies(implies(X_58,X_57),X_57))))) )],[refute_0_414,refute_0_437]) ).
cnf(refute_0_439,plain,
( implies(X_58,implies(implies(X_58,X_57),X_57)) != not(falsehood)
| not(falsehood) != truth
| implies(X_58,implies(implies(X_58,X_57),X_57)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_58,implies(implies(X_58,X_57),X_57)),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_440,plain,
( implies(X_58,implies(implies(X_58,X_57),X_57)) != not(falsehood)
| implies(X_58,implies(implies(X_58,X_57),X_57)) = truth ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_187,refute_0_439]) ).
cnf(refute_0_441,plain,
implies(X_58,implies(implies(X_58,X_57),X_57)) = truth,
inference(resolve,[$cnf( $equal(implies(X_58,implies(implies(X_58,X_57),X_57)),not(falsehood)) )],[refute_0_438,refute_0_440]) ).
cnf(refute_0_442,plain,
implies(X_50,implies(implies(X_50,X_67),X_67)) = truth,
inference(subst,[],[refute_0_441:[bind(X_57,$fot(X_67)),bind(X_58,$fot(X_50))]]) ).
cnf(refute_0_443,plain,
( implies(X_50,implies(implies(X_50,X_67),X_67)) != truth
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(X_50,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67))
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(truth,implies(implies(X_50,X_67),X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_50,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_444,plain,
( implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(X_50,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67))
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(truth,implies(implies(X_50,X_67),X_67)) ),
inference(resolve,[$cnf( $equal(implies(X_50,implies(implies(X_50,X_67),X_67)),truth) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(truth,implies(implies(X_50,X_67),X_67)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_50,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67))) )],[refute_0_413,refute_0_444]) ).
cnf(refute_0_446,plain,
implies(truth,X_18) = not(and_star(truth,not(X_18))),
inference(subst,[],[refute_0_82:[bind(X,$fot(truth)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_447,plain,
and_star(X,truth) = and_star(truth,X),
inference(subst,[],[and_star_commutativity:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_448,plain,
( and_star(X,truth) != X
| and_star(X,truth) != and_star(truth,X)
| and_star(truth,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X,truth),X) ),[0],$fot(and_star(truth,X))]]) ).
cnf(refute_0_449,plain,
( and_star(X,truth) != X
| and_star(truth,X) = X ),
inference(resolve,[$cnf( $equal(and_star(X,truth),and_star(truth,X)) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
and_star(truth,X) = X,
inference(resolve,[$cnf( $equal(and_star(X,truth),X) )],[axiom_4,refute_0_449]) ).
cnf(refute_0_451,plain,
and_star(truth,not(X_18)) = not(X_18),
inference(subst,[],[refute_0_450:[bind(X,$fot(not(X_18)))]]) ).
cnf(refute_0_452,plain,
( and_star(truth,not(X_18)) != not(X_18)
| implies(truth,X_18) != not(and_star(truth,not(X_18)))
| implies(truth,X_18) = not(not(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,X_18),not(and_star(truth,not(X_18)))) ),[1,0],$fot(not(X_18))]]) ).
cnf(refute_0_453,plain,
( implies(truth,X_18) != not(and_star(truth,not(X_18)))
| implies(truth,X_18) = not(not(X_18)) ),
inference(resolve,[$cnf( $equal(and_star(truth,not(X_18)),not(X_18)) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
implies(truth,X_18) = not(not(X_18)),
inference(resolve,[$cnf( $equal(implies(truth,X_18),not(and_star(truth,not(X_18)))) )],[refute_0_446,refute_0_453]) ).
cnf(refute_0_455,plain,
not(not(X_18)) = X_18,
inference(subst,[],[refute_0_61:[bind(X_6,$fot(X_18))]]) ).
cnf(refute_0_456,plain,
( implies(truth,X_18) != not(not(X_18))
| not(not(X_18)) != X_18
| implies(truth,X_18) = X_18 ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(truth,X_18),X_18) ),[0],$fot(not(not(X_18)))]]) ).
cnf(refute_0_457,plain,
( implies(truth,X_18) != not(not(X_18))
| implies(truth,X_18) = X_18 ),
inference(resolve,[$cnf( $equal(not(not(X_18)),X_18) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
implies(truth,X_18) = X_18,
inference(resolve,[$cnf( $equal(implies(truth,X_18),not(not(X_18))) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(truth,implies(implies(X_50,X_67),X_67)) = implies(implies(X_50,X_67),X_67),
inference(subst,[],[refute_0_458:[bind(X_18,$fot(implies(implies(X_50,X_67),X_67)))]]) ).
cnf(refute_0_460,plain,
( implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(truth,implies(implies(X_50,X_67),X_67))
| implies(truth,implies(implies(X_50,X_67),X_67)) != implies(implies(X_50,X_67),X_67)
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_50,X_67),X_67) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_50,X_67),X_67)) ),[0],$fot(implies(truth,implies(implies(X_50,X_67),X_67)))]]) ).
cnf(refute_0_461,plain,
( implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(truth,implies(implies(X_50,X_67),X_67))
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_50,X_67),X_67) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_50,X_67),X_67)),implies(implies(X_50,X_67),X_67)) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_50,X_67),X_67),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(truth,implies(implies(X_50,X_67),X_67))) )],[refute_0_445,refute_0_461]) ).
cnf(refute_0_463,plain,
implies(X_17,not(implies(X_17,X_33))) = not(and_star(X_17,implies(X_17,X_33))),
inference(subst,[],[refute_0_300:[bind(X_6,$fot(implies(X_17,X_33)))]]) ).
cnf(refute_0_464,plain,
and_star(X_17,implies(X_17,X_33)) = and_star(X_33,implies(X_33,X_17)),
inference(subst,[],[refute_0_339:[bind(X,$fot(X_33)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_465,plain,
( and_star(X_17,implies(X_17,X_33)) != and_star(X_33,implies(X_33,X_17))
| implies(X_17,not(implies(X_17,X_33))) != not(and_star(X_17,implies(X_17,X_33)))
| implies(X_17,not(implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,not(implies(X_17,X_33))),not(and_star(X_17,implies(X_17,X_33)))) ),[1,0],$fot(and_star(X_33,implies(X_33,X_17)))]]) ).
cnf(refute_0_466,plain,
( implies(X_17,not(implies(X_17,X_33))) != not(and_star(X_17,implies(X_17,X_33)))
| implies(X_17,not(implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))) ),
inference(resolve,[$cnf( $equal(and_star(X_17,implies(X_17,X_33)),and_star(X_33,implies(X_33,X_17))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
implies(X_17,not(implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))),
inference(resolve,[$cnf( $equal(implies(X_17,not(implies(X_17,X_33))),not(and_star(X_17,implies(X_17,X_33)))) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
( implies(X_17,not(implies(X_17,X_33))) != not(and_star(X_17,implies(X_17,X_33)))
| implies(X_17,not(implies(X_17,X_33))) != not(and_star(X_33,implies(X_33,X_17)))
| not(and_star(X_17,implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,not(implies(X_17,X_33))),not(and_star(X_33,implies(X_33,X_17)))) ),[0],$fot(not(and_star(X_17,implies(X_17,X_33))))]]) ).
cnf(refute_0_469,plain,
( implies(X_17,not(implies(X_17,X_33))) != not(and_star(X_33,implies(X_33,X_17)))
| not(and_star(X_17,implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))) ),
inference(resolve,[$cnf( $equal(implies(X_17,not(implies(X_17,X_33))),not(and_star(X_17,implies(X_17,X_33)))) )],[refute_0_463,refute_0_468]) ).
cnf(refute_0_470,plain,
not(and_star(X_17,implies(X_17,X_33))) = not(and_star(X_33,implies(X_33,X_17))),
inference(resolve,[$cnf( $equal(implies(X_17,not(implies(X_17,X_33))),not(and_star(X_33,implies(X_33,X_17)))) )],[refute_0_467,refute_0_469]) ).
cnf(refute_0_471,plain,
not(and_star(X_44,implies(X_44,not(X_6)))) = not(and_star(not(X_6),implies(not(X_6),X_44))),
inference(subst,[],[refute_0_470:[bind(X_17,$fot(X_44)),bind(X_33,$fot(not(X_6)))]]) ).
cnf(refute_0_472,plain,
implies(X_44,not(X_6)) = not(and_star(X_44,X_6)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(X_44))]]) ).
cnf(refute_0_473,plain,
( implies(X_44,not(X_6)) != not(and_star(X_44,X_6))
| not(and_star(X_44,implies(X_44,not(X_6)))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = not(and_star(not(X_6),implies(not(X_6),X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X_44,implies(X_44,not(X_6)))),not(and_star(not(X_6),implies(not(X_6),X_44)))) ),[0,0,1],$fot(not(and_star(X_44,X_6)))]]) ).
cnf(refute_0_474,plain,
( not(and_star(X_44,implies(X_44,not(X_6)))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = not(and_star(not(X_6),implies(not(X_6),X_44))) ),
inference(resolve,[$cnf( $equal(implies(X_44,not(X_6)),not(and_star(X_44,X_6))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
not(and_star(X_44,not(and_star(X_44,X_6)))) = not(and_star(not(X_6),implies(not(X_6),X_44))),
inference(resolve,[$cnf( $equal(not(and_star(X_44,implies(X_44,not(X_6)))),not(and_star(not(X_6),implies(not(X_6),X_44)))) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
not(not(implies(X_44,and_star(X_44,X_6)))) = implies(X_44,and_star(X_44,X_6)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_44,and_star(X_44,X_6))))]]) ).
cnf(refute_0_477,plain,
and_star(X_44,not(and_star(X_44,X_6))) = not(implies(X_44,and_star(X_44,X_6))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_44)),bind(X_18,$fot(and_star(X_44,X_6)))]]) ).
cnf(refute_0_478,plain,
not(and_star(X_44,not(and_star(X_44,X_6)))) = not(and_star(X_44,not(and_star(X_44,X_6)))),
introduced(tautology,[refl,[$fot(not(and_star(X_44,not(and_star(X_44,X_6)))))]]) ).
cnf(refute_0_479,plain,
( and_star(X_44,not(and_star(X_44,X_6))) != not(implies(X_44,and_star(X_44,X_6)))
| not(and_star(X_44,not(and_star(X_44,X_6)))) != not(and_star(X_44,not(and_star(X_44,X_6))))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = not(not(implies(X_44,and_star(X_44,X_6)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),not(and_star(X_44,not(and_star(X_44,X_6))))) ),[1,0],$fot(not(implies(X_44,and_star(X_44,X_6))))]]) ).
cnf(refute_0_480,plain,
( and_star(X_44,not(and_star(X_44,X_6))) != not(implies(X_44,and_star(X_44,X_6)))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = not(not(implies(X_44,and_star(X_44,X_6)))) ),
inference(resolve,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),not(and_star(X_44,not(and_star(X_44,X_6))))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
not(and_star(X_44,not(and_star(X_44,X_6)))) = not(not(implies(X_44,and_star(X_44,X_6)))),
inference(resolve,[$cnf( $equal(and_star(X_44,not(and_star(X_44,X_6))),not(implies(X_44,and_star(X_44,X_6)))) )],[refute_0_477,refute_0_480]) ).
cnf(refute_0_482,plain,
( not(and_star(X_44,not(and_star(X_44,X_6)))) != not(not(implies(X_44,and_star(X_44,X_6))))
| not(not(implies(X_44,and_star(X_44,X_6)))) != implies(X_44,and_star(X_44,X_6))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = implies(X_44,and_star(X_44,X_6)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(X_44,not(and_star(X_44,X_6)))))),bind(Y0,$fot(not(not(implies(X_44,and_star(X_44,X_6)))))),bind(Z0,$fot(implies(X_44,and_star(X_44,X_6))))]]) ).
cnf(refute_0_483,plain,
( not(not(implies(X_44,and_star(X_44,X_6)))) != implies(X_44,and_star(X_44,X_6))
| not(and_star(X_44,not(and_star(X_44,X_6)))) = implies(X_44,and_star(X_44,X_6)) ),
inference(resolve,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),not(not(implies(X_44,and_star(X_44,X_6))))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
not(and_star(X_44,not(and_star(X_44,X_6)))) = implies(X_44,and_star(X_44,X_6)),
inference(resolve,[$cnf( $equal(not(not(implies(X_44,and_star(X_44,X_6)))),implies(X_44,and_star(X_44,X_6))) )],[refute_0_476,refute_0_483]) ).
cnf(refute_0_485,plain,
( not(and_star(X_44,not(and_star(X_44,X_6)))) != implies(X_44,and_star(X_44,X_6))
| not(and_star(X_44,not(and_star(X_44,X_6)))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| implies(X_44,and_star(X_44,X_6)) = not(and_star(not(X_6),implies(not(X_6),X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),not(and_star(not(X_6),implies(not(X_6),X_44)))) ),[0],$fot(implies(X_44,and_star(X_44,X_6)))]]) ).
cnf(refute_0_486,plain,
( not(and_star(X_44,not(and_star(X_44,X_6)))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| implies(X_44,and_star(X_44,X_6)) = not(and_star(not(X_6),implies(not(X_6),X_44))) ),
inference(resolve,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),implies(X_44,and_star(X_44,X_6))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
not(not(implies(implies(not(X_6),X_44),X_6))) = implies(implies(not(X_6),X_44),X_6),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(not(X_6),X_44),X_6)))]]) ).
cnf(refute_0_488,plain,
and_star(not(X_6),implies(not(X_6),X_44)) = not(implies(implies(not(X_6),X_44),X_6)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(not(X_6),X_44))),bind(X_28,$fot(X_6))]]) ).
cnf(refute_0_489,plain,
not(and_star(not(X_6),implies(not(X_6),X_44))) = not(and_star(not(X_6),implies(not(X_6),X_44))),
introduced(tautology,[refl,[$fot(not(and_star(not(X_6),implies(not(X_6),X_44))))]]) ).
cnf(refute_0_490,plain,
( and_star(not(X_6),implies(not(X_6),X_44)) != not(implies(implies(not(X_6),X_44),X_6))
| not(and_star(not(X_6),implies(not(X_6),X_44))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| not(and_star(not(X_6),implies(not(X_6),X_44))) = not(not(implies(implies(not(X_6),X_44),X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_6),implies(not(X_6),X_44))),not(and_star(not(X_6),implies(not(X_6),X_44)))) ),[1,0],$fot(not(implies(implies(not(X_6),X_44),X_6)))]]) ).
cnf(refute_0_491,plain,
( and_star(not(X_6),implies(not(X_6),X_44)) != not(implies(implies(not(X_6),X_44),X_6))
| not(and_star(not(X_6),implies(not(X_6),X_44))) = not(not(implies(implies(not(X_6),X_44),X_6))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(not(X_6),X_44))),not(and_star(not(X_6),implies(not(X_6),X_44)))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
not(and_star(not(X_6),implies(not(X_6),X_44))) = not(not(implies(implies(not(X_6),X_44),X_6))),
inference(resolve,[$cnf( $equal(and_star(not(X_6),implies(not(X_6),X_44)),not(implies(implies(not(X_6),X_44),X_6))) )],[refute_0_488,refute_0_491]) ).
cnf(refute_0_493,plain,
( not(and_star(not(X_6),implies(not(X_6),X_44))) != not(not(implies(implies(not(X_6),X_44),X_6)))
| not(not(implies(implies(not(X_6),X_44),X_6))) != implies(implies(not(X_6),X_44),X_6)
| not(and_star(not(X_6),implies(not(X_6),X_44))) = implies(implies(not(X_6),X_44),X_6) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_6),implies(not(X_6),X_44))))),bind(Y0,$fot(not(not(implies(implies(not(X_6),X_44),X_6))))),bind(Z0,$fot(implies(implies(not(X_6),X_44),X_6)))]]) ).
cnf(refute_0_494,plain,
( not(not(implies(implies(not(X_6),X_44),X_6))) != implies(implies(not(X_6),X_44),X_6)
| not(and_star(not(X_6),implies(not(X_6),X_44))) = implies(implies(not(X_6),X_44),X_6) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(not(X_6),X_44))),not(not(implies(implies(not(X_6),X_44),X_6)))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
not(and_star(not(X_6),implies(not(X_6),X_44))) = implies(implies(not(X_6),X_44),X_6),
inference(resolve,[$cnf( $equal(not(not(implies(implies(not(X_6),X_44),X_6))),implies(implies(not(X_6),X_44),X_6)) )],[refute_0_487,refute_0_494]) ).
cnf(refute_0_496,plain,
( implies(X_44,and_star(X_44,X_6)) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| not(and_star(not(X_6),implies(not(X_6),X_44))) != implies(implies(not(X_6),X_44),X_6)
| implies(X_44,and_star(X_44,X_6)) = implies(implies(not(X_6),X_44),X_6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_44,and_star(X_44,X_6)),implies(implies(not(X_6),X_44),X_6)) ),[0],$fot(not(and_star(not(X_6),implies(not(X_6),X_44))))]]) ).
cnf(refute_0_497,plain,
( implies(X_44,and_star(X_44,X_6)) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| implies(X_44,and_star(X_44,X_6)) = implies(implies(not(X_6),X_44),X_6) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(not(X_6),X_44))),implies(implies(not(X_6),X_44),X_6)) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
( not(and_star(X_44,not(and_star(X_44,X_6)))) != not(and_star(not(X_6),implies(not(X_6),X_44)))
| implies(X_44,and_star(X_44,X_6)) = implies(implies(not(X_6),X_44),X_6) ),
inference(resolve,[$cnf( $equal(implies(X_44,and_star(X_44,X_6)),not(and_star(not(X_6),implies(not(X_6),X_44)))) )],[refute_0_486,refute_0_497]) ).
cnf(refute_0_499,plain,
implies(X_44,and_star(X_44,X_6)) = implies(implies(not(X_6),X_44),X_6),
inference(resolve,[$cnf( $equal(not(and_star(X_44,not(and_star(X_44,X_6)))),not(and_star(not(X_6),implies(not(X_6),X_44)))) )],[refute_0_475,refute_0_498]) ).
cnf(refute_0_500,plain,
implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6),
inference(subst,[],[refute_0_499:[bind(X_44,$fot(and_star(not(X_6),X_49)))]]) ).
cnf(refute_0_501,plain,
implies(not(X_6),and_star(not(X_6),X_49)) = implies(implies(not(X_49),not(X_6)),X_49),
inference(subst,[],[refute_0_499:[bind(X_44,$fot(not(X_6))),bind(X_6,$fot(X_49))]]) ).
cnf(refute_0_502,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)
| implies(not(X_6),and_star(not(X_6),X_49)) != implies(implies(not(X_49),not(X_6)),X_49)
| implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)) ),[1,0],$fot(implies(implies(not(X_49),not(X_6)),X_49))]]) ).
cnf(refute_0_503,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)
| implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(not(X_6),and_star(not(X_6),X_49)),implies(implies(not(X_49),not(X_6)),X_49)) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6),
inference(resolve,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)) )],[refute_0_500,refute_0_503]) ).
cnf(refute_0_505,plain,
not(not(implies(implies(X_49,X_6),X_6))) = implies(implies(X_49,X_6),X_6),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(X_49,X_6),X_6)))]]) ).
cnf(refute_0_506,plain,
and_star(not(X_6),implies(X_49,X_6)) = not(implies(implies(X_49,X_6),X_6)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(X_49,X_6))),bind(X_28,$fot(X_6))]]) ).
cnf(refute_0_507,plain,
not(and_star(not(X_6),implies(X_49,X_6))) = not(and_star(not(X_6),implies(X_49,X_6))),
introduced(tautology,[refl,[$fot(not(and_star(not(X_6),implies(X_49,X_6))))]]) ).
cnf(refute_0_508,plain,
( and_star(not(X_6),implies(X_49,X_6)) != not(implies(implies(X_49,X_6),X_6))
| not(and_star(not(X_6),implies(X_49,X_6))) != not(and_star(not(X_6),implies(X_49,X_6)))
| not(and_star(not(X_6),implies(X_49,X_6))) = not(not(implies(implies(X_49,X_6),X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_6),implies(X_49,X_6))),not(and_star(not(X_6),implies(X_49,X_6)))) ),[1,0],$fot(not(implies(implies(X_49,X_6),X_6)))]]) ).
cnf(refute_0_509,plain,
( and_star(not(X_6),implies(X_49,X_6)) != not(implies(implies(X_49,X_6),X_6))
| not(and_star(not(X_6),implies(X_49,X_6))) = not(not(implies(implies(X_49,X_6),X_6))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(X_49,X_6))),not(and_star(not(X_6),implies(X_49,X_6)))) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
not(and_star(not(X_6),implies(X_49,X_6))) = not(not(implies(implies(X_49,X_6),X_6))),
inference(resolve,[$cnf( $equal(and_star(not(X_6),implies(X_49,X_6)),not(implies(implies(X_49,X_6),X_6))) )],[refute_0_506,refute_0_509]) ).
cnf(refute_0_511,plain,
( not(and_star(not(X_6),implies(X_49,X_6))) != not(not(implies(implies(X_49,X_6),X_6)))
| not(not(implies(implies(X_49,X_6),X_6))) != implies(implies(X_49,X_6),X_6)
| not(and_star(not(X_6),implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_6),implies(X_49,X_6))))),bind(Y0,$fot(not(not(implies(implies(X_49,X_6),X_6))))),bind(Z0,$fot(implies(implies(X_49,X_6),X_6)))]]) ).
cnf(refute_0_512,plain,
( not(not(implies(implies(X_49,X_6),X_6))) != implies(implies(X_49,X_6),X_6)
| not(and_star(not(X_6),implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(X_49,X_6))),not(not(implies(implies(X_49,X_6),X_6)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
not(and_star(not(X_6),implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6),
inference(resolve,[$cnf( $equal(not(not(implies(implies(X_49,X_6),X_6))),implies(implies(X_49,X_6),X_6)) )],[refute_0_505,refute_0_512]) ).
cnf(refute_0_514,plain,
implies(not(X_6),not(implies(X_49,X_6))) = not(and_star(not(X_6),implies(X_49,X_6))),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(not(X_6))),bind(X_6,$fot(implies(X_49,X_6)))]]) ).
cnf(refute_0_515,plain,
( implies(not(X_6),not(implies(X_49,X_6))) != not(and_star(not(X_6),implies(X_49,X_6)))
| not(and_star(not(X_6),implies(X_49,X_6))) != implies(implies(X_49,X_6),X_6)
| implies(not(X_6),not(implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_6),not(implies(X_49,X_6))))),bind(Y0,$fot(not(and_star(not(X_6),implies(X_49,X_6))))),bind(Z0,$fot(implies(implies(X_49,X_6),X_6)))]]) ).
cnf(refute_0_516,plain,
( not(and_star(not(X_6),implies(X_49,X_6))) != implies(implies(X_49,X_6),X_6)
| implies(not(X_6),not(implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6) ),
inference(resolve,[$cnf( $equal(implies(not(X_6),not(implies(X_49,X_6))),not(and_star(not(X_6),implies(X_49,X_6)))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
implies(not(X_6),not(implies(X_49,X_6))) = implies(implies(X_49,X_6),X_6),
inference(resolve,[$cnf( $equal(not(and_star(not(X_6),implies(X_49,X_6))),implies(implies(X_49,X_6),X_6)) )],[refute_0_513,refute_0_516]) ).
cnf(refute_0_518,plain,
and_star(not(X_6),X_49) = not(implies(X_49,X_6)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_49)),bind(X_28,$fot(X_6))]]) ).
cnf(refute_0_519,plain,
implies(not(X_6),and_star(not(X_6),X_49)) = implies(not(X_6),and_star(not(X_6),X_49)),
introduced(tautology,[refl,[$fot(implies(not(X_6),and_star(not(X_6),X_49)))]]) ).
cnf(refute_0_520,plain,
( and_star(not(X_6),X_49) != not(implies(X_49,X_6))
| implies(not(X_6),and_star(not(X_6),X_49)) != implies(not(X_6),and_star(not(X_6),X_49))
| implies(not(X_6),and_star(not(X_6),X_49)) = implies(not(X_6),not(implies(X_49,X_6))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_6),and_star(not(X_6),X_49)),implies(not(X_6),and_star(not(X_6),X_49))) ),[1,1],$fot(not(implies(X_49,X_6)))]]) ).
cnf(refute_0_521,plain,
( and_star(not(X_6),X_49) != not(implies(X_49,X_6))
| implies(not(X_6),and_star(not(X_6),X_49)) = implies(not(X_6),not(implies(X_49,X_6))) ),
inference(resolve,[$cnf( $equal(implies(not(X_6),and_star(not(X_6),X_49)),implies(not(X_6),and_star(not(X_6),X_49))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
implies(not(X_6),and_star(not(X_6),X_49)) = implies(not(X_6),not(implies(X_49,X_6))),
inference(resolve,[$cnf( $equal(and_star(not(X_6),X_49),not(implies(X_49,X_6))) )],[refute_0_518,refute_0_521]) ).
cnf(refute_0_523,plain,
( implies(not(X_6),and_star(not(X_6),X_49)) != implies(not(X_6),not(implies(X_49,X_6)))
| implies(not(X_6),not(implies(X_49,X_6))) != implies(implies(X_49,X_6),X_6)
| implies(not(X_6),and_star(not(X_6),X_49)) = implies(implies(X_49,X_6),X_6) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_6),and_star(not(X_6),X_49)))),bind(Y0,$fot(implies(not(X_6),not(implies(X_49,X_6))))),bind(Z0,$fot(implies(implies(X_49,X_6),X_6)))]]) ).
cnf(refute_0_524,plain,
( implies(not(X_6),not(implies(X_49,X_6))) != implies(implies(X_49,X_6),X_6)
| implies(not(X_6),and_star(not(X_6),X_49)) = implies(implies(X_49,X_6),X_6) ),
inference(resolve,[$cnf( $equal(implies(not(X_6),and_star(not(X_6),X_49)),implies(not(X_6),not(implies(X_49,X_6)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
implies(not(X_6),and_star(not(X_6),X_49)) = implies(implies(X_49,X_6),X_6),
inference(resolve,[$cnf( $equal(implies(not(X_6),not(implies(X_49,X_6))),implies(implies(X_49,X_6),X_6)) )],[refute_0_517,refute_0_524]) ).
cnf(refute_0_526,plain,
implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) = implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6),
introduced(tautology,[refl,[$fot(implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6))]]) ).
cnf(refute_0_527,plain,
( implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) != implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)
| implies(not(X_6),and_star(not(X_6),X_49)) != implies(implies(X_49,X_6),X_6)
| implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) = implies(implies(implies(X_49,X_6),X_6),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6),implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)) ),[1,0],$fot(implies(implies(X_49,X_6),X_6))]]) ).
cnf(refute_0_528,plain,
( implies(not(X_6),and_star(not(X_6),X_49)) != implies(implies(X_49,X_6),X_6)
| implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) = implies(implies(implies(X_49,X_6),X_6),X_6) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6),implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) = implies(implies(implies(X_49,X_6),X_6),X_6),
inference(resolve,[$cnf( $equal(implies(not(X_6),and_star(not(X_6),X_49)),implies(implies(X_49,X_6),X_6)) )],[refute_0_525,refute_0_528]) ).
cnf(refute_0_530,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)
| implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) != implies(implies(implies(X_49,X_6),X_6),X_6)
| implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(X_49,X_6),X_6),X_6) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)))),bind(Y0,$fot(implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6))),bind(Z0,$fot(implies(implies(implies(X_49,X_6),X_6),X_6)))]]) ).
cnf(refute_0_531,plain,
( implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6) != implies(implies(implies(X_49,X_6),X_6),X_6)
| implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(X_49,X_6),X_6),X_6) ),
inference(resolve,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6)) )],[refute_0_500,refute_0_530]) ).
cnf(refute_0_532,plain,
implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) = implies(implies(implies(X_49,X_6),X_6),X_6),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),and_star(not(X_6),X_49)),X_6),implies(implies(implies(X_49,X_6),X_6),X_6)) )],[refute_0_529,refute_0_531]) ).
cnf(refute_0_533,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(implies(X_49,X_6),X_6),X_6)
| implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)) ),[0],$fot(implies(implies(implies(X_49,X_6),X_6),X_6))]]) ).
cnf(refute_0_534,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(implies(X_49,X_6),X_6),X_6)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
not(not(implies(X_6,X_49))) = implies(X_6,X_49),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_6,X_49)))]]) ).
cnf(refute_0_536,plain,
and_star(not(X_49),X_6) = not(implies(X_6,X_49)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_6)),bind(X_28,$fot(X_49))]]) ).
cnf(refute_0_537,plain,
not(and_star(not(X_49),X_6)) = not(and_star(not(X_49),X_6)),
introduced(tautology,[refl,[$fot(not(and_star(not(X_49),X_6)))]]) ).
cnf(refute_0_538,plain,
( and_star(not(X_49),X_6) != not(implies(X_6,X_49))
| not(and_star(not(X_49),X_6)) != not(and_star(not(X_49),X_6))
| not(and_star(not(X_49),X_6)) = not(not(implies(X_6,X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_49),X_6)),not(and_star(not(X_49),X_6))) ),[1,0],$fot(not(implies(X_6,X_49)))]]) ).
cnf(refute_0_539,plain,
( and_star(not(X_49),X_6) != not(implies(X_6,X_49))
| not(and_star(not(X_49),X_6)) = not(not(implies(X_6,X_49))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_49),X_6)),not(and_star(not(X_49),X_6))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
not(and_star(not(X_49),X_6)) = not(not(implies(X_6,X_49))),
inference(resolve,[$cnf( $equal(and_star(not(X_49),X_6),not(implies(X_6,X_49))) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
( not(and_star(not(X_49),X_6)) != not(not(implies(X_6,X_49)))
| not(not(implies(X_6,X_49))) != implies(X_6,X_49)
| not(and_star(not(X_49),X_6)) = implies(X_6,X_49) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_49),X_6)))),bind(Y0,$fot(not(not(implies(X_6,X_49))))),bind(Z0,$fot(implies(X_6,X_49)))]]) ).
cnf(refute_0_542,plain,
( not(not(implies(X_6,X_49))) != implies(X_6,X_49)
| not(and_star(not(X_49),X_6)) = implies(X_6,X_49) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_49),X_6)),not(not(implies(X_6,X_49)))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
not(and_star(not(X_49),X_6)) = implies(X_6,X_49),
inference(resolve,[$cnf( $equal(not(not(implies(X_6,X_49))),implies(X_6,X_49)) )],[refute_0_535,refute_0_542]) ).
cnf(refute_0_544,plain,
implies(not(X_49),not(X_6)) = not(and_star(not(X_49),X_6)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(not(X_49)))]]) ).
cnf(refute_0_545,plain,
( implies(not(X_49),not(X_6)) != not(and_star(not(X_49),X_6))
| not(and_star(not(X_49),X_6)) != implies(X_6,X_49)
| implies(not(X_49),not(X_6)) = implies(X_6,X_49) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_49),not(X_6)))),bind(Y0,$fot(not(and_star(not(X_49),X_6)))),bind(Z0,$fot(implies(X_6,X_49)))]]) ).
cnf(refute_0_546,plain,
( not(and_star(not(X_49),X_6)) != implies(X_6,X_49)
| implies(not(X_49),not(X_6)) = implies(X_6,X_49) ),
inference(resolve,[$cnf( $equal(implies(not(X_49),not(X_6)),not(and_star(not(X_49),X_6))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
implies(not(X_49),not(X_6)) = implies(X_6,X_49),
inference(resolve,[$cnf( $equal(not(and_star(not(X_49),X_6)),implies(X_6,X_49)) )],[refute_0_543,refute_0_546]) ).
cnf(refute_0_548,plain,
implies(implies(not(X_49),not(X_6)),X_49) = implies(implies(not(X_49),not(X_6)),X_49),
introduced(tautology,[refl,[$fot(implies(implies(not(X_49),not(X_6)),X_49))]]) ).
cnf(refute_0_549,plain,
( implies(implies(not(X_49),not(X_6)),X_49) != implies(implies(not(X_49),not(X_6)),X_49)
| implies(not(X_49),not(X_6)) != implies(X_6,X_49)
| implies(implies(not(X_49),not(X_6)),X_49) = implies(implies(X_6,X_49),X_49) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_49),not(X_6)),X_49),implies(implies(not(X_49),not(X_6)),X_49)) ),[1,0],$fot(implies(X_6,X_49))]]) ).
cnf(refute_0_550,plain,
( implies(not(X_49),not(X_6)) != implies(X_6,X_49)
| implies(implies(not(X_49),not(X_6)),X_49) = implies(implies(X_6,X_49),X_49) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_49),not(X_6)),X_49),implies(implies(not(X_49),not(X_6)),X_49)) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
implies(implies(not(X_49),not(X_6)),X_49) = implies(implies(X_6,X_49),X_49),
inference(resolve,[$cnf( $equal(implies(not(X_49),not(X_6)),implies(X_6,X_49)) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) = implies(implies(implies(not(X_49),not(X_6)),X_49),X_6),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_49),not(X_6)),X_49),X_6))]]) ).
cnf(refute_0_553,plain,
( implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(not(X_49),not(X_6)),X_49) != implies(implies(X_6,X_49),X_49)
| implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_49),not(X_6)),X_49),X_6),implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)) ),[1,0],$fot(implies(implies(X_6,X_49),X_49))]]) ).
cnf(refute_0_554,plain,
( implies(implies(not(X_49),not(X_6)),X_49) != implies(implies(X_6,X_49),X_49)
| implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_49),not(X_6)),X_49),X_6),implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)) )],[refute_0_552,refute_0_553]) ).
cnf(refute_0_555,plain,
implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6),
inference(resolve,[$cnf( $equal(implies(implies(not(X_49),not(X_6)),X_49),implies(implies(X_6,X_49),X_49)) )],[refute_0_551,refute_0_554]) ).
cnf(refute_0_556,plain,
( implies(implies(implies(X_49,X_6),X_6),X_6) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(implies(not(X_49),not(X_6)),X_49),X_6) != implies(implies(implies(X_6,X_49),X_49),X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_49,X_6),X_6),X_6),implies(implies(implies(X_6,X_49),X_49),X_6)) ),[0],$fot(implies(implies(implies(not(X_49),not(X_6)),X_49),X_6))]]) ).
cnf(refute_0_557,plain,
( implies(implies(implies(X_49,X_6),X_6),X_6) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_49),not(X_6)),X_49),X_6),implies(implies(implies(X_6,X_49),X_49),X_6)) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
( implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)) != implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_49,X_6),X_6),X_6),implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)) )],[refute_0_534,refute_0_557]) ).
cnf(refute_0_559,plain,
implies(implies(implies(X_49,X_6),X_6),X_6) = implies(implies(implies(X_6,X_49),X_49),X_6),
inference(resolve,[$cnf( $equal(implies(and_star(not(X_6),X_49),and_star(and_star(not(X_6),X_49),X_6)),implies(implies(implies(not(X_49),not(X_6)),X_49),X_6)) )],[refute_0_504,refute_0_558]) ).
cnf(refute_0_560,plain,
implies(implies(implies(X_77,X_50),X_50),X_50) = implies(implies(X_50,implies(X_77,X_50)),implies(X_77,X_50)),
inference(subst,[],[refute_0_412:[bind(X_51,$fot(implies(X_77,X_50)))]]) ).
cnf(refute_0_561,plain,
implies(X_50,implies(X_77,X_50)) = truth,
inference(subst,[],[refute_0_229:[bind(X_74,$fot(X_50)),bind(X_75,$fot(X_77))]]) ).
cnf(refute_0_562,plain,
( implies(X_50,implies(X_77,X_50)) != truth
| implies(implies(implies(X_77,X_50),X_50),X_50) != implies(implies(X_50,implies(X_77,X_50)),implies(X_77,X_50))
| implies(implies(implies(X_77,X_50),X_50),X_50) = implies(truth,implies(X_77,X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_77,X_50),X_50),X_50),implies(implies(X_50,implies(X_77,X_50)),implies(X_77,X_50))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_563,plain,
( implies(implies(implies(X_77,X_50),X_50),X_50) != implies(implies(X_50,implies(X_77,X_50)),implies(X_77,X_50))
| implies(implies(implies(X_77,X_50),X_50),X_50) = implies(truth,implies(X_77,X_50)) ),
inference(resolve,[$cnf( $equal(implies(X_50,implies(X_77,X_50)),truth) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
implies(implies(implies(X_77,X_50),X_50),X_50) = implies(truth,implies(X_77,X_50)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_77,X_50),X_50),X_50),implies(implies(X_50,implies(X_77,X_50)),implies(X_77,X_50))) )],[refute_0_560,refute_0_563]) ).
cnf(refute_0_565,plain,
implies(truth,implies(X_77,X_50)) = implies(X_77,X_50),
inference(subst,[],[refute_0_458:[bind(X_18,$fot(implies(X_77,X_50)))]]) ).
cnf(refute_0_566,plain,
( implies(implies(implies(X_77,X_50),X_50),X_50) != implies(truth,implies(X_77,X_50))
| implies(truth,implies(X_77,X_50)) != implies(X_77,X_50)
| implies(implies(implies(X_77,X_50),X_50),X_50) = implies(X_77,X_50) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_77,X_50),X_50),X_50),implies(X_77,X_50)) ),[0],$fot(implies(truth,implies(X_77,X_50)))]]) ).
cnf(refute_0_567,plain,
( implies(implies(implies(X_77,X_50),X_50),X_50) != implies(truth,implies(X_77,X_50))
| implies(implies(implies(X_77,X_50),X_50),X_50) = implies(X_77,X_50) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_77,X_50)),implies(X_77,X_50)) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
implies(implies(implies(X_77,X_50),X_50),X_50) = implies(X_77,X_50),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_77,X_50),X_50),X_50),implies(truth,implies(X_77,X_50))) )],[refute_0_564,refute_0_567]) ).
cnf(refute_0_569,plain,
implies(implies(implies(X_49,X_6),X_6),X_6) = implies(X_49,X_6),
inference(subst,[],[refute_0_568:[bind(X_50,$fot(X_6)),bind(X_77,$fot(X_49))]]) ).
cnf(refute_0_570,plain,
( implies(implies(implies(X_49,X_6),X_6),X_6) != implies(X_49,X_6)
| implies(implies(implies(X_49,X_6),X_6),X_6) != implies(implies(implies(X_6,X_49),X_49),X_6)
| implies(X_49,X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_49,X_6),X_6),X_6),implies(implies(implies(X_6,X_49),X_49),X_6)) ),[0],$fot(implies(X_49,X_6))]]) ).
cnf(refute_0_571,plain,
( implies(implies(implies(X_49,X_6),X_6),X_6) != implies(implies(implies(X_6,X_49),X_49),X_6)
| implies(X_49,X_6) = implies(implies(implies(X_6,X_49),X_49),X_6) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_49,X_6),X_6),X_6),implies(X_49,X_6)) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
implies(X_49,X_6) = implies(implies(implies(X_6,X_49),X_49),X_6),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_49,X_6),X_6),X_6),implies(implies(implies(X_6,X_49),X_49),X_6)) )],[refute_0_559,refute_0_571]) ).
cnf(refute_0_573,plain,
( implies(X_49,X_6) != implies(implies(implies(X_6,X_49),X_49),X_6)
| implies(implies(implies(X_6,X_49),X_49),X_6) = implies(X_49,X_6) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_49,X_6))),bind(Y0,$fot(implies(implies(implies(X_6,X_49),X_49),X_6)))]]) ).
cnf(refute_0_574,plain,
implies(implies(implies(X_6,X_49),X_49),X_6) = implies(X_49,X_6),
inference(resolve,[$cnf( $equal(implies(X_49,X_6),implies(implies(implies(X_6,X_49),X_49),X_6)) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
implies(implies(implies(X_50,X_67),X_67),X_50) = implies(X_67,X_50),
inference(subst,[],[refute_0_574:[bind(X_49,$fot(X_67)),bind(X_6,$fot(X_50))]]) ).
cnf(refute_0_576,plain,
implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50))]]) ).
cnf(refute_0_577,plain,
( implies(implies(implies(X_50,X_67),X_67),X_50) != implies(X_67,X_50)
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50)
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_67,X_50),X_50) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50)) ),[1,0],$fot(implies(X_67,X_50))]]) ).
cnf(refute_0_578,plain,
( implies(implies(implies(X_50,X_67),X_67),X_50) != implies(X_67,X_50)
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_67,X_50),X_50) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50)) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) = implies(implies(X_67,X_50),X_50),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_50,X_67),X_67),X_50),implies(X_67,X_50)) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
( implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(X_50,X_67),X_67)
| implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(X_67,X_50),X_50)
| implies(implies(X_67,X_50),X_50) = implies(implies(X_50,X_67),X_67) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_50,X_67),X_67)) ),[0],$fot(implies(implies(X_67,X_50),X_50))]]) ).
cnf(refute_0_581,plain,
( implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50) != implies(implies(X_50,X_67),X_67)
| implies(implies(X_67,X_50),X_50) = implies(implies(X_50,X_67),X_67) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_67,X_50),X_50)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
implies(implies(X_67,X_50),X_50) = implies(implies(X_50,X_67),X_67),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_50,X_67),X_67),X_50),X_50),implies(implies(X_50,X_67),X_67)) )],[refute_0_462,refute_0_581]) ).
cnf(refute_0_583,plain,
( implies(implies(X_67,X_50),X_50) != implies(implies(X_50,X_67),X_67)
| implies(implies(X_50,X_67),X_67) = implies(implies(X_67,X_50),X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_67,X_50),X_50))),bind(Y0,$fot(implies(implies(X_50,X_67),X_67)))]]) ).
cnf(refute_0_584,plain,
implies(implies(X_50,X_67),X_67) = implies(implies(X_67,X_50),X_50),
inference(resolve,[$cnf( $equal(implies(implies(X_67,X_50),X_50),implies(implies(X_50,X_67),X_67)) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
implies(implies(b,a),a) = implies(implies(a,b),b),
inference(subst,[],[refute_0_584:[bind(X_50,$fot(b)),bind(X_67,$fot(a))]]) ).
cnf(refute_0_586,plain,
implies(not(X_37),X_38) = not(not(implies(not(X_37),X_38))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(not(X_37),X_38)))]]) ).
cnf(refute_0_587,plain,
and_star(not(X_32),not(X_18)) = not(implies(not(X_32),X_18)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(not(X_32)))]]) ).
cnf(refute_0_588,plain,
and_star(not(X_32),not(X_18)) = not(implies(not(X_18),X_32)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(not(X_18))),bind(X_28,$fot(X_32))]]) ).
cnf(refute_0_589,plain,
( and_star(not(X_32),not(X_18)) != not(implies(not(X_18),X_32))
| and_star(not(X_32),not(X_18)) != not(implies(not(X_32),X_18))
| not(implies(not(X_18),X_32)) = not(implies(not(X_32),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_32),not(X_18)),not(implies(not(X_32),X_18))) ),[0],$fot(not(implies(not(X_18),X_32)))]]) ).
cnf(refute_0_590,plain,
( and_star(not(X_32),not(X_18)) != not(implies(not(X_32),X_18))
| not(implies(not(X_18),X_32)) = not(implies(not(X_32),X_18)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_32),not(X_18)),not(implies(not(X_18),X_32))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
not(implies(not(X_18),X_32)) = not(implies(not(X_32),X_18)),
inference(resolve,[$cnf( $equal(and_star(not(X_32),not(X_18)),not(implies(not(X_32),X_18))) )],[refute_0_587,refute_0_590]) ).
cnf(refute_0_592,plain,
not(implies(not(X_37),X_38)) = not(implies(not(X_38),X_37)),
inference(subst,[],[refute_0_591:[bind(X_18,$fot(X_37)),bind(X_32,$fot(X_38))]]) ).
cnf(refute_0_593,plain,
( implies(not(X_37),X_38) != not(not(implies(not(X_37),X_38)))
| not(implies(not(X_37),X_38)) != not(implies(not(X_38),X_37))
| implies(not(X_37),X_38) = not(not(implies(not(X_38),X_37))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_37),X_38),not(not(implies(not(X_37),X_38)))) ),[1,0],$fot(not(implies(not(X_38),X_37)))]]) ).
cnf(refute_0_594,plain,
( implies(not(X_37),X_38) != not(not(implies(not(X_37),X_38)))
| implies(not(X_37),X_38) = not(not(implies(not(X_38),X_37))) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_37),X_38)),not(implies(not(X_38),X_37))) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
implies(not(X_37),X_38) = not(not(implies(not(X_38),X_37))),
inference(resolve,[$cnf( $equal(implies(not(X_37),X_38),not(not(implies(not(X_37),X_38)))) )],[refute_0_586,refute_0_594]) ).
cnf(refute_0_596,plain,
not(not(implies(not(X_38),X_37))) = implies(not(X_38),X_37),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(not(X_38),X_37)))]]) ).
cnf(refute_0_597,plain,
( implies(not(X_37),X_38) != not(not(implies(not(X_38),X_37)))
| not(not(implies(not(X_38),X_37))) != implies(not(X_38),X_37)
| implies(not(X_37),X_38) = implies(not(X_38),X_37) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_37),X_38),implies(not(X_38),X_37)) ),[0],$fot(not(not(implies(not(X_38),X_37))))]]) ).
cnf(refute_0_598,plain,
( implies(not(X_37),X_38) != not(not(implies(not(X_38),X_37)))
| implies(not(X_37),X_38) = implies(not(X_38),X_37) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(X_38),X_37))),implies(not(X_38),X_37)) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
implies(not(X_37),X_38) = implies(not(X_38),X_37),
inference(resolve,[$cnf( $equal(implies(not(X_37),X_38),not(not(implies(not(X_38),X_37)))) )],[refute_0_595,refute_0_598]) ).
cnf(refute_0_600,plain,
implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(implies(implies(X_51,X_50),X_50)),X_37),
inference(subst,[],[refute_0_599:[bind(X_38,$fot(implies(implies(X_51,X_50),X_50)))]]) ).
cnf(refute_0_601,plain,
( implies(not(X_37),implies(implies(X_51,X_50),X_50)) != implies(not(implies(implies(X_51,X_50),X_50)),X_37)
| not(implies(implies(X_51,X_50),X_50)) != not(implies(implies(X_50,X_51),X_51))
| implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(implies(implies(X_50,X_51),X_51)),X_37) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_37),implies(implies(X_51,X_50),X_50)),implies(not(implies(implies(X_51,X_50),X_50)),X_37)) ),[1,0],$fot(not(implies(implies(X_50,X_51),X_51)))]]) ).
cnf(refute_0_602,plain,
( implies(not(X_37),implies(implies(X_51,X_50),X_50)) != implies(not(implies(implies(X_51,X_50),X_50)),X_37)
| implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(implies(implies(X_50,X_51),X_51)),X_37) ),
inference(resolve,[$cnf( $equal(not(implies(implies(X_51,X_50),X_50)),not(implies(implies(X_50,X_51),X_51))) )],[refute_0_405,refute_0_601]) ).
cnf(refute_0_603,plain,
implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(implies(implies(X_50,X_51),X_51)),X_37),
inference(resolve,[$cnf( $equal(implies(not(X_37),implies(implies(X_51,X_50),X_50)),implies(not(implies(implies(X_51,X_50),X_50)),X_37)) )],[refute_0_600,refute_0_602]) ).
cnf(refute_0_604,plain,
implies(and_star(X_55,X_56),X_54) = not(not(implies(and_star(X_55,X_56),X_54))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(and_star(X_55,X_56),X_54)))]]) ).
cnf(refute_0_605,plain,
not(implies(X_55,implies(X_56,X_54))) = not(implies(and_star(X_55,X_56),X_54)),
inference(subst,[],[refute_0_116:[bind(X_18,$fot(X_54)),bind(X_39,$fot(X_55)),bind(X_40,$fot(X_56))]]) ).
cnf(refute_0_606,plain,
( not(implies(X_55,implies(X_56,X_54))) != not(implies(and_star(X_55,X_56),X_54))
| not(implies(and_star(X_55,X_56),X_54)) = not(implies(X_55,implies(X_56,X_54))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(implies(X_55,implies(X_56,X_54))))),bind(Y0,$fot(not(implies(and_star(X_55,X_56),X_54))))]]) ).
cnf(refute_0_607,plain,
not(implies(and_star(X_55,X_56),X_54)) = not(implies(X_55,implies(X_56,X_54))),
inference(resolve,[$cnf( $equal(not(implies(X_55,implies(X_56,X_54))),not(implies(and_star(X_55,X_56),X_54))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
( implies(and_star(X_55,X_56),X_54) != not(not(implies(and_star(X_55,X_56),X_54)))
| not(implies(and_star(X_55,X_56),X_54)) != not(implies(X_55,implies(X_56,X_54)))
| implies(and_star(X_55,X_56),X_54) = not(not(implies(X_55,implies(X_56,X_54)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and_star(X_55,X_56),X_54),not(not(implies(and_star(X_55,X_56),X_54)))) ),[1,0],$fot(not(implies(X_55,implies(X_56,X_54))))]]) ).
cnf(refute_0_609,plain,
( implies(and_star(X_55,X_56),X_54) != not(not(implies(and_star(X_55,X_56),X_54)))
| implies(and_star(X_55,X_56),X_54) = not(not(implies(X_55,implies(X_56,X_54)))) ),
inference(resolve,[$cnf( $equal(not(implies(and_star(X_55,X_56),X_54)),not(implies(X_55,implies(X_56,X_54)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
implies(and_star(X_55,X_56),X_54) = not(not(implies(X_55,implies(X_56,X_54)))),
inference(resolve,[$cnf( $equal(implies(and_star(X_55,X_56),X_54),not(not(implies(and_star(X_55,X_56),X_54)))) )],[refute_0_604,refute_0_609]) ).
cnf(refute_0_611,plain,
not(not(implies(X_55,implies(X_56,X_54)))) = implies(X_55,implies(X_56,X_54)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_55,implies(X_56,X_54))))]]) ).
cnf(refute_0_612,plain,
( implies(and_star(X_55,X_56),X_54) != not(not(implies(X_55,implies(X_56,X_54))))
| not(not(implies(X_55,implies(X_56,X_54)))) != implies(X_55,implies(X_56,X_54))
| implies(and_star(X_55,X_56),X_54) = implies(X_55,implies(X_56,X_54)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(and_star(X_55,X_56),X_54),implies(X_55,implies(X_56,X_54))) ),[0],$fot(not(not(implies(X_55,implies(X_56,X_54)))))]]) ).
cnf(refute_0_613,plain,
( implies(and_star(X_55,X_56),X_54) != not(not(implies(X_55,implies(X_56,X_54))))
| implies(and_star(X_55,X_56),X_54) = implies(X_55,implies(X_56,X_54)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_55,implies(X_56,X_54)))),implies(X_55,implies(X_56,X_54))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
implies(and_star(X_55,X_56),X_54) = implies(X_55,implies(X_56,X_54)),
inference(resolve,[$cnf( $equal(implies(and_star(X_55,X_56),X_54),not(not(implies(X_55,implies(X_56,X_54))))) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
implies(and_star(not(X_28),X_92),X_90) = implies(not(X_28),implies(X_92,X_90)),
inference(subst,[],[refute_0_614:[bind(X_54,$fot(X_90)),bind(X_55,$fot(not(X_28))),bind(X_56,$fot(X_92))]]) ).
cnf(refute_0_616,plain,
and_star(not(X_28),X_92) = not(implies(X_92,X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_92))]]) ).
cnf(refute_0_617,plain,
( and_star(not(X_28),X_92) != not(implies(X_92,X_28))
| implies(and_star(not(X_28),X_92),X_90) != implies(not(X_28),implies(X_92,X_90))
| implies(not(implies(X_92,X_28)),X_90) = implies(not(X_28),implies(X_92,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and_star(not(X_28),X_92),X_90),implies(not(X_28),implies(X_92,X_90))) ),[0,0],$fot(not(implies(X_92,X_28)))]]) ).
cnf(refute_0_618,plain,
( implies(and_star(not(X_28),X_92),X_90) != implies(not(X_28),implies(X_92,X_90))
| implies(not(implies(X_92,X_28)),X_90) = implies(not(X_28),implies(X_92,X_90)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),X_92),not(implies(X_92,X_28))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
implies(not(implies(X_92,X_28)),X_90) = implies(not(X_28),implies(X_92,X_90)),
inference(resolve,[$cnf( $equal(implies(and_star(not(X_28),X_92),X_90),implies(not(X_28),implies(X_92,X_90))) )],[refute_0_615,refute_0_618]) ).
cnf(refute_0_620,plain,
implies(not(implies(implies(X_50,X_51),X_51)),X_37) = implies(not(X_51),implies(implies(X_50,X_51),X_37)),
inference(subst,[],[refute_0_619:[bind(X_28,$fot(X_51)),bind(X_90,$fot(X_37)),bind(X_92,$fot(implies(X_50,X_51)))]]) ).
cnf(refute_0_621,plain,
( implies(not(X_37),implies(implies(X_51,X_50),X_50)) != implies(not(implies(implies(X_50,X_51),X_51)),X_37)
| implies(not(implies(implies(X_50,X_51),X_51)),X_37) != implies(not(X_51),implies(implies(X_50,X_51),X_37))
| implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(X_51),implies(implies(X_50,X_51),X_37)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_37),implies(implies(X_51,X_50),X_50)),implies(not(X_51),implies(implies(X_50,X_51),X_37))) ),[0],$fot(implies(not(implies(implies(X_50,X_51),X_51)),X_37))]]) ).
cnf(refute_0_622,plain,
( implies(not(X_37),implies(implies(X_51,X_50),X_50)) != implies(not(implies(implies(X_50,X_51),X_51)),X_37)
| implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(X_51),implies(implies(X_50,X_51),X_37)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_50,X_51),X_51)),X_37),implies(not(X_51),implies(implies(X_50,X_51),X_37))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
implies(not(X_37),implies(implies(X_51,X_50),X_50)) = implies(not(X_51),implies(implies(X_50,X_51),X_37)),
inference(resolve,[$cnf( $equal(implies(not(X_37),implies(implies(X_51,X_50),X_50)),implies(not(implies(implies(X_50,X_51),X_51)),X_37)) )],[refute_0_603,refute_0_622]) ).
cnf(refute_0_624,plain,
implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))),
inference(subst,[],[refute_0_623:[bind(X_37,$fot(and_star(X_250,X_51))),bind(X_50,$fot(implies(not(X_250),X_51)))]]) ).
cnf(refute_0_625,plain,
implies(implies(X_64,and_star(X_64,X_38)),and_star(X_64,X_38)) = implies(implies(and_star(X_64,X_38),X_64),X_64),
inference(subst,[],[refute_0_412:[bind(X_50,$fot(and_star(X_64,X_38))),bind(X_51,$fot(X_64))]]) ).
cnf(refute_0_626,plain,
not(and_star(not(X_38),implies(not(X_38),X_45))) = not(and_star(X_45,implies(X_45,not(X_38)))),
inference(subst,[],[refute_0_470:[bind(X_17,$fot(not(X_38))),bind(X_33,$fot(X_45))]]) ).
cnf(refute_0_627,plain,
implies(not(X_45),X_38) = implies(not(X_38),X_45),
inference(subst,[],[refute_0_599:[bind(X_37,$fot(X_45))]]) ).
cnf(refute_0_628,plain,
( implies(not(X_45),X_38) != implies(not(X_38),X_45)
| implies(not(X_38),X_45) = implies(not(X_45),X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_45),X_38))),bind(Y0,$fot(implies(not(X_38),X_45)))]]) ).
cnf(refute_0_629,plain,
implies(not(X_38),X_45) = implies(not(X_45),X_38),
inference(resolve,[$cnf( $equal(implies(not(X_45),X_38),implies(not(X_38),X_45)) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
( implies(not(X_38),X_45) != implies(not(X_45),X_38)
| not(and_star(not(X_38),implies(not(X_38),X_45))) != not(and_star(X_45,implies(X_45,not(X_38))))
| not(and_star(not(X_38),implies(not(X_45),X_38))) = not(and_star(X_45,implies(X_45,not(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_38),X_45))),not(and_star(X_45,implies(X_45,not(X_38))))) ),[0,0,1],$fot(implies(not(X_45),X_38))]]) ).
cnf(refute_0_631,plain,
( not(and_star(not(X_38),implies(not(X_38),X_45))) != not(and_star(X_45,implies(X_45,not(X_38))))
| not(and_star(not(X_38),implies(not(X_45),X_38))) = not(and_star(X_45,implies(X_45,not(X_38)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_38),X_45),implies(not(X_45),X_38)) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
not(and_star(not(X_38),implies(not(X_45),X_38))) = not(and_star(X_45,implies(X_45,not(X_38)))),
inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_38),X_45))),not(and_star(X_45,implies(X_45,not(X_38))))) )],[refute_0_626,refute_0_631]) ).
cnf(refute_0_633,plain,
not(not(implies(implies(not(X_45),X_38),X_38))) = implies(implies(not(X_45),X_38),X_38),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(not(X_45),X_38),X_38)))]]) ).
cnf(refute_0_634,plain,
and_star(not(X_38),implies(not(X_45),X_38)) = not(implies(implies(not(X_45),X_38),X_38)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(not(X_45),X_38))),bind(X_28,$fot(X_38))]]) ).
cnf(refute_0_635,plain,
not(and_star(not(X_38),implies(not(X_45),X_38))) = not(and_star(not(X_38),implies(not(X_45),X_38))),
introduced(tautology,[refl,[$fot(not(and_star(not(X_38),implies(not(X_45),X_38))))]]) ).
cnf(refute_0_636,plain,
( and_star(not(X_38),implies(not(X_45),X_38)) != not(implies(implies(not(X_45),X_38),X_38))
| not(and_star(not(X_38),implies(not(X_45),X_38))) != not(and_star(not(X_38),implies(not(X_45),X_38)))
| not(and_star(not(X_38),implies(not(X_45),X_38))) = not(not(implies(implies(not(X_45),X_38),X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),not(and_star(not(X_38),implies(not(X_45),X_38)))) ),[1,0],$fot(not(implies(implies(not(X_45),X_38),X_38)))]]) ).
cnf(refute_0_637,plain,
( and_star(not(X_38),implies(not(X_45),X_38)) != not(implies(implies(not(X_45),X_38),X_38))
| not(and_star(not(X_38),implies(not(X_45),X_38))) = not(not(implies(implies(not(X_45),X_38),X_38))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),not(and_star(not(X_38),implies(not(X_45),X_38)))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
not(and_star(not(X_38),implies(not(X_45),X_38))) = not(not(implies(implies(not(X_45),X_38),X_38))),
inference(resolve,[$cnf( $equal(and_star(not(X_38),implies(not(X_45),X_38)),not(implies(implies(not(X_45),X_38),X_38))) )],[refute_0_634,refute_0_637]) ).
cnf(refute_0_639,plain,
( not(and_star(not(X_38),implies(not(X_45),X_38))) != not(not(implies(implies(not(X_45),X_38),X_38)))
| not(not(implies(implies(not(X_45),X_38),X_38))) != implies(implies(not(X_45),X_38),X_38)
| not(and_star(not(X_38),implies(not(X_45),X_38))) = implies(implies(not(X_45),X_38),X_38) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_38),implies(not(X_45),X_38))))),bind(Y0,$fot(not(not(implies(implies(not(X_45),X_38),X_38))))),bind(Z0,$fot(implies(implies(not(X_45),X_38),X_38)))]]) ).
cnf(refute_0_640,plain,
( not(not(implies(implies(not(X_45),X_38),X_38))) != implies(implies(not(X_45),X_38),X_38)
| not(and_star(not(X_38),implies(not(X_45),X_38))) = implies(implies(not(X_45),X_38),X_38) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),not(not(implies(implies(not(X_45),X_38),X_38)))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
not(and_star(not(X_38),implies(not(X_45),X_38))) = implies(implies(not(X_45),X_38),X_38),
inference(resolve,[$cnf( $equal(not(not(implies(implies(not(X_45),X_38),X_38))),implies(implies(not(X_45),X_38),X_38)) )],[refute_0_633,refute_0_640]) ).
cnf(refute_0_642,plain,
( not(and_star(not(X_38),implies(not(X_45),X_38))) != implies(implies(not(X_45),X_38),X_38)
| not(and_star(not(X_38),implies(not(X_45),X_38))) != not(and_star(X_45,implies(X_45,not(X_38))))
| implies(implies(not(X_45),X_38),X_38) = not(and_star(X_45,implies(X_45,not(X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),not(and_star(X_45,implies(X_45,not(X_38))))) ),[0],$fot(implies(implies(not(X_45),X_38),X_38))]]) ).
cnf(refute_0_643,plain,
( not(and_star(not(X_38),implies(not(X_45),X_38))) != not(and_star(X_45,implies(X_45,not(X_38))))
| implies(implies(not(X_45),X_38),X_38) = not(and_star(X_45,implies(X_45,not(X_38)))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),implies(implies(not(X_45),X_38),X_38)) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
not(not(implies(X_45,and_star(X_45,X_38)))) = implies(X_45,and_star(X_45,X_38)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_45,and_star(X_45,X_38))))]]) ).
cnf(refute_0_645,plain,
and_star(X_45,not(and_star(X_45,X_38))) = not(implies(X_45,and_star(X_45,X_38))),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_45)),bind(X_18,$fot(and_star(X_45,X_38)))]]) ).
cnf(refute_0_646,plain,
implies(X_45,not(X_38)) = not(and_star(X_45,X_38)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(X_45)),bind(X_6,$fot(X_38))]]) ).
cnf(refute_0_647,plain,
and_star(X_45,implies(X_45,not(X_38))) = and_star(X_45,implies(X_45,not(X_38))),
introduced(tautology,[refl,[$fot(and_star(X_45,implies(X_45,not(X_38))))]]) ).
cnf(refute_0_648,plain,
( and_star(X_45,implies(X_45,not(X_38))) != and_star(X_45,implies(X_45,not(X_38)))
| implies(X_45,not(X_38)) != not(and_star(X_45,X_38))
| and_star(X_45,implies(X_45,not(X_38))) = and_star(X_45,not(and_star(X_45,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X_45,implies(X_45,not(X_38))),and_star(X_45,implies(X_45,not(X_38)))) ),[1,1],$fot(not(and_star(X_45,X_38)))]]) ).
cnf(refute_0_649,plain,
( implies(X_45,not(X_38)) != not(and_star(X_45,X_38))
| and_star(X_45,implies(X_45,not(X_38))) = and_star(X_45,not(and_star(X_45,X_38))) ),
inference(resolve,[$cnf( $equal(and_star(X_45,implies(X_45,not(X_38))),and_star(X_45,implies(X_45,not(X_38)))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
and_star(X_45,implies(X_45,not(X_38))) = and_star(X_45,not(and_star(X_45,X_38))),
inference(resolve,[$cnf( $equal(implies(X_45,not(X_38)),not(and_star(X_45,X_38))) )],[refute_0_646,refute_0_649]) ).
cnf(refute_0_651,plain,
( and_star(X_45,implies(X_45,not(X_38))) != and_star(X_45,not(and_star(X_45,X_38)))
| and_star(X_45,not(and_star(X_45,X_38))) != not(implies(X_45,and_star(X_45,X_38)))
| and_star(X_45,implies(X_45,not(X_38))) = not(implies(X_45,and_star(X_45,X_38))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(and_star(X_45,implies(X_45,not(X_38))))),bind(Y0,$fot(and_star(X_45,not(and_star(X_45,X_38))))),bind(Z0,$fot(not(implies(X_45,and_star(X_45,X_38)))))]]) ).
cnf(refute_0_652,plain,
( and_star(X_45,not(and_star(X_45,X_38))) != not(implies(X_45,and_star(X_45,X_38)))
| and_star(X_45,implies(X_45,not(X_38))) = not(implies(X_45,and_star(X_45,X_38))) ),
inference(resolve,[$cnf( $equal(and_star(X_45,implies(X_45,not(X_38))),and_star(X_45,not(and_star(X_45,X_38)))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
and_star(X_45,implies(X_45,not(X_38))) = not(implies(X_45,and_star(X_45,X_38))),
inference(resolve,[$cnf( $equal(and_star(X_45,not(and_star(X_45,X_38))),not(implies(X_45,and_star(X_45,X_38)))) )],[refute_0_645,refute_0_652]) ).
cnf(refute_0_654,plain,
not(and_star(X_45,implies(X_45,not(X_38)))) = not(and_star(X_45,implies(X_45,not(X_38)))),
introduced(tautology,[refl,[$fot(not(and_star(X_45,implies(X_45,not(X_38)))))]]) ).
cnf(refute_0_655,plain,
( and_star(X_45,implies(X_45,not(X_38))) != not(implies(X_45,and_star(X_45,X_38)))
| not(and_star(X_45,implies(X_45,not(X_38)))) != not(and_star(X_45,implies(X_45,not(X_38))))
| not(and_star(X_45,implies(X_45,not(X_38)))) = not(not(implies(X_45,and_star(X_45,X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X_45,implies(X_45,not(X_38)))),not(and_star(X_45,implies(X_45,not(X_38))))) ),[1,0],$fot(not(implies(X_45,and_star(X_45,X_38))))]]) ).
cnf(refute_0_656,plain,
( and_star(X_45,implies(X_45,not(X_38))) != not(implies(X_45,and_star(X_45,X_38)))
| not(and_star(X_45,implies(X_45,not(X_38)))) = not(not(implies(X_45,and_star(X_45,X_38)))) ),
inference(resolve,[$cnf( $equal(not(and_star(X_45,implies(X_45,not(X_38)))),not(and_star(X_45,implies(X_45,not(X_38))))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
not(and_star(X_45,implies(X_45,not(X_38)))) = not(not(implies(X_45,and_star(X_45,X_38)))),
inference(resolve,[$cnf( $equal(and_star(X_45,implies(X_45,not(X_38))),not(implies(X_45,and_star(X_45,X_38)))) )],[refute_0_653,refute_0_656]) ).
cnf(refute_0_658,plain,
( not(and_star(X_45,implies(X_45,not(X_38)))) != not(not(implies(X_45,and_star(X_45,X_38))))
| not(not(implies(X_45,and_star(X_45,X_38)))) != implies(X_45,and_star(X_45,X_38))
| not(and_star(X_45,implies(X_45,not(X_38)))) = implies(X_45,and_star(X_45,X_38)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(X_45,implies(X_45,not(X_38)))))),bind(Y0,$fot(not(not(implies(X_45,and_star(X_45,X_38)))))),bind(Z0,$fot(implies(X_45,and_star(X_45,X_38))))]]) ).
cnf(refute_0_659,plain,
( not(not(implies(X_45,and_star(X_45,X_38)))) != implies(X_45,and_star(X_45,X_38))
| not(and_star(X_45,implies(X_45,not(X_38)))) = implies(X_45,and_star(X_45,X_38)) ),
inference(resolve,[$cnf( $equal(not(and_star(X_45,implies(X_45,not(X_38)))),not(not(implies(X_45,and_star(X_45,X_38))))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
not(and_star(X_45,implies(X_45,not(X_38)))) = implies(X_45,and_star(X_45,X_38)),
inference(resolve,[$cnf( $equal(not(not(implies(X_45,and_star(X_45,X_38)))),implies(X_45,and_star(X_45,X_38))) )],[refute_0_644,refute_0_659]) ).
cnf(refute_0_661,plain,
( implies(implies(not(X_45),X_38),X_38) != not(and_star(X_45,implies(X_45,not(X_38))))
| not(and_star(X_45,implies(X_45,not(X_38)))) != implies(X_45,and_star(X_45,X_38))
| implies(implies(not(X_45),X_38),X_38) = implies(X_45,and_star(X_45,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(not(X_45),X_38),X_38),implies(X_45,and_star(X_45,X_38))) ),[0],$fot(not(and_star(X_45,implies(X_45,not(X_38)))))]]) ).
cnf(refute_0_662,plain,
( implies(implies(not(X_45),X_38),X_38) != not(and_star(X_45,implies(X_45,not(X_38))))
| implies(implies(not(X_45),X_38),X_38) = implies(X_45,and_star(X_45,X_38)) ),
inference(resolve,[$cnf( $equal(not(and_star(X_45,implies(X_45,not(X_38)))),implies(X_45,and_star(X_45,X_38))) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
( not(and_star(not(X_38),implies(not(X_45),X_38))) != not(and_star(X_45,implies(X_45,not(X_38))))
| implies(implies(not(X_45),X_38),X_38) = implies(X_45,and_star(X_45,X_38)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_45),X_38),X_38),not(and_star(X_45,implies(X_45,not(X_38))))) )],[refute_0_643,refute_0_662]) ).
cnf(refute_0_664,plain,
implies(implies(not(X_45),X_38),X_38) = implies(X_45,and_star(X_45,X_38)),
inference(resolve,[$cnf( $equal(not(and_star(not(X_38),implies(not(X_45),X_38))),not(and_star(X_45,implies(X_45,not(X_38))))) )],[refute_0_632,refute_0_663]) ).
cnf(refute_0_665,plain,
implies(implies(not(X_64),X_38),X_38) = implies(X_64,and_star(X_64,X_38)),
inference(subst,[],[refute_0_664:[bind(X_45,$fot(X_64))]]) ).
cnf(refute_0_666,plain,
( implies(implies(not(X_64),X_38),X_38) != implies(X_64,and_star(X_64,X_38))
| implies(X_64,and_star(X_64,X_38)) = implies(implies(not(X_64),X_38),X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_64),X_38),X_38))),bind(Y0,$fot(implies(X_64,and_star(X_64,X_38))))]]) ).
cnf(refute_0_667,plain,
implies(X_64,and_star(X_64,X_38)) = implies(implies(not(X_64),X_38),X_38),
inference(resolve,[$cnf( $equal(implies(implies(not(X_64),X_38),X_38),implies(X_64,and_star(X_64,X_38))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
( implies(X_64,and_star(X_64,X_38)) != implies(implies(not(X_64),X_38),X_38)
| implies(implies(X_64,and_star(X_64,X_38)),and_star(X_64,X_38)) != implies(implies(and_star(X_64,X_38),X_64),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(and_star(X_64,X_38),X_64),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_64,and_star(X_64,X_38)),and_star(X_64,X_38)),implies(implies(and_star(X_64,X_38),X_64),X_64)) ),[0,0],$fot(implies(implies(not(X_64),X_38),X_38))]]) ).
cnf(refute_0_669,plain,
( implies(implies(X_64,and_star(X_64,X_38)),and_star(X_64,X_38)) != implies(implies(and_star(X_64,X_38),X_64),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(and_star(X_64,X_38),X_64),X_64) ),
inference(resolve,[$cnf( $equal(implies(X_64,and_star(X_64,X_38)),implies(implies(not(X_64),X_38),X_38)) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(and_star(X_64,X_38),X_64),X_64),
inference(resolve,[$cnf( $equal(implies(implies(X_64,and_star(X_64,X_38)),and_star(X_64,X_38)),implies(implies(and_star(X_64,X_38),X_64),X_64)) )],[refute_0_625,refute_0_669]) ).
cnf(refute_0_671,plain,
implies(and_star(X_64,X_38),X_64) = implies(X_64,implies(X_38,X_64)),
inference(subst,[],[refute_0_614:[bind(X_54,$fot(X_64)),bind(X_55,$fot(X_64)),bind(X_56,$fot(X_38))]]) ).
cnf(refute_0_672,plain,
implies(implies(and_star(X_64,X_38),X_64),X_64) = implies(implies(and_star(X_64,X_38),X_64),X_64),
introduced(tautology,[refl,[$fot(implies(implies(and_star(X_64,X_38),X_64),X_64))]]) ).
cnf(refute_0_673,plain,
( implies(and_star(X_64,X_38),X_64) != implies(X_64,implies(X_38,X_64))
| implies(implies(and_star(X_64,X_38),X_64),X_64) != implies(implies(and_star(X_64,X_38),X_64),X_64)
| implies(implies(and_star(X_64,X_38),X_64),X_64) = implies(implies(X_64,implies(X_38,X_64)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(and_star(X_64,X_38),X_64),X_64),implies(implies(and_star(X_64,X_38),X_64),X_64)) ),[1,0],$fot(implies(X_64,implies(X_38,X_64)))]]) ).
cnf(refute_0_674,plain,
( implies(and_star(X_64,X_38),X_64) != implies(X_64,implies(X_38,X_64))
| implies(implies(and_star(X_64,X_38),X_64),X_64) = implies(implies(X_64,implies(X_38,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(implies(implies(and_star(X_64,X_38),X_64),X_64),implies(implies(and_star(X_64,X_38),X_64),X_64)) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
implies(implies(and_star(X_64,X_38),X_64),X_64) = implies(implies(X_64,implies(X_38,X_64)),X_64),
inference(resolve,[$cnf( $equal(implies(and_star(X_64,X_38),X_64),implies(X_64,implies(X_38,X_64))) )],[refute_0_671,refute_0_674]) ).
cnf(refute_0_676,plain,
( implies(implies(and_star(X_64,X_38),X_64),X_64) != implies(implies(X_64,implies(X_38,X_64)),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) != implies(implies(and_star(X_64,X_38),X_64),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(X_64,implies(X_38,X_64)),X_64) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)),implies(implies(and_star(X_64,X_38),X_64),X_64)) ),[1],$fot(implies(implies(X_64,implies(X_38,X_64)),X_64))]]) ).
cnf(refute_0_677,plain,
( implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) != implies(implies(and_star(X_64,X_38),X_64),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(X_64,implies(X_38,X_64)),X_64) ),
inference(resolve,[$cnf( $equal(implies(implies(and_star(X_64,X_38),X_64),X_64),implies(implies(X_64,implies(X_38,X_64)),X_64)) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = implies(implies(X_64,implies(X_38,X_64)),X_64),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)),implies(implies(and_star(X_64,X_38),X_64),X_64)) )],[refute_0_670,refute_0_677]) ).
cnf(refute_0_679,plain,
implies(truth,X_64) = X_64,
inference(subst,[],[refute_0_458:[bind(X_18,$fot(X_64))]]) ).
cnf(refute_0_680,plain,
implies(X_64,implies(X_38,X_64)) = truth,
inference(subst,[],[refute_0_229:[bind(X_74,$fot(X_64)),bind(X_75,$fot(X_38))]]) ).
cnf(refute_0_681,plain,
implies(implies(X_64,implies(X_38,X_64)),X_64) = implies(implies(X_64,implies(X_38,X_64)),X_64),
introduced(tautology,[refl,[$fot(implies(implies(X_64,implies(X_38,X_64)),X_64))]]) ).
cnf(refute_0_682,plain,
( implies(X_64,implies(X_38,X_64)) != truth
| implies(implies(X_64,implies(X_38,X_64)),X_64) != implies(implies(X_64,implies(X_38,X_64)),X_64)
| implies(implies(X_64,implies(X_38,X_64)),X_64) = implies(truth,X_64) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_64,implies(X_38,X_64)),X_64),implies(implies(X_64,implies(X_38,X_64)),X_64)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_683,plain,
( implies(X_64,implies(X_38,X_64)) != truth
| implies(implies(X_64,implies(X_38,X_64)),X_64) = implies(truth,X_64) ),
inference(resolve,[$cnf( $equal(implies(implies(X_64,implies(X_38,X_64)),X_64),implies(implies(X_64,implies(X_38,X_64)),X_64)) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
implies(implies(X_64,implies(X_38,X_64)),X_64) = implies(truth,X_64),
inference(resolve,[$cnf( $equal(implies(X_64,implies(X_38,X_64)),truth) )],[refute_0_680,refute_0_683]) ).
cnf(refute_0_685,plain,
( implies(implies(X_64,implies(X_38,X_64)),X_64) != implies(truth,X_64)
| implies(truth,X_64) != X_64
| implies(implies(X_64,implies(X_38,X_64)),X_64) = X_64 ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(X_64,implies(X_38,X_64)),X_64))),bind(Y0,$fot(implies(truth,X_64))),bind(Z0,$fot(X_64))]]) ).
cnf(refute_0_686,plain,
( implies(truth,X_64) != X_64
| implies(implies(X_64,implies(X_38,X_64)),X_64) = X_64 ),
inference(resolve,[$cnf( $equal(implies(implies(X_64,implies(X_38,X_64)),X_64),implies(truth,X_64)) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
implies(implies(X_64,implies(X_38,X_64)),X_64) = X_64,
inference(resolve,[$cnf( $equal(implies(truth,X_64),X_64) )],[refute_0_679,refute_0_686]) ).
cnf(refute_0_688,plain,
( implies(implies(X_64,implies(X_38,X_64)),X_64) != X_64
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) != implies(implies(X_64,implies(X_38,X_64)),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = X_64 ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)),implies(implies(X_64,implies(X_38,X_64)),X_64)) ),[1],$fot(X_64)]]) ).
cnf(refute_0_689,plain,
( implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) != implies(implies(X_64,implies(X_38,X_64)),X_64)
| implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = X_64 ),
inference(resolve,[$cnf( $equal(implies(implies(X_64,implies(X_38,X_64)),X_64),X_64) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)) = X_64,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_64),X_38),X_38),and_star(X_64,X_38)),implies(implies(X_64,implies(X_38,X_64)),X_64)) )],[refute_0_678,refute_0_689]) ).
cnf(refute_0_691,plain,
implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)) = X_250,
inference(subst,[],[refute_0_690:[bind(X_38,$fot(X_51)),bind(X_64,$fot(X_250))]]) ).
cnf(refute_0_692,plain,
( implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)) != X_250
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),X_250) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))) ),[1,1],$fot(X_250)]]) ).
cnf(refute_0_693,plain,
( implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),X_250) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)),X_250) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),X_250),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))) )],[refute_0_624,refute_0_693]) ).
cnf(refute_0_695,plain,
implies(not(X_226),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_227)) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)),
inference(subst,[],[refute_0_623:[bind(X_37,$fot(X_226)),bind(X_50,$fot(X_227)),bind(X_51,$fot(implies(not(and_star(X_62,X_61)),X_227)))]]) ).
cnf(refute_0_696,plain,
implies(implies(not(and_star(X_61,X_62)),X_38),X_38) = implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)),
inference(subst,[],[refute_0_664:[bind(X_45,$fot(and_star(X_61,X_62)))]]) ).
cnf(refute_0_697,plain,
implies(X_29,not(X_30)) = not(and_star(X_29,X_30)),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(X_29)),bind(X_6,$fot(X_30))]]) ).
cnf(refute_0_698,plain,
and_star(X_30,X_29) = and_star(X_29,X_30),
inference(subst,[],[and_star_commutativity:[bind(X,$fot(X_30)),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_699,plain,
( and_star(X_30,X_29) != and_star(X_29,X_30)
| and_star(X_29,X_30) = and_star(X_30,X_29) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and_star(X_30,X_29))),bind(Y0,$fot(and_star(X_29,X_30)))]]) ).
cnf(refute_0_700,plain,
and_star(X_29,X_30) = and_star(X_30,X_29),
inference(resolve,[$cnf( $equal(and_star(X_30,X_29),and_star(X_29,X_30)) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
( and_star(X_29,X_30) != and_star(X_30,X_29)
| implies(X_29,not(X_30)) != not(and_star(X_29,X_30))
| implies(X_29,not(X_30)) = not(and_star(X_30,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,not(X_30)),not(and_star(X_29,X_30))) ),[1,0],$fot(and_star(X_30,X_29))]]) ).
cnf(refute_0_702,plain,
( implies(X_29,not(X_30)) != not(and_star(X_29,X_30))
| implies(X_29,not(X_30)) = not(and_star(X_30,X_29)) ),
inference(resolve,[$cnf( $equal(and_star(X_29,X_30),and_star(X_30,X_29)) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
implies(X_29,not(X_30)) = not(and_star(X_30,X_29)),
inference(resolve,[$cnf( $equal(implies(X_29,not(X_30)),not(and_star(X_29,X_30))) )],[refute_0_697,refute_0_702]) ).
cnf(refute_0_704,plain,
( implies(X_29,not(X_30)) != not(and_star(X_29,X_30))
| implies(X_29,not(X_30)) != not(and_star(X_30,X_29))
| not(and_star(X_29,X_30)) = not(and_star(X_30,X_29)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,not(X_30)),not(and_star(X_30,X_29))) ),[0],$fot(not(and_star(X_29,X_30)))]]) ).
cnf(refute_0_705,plain,
( implies(X_29,not(X_30)) != not(and_star(X_30,X_29))
| not(and_star(X_29,X_30)) = not(and_star(X_30,X_29)) ),
inference(resolve,[$cnf( $equal(implies(X_29,not(X_30)),not(and_star(X_29,X_30))) )],[refute_0_697,refute_0_704]) ).
cnf(refute_0_706,plain,
not(and_star(X_29,X_30)) = not(and_star(X_30,X_29)),
inference(resolve,[$cnf( $equal(implies(X_29,not(X_30)),not(and_star(X_30,X_29))) )],[refute_0_703,refute_0_705]) ).
cnf(refute_0_707,plain,
not(and_star(X_61,X_62)) = not(and_star(X_62,X_61)),
inference(subst,[],[refute_0_706:[bind(X_29,$fot(X_61)),bind(X_30,$fot(X_62))]]) ).
cnf(refute_0_708,plain,
( implies(implies(not(and_star(X_61,X_62)),X_38),X_38) != implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))
| not(and_star(X_61,X_62)) != not(and_star(X_62,X_61))
| implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(and_star(X_61,X_62)),X_38),X_38),implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))) ),[0,0,0],$fot(not(and_star(X_62,X_61)))]]) ).
cnf(refute_0_709,plain,
( implies(implies(not(and_star(X_61,X_62)),X_38),X_38) != implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))
| implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) ),
inference(resolve,[$cnf( $equal(not(and_star(X_61,X_62)),not(and_star(X_62,X_61))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)),
inference(resolve,[$cnf( $equal(implies(implies(not(and_star(X_61,X_62)),X_38),X_38),implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))) )],[refute_0_696,refute_0_709]) ).
cnf(refute_0_711,plain,
and_star(and_star(X_61,X_62),X_38) = and_star(X_61,and_star(X_62,X_38)),
inference(subst,[],[and_star_associativity:[bind(X,$fot(X_61)),bind(Y,$fot(X_62)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_712,plain,
implies(X_62,and_star(and_star(X_61,X_62),X_38)) = implies(X_62,and_star(and_star(X_61,X_62),X_38)),
introduced(tautology,[refl,[$fot(implies(X_62,and_star(and_star(X_61,X_62),X_38)))]]) ).
cnf(refute_0_713,plain,
( and_star(and_star(X_61,X_62),X_38) != and_star(X_61,and_star(X_62,X_38))
| implies(X_62,and_star(and_star(X_61,X_62),X_38)) != implies(X_62,and_star(and_star(X_61,X_62),X_38))
| implies(X_62,and_star(and_star(X_61,X_62),X_38)) = implies(X_62,and_star(X_61,and_star(X_62,X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_62,and_star(and_star(X_61,X_62),X_38)),implies(X_62,and_star(and_star(X_61,X_62),X_38))) ),[1,1],$fot(and_star(X_61,and_star(X_62,X_38)))]]) ).
cnf(refute_0_714,plain,
( and_star(and_star(X_61,X_62),X_38) != and_star(X_61,and_star(X_62,X_38))
| implies(X_62,and_star(and_star(X_61,X_62),X_38)) = implies(X_62,and_star(X_61,and_star(X_62,X_38))) ),
inference(resolve,[$cnf( $equal(implies(X_62,and_star(and_star(X_61,X_62),X_38)),implies(X_62,and_star(and_star(X_61,X_62),X_38))) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
implies(X_62,and_star(and_star(X_61,X_62),X_38)) = implies(X_62,and_star(X_61,and_star(X_62,X_38))),
inference(resolve,[$cnf( $equal(and_star(and_star(X_61,X_62),X_38),and_star(X_61,and_star(X_62,X_38))) )],[refute_0_711,refute_0_714]) ).
cnf(refute_0_716,plain,
implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) = implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))),
introduced(tautology,[refl,[$fot(implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))))]]) ).
cnf(refute_0_717,plain,
( implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) != implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38)))
| implies(X_62,and_star(and_star(X_61,X_62),X_38)) != implies(X_62,and_star(X_61,and_star(X_62,X_38)))
| implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))),implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38)))) ),[1,1],$fot(implies(X_62,and_star(X_61,and_star(X_62,X_38))))]]) ).
cnf(refute_0_718,plain,
( implies(X_62,and_star(and_star(X_61,X_62),X_38)) != implies(X_62,and_star(X_61,and_star(X_62,X_38)))
| implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
inference(resolve,[$cnf( $equal(implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))),implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38)))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))),
inference(resolve,[$cnf( $equal(implies(X_62,and_star(and_star(X_61,X_62),X_38)),implies(X_62,and_star(X_61,and_star(X_62,X_38)))) )],[refute_0_715,refute_0_718]) ).
cnf(refute_0_720,plain,
implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) = implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))),
inference(subst,[],[refute_0_614:[bind(X_54,$fot(and_star(and_star(X_61,X_62),X_38))),bind(X_55,$fot(X_61)),bind(X_56,$fot(X_62))]]) ).
cnf(refute_0_721,plain,
( implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) != implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))
| implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) != implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38)))
| implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)))),bind(Y0,$fot(implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))))),bind(Z0,$fot(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))))]]) ).
cnf(refute_0_722,plain,
( implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))) != implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))
| implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
inference(resolve,[$cnf( $equal(implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)),implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38)))) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))),
inference(resolve,[$cnf( $equal(implies(X_61,implies(X_62,and_star(and_star(X_61,X_62),X_38))),implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))) )],[refute_0_719,refute_0_722]) ).
cnf(refute_0_724,plain,
( implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)) != implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))
| implies(implies(not(and_star(X_62,X_61)),X_38),X_38) != implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))
| implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(and_star(X_62,X_61)),X_38),X_38),implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))) ),[1],$fot(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))))]]) ).
cnf(refute_0_725,plain,
( implies(implies(not(and_star(X_62,X_61)),X_38),X_38) != implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))
| implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))) ),
inference(resolve,[$cnf( $equal(implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38)),implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38))))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
implies(implies(not(and_star(X_62,X_61)),X_38),X_38) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_38)))),
inference(resolve,[$cnf( $equal(implies(implies(not(and_star(X_62,X_61)),X_38),X_38),implies(and_star(X_61,X_62),and_star(and_star(X_61,X_62),X_38))) )],[refute_0_710,refute_0_725]) ).
cnf(refute_0_727,plain,
implies(implies(not(and_star(X_62,X_61)),X_227),X_227) = implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),
inference(subst,[],[refute_0_726:[bind(X_38,$fot(X_227))]]) ).
cnf(refute_0_728,plain,
( implies(implies(not(and_star(X_62,X_61)),X_227),X_227) != implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227))))
| implies(not(X_226),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_227)) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_227)),implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))) ),[0,1,0],$fot(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))))]]) ).
cnf(refute_0_729,plain,
( implies(not(X_226),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_227)) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227))))) )],[refute_0_727,refute_0_728]) ).
cnf(refute_0_730,plain,
implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_227)),implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))) )],[refute_0_695,refute_0_729]) ).
cnf(refute_0_731,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),X_51),
inference(subst,[],[refute_0_412:[bind(X_50,$fot(implies(not(and_star(X_186,X_185)),X_51)))]]) ).
cnf(refute_0_732,plain,
implies(implies(not(and_star(X_186,X_185)),X_51),X_51) = implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),
inference(subst,[],[refute_0_726:[bind(X_38,$fot(X_51)),bind(X_61,$fot(X_185)),bind(X_62,$fot(X_186))]]) ).
cnf(refute_0_733,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),X_51)
| implies(implies(not(and_star(X_186,X_185)),X_51),X_51) != implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51))))
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),X_51)) ),[1,0],$fot(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))))]]) ).
cnf(refute_0_734,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),X_51)
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) ),
inference(resolve,[$cnf( $equal(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51))))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(implies(implies(not(and_star(X_186,X_185)),X_51),X_51),X_51)) )],[refute_0_731,refute_0_734]) ).
cnf(refute_0_736,plain,
implies(truth,and_star(X_186,X_185)) = and_star(X_186,X_185),
inference(subst,[],[refute_0_458:[bind(X_18,$fot(and_star(X_186,X_185)))]]) ).
cnf(refute_0_737,plain,
implies(X_51,implies(not(and_star(X_186,X_185)),X_51)) = truth,
inference(subst,[],[refute_0_229:[bind(X_74,$fot(X_51)),bind(X_75,$fot(not(and_star(X_186,X_185))))]]) ).
cnf(refute_0_738,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)),
introduced(tautology,[refl,[$fot(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))]]) ).
cnf(refute_0_739,plain,
( implies(X_51,implies(not(and_star(X_186,X_185)),X_51)) != truth
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) != implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = implies(truth,and_star(X_186,X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_740,plain,
( implies(X_51,implies(not(and_star(X_186,X_185)),X_51)) != truth
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = implies(truth,and_star(X_186,X_185)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) )],[refute_0_738,refute_0_739]) ).
cnf(refute_0_741,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = implies(truth,and_star(X_186,X_185)),
inference(resolve,[$cnf( $equal(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),truth) )],[refute_0_737,refute_0_740]) ).
cnf(refute_0_742,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) != implies(truth,and_star(X_186,X_185))
| implies(truth,and_star(X_186,X_185)) != and_star(X_186,X_185)
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = and_star(X_186,X_185) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))),bind(Y0,$fot(implies(truth,and_star(X_186,X_185)))),bind(Z0,$fot(and_star(X_186,X_185)))]]) ).
cnf(refute_0_743,plain,
( implies(truth,and_star(X_186,X_185)) != and_star(X_186,X_185)
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = and_star(X_186,X_185) ),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)),implies(truth,and_star(X_186,X_185))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) = and_star(X_186,X_185),
inference(resolve,[$cnf( $equal(implies(truth,and_star(X_186,X_185)),and_star(X_186,X_185)) )],[refute_0_736,refute_0_743]) ).
cnf(refute_0_745,plain,
implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) = implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))),
introduced(tautology,[refl,[$fot(implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))))]]) ).
cnf(refute_0_746,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) != and_star(X_186,X_185)
| implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) != implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))
| implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) = implies(not(X_51),and_star(X_186,X_185)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))),implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))) ),[1,1],$fot(and_star(X_186,X_185))]]) ).
cnf(refute_0_747,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)) != and_star(X_186,X_185)
| implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) = implies(not(X_51),and_star(X_186,X_185)) ),
inference(resolve,[$cnf( $equal(implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))),implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) = implies(not(X_51),and_star(X_186,X_185)),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)),and_star(X_186,X_185)) )],[refute_0_744,refute_0_747]) ).
cnf(refute_0_749,plain,
implies(not(X_174),implies(X_175,X_173)) = not(not(implies(not(X_174),implies(X_175,X_173)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(not(X_174),implies(X_175,X_173))))]]) ).
cnf(refute_0_750,plain,
not(implies(not(implies(X_72,X_71)),X_32)) = not(implies(not(X_32),implies(X_72,X_71))),
inference(subst,[],[refute_0_591:[bind(X_18,$fot(implies(X_72,X_71)))]]) ).
cnf(refute_0_751,plain,
not(implies(not(X_32),implies(X_72,X_71))) = not(implies(X_72,implies(not(X_32),X_71))),
inference(subst,[],[refute_0_127:[bind(X_28,$fot(X_71)),bind(X_40,$fot(X_72)),bind(X_41,$fot(not(X_32)))]]) ).
cnf(refute_0_752,plain,
( not(implies(not(X_32),implies(X_72,X_71))) != not(implies(X_72,implies(not(X_32),X_71)))
| not(implies(not(implies(X_72,X_71)),X_32)) != not(implies(not(X_32),implies(X_72,X_71)))
| not(implies(not(implies(X_72,X_71)),X_32)) = not(implies(X_72,implies(not(X_32),X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(implies(X_72,X_71)),X_32)),not(implies(not(X_32),implies(X_72,X_71)))) ),[1],$fot(not(implies(X_72,implies(not(X_32),X_71))))]]) ).
cnf(refute_0_753,plain,
( not(implies(not(implies(X_72,X_71)),X_32)) != not(implies(not(X_32),implies(X_72,X_71)))
| not(implies(not(implies(X_72,X_71)),X_32)) = not(implies(X_72,implies(not(X_32),X_71))) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_32),implies(X_72,X_71))),not(implies(X_72,implies(not(X_32),X_71)))) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
not(implies(not(implies(X_72,X_71)),X_32)) = not(implies(X_72,implies(not(X_32),X_71))),
inference(resolve,[$cnf( $equal(not(implies(not(implies(X_72,X_71)),X_32)),not(implies(not(X_32),implies(X_72,X_71)))) )],[refute_0_750,refute_0_753]) ).
cnf(refute_0_755,plain,
not(implies(not(X_28),implies(X_56,X_54))) = not(implies(and_star(not(X_28),X_56),X_54)),
inference(subst,[],[refute_0_116:[bind(X_18,$fot(X_54)),bind(X_39,$fot(not(X_28))),bind(X_40,$fot(X_56))]]) ).
cnf(refute_0_756,plain,
and_star(not(X_28),X_56) = not(implies(X_56,X_28)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(X_56))]]) ).
cnf(refute_0_757,plain,
( and_star(not(X_28),X_56) != not(implies(X_56,X_28))
| not(implies(not(X_28),implies(X_56,X_54))) != not(implies(and_star(not(X_28),X_56),X_54))
| not(implies(not(X_28),implies(X_56,X_54))) = not(implies(not(implies(X_56,X_28)),X_54)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_28),implies(X_56,X_54))),not(implies(and_star(not(X_28),X_56),X_54))) ),[1,0,0],$fot(not(implies(X_56,X_28)))]]) ).
cnf(refute_0_758,plain,
( not(implies(not(X_28),implies(X_56,X_54))) != not(implies(and_star(not(X_28),X_56),X_54))
| not(implies(not(X_28),implies(X_56,X_54))) = not(implies(not(implies(X_56,X_28)),X_54)) ),
inference(resolve,[$cnf( $equal(and_star(not(X_28),X_56),not(implies(X_56,X_28))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
not(implies(not(X_28),implies(X_56,X_54))) = not(implies(not(implies(X_56,X_28)),X_54)),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),implies(X_56,X_54))),not(implies(and_star(not(X_28),X_56),X_54))) )],[refute_0_755,refute_0_758]) ).
cnf(refute_0_760,plain,
( not(implies(not(X_28),implies(X_56,X_54))) != not(implies(not(implies(X_56,X_28)),X_54))
| not(implies(not(implies(X_56,X_28)),X_54)) = not(implies(not(X_28),implies(X_56,X_54))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(implies(not(X_28),implies(X_56,X_54))))),bind(Y0,$fot(not(implies(not(implies(X_56,X_28)),X_54))))]]) ).
cnf(refute_0_761,plain,
not(implies(not(implies(X_56,X_28)),X_54)) = not(implies(not(X_28),implies(X_56,X_54))),
inference(resolve,[$cnf( $equal(not(implies(not(X_28),implies(X_56,X_54))),not(implies(not(implies(X_56,X_28)),X_54))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
not(implies(not(implies(X_72,X_71)),X_32)) = not(implies(not(X_71),implies(X_72,X_32))),
inference(subst,[],[refute_0_761:[bind(X_28,$fot(X_71)),bind(X_54,$fot(X_32)),bind(X_56,$fot(X_72))]]) ).
cnf(refute_0_763,plain,
( not(implies(not(implies(X_72,X_71)),X_32)) != not(implies(X_72,implies(not(X_32),X_71)))
| not(implies(not(implies(X_72,X_71)),X_32)) != not(implies(not(X_71),implies(X_72,X_32)))
| not(implies(not(X_71),implies(X_72,X_32))) = not(implies(X_72,implies(not(X_32),X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(implies(X_72,X_71)),X_32)),not(implies(X_72,implies(not(X_32),X_71)))) ),[0],$fot(not(implies(not(X_71),implies(X_72,X_32))))]]) ).
cnf(refute_0_764,plain,
( not(implies(not(implies(X_72,X_71)),X_32)) != not(implies(X_72,implies(not(X_32),X_71)))
| not(implies(not(X_71),implies(X_72,X_32))) = not(implies(X_72,implies(not(X_32),X_71))) ),
inference(resolve,[$cnf( $equal(not(implies(not(implies(X_72,X_71)),X_32)),not(implies(not(X_71),implies(X_72,X_32)))) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
not(implies(not(X_71),implies(X_72,X_32))) = not(implies(X_72,implies(not(X_32),X_71))),
inference(resolve,[$cnf( $equal(not(implies(not(implies(X_72,X_71)),X_32)),not(implies(X_72,implies(not(X_32),X_71)))) )],[refute_0_754,refute_0_764]) ).
cnf(refute_0_766,plain,
not(implies(not(X_174),implies(X_175,X_173))) = not(implies(X_175,implies(not(X_173),X_174))),
inference(subst,[],[refute_0_765:[bind(X_32,$fot(X_173)),bind(X_71,$fot(X_174)),bind(X_72,$fot(X_175))]]) ).
cnf(refute_0_767,plain,
( implies(not(X_174),implies(X_175,X_173)) != not(not(implies(not(X_174),implies(X_175,X_173))))
| not(implies(not(X_174),implies(X_175,X_173))) != not(implies(X_175,implies(not(X_173),X_174)))
| implies(not(X_174),implies(X_175,X_173)) = not(not(implies(X_175,implies(not(X_173),X_174)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_174),implies(X_175,X_173)),not(not(implies(not(X_174),implies(X_175,X_173))))) ),[1,0],$fot(not(implies(X_175,implies(not(X_173),X_174))))]]) ).
cnf(refute_0_768,plain,
( implies(not(X_174),implies(X_175,X_173)) != not(not(implies(not(X_174),implies(X_175,X_173))))
| implies(not(X_174),implies(X_175,X_173)) = not(not(implies(X_175,implies(not(X_173),X_174)))) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_174),implies(X_175,X_173))),not(implies(X_175,implies(not(X_173),X_174)))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
implies(not(X_174),implies(X_175,X_173)) = not(not(implies(X_175,implies(not(X_173),X_174)))),
inference(resolve,[$cnf( $equal(implies(not(X_174),implies(X_175,X_173)),not(not(implies(not(X_174),implies(X_175,X_173))))) )],[refute_0_749,refute_0_768]) ).
cnf(refute_0_770,plain,
not(not(implies(X_175,implies(not(X_173),X_174)))) = implies(X_175,implies(not(X_173),X_174)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_175,implies(not(X_173),X_174))))]]) ).
cnf(refute_0_771,plain,
( implies(not(X_174),implies(X_175,X_173)) != not(not(implies(X_175,implies(not(X_173),X_174))))
| not(not(implies(X_175,implies(not(X_173),X_174)))) != implies(X_175,implies(not(X_173),X_174))
| implies(not(X_174),implies(X_175,X_173)) = implies(X_175,implies(not(X_173),X_174)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_174),implies(X_175,X_173)),implies(X_175,implies(not(X_173),X_174))) ),[0],$fot(not(not(implies(X_175,implies(not(X_173),X_174)))))]]) ).
cnf(refute_0_772,plain,
( implies(not(X_174),implies(X_175,X_173)) != not(not(implies(X_175,implies(not(X_173),X_174))))
| implies(not(X_174),implies(X_175,X_173)) = implies(X_175,implies(not(X_173),X_174)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_175,implies(not(X_173),X_174)))),implies(X_175,implies(not(X_173),X_174))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
implies(not(X_174),implies(X_175,X_173)) = implies(X_175,implies(not(X_173),X_174)),
inference(resolve,[$cnf( $equal(implies(not(X_174),implies(X_175,X_173)),not(not(implies(X_175,implies(not(X_173),X_174))))) )],[refute_0_769,refute_0_772]) ).
cnf(refute_0_774,plain,
( implies(not(X_174),implies(X_175,X_173)) != implies(X_175,implies(not(X_173),X_174))
| implies(X_175,implies(not(X_173),X_174)) = implies(not(X_174),implies(X_175,X_173)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_174),implies(X_175,X_173)))),bind(Y0,$fot(implies(X_175,implies(not(X_173),X_174))))]]) ).
cnf(refute_0_775,plain,
implies(X_175,implies(not(X_173),X_174)) = implies(not(X_174),implies(X_175,X_173)),
inference(resolve,[$cnf( $equal(implies(not(X_174),implies(X_175,X_173)),implies(X_175,implies(not(X_173),X_174))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))),
inference(subst,[],[refute_0_775:[bind(X_173,$fot(and_star(X_186,X_185))),bind(X_174,$fot(X_51)),bind(X_175,$fot(implies(X_51,implies(not(and_star(X_186,X_185)),X_51))))]]) ).
cnf(refute_0_777,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))
| implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) != implies(not(X_51),and_star(X_186,X_185))
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(not(X_51),and_star(X_186,X_185)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)))),bind(Y0,$fot(implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))))),bind(Z0,$fot(implies(not(X_51),and_star(X_186,X_185))))]]) ).
cnf(refute_0_778,plain,
( implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))) != implies(not(X_51),and_star(X_186,X_185))
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(not(X_51),and_star(X_186,X_185)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185)))) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) = implies(not(X_51),and_star(X_186,X_185)),
inference(resolve,[$cnf( $equal(implies(not(X_51),implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),and_star(X_186,X_185))),implies(not(X_51),and_star(X_186,X_185))) )],[refute_0_748,refute_0_778]) ).
cnf(refute_0_780,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)
| implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(not(X_51),and_star(X_186,X_185))
| implies(not(X_51),and_star(X_186,X_185)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)) ),[0],$fot(implies(not(X_51),and_star(X_186,X_185)))]]) ).
cnf(refute_0_781,plain,
( implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)) != implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)
| implies(not(X_51),and_star(X_186,X_185)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) ),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(not(X_51),and_star(X_186,X_185))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
implies(not(X_51),and_star(X_186,X_185)) = implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51),
inference(resolve,[$cnf( $equal(implies(implies(X_51,implies(not(and_star(X_186,X_185)),X_51)),implies(not(and_star(X_186,X_185)),X_51)),implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)) )],[refute_0_735,refute_0_781]) ).
cnf(refute_0_783,plain,
( implies(not(X_51),and_star(X_186,X_185)) != implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)
| implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) = implies(not(X_51),and_star(X_186,X_185)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_51),and_star(X_186,X_185)))),bind(Y0,$fot(implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)))]]) ).
cnf(refute_0_784,plain,
implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51) = implies(not(X_51),and_star(X_186,X_185)),
inference(resolve,[$cnf( $equal(implies(not(X_51),and_star(X_186,X_185)),implies(implies(X_185,implies(X_186,and_star(X_185,and_star(X_186,X_51)))),X_51)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227) = implies(not(X_227),and_star(X_62,X_61)),
inference(subst,[],[refute_0_784:[bind(X_185,$fot(X_61)),bind(X_186,$fot(X_62)),bind(X_51,$fot(X_227))]]) ).
cnf(refute_0_786,plain,
implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),
introduced(tautology,[refl,[$fot(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)))]]) ).
cnf(refute_0_787,plain,
( implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227) != implies(not(X_227),and_star(X_62,X_61))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) != implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227))) ),[1,1],$fot(implies(not(X_227),and_star(X_62,X_61)))]]) ).
cnf(refute_0_788,plain,
( implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227) != implies(not(X_227),and_star(X_62,X_61))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227))) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) = implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),
inference(resolve,[$cnf( $equal(implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227),implies(not(X_227),and_star(X_62,X_61))) )],[refute_0_785,refute_0_788]) ).
cnf(refute_0_790,plain,
( implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) != implies(not(X_226),implies(not(X_227),and_star(X_62,X_61)))
| implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))) ),[0],$fot(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))))]]) ).
cnf(refute_0_791,plain,
( implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),implies(not(X_226),implies(not(X_227),and_star(X_62,X_61)))) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
implies(implies(X_228,X_71),implies(not(X_226),X_71)) = implies(not(X_226),implies(implies(X_228,X_71),X_71)),
inference(subst,[],[refute_0_135:[bind(X_72,$fot(not(X_226))),bind(X_73,$fot(implies(X_228,X_71)))]]) ).
cnf(refute_0_793,plain,
implies(not(X_226),implies(implies(X_228,X_71),X_71)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)),
inference(subst,[],[refute_0_623:[bind(X_37,$fot(X_226)),bind(X_50,$fot(X_71)),bind(X_51,$fot(X_228))]]) ).
cnf(refute_0_794,plain,
( implies(implies(X_228,X_71),implies(not(X_226),X_71)) != implies(not(X_226),implies(implies(X_228,X_71),X_71))
| implies(not(X_226),implies(implies(X_228,X_71),X_71)) != implies(not(X_228),implies(implies(X_71,X_228),X_226))
| implies(implies(X_228,X_71),implies(not(X_226),X_71)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_228,X_71),implies(not(X_226),X_71)),implies(not(X_228),implies(implies(X_71,X_228),X_226))) ),[0],$fot(implies(not(X_226),implies(implies(X_228,X_71),X_71)))]]) ).
cnf(refute_0_795,plain,
( implies(implies(X_228,X_71),implies(not(X_226),X_71)) != implies(not(X_226),implies(implies(X_228,X_71),X_71))
| implies(implies(X_228,X_71),implies(not(X_226),X_71)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(X_228,X_71),X_71)),implies(not(X_228),implies(implies(X_71,X_228),X_226))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
implies(implies(X_228,X_71),implies(not(X_226),X_71)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)),
inference(resolve,[$cnf( $equal(implies(implies(X_228,X_71),implies(not(X_226),X_71)),implies(not(X_226),implies(implies(X_228,X_71),X_71))) )],[refute_0_792,refute_0_795]) ).
cnf(refute_0_797,plain,
implies(not(X_222),implies(X_72,X_71)) = implies(X_72,implies(not(X_222),X_71)),
inference(subst,[],[refute_0_135:[bind(X_73,$fot(not(X_222)))]]) ).
cnf(refute_0_798,plain,
implies(X_107,implies(not(X_109),X_108)) = not(not(implies(X_107,implies(not(X_109),X_108)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_107,implies(not(X_109),X_108))))]]) ).
cnf(refute_0_799,plain,
and_star(not(implies(not(X_37),X_38)),Y) = not(implies(Y,implies(not(X_37),X_38))),
inference(subst,[],[refute_0_92:[bind(X_28,$fot(implies(not(X_37),X_38)))]]) ).
cnf(refute_0_800,plain,
( and_star(not(implies(not(X_37),X_38)),Y) != not(implies(Y,implies(not(X_37),X_38)))
| not(implies(not(X_37),X_38)) != not(implies(not(X_38),X_37))
| and_star(not(implies(not(X_38),X_37)),Y) = not(implies(Y,implies(not(X_37),X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(implies(not(X_37),X_38)),Y),not(implies(Y,implies(not(X_37),X_38)))) ),[0,0],$fot(not(implies(not(X_38),X_37)))]]) ).
cnf(refute_0_801,plain,
( and_star(not(implies(not(X_37),X_38)),Y) != not(implies(Y,implies(not(X_37),X_38)))
| and_star(not(implies(not(X_38),X_37)),Y) = not(implies(Y,implies(not(X_37),X_38))) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_37),X_38)),not(implies(not(X_38),X_37))) )],[refute_0_592,refute_0_800]) ).
cnf(refute_0_802,plain,
and_star(not(implies(not(X_38),X_37)),Y) = not(implies(Y,implies(not(X_37),X_38))),
inference(resolve,[$cnf( $equal(and_star(not(implies(not(X_37),X_38)),Y),not(implies(Y,implies(not(X_37),X_38)))) )],[refute_0_799,refute_0_801]) ).
cnf(refute_0_803,plain,
and_star(not(implies(not(X_38),X_37)),Y) = not(implies(Y,implies(not(X_38),X_37))),
inference(subst,[],[refute_0_92:[bind(X_28,$fot(implies(not(X_38),X_37)))]]) ).
cnf(refute_0_804,plain,
( and_star(not(implies(not(X_38),X_37)),Y) != not(implies(Y,implies(not(X_37),X_38)))
| and_star(not(implies(not(X_38),X_37)),Y) != not(implies(Y,implies(not(X_38),X_37)))
| not(implies(Y,implies(not(X_38),X_37))) = not(implies(Y,implies(not(X_37),X_38))) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(implies(not(X_38),X_37)),Y),not(implies(Y,implies(not(X_37),X_38)))) ),[0],$fot(not(implies(Y,implies(not(X_38),X_37))))]]) ).
cnf(refute_0_805,plain,
( and_star(not(implies(not(X_38),X_37)),Y) != not(implies(Y,implies(not(X_37),X_38)))
| not(implies(Y,implies(not(X_38),X_37))) = not(implies(Y,implies(not(X_37),X_38))) ),
inference(resolve,[$cnf( $equal(and_star(not(implies(not(X_38),X_37)),Y),not(implies(Y,implies(not(X_38),X_37)))) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
not(implies(Y,implies(not(X_38),X_37))) = not(implies(Y,implies(not(X_37),X_38))),
inference(resolve,[$cnf( $equal(and_star(not(implies(not(X_38),X_37)),Y),not(implies(Y,implies(not(X_37),X_38)))) )],[refute_0_802,refute_0_805]) ).
cnf(refute_0_807,plain,
not(implies(X_107,implies(not(X_109),X_108))) = not(implies(X_107,implies(not(X_108),X_109))),
inference(subst,[],[refute_0_806:[bind(Y,$fot(X_107)),bind(X_37,$fot(X_108)),bind(X_38,$fot(X_109))]]) ).
cnf(refute_0_808,plain,
( implies(X_107,implies(not(X_109),X_108)) != not(not(implies(X_107,implies(not(X_109),X_108))))
| not(implies(X_107,implies(not(X_109),X_108))) != not(implies(X_107,implies(not(X_108),X_109)))
| implies(X_107,implies(not(X_109),X_108)) = not(not(implies(X_107,implies(not(X_108),X_109)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_107,implies(not(X_109),X_108)),not(not(implies(X_107,implies(not(X_109),X_108))))) ),[1,0],$fot(not(implies(X_107,implies(not(X_108),X_109))))]]) ).
cnf(refute_0_809,plain,
( implies(X_107,implies(not(X_109),X_108)) != not(not(implies(X_107,implies(not(X_109),X_108))))
| implies(X_107,implies(not(X_109),X_108)) = not(not(implies(X_107,implies(not(X_108),X_109)))) ),
inference(resolve,[$cnf( $equal(not(implies(X_107,implies(not(X_109),X_108))),not(implies(X_107,implies(not(X_108),X_109)))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
implies(X_107,implies(not(X_109),X_108)) = not(not(implies(X_107,implies(not(X_108),X_109)))),
inference(resolve,[$cnf( $equal(implies(X_107,implies(not(X_109),X_108)),not(not(implies(X_107,implies(not(X_109),X_108))))) )],[refute_0_798,refute_0_809]) ).
cnf(refute_0_811,plain,
not(not(implies(X_107,implies(not(X_108),X_109)))) = implies(X_107,implies(not(X_108),X_109)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(X_107,implies(not(X_108),X_109))))]]) ).
cnf(refute_0_812,plain,
( implies(X_107,implies(not(X_109),X_108)) != not(not(implies(X_107,implies(not(X_108),X_109))))
| not(not(implies(X_107,implies(not(X_108),X_109)))) != implies(X_107,implies(not(X_108),X_109))
| implies(X_107,implies(not(X_109),X_108)) = implies(X_107,implies(not(X_108),X_109)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_107,implies(not(X_109),X_108)),implies(X_107,implies(not(X_108),X_109))) ),[0],$fot(not(not(implies(X_107,implies(not(X_108),X_109)))))]]) ).
cnf(refute_0_813,plain,
( implies(X_107,implies(not(X_109),X_108)) != not(not(implies(X_107,implies(not(X_108),X_109))))
| implies(X_107,implies(not(X_109),X_108)) = implies(X_107,implies(not(X_108),X_109)) ),
inference(resolve,[$cnf( $equal(not(not(implies(X_107,implies(not(X_108),X_109)))),implies(X_107,implies(not(X_108),X_109))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
implies(X_107,implies(not(X_109),X_108)) = implies(X_107,implies(not(X_108),X_109)),
inference(resolve,[$cnf( $equal(implies(X_107,implies(not(X_109),X_108)),not(not(implies(X_107,implies(not(X_108),X_109))))) )],[refute_0_810,refute_0_813]) ).
cnf(refute_0_815,plain,
implies(X_72,implies(not(X_222),X_71)) = implies(X_72,implies(not(X_71),X_222)),
inference(subst,[],[refute_0_814:[bind(X_107,$fot(X_72)),bind(X_108,$fot(X_71)),bind(X_109,$fot(X_222))]]) ).
cnf(refute_0_816,plain,
( implies(X_72,implies(not(X_222),X_71)) != implies(X_72,implies(not(X_71),X_222))
| implies(not(X_222),implies(X_72,X_71)) != implies(X_72,implies(not(X_222),X_71))
| implies(not(X_222),implies(X_72,X_71)) = implies(X_72,implies(not(X_71),X_222)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_222),implies(X_72,X_71)),implies(X_72,implies(not(X_222),X_71))) ),[1],$fot(implies(X_72,implies(not(X_71),X_222)))]]) ).
cnf(refute_0_817,plain,
( implies(not(X_222),implies(X_72,X_71)) != implies(X_72,implies(not(X_222),X_71))
| implies(not(X_222),implies(X_72,X_71)) = implies(X_72,implies(not(X_71),X_222)) ),
inference(resolve,[$cnf( $equal(implies(X_72,implies(not(X_222),X_71)),implies(X_72,implies(not(X_71),X_222))) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
implies(not(X_222),implies(X_72,X_71)) = implies(X_72,implies(not(X_71),X_222)),
inference(resolve,[$cnf( $equal(implies(not(X_222),implies(X_72,X_71)),implies(X_72,implies(not(X_222),X_71))) )],[refute_0_797,refute_0_817]) ).
cnf(refute_0_819,plain,
( implies(not(X_222),implies(X_72,X_71)) != implies(X_72,implies(not(X_71),X_222))
| implies(X_72,implies(not(X_71),X_222)) = implies(not(X_222),implies(X_72,X_71)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_222),implies(X_72,X_71)))),bind(Y0,$fot(implies(X_72,implies(not(X_71),X_222))))]]) ).
cnf(refute_0_820,plain,
implies(X_72,implies(not(X_71),X_222)) = implies(not(X_222),implies(X_72,X_71)),
inference(resolve,[$cnf( $equal(implies(not(X_222),implies(X_72,X_71)),implies(X_72,implies(not(X_71),X_222))) )],[refute_0_818,refute_0_819]) ).
cnf(refute_0_821,plain,
implies(implies(X_228,X_71),implies(not(X_226),X_71)) = implies(not(X_71),implies(implies(X_228,X_71),X_226)),
inference(subst,[],[refute_0_820:[bind(X_222,$fot(X_71)),bind(X_71,$fot(X_226)),bind(X_72,$fot(implies(X_228,X_71)))]]) ).
cnf(refute_0_822,plain,
( implies(implies(X_228,X_71),implies(not(X_226),X_71)) != implies(not(X_228),implies(implies(X_71,X_228),X_226))
| implies(implies(X_228,X_71),implies(not(X_226),X_71)) != implies(not(X_71),implies(implies(X_228,X_71),X_226))
| implies(not(X_71),implies(implies(X_228,X_71),X_226)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_228,X_71),implies(not(X_226),X_71)),implies(not(X_228),implies(implies(X_71,X_228),X_226))) ),[0],$fot(implies(not(X_71),implies(implies(X_228,X_71),X_226)))]]) ).
cnf(refute_0_823,plain,
( implies(implies(X_228,X_71),implies(not(X_226),X_71)) != implies(not(X_228),implies(implies(X_71,X_228),X_226))
| implies(not(X_71),implies(implies(X_228,X_71),X_226)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_228,X_71),implies(not(X_226),X_71)),implies(not(X_71),implies(implies(X_228,X_71),X_226))) )],[refute_0_821,refute_0_822]) ).
cnf(refute_0_824,plain,
implies(not(X_71),implies(implies(X_228,X_71),X_226)) = implies(not(X_228),implies(implies(X_71,X_228),X_226)),
inference(resolve,[$cnf( $equal(implies(implies(X_228,X_71),implies(not(X_226),X_71)),implies(not(X_228),implies(implies(X_71,X_228),X_226))) )],[refute_0_796,refute_0_823]) ).
cnf(refute_0_825,plain,
( implies(not(X_71),implies(implies(X_228,X_71),X_226)) != implies(not(X_228),implies(implies(X_71,X_228),X_226))
| implies(not(X_228),implies(implies(X_71,X_228),X_226)) = implies(not(X_71),implies(implies(X_228,X_71),X_226)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_71),implies(implies(X_228,X_71),X_226)))),bind(Y0,$fot(implies(not(X_228),implies(implies(X_71,X_228),X_226))))]]) ).
cnf(refute_0_826,plain,
implies(not(X_228),implies(implies(X_71,X_228),X_226)) = implies(not(X_71),implies(implies(X_228,X_71),X_226)),
inference(resolve,[$cnf( $equal(implies(not(X_71),implies(implies(X_228,X_71),X_226)),implies(not(X_228),implies(implies(X_71,X_228),X_226))) )],[refute_0_824,refute_0_825]) ).
cnf(refute_0_827,plain,
implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) = implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)),
inference(subst,[],[refute_0_826:[bind(X_228,$fot(implies(not(and_star(X_62,X_61)),X_227))),bind(X_71,$fot(X_227))]]) ).
cnf(refute_0_828,plain,
( implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)) != implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))) ),[0],$fot(implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)))]]) ).
cnf(refute_0_829,plain,
( implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226)),implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
( implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)) != implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))) )],[refute_0_791,refute_0_829]) ).
cnf(refute_0_831,plain,
implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(X_61,implies(X_62,and_star(X_61,and_star(X_62,X_227)))),X_227)),implies(not(implies(not(and_star(X_62,X_61)),X_227)),implies(implies(X_227,implies(not(and_star(X_62,X_61)),X_227)),X_226))) )],[refute_0_730,refute_0_830]) ).
cnf(refute_0_832,plain,
implies(not(X_226),implies(implies(implies(X_50,X_227),X_227),X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)),
inference(subst,[],[refute_0_623:[bind(X_37,$fot(X_226)),bind(X_50,$fot(X_227)),bind(X_51,$fot(implies(X_50,X_227)))]]) ).
cnf(refute_0_833,plain,
implies(implies(X_227,X_50),X_50) = implies(implies(X_50,X_227),X_227),
inference(subst,[],[refute_0_412:[bind(X_51,$fot(X_227))]]) ).
cnf(refute_0_834,plain,
( implies(implies(X_227,X_50),X_50) != implies(implies(X_50,X_227),X_227)
| implies(implies(X_50,X_227),X_227) = implies(implies(X_227,X_50),X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_227,X_50),X_50))),bind(Y0,$fot(implies(implies(X_50,X_227),X_227)))]]) ).
cnf(refute_0_835,plain,
implies(implies(X_50,X_227),X_227) = implies(implies(X_227,X_50),X_50),
inference(resolve,[$cnf( $equal(implies(implies(X_227,X_50),X_50),implies(implies(X_50,X_227),X_227)) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
( implies(implies(X_50,X_227),X_227) != implies(implies(X_227,X_50),X_50)
| implies(not(X_226),implies(implies(implies(X_50,X_227),X_227),X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_50,X_227),X_227),X_227)),implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))) ),[0,1,0],$fot(implies(implies(X_227,X_50),X_50))]]) ).
cnf(refute_0_837,plain,
( implies(not(X_226),implies(implies(implies(X_50,X_227),X_227),X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_50,X_227),X_227),implies(implies(X_227,X_50),X_50)) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_50,X_227),X_227),X_227)),implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))) )],[refute_0_832,refute_0_837]) ).
cnf(refute_0_839,plain,
implies(implies(implies(X_227,X_50),X_50),X_227) = implies(X_50,X_227),
inference(subst,[],[refute_0_574:[bind(X_49,$fot(X_50)),bind(X_6,$fot(X_227))]]) ).
cnf(refute_0_840,plain,
implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),
introduced(tautology,[refl,[$fot(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)))]]) ).
cnf(refute_0_841,plain,
( implies(implies(implies(X_227,X_50),X_50),X_227) != implies(X_50,X_227)
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) != implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227))
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(X_226),implies(X_50,X_227)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227))) ),[1,1],$fot(implies(X_50,X_227))]]) ).
cnf(refute_0_842,plain,
( implies(implies(implies(X_227,X_50),X_50),X_227) != implies(X_50,X_227)
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(X_226),implies(X_50,X_227)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) = implies(not(X_226),implies(X_50,X_227)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_227,X_50),X_50),X_227),implies(X_50,X_227)) )],[refute_0_839,refute_0_842]) ).
cnf(refute_0_844,plain,
( implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) != implies(not(X_226),implies(X_50,X_227))
| implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(X_50,X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))) ),[0],$fot(implies(not(X_226),implies(X_50,X_227)))]]) ).
cnf(refute_0_845,plain,
( implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(X_50,X_227)) = implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),implies(not(X_226),implies(X_50,X_227))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) = implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)),
inference(subst,[],[refute_0_826:[bind(X_228,$fot(implies(X_50,X_227))),bind(X_71,$fot(X_227))]]) ).
cnf(refute_0_847,plain,
( implies(not(X_226),implies(X_50,X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)) != implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))
| implies(not(X_226),implies(X_50,X_227)) = implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_226),implies(X_50,X_227)),implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))) ),[0],$fot(implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)))]]) ).
cnf(refute_0_848,plain,
( implies(not(X_226),implies(X_50,X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(X_50,X_227)) = implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226)),implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
( implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)) != implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))
| implies(not(X_226),implies(X_50,X_227)) = implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)) ),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(X_50,X_227)),implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))) )],[refute_0_845,refute_0_848]) ).
cnf(refute_0_850,plain,
implies(not(X_226),implies(X_50,X_227)) = implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(implies(implies(X_227,X_50),X_50),X_227)),implies(not(implies(X_50,X_227)),implies(implies(X_227,implies(X_50,X_227)),X_226))) )],[refute_0_838,refute_0_849]) ).
cnf(refute_0_851,plain,
( implies(not(X_226),implies(X_50,X_227)) != implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))
| implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)) = implies(not(X_226),implies(X_50,X_227)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_226),implies(X_50,X_227)))),bind(Y0,$fot(implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))))]]) ).
cnf(refute_0_852,plain,
implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226)) = implies(not(X_226),implies(X_50,X_227)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(X_50,X_227)),implies(not(X_227),implies(implies(implies(X_50,X_227),X_227),X_226))) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)) = implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)),
inference(subst,[],[refute_0_852:[bind(X_50,$fot(not(and_star(X_62,X_61))))]]) ).
cnf(refute_0_854,plain,
( implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) != implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))
| implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)) != implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))) ),[0],$fot(implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)))]]) ).
cnf(refute_0_855,plain,
( implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) != implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))
| implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)) ),
inference(resolve,[$cnf( $equal(implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226)),implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) = implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),implies(not(X_227),implies(implies(implies(not(and_star(X_62,X_61)),X_227),X_227),X_226))) )],[refute_0_831,refute_0_855]) ).
cnf(refute_0_857,plain,
( implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) != implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))
| implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)) = implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))))),bind(Y0,$fot(implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))))]]) ).
cnf(refute_0_858,plain,
implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227)) = implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),
inference(resolve,[$cnf( $equal(implies(not(X_226),implies(not(X_227),and_star(X_62,X_61))),implies(not(X_226),implies(not(and_star(X_62,X_61)),X_227))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))),
inference(subst,[],[refute_0_858:[bind(X_226,$fot(X_51)),bind(X_227,$fot(X_250)),bind(X_61,$fot(X_51)),bind(X_62,$fot(X_250))]]) ).
cnf(refute_0_860,plain,
implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) = implies(implies(X_50,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242))),
inference(subst,[],[refute_0_412:[bind(X_51,$fot(implies(X_241,implies(not(X_50),X_242))))]]) ).
cnf(refute_0_861,plain,
implies(X_74,implies(and_star(X_91,X_92),X_74)) = truth,
inference(subst,[],[refute_0_229:[bind(X_75,$fot(and_star(X_91,X_92)))]]) ).
cnf(refute_0_862,plain,
implies(and_star(X_91,X_92),X_74) = implies(X_91,implies(X_92,X_74)),
inference(subst,[],[refute_0_614:[bind(X_54,$fot(X_74)),bind(X_55,$fot(X_91)),bind(X_56,$fot(X_92))]]) ).
cnf(refute_0_863,plain,
( implies(X_74,implies(and_star(X_91,X_92),X_74)) != truth
| implies(and_star(X_91,X_92),X_74) != implies(X_91,implies(X_92,X_74))
| implies(X_74,implies(X_91,implies(X_92,X_74))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_74,implies(and_star(X_91,X_92),X_74)),truth) ),[0,1],$fot(implies(X_91,implies(X_92,X_74)))]]) ).
cnf(refute_0_864,plain,
( implies(X_74,implies(and_star(X_91,X_92),X_74)) != truth
| implies(X_74,implies(X_91,implies(X_92,X_74))) = truth ),
inference(resolve,[$cnf( $equal(implies(and_star(X_91,X_92),X_74),implies(X_91,implies(X_92,X_74))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
implies(X_74,implies(X_91,implies(X_92,X_74))) = truth,
inference(resolve,[$cnf( $equal(implies(X_74,implies(and_star(X_91,X_92),X_74)),truth) )],[refute_0_861,refute_0_864]) ).
cnf(refute_0_866,plain,
implies(X_117,implies(X_118,implies(not(X_38),X_117))) = truth,
inference(subst,[],[refute_0_865:[bind(X_74,$fot(X_117)),bind(X_91,$fot(X_118)),bind(X_92,$fot(not(X_38)))]]) ).
cnf(refute_0_867,plain,
implies(not(X_117),X_38) = implies(not(X_38),X_117),
inference(subst,[],[refute_0_599:[bind(X_37,$fot(X_117))]]) ).
cnf(refute_0_868,plain,
( implies(not(X_117),X_38) != implies(not(X_38),X_117)
| implies(not(X_38),X_117) = implies(not(X_117),X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_117),X_38))),bind(Y0,$fot(implies(not(X_38),X_117)))]]) ).
cnf(refute_0_869,plain,
implies(not(X_38),X_117) = implies(not(X_117),X_38),
inference(resolve,[$cnf( $equal(implies(not(X_117),X_38),implies(not(X_38),X_117)) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
( implies(X_117,implies(X_118,implies(not(X_38),X_117))) != truth
| implies(not(X_38),X_117) != implies(not(X_117),X_38)
| implies(X_117,implies(X_118,implies(not(X_117),X_38))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_117,implies(X_118,implies(not(X_38),X_117))),truth) ),[0,1,1],$fot(implies(not(X_117),X_38))]]) ).
cnf(refute_0_871,plain,
( implies(X_117,implies(X_118,implies(not(X_38),X_117))) != truth
| implies(X_117,implies(X_118,implies(not(X_117),X_38))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_38),X_117),implies(not(X_117),X_38)) )],[refute_0_869,refute_0_870]) ).
cnf(refute_0_872,plain,
implies(X_117,implies(X_118,implies(not(X_117),X_38))) = truth,
inference(resolve,[$cnf( $equal(implies(X_117,implies(X_118,implies(not(X_38),X_117))),truth) )],[refute_0_866,refute_0_871]) ).
cnf(refute_0_873,plain,
implies(X_50,implies(X_241,implies(not(X_50),X_242))) = truth,
inference(subst,[],[refute_0_872:[bind(X_117,$fot(X_50)),bind(X_118,$fot(X_241)),bind(X_38,$fot(X_242))]]) ).
cnf(refute_0_874,plain,
( implies(X_50,implies(X_241,implies(not(X_50),X_242))) != truth
| implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(implies(X_50,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242)))
| implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) = implies(truth,implies(X_241,implies(not(X_50),X_242))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50),implies(implies(X_50,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_875,plain,
( implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(implies(X_50,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242)))
| implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) = implies(truth,implies(X_241,implies(not(X_50),X_242))) ),
inference(resolve,[$cnf( $equal(implies(X_50,implies(X_241,implies(not(X_50),X_242))),truth) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) = implies(truth,implies(X_241,implies(not(X_50),X_242))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50),implies(implies(X_50,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242)))) )],[refute_0_860,refute_0_875]) ).
cnf(refute_0_877,plain,
implies(implies(implies(not(X_63),X_44),X_63),X_63) = implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)),
inference(subst,[],[refute_0_412:[bind(X_50,$fot(X_63)),bind(X_51,$fot(implies(not(X_63),X_44)))]]) ).
cnf(refute_0_878,plain,
implies(X_44,and_star(X_44,X_63)) = implies(implies(not(X_63),X_44),X_63),
inference(subst,[],[refute_0_499:[bind(X_6,$fot(X_63))]]) ).
cnf(refute_0_879,plain,
( implies(X_44,and_star(X_44,X_63)) != implies(implies(not(X_63),X_44),X_63)
| implies(implies(not(X_63),X_44),X_63) = implies(X_44,and_star(X_44,X_63)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_44,and_star(X_44,X_63)))),bind(Y0,$fot(implies(implies(not(X_63),X_44),X_63)))]]) ).
cnf(refute_0_880,plain,
implies(implies(not(X_63),X_44),X_63) = implies(X_44,and_star(X_44,X_63)),
inference(resolve,[$cnf( $equal(implies(X_44,and_star(X_44,X_63)),implies(implies(not(X_63),X_44),X_63)) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
( implies(implies(implies(not(X_63),X_44),X_63),X_63) != implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))
| implies(implies(not(X_63),X_44),X_63) != implies(X_44,and_star(X_44,X_63))
| implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_63),X_44),X_63),X_63),implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))) ),[0,0],$fot(implies(X_44,and_star(X_44,X_63)))]]) ).
cnf(refute_0_882,plain,
( implies(implies(implies(not(X_63),X_44),X_63),X_63) != implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))
| implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_63),X_44),X_63),implies(X_44,and_star(X_44,X_63))) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_63),X_44),X_63),X_63),implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))) )],[refute_0_877,refute_0_882]) ).
cnf(refute_0_884,plain,
( implies(implies(X_51,X_50),X_50) != implies(implies(X_50,X_51),X_51)
| implies(implies(X_50,X_51),X_51) = implies(implies(X_51,X_50),X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_51,X_50),X_50))),bind(Y0,$fot(implies(implies(X_50,X_51),X_51)))]]) ).
cnf(refute_0_885,plain,
implies(implies(X_50,X_51),X_51) = implies(implies(X_51,X_50),X_50),
inference(resolve,[$cnf( $equal(implies(implies(X_51,X_50),X_50),implies(implies(X_50,X_51),X_51)) )],[refute_0_412,refute_0_884]) ).
cnf(refute_0_886,plain,
implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)) = implies(implies(implies(not(X_63),X_44),X_63),X_63),
inference(subst,[],[refute_0_885:[bind(X_50,$fot(X_63)),bind(X_51,$fot(implies(not(X_63),X_44)))]]) ).
cnf(refute_0_887,plain,
( implies(implies(X_44,and_star(X_44,X_63)),X_63) != implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))
| implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)) != implies(implies(implies(not(X_63),X_44),X_63),X_63)
| implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_44,and_star(X_44,X_63)),X_63),implies(implies(implies(not(X_63),X_44),X_63),X_63)) ),[0],$fot(implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)))]]) ).
cnf(refute_0_888,plain,
( implies(implies(X_44,and_star(X_44,X_63)),X_63) != implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))
| implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44)),implies(implies(implies(not(X_63),X_44),X_63),X_63)) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63),
inference(resolve,[$cnf( $equal(implies(implies(X_44,and_star(X_44,X_63)),X_63),implies(implies(X_63,implies(not(X_63),X_44)),implies(not(X_63),X_44))) )],[refute_0_883,refute_0_888]) ).
cnf(refute_0_890,plain,
implies(implies(implies(not(X_45),X_63),X_63),X_63) = implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)),
inference(subst,[],[refute_0_412:[bind(X_50,$fot(X_63)),bind(X_51,$fot(implies(not(X_45),X_63)))]]) ).
cnf(refute_0_891,plain,
implies(implies(not(X_45),X_63),X_63) = implies(X_45,and_star(X_45,X_63)),
inference(subst,[],[refute_0_664:[bind(X_38,$fot(X_63))]]) ).
cnf(refute_0_892,plain,
( implies(implies(implies(not(X_45),X_63),X_63),X_63) != implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))
| implies(implies(not(X_45),X_63),X_63) != implies(X_45,and_star(X_45,X_63))
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_45),X_63),X_63),X_63),implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))) ),[0,0],$fot(implies(X_45,and_star(X_45,X_63)))]]) ).
cnf(refute_0_893,plain,
( implies(implies(implies(not(X_45),X_63),X_63),X_63) != implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_45),X_63),X_63),implies(X_45,and_star(X_45,X_63))) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_45),X_63),X_63),X_63),implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))) )],[refute_0_890,refute_0_893]) ).
cnf(refute_0_895,plain,
implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)) = implies(implies(implies(not(X_45),X_63),X_63),X_63),
inference(subst,[],[refute_0_885:[bind(X_50,$fot(X_63)),bind(X_51,$fot(implies(not(X_45),X_63)))]]) ).
cnf(refute_0_896,plain,
( implies(implies(X_45,and_star(X_45,X_63)),X_63) != implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))
| implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)) != implies(implies(implies(not(X_45),X_63),X_63),X_63)
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(implies(not(X_45),X_63),X_63),X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_45,and_star(X_45,X_63)),X_63),implies(implies(implies(not(X_45),X_63),X_63),X_63)) ),[0],$fot(implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)))]]) ).
cnf(refute_0_897,plain,
( implies(implies(X_45,and_star(X_45,X_63)),X_63) != implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(implies(not(X_45),X_63),X_63),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63)),implies(implies(implies(not(X_45),X_63),X_63),X_63)) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(implies(implies(not(X_45),X_63),X_63),X_63),
inference(resolve,[$cnf( $equal(implies(implies(X_45,and_star(X_45,X_63)),X_63),implies(implies(X_63,implies(not(X_45),X_63)),implies(not(X_45),X_63))) )],[refute_0_894,refute_0_897]) ).
cnf(refute_0_899,plain,
implies(implies(implies(not(X_45),X_63),X_63),X_63) = implies(not(X_45),X_63),
inference(subst,[],[refute_0_568:[bind(X_50,$fot(X_63)),bind(X_77,$fot(not(X_45)))]]) ).
cnf(refute_0_900,plain,
( implies(implies(X_45,and_star(X_45,X_63)),X_63) != implies(implies(implies(not(X_45),X_63),X_63),X_63)
| implies(implies(implies(not(X_45),X_63),X_63),X_63) != implies(not(X_45),X_63)
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(not(X_45),X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_45,and_star(X_45,X_63)),X_63),implies(not(X_45),X_63)) ),[0],$fot(implies(implies(implies(not(X_45),X_63),X_63),X_63))]]) ).
cnf(refute_0_901,plain,
( implies(implies(X_45,and_star(X_45,X_63)),X_63) != implies(implies(implies(not(X_45),X_63),X_63),X_63)
| implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(not(X_45),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_45),X_63),X_63),X_63),implies(not(X_45),X_63)) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
implies(implies(X_45,and_star(X_45,X_63)),X_63) = implies(not(X_45),X_63),
inference(resolve,[$cnf( $equal(implies(implies(X_45,and_star(X_45,X_63)),X_63),implies(implies(implies(not(X_45),X_63),X_63),X_63)) )],[refute_0_898,refute_0_901]) ).
cnf(refute_0_903,plain,
implies(implies(X_44,and_star(X_44,X_63)),X_63) = implies(not(X_44),X_63),
inference(subst,[],[refute_0_902:[bind(X_45,$fot(X_44))]]) ).
cnf(refute_0_904,plain,
( implies(implies(X_44,and_star(X_44,X_63)),X_63) != implies(implies(implies(not(X_63),X_44),X_63),X_63)
| implies(implies(X_44,and_star(X_44,X_63)),X_63) != implies(not(X_44),X_63)
| implies(not(X_44),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_44,and_star(X_44,X_63)),X_63),implies(implies(implies(not(X_63),X_44),X_63),X_63)) ),[0],$fot(implies(not(X_44),X_63))]]) ).
cnf(refute_0_905,plain,
( implies(implies(X_44,and_star(X_44,X_63)),X_63) != implies(implies(implies(not(X_63),X_44),X_63),X_63)
| implies(not(X_44),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(X_44,and_star(X_44,X_63)),X_63),implies(not(X_44),X_63)) )],[refute_0_903,refute_0_904]) ).
cnf(refute_0_906,plain,
implies(not(X_44),X_63) = implies(implies(implies(not(X_63),X_44),X_63),X_63),
inference(resolve,[$cnf( $equal(implies(implies(X_44,and_star(X_44,X_63)),X_63),implies(implies(implies(not(X_63),X_44),X_63),X_63)) )],[refute_0_889,refute_0_905]) ).
cnf(refute_0_907,plain,
implies(not(implies(X_73,X_71)),X_183) = implies(implies(implies(not(X_183),implies(X_73,X_71)),X_183),X_183),
inference(subst,[],[refute_0_906:[bind(X_44,$fot(implies(X_73,X_71))),bind(X_63,$fot(X_183))]]) ).
cnf(refute_0_908,plain,
implies(X_73,implies(not(X_183),X_71)) = implies(not(X_183),implies(X_73,X_71)),
inference(subst,[],[refute_0_135:[bind(X_72,$fot(not(X_183)))]]) ).
cnf(refute_0_909,plain,
( implies(X_73,implies(not(X_183),X_71)) != implies(not(X_183),implies(X_73,X_71))
| implies(not(X_183),implies(X_73,X_71)) = implies(X_73,implies(not(X_183),X_71)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_73,implies(not(X_183),X_71)))),bind(Y0,$fot(implies(not(X_183),implies(X_73,X_71))))]]) ).
cnf(refute_0_910,plain,
implies(not(X_183),implies(X_73,X_71)) = implies(X_73,implies(not(X_183),X_71)),
inference(resolve,[$cnf( $equal(implies(X_73,implies(not(X_183),X_71)),implies(not(X_183),implies(X_73,X_71))) )],[refute_0_908,refute_0_909]) ).
cnf(refute_0_911,plain,
( implies(not(X_183),implies(X_73,X_71)) != implies(X_73,implies(not(X_183),X_71))
| implies(not(implies(X_73,X_71)),X_183) != implies(implies(implies(not(X_183),implies(X_73,X_71)),X_183),X_183)
| implies(not(implies(X_73,X_71)),X_183) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_73,X_71)),X_183),implies(implies(implies(not(X_183),implies(X_73,X_71)),X_183),X_183)) ),[1,0,0],$fot(implies(X_73,implies(not(X_183),X_71)))]]) ).
cnf(refute_0_912,plain,
( implies(not(implies(X_73,X_71)),X_183) != implies(implies(implies(not(X_183),implies(X_73,X_71)),X_183),X_183)
| implies(not(implies(X_73,X_71)),X_183) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) ),
inference(resolve,[$cnf( $equal(implies(not(X_183),implies(X_73,X_71)),implies(X_73,implies(not(X_183),X_71))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
implies(not(implies(X_73,X_71)),X_183) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183),
inference(resolve,[$cnf( $equal(implies(not(implies(X_73,X_71)),X_183),implies(implies(implies(not(X_183),implies(X_73,X_71)),X_183),X_183)) )],[refute_0_907,refute_0_912]) ).
cnf(refute_0_914,plain,
implies(not(implies(X_73,X_71)),X_183) = implies(not(X_71),implies(X_73,X_183)),
inference(subst,[],[refute_0_619:[bind(X_28,$fot(X_71)),bind(X_90,$fot(X_183)),bind(X_92,$fot(X_73))]]) ).
cnf(refute_0_915,plain,
( implies(not(implies(X_73,X_71)),X_183) != implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)
| implies(not(implies(X_73,X_71)),X_183) != implies(not(X_71),implies(X_73,X_183))
| implies(not(X_71),implies(X_73,X_183)) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_73,X_71)),X_183),implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)) ),[0],$fot(implies(not(X_71),implies(X_73,X_183)))]]) ).
cnf(refute_0_916,plain,
( implies(not(implies(X_73,X_71)),X_183) != implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)
| implies(not(X_71),implies(X_73,X_183)) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_73,X_71)),X_183),implies(not(X_71),implies(X_73,X_183))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
implies(not(X_71),implies(X_73,X_183)) = implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183),
inference(resolve,[$cnf( $equal(implies(not(implies(X_73,X_71)),X_183),implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)) )],[refute_0_913,refute_0_916]) ).
cnf(refute_0_918,plain,
( implies(not(X_71),implies(X_73,X_183)) != implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)
| implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) = implies(not(X_71),implies(X_73,X_183)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_71),implies(X_73,X_183)))),bind(Y0,$fot(implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)))]]) ).
cnf(refute_0_919,plain,
implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183) = implies(not(X_71),implies(X_73,X_183)),
inference(resolve,[$cnf( $equal(implies(not(X_71),implies(X_73,X_183)),implies(implies(implies(X_73,implies(not(X_183),X_71)),X_183),X_183)) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) = implies(not(X_242),implies(X_241,X_50)),
inference(subst,[],[refute_0_919:[bind(X_183,$fot(X_50)),bind(X_71,$fot(X_242)),bind(X_73,$fot(X_241))]]) ).
cnf(refute_0_921,plain,
( implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(not(X_242),implies(X_241,X_50))
| implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(truth,implies(X_241,implies(not(X_50),X_242)))
| implies(not(X_242),implies(X_241,X_50)) = implies(truth,implies(X_241,implies(not(X_50),X_242))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50),implies(truth,implies(X_241,implies(not(X_50),X_242)))) ),[0],$fot(implies(not(X_242),implies(X_241,X_50)))]]) ).
cnf(refute_0_922,plain,
( implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(truth,implies(X_241,implies(not(X_50),X_242)))
| implies(not(X_242),implies(X_241,X_50)) = implies(truth,implies(X_241,implies(not(X_50),X_242))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50),implies(not(X_242),implies(X_241,X_50))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
implies(truth,implies(X_241,implies(not(X_50),X_242))) = implies(X_241,implies(not(X_50),X_242)),
inference(subst,[],[refute_0_458:[bind(X_18,$fot(implies(X_241,implies(not(X_50),X_242))))]]) ).
cnf(refute_0_924,plain,
( implies(not(X_242),implies(X_241,X_50)) != implies(truth,implies(X_241,implies(not(X_50),X_242)))
| implies(truth,implies(X_241,implies(not(X_50),X_242))) != implies(X_241,implies(not(X_50),X_242))
| implies(not(X_242),implies(X_241,X_50)) = implies(X_241,implies(not(X_50),X_242)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_242),implies(X_241,X_50)),implies(X_241,implies(not(X_50),X_242))) ),[0],$fot(implies(truth,implies(X_241,implies(not(X_50),X_242))))]]) ).
cnf(refute_0_925,plain,
( implies(not(X_242),implies(X_241,X_50)) != implies(truth,implies(X_241,implies(not(X_50),X_242)))
| implies(not(X_242),implies(X_241,X_50)) = implies(X_241,implies(not(X_50),X_242)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_241,implies(not(X_50),X_242))),implies(X_241,implies(not(X_50),X_242))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
( implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50) != implies(truth,implies(X_241,implies(not(X_50),X_242)))
| implies(not(X_242),implies(X_241,X_50)) = implies(X_241,implies(not(X_50),X_242)) ),
inference(resolve,[$cnf( $equal(implies(not(X_242),implies(X_241,X_50)),implies(truth,implies(X_241,implies(not(X_50),X_242)))) )],[refute_0_922,refute_0_925]) ).
cnf(refute_0_927,plain,
implies(not(X_242),implies(X_241,X_50)) = implies(X_241,implies(not(X_50),X_242)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_241,implies(not(X_50),X_242)),X_50),X_50),implies(truth,implies(X_241,implies(not(X_50),X_242)))) )],[refute_0_876,refute_0_926]) ).
cnf(refute_0_928,plain,
( implies(not(X_242),implies(X_241,X_50)) != implies(X_241,implies(not(X_50),X_242))
| implies(X_241,implies(not(X_50),X_242)) = implies(not(X_242),implies(X_241,X_50)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_242),implies(X_241,X_50)))),bind(Y0,$fot(implies(X_241,implies(not(X_50),X_242))))]]) ).
cnf(refute_0_929,plain,
implies(X_241,implies(not(X_50),X_242)) = implies(not(X_242),implies(X_241,X_50)),
inference(resolve,[$cnf( $equal(implies(not(X_242),implies(X_241,X_50)),implies(X_241,implies(not(X_50),X_242))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) = implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)),
inference(subst,[],[refute_0_929:[bind(X_241,$fot(not(and_star(X_250,X_51)))),bind(X_242,$fot(X_51)),bind(X_50,$fot(X_250))]]) ).
cnf(refute_0_931,plain,
( implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) != implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250))
| implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)))),bind(Y0,$fot(implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)))),bind(Z0,$fot(implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))))]]) ).
cnf(refute_0_932,plain,
( implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)),implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))),
inference(resolve,[$cnf( $equal(implies(not(X_51),implies(not(and_star(X_250,X_51)),X_250)),implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))) )],[refute_0_859,refute_0_932]) ).
cnf(refute_0_934,plain,
implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) = implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)),
inference(subst,[],[refute_0_852:[bind(X_226,$fot(and_star(X_250,X_51))),bind(X_227,$fot(X_51)),bind(X_50,$fot(not(X_250)))]]) ).
cnf(refute_0_935,plain,
( implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) != implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51))
| implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))))),bind(Y0,$fot(implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)))),bind(Z0,$fot(implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))))]]) ).
cnf(refute_0_936,plain,
( implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(resolve,[$cnf( $equal(implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))),implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(not(X_250),X_51)),implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))) )],[refute_0_933,refute_0_936]) ).
cnf(refute_0_938,plain,
implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) = implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))),
inference(subst,[],[refute_0_929:[bind(X_241,$fot(implies(implies(not(X_250),X_51),X_51))),bind(X_242,$fot(X_51)),bind(X_50,$fot(and_star(X_250,X_51)))]]) ).
cnf(refute_0_939,plain,
( implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) != implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))
| implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)))),bind(Y0,$fot(implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))))),bind(Z0,$fot(implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))))]]) ).
cnf(refute_0_940,plain,
( implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)),implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51)))) )],[refute_0_938,refute_0_939]) ).
cnf(refute_0_941,plain,
implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))),
inference(resolve,[$cnf( $equal(implies(not(X_51),implies(implies(implies(not(X_250),X_51),X_51),and_star(X_250,X_51))),implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))) )],[refute_0_937,refute_0_940]) ).
cnf(refute_0_942,plain,
implies(X_245,implies(implies(X_244,X_243),X_243)) = not(not(implies(X_245,implies(implies(X_244,X_243),X_243)))),
inference(subst,[],[refute_0_54:[bind(X_6,$fot(implies(X_245,implies(implies(X_244,X_243),X_243))))]]) ).
cnf(refute_0_943,plain,
not(implies(X_73,implies(implies(X_50,X_71),X_71))) = not(implies(implies(X_50,X_71),implies(X_73,X_71))),
inference(subst,[],[refute_0_127:[bind(X_28,$fot(X_71)),bind(X_40,$fot(implies(X_50,X_71))),bind(X_41,$fot(X_73))]]) ).
cnf(refute_0_944,plain,
implies(implies(X_71,X_50),X_50) = implies(implies(X_50,X_71),X_71),
inference(subst,[],[refute_0_412:[bind(X_51,$fot(X_71))]]) ).
cnf(refute_0_945,plain,
( implies(implies(X_71,X_50),X_50) != implies(implies(X_50,X_71),X_71)
| implies(implies(X_50,X_71),X_71) = implies(implies(X_71,X_50),X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_71,X_50),X_50))),bind(Y0,$fot(implies(implies(X_50,X_71),X_71)))]]) ).
cnf(refute_0_946,plain,
implies(implies(X_50,X_71),X_71) = implies(implies(X_71,X_50),X_50),
inference(resolve,[$cnf( $equal(implies(implies(X_71,X_50),X_50),implies(implies(X_50,X_71),X_71)) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
( implies(implies(X_50,X_71),X_71) != implies(implies(X_71,X_50),X_50)
| not(implies(X_73,implies(implies(X_50,X_71),X_71))) != not(implies(implies(X_50,X_71),implies(X_73,X_71)))
| not(implies(X_73,implies(implies(X_71,X_50),X_50))) = not(implies(implies(X_50,X_71),implies(X_73,X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_73,implies(implies(X_50,X_71),X_71))),not(implies(implies(X_50,X_71),implies(X_73,X_71)))) ),[0,0,1],$fot(implies(implies(X_71,X_50),X_50))]]) ).
cnf(refute_0_948,plain,
( not(implies(X_73,implies(implies(X_50,X_71),X_71))) != not(implies(implies(X_50,X_71),implies(X_73,X_71)))
| not(implies(X_73,implies(implies(X_71,X_50),X_50))) = not(implies(implies(X_50,X_71),implies(X_73,X_71))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_50,X_71),X_71),implies(implies(X_71,X_50),X_50)) )],[refute_0_946,refute_0_947]) ).
cnf(refute_0_949,plain,
not(implies(X_73,implies(implies(X_71,X_50),X_50))) = not(implies(implies(X_50,X_71),implies(X_73,X_71))),
inference(resolve,[$cnf( $equal(not(implies(X_73,implies(implies(X_50,X_71),X_71))),not(implies(implies(X_50,X_71),implies(X_73,X_71)))) )],[refute_0_943,refute_0_948]) ).
cnf(refute_0_950,plain,
not(implies(X_245,implies(implies(X_244,X_243),X_243))) = not(implies(implies(X_243,X_244),implies(X_245,X_244))),
inference(subst,[],[refute_0_949:[bind(X_50,$fot(X_243)),bind(X_71,$fot(X_244)),bind(X_73,$fot(X_245))]]) ).
cnf(refute_0_951,plain,
( implies(X_245,implies(implies(X_244,X_243),X_243)) != not(not(implies(X_245,implies(implies(X_244,X_243),X_243))))
| not(implies(X_245,implies(implies(X_244,X_243),X_243))) != not(implies(implies(X_243,X_244),implies(X_245,X_244)))
| implies(X_245,implies(implies(X_244,X_243),X_243)) = not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_245,implies(implies(X_244,X_243),X_243)),not(not(implies(X_245,implies(implies(X_244,X_243),X_243))))) ),[1,0],$fot(not(implies(implies(X_243,X_244),implies(X_245,X_244))))]]) ).
cnf(refute_0_952,plain,
( implies(X_245,implies(implies(X_244,X_243),X_243)) != not(not(implies(X_245,implies(implies(X_244,X_243),X_243))))
| implies(X_245,implies(implies(X_244,X_243),X_243)) = not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))) ),
inference(resolve,[$cnf( $equal(not(implies(X_245,implies(implies(X_244,X_243),X_243))),not(implies(implies(X_243,X_244),implies(X_245,X_244)))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
implies(X_245,implies(implies(X_244,X_243),X_243)) = not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))),
inference(resolve,[$cnf( $equal(implies(X_245,implies(implies(X_244,X_243),X_243)),not(not(implies(X_245,implies(implies(X_244,X_243),X_243))))) )],[refute_0_942,refute_0_952]) ).
cnf(refute_0_954,plain,
not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))) = implies(implies(X_243,X_244),implies(X_245,X_244)),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(X_243,X_244),implies(X_245,X_244))))]]) ).
cnf(refute_0_955,plain,
( implies(X_245,implies(implies(X_244,X_243),X_243)) != not(not(implies(implies(X_243,X_244),implies(X_245,X_244))))
| not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))) != implies(implies(X_243,X_244),implies(X_245,X_244))
| implies(X_245,implies(implies(X_244,X_243),X_243)) = implies(implies(X_243,X_244),implies(X_245,X_244)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_245,implies(implies(X_244,X_243),X_243)),implies(implies(X_243,X_244),implies(X_245,X_244))) ),[0],$fot(not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))))]]) ).
cnf(refute_0_956,plain,
( implies(X_245,implies(implies(X_244,X_243),X_243)) != not(not(implies(implies(X_243,X_244),implies(X_245,X_244))))
| implies(X_245,implies(implies(X_244,X_243),X_243)) = implies(implies(X_243,X_244),implies(X_245,X_244)) ),
inference(resolve,[$cnf( $equal(not(not(implies(implies(X_243,X_244),implies(X_245,X_244)))),implies(implies(X_243,X_244),implies(X_245,X_244))) )],[refute_0_954,refute_0_955]) ).
cnf(refute_0_957,plain,
implies(X_245,implies(implies(X_244,X_243),X_243)) = implies(implies(X_243,X_244),implies(X_245,X_244)),
inference(resolve,[$cnf( $equal(implies(X_245,implies(implies(X_244,X_243),X_243)),not(not(implies(implies(X_243,X_244),implies(X_245,X_244))))) )],[refute_0_953,refute_0_956]) ).
cnf(refute_0_958,plain,
implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)),
inference(subst,[],[refute_0_957:[bind(X_243,$fot(implies(not(X_250),X_51))),bind(X_244,$fot(X_51)),bind(X_245,$fot(not(and_star(X_250,X_51))))]]) ).
cnf(refute_0_959,plain,
( implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51))
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))))),bind(Y0,$fot(implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)))),bind(Z0,$fot(implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))))]]) ).
cnf(refute_0_960,plain,
( implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) ),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) = implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_250),X_51),X_51),implies(not(and_star(X_250,X_51)),X_51)),implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))) )],[refute_0_941,refute_0_960]) ).
cnf(refute_0_962,plain,
( implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(not(X_51),X_250)
| implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))
| implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) = implies(not(X_51),X_250) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(not(X_51),X_250)) ),[0],$fot(implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))))]]) ).
cnf(refute_0_963,plain,
( implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))) != implies(not(X_51),X_250)
| implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) = implies(not(X_51),X_250) ),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(not(X_51),implies(not(X_250),and_star(X_250,X_51)))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
implies(not(X_51),implies(not(X_250),and_star(X_250,X_51))) = implies(not(X_51),X_250),
inference(resolve,[$cnf( $equal(implies(not(and_star(X_250,X_51)),implies(implies(X_51,implies(not(X_250),X_51)),implies(not(X_250),X_51))),implies(not(X_51),X_250)) )],[refute_0_694,refute_0_963]) ).
cnf(refute_0_965,plain,
implies(not(not(X_18)),implies(not(X_381),and_star(X_381,not(X_18)))) = implies(not(not(X_18)),X_381),
inference(subst,[],[refute_0_964:[bind(X_250,$fot(X_381)),bind(X_51,$fot(not(X_18)))]]) ).
cnf(refute_0_966,plain,
and_star(X_381,not(X_18)) = not(implies(X_381,X_18)),
inference(subst,[],[refute_0_88:[bind(X_17,$fot(X_381))]]) ).
cnf(refute_0_967,plain,
( and_star(X_381,not(X_18)) != not(implies(X_381,X_18))
| implies(not(not(X_18)),implies(not(X_381),and_star(X_381,not(X_18)))) != implies(not(not(X_18)),X_381)
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(not(not(X_18)),X_381) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),and_star(X_381,not(X_18)))),implies(not(not(X_18)),X_381)) ),[0,1,1],$fot(not(implies(X_381,X_18)))]]) ).
cnf(refute_0_968,plain,
( implies(not(not(X_18)),implies(not(X_381),and_star(X_381,not(X_18)))) != implies(not(not(X_18)),X_381)
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(not(not(X_18)),X_381) ),
inference(resolve,[$cnf( $equal(and_star(X_381,not(X_18)),not(implies(X_381,X_18))) )],[refute_0_966,refute_0_967]) ).
cnf(refute_0_969,plain,
implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(not(not(X_18)),X_381),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),and_star(X_381,not(X_18)))),implies(not(not(X_18)),X_381)) )],[refute_0_965,refute_0_968]) ).
cnf(refute_0_970,plain,
not(not(implies(implies(X_381,X_18),X_381))) = implies(implies(X_381,X_18),X_381),
inference(subst,[],[refute_0_61:[bind(X_6,$fot(implies(implies(X_381,X_18),X_381)))]]) ).
cnf(refute_0_971,plain,
and_star(not(X_381),implies(X_381,X_18)) = not(implies(implies(X_381,X_18),X_381)),
inference(subst,[],[refute_0_92:[bind(Y,$fot(implies(X_381,X_18))),bind(X_28,$fot(X_381))]]) ).
cnf(refute_0_972,plain,
not(and_star(not(X_381),implies(X_381,X_18))) = not(and_star(not(X_381),implies(X_381,X_18))),
introduced(tautology,[refl,[$fot(not(and_star(not(X_381),implies(X_381,X_18))))]]) ).
cnf(refute_0_973,plain,
( and_star(not(X_381),implies(X_381,X_18)) != not(implies(implies(X_381,X_18),X_381))
| not(and_star(not(X_381),implies(X_381,X_18))) != not(and_star(not(X_381),implies(X_381,X_18)))
| not(and_star(not(X_381),implies(X_381,X_18))) = not(not(implies(implies(X_381,X_18),X_381))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(not(X_381),implies(X_381,X_18))),not(and_star(not(X_381),implies(X_381,X_18)))) ),[1,0],$fot(not(implies(implies(X_381,X_18),X_381)))]]) ).
cnf(refute_0_974,plain,
( and_star(not(X_381),implies(X_381,X_18)) != not(implies(implies(X_381,X_18),X_381))
| not(and_star(not(X_381),implies(X_381,X_18))) = not(not(implies(implies(X_381,X_18),X_381))) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_381),implies(X_381,X_18))),not(and_star(not(X_381),implies(X_381,X_18)))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
not(and_star(not(X_381),implies(X_381,X_18))) = not(not(implies(implies(X_381,X_18),X_381))),
inference(resolve,[$cnf( $equal(and_star(not(X_381),implies(X_381,X_18)),not(implies(implies(X_381,X_18),X_381))) )],[refute_0_971,refute_0_974]) ).
cnf(refute_0_976,plain,
( not(and_star(not(X_381),implies(X_381,X_18))) != not(not(implies(implies(X_381,X_18),X_381)))
| not(not(implies(implies(X_381,X_18),X_381))) != implies(implies(X_381,X_18),X_381)
| not(and_star(not(X_381),implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(not(and_star(not(X_381),implies(X_381,X_18))))),bind(Y0,$fot(not(not(implies(implies(X_381,X_18),X_381))))),bind(Z0,$fot(implies(implies(X_381,X_18),X_381)))]]) ).
cnf(refute_0_977,plain,
( not(not(implies(implies(X_381,X_18),X_381))) != implies(implies(X_381,X_18),X_381)
| not(and_star(not(X_381),implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381) ),
inference(resolve,[$cnf( $equal(not(and_star(not(X_381),implies(X_381,X_18))),not(not(implies(implies(X_381,X_18),X_381)))) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
not(and_star(not(X_381),implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381),
inference(resolve,[$cnf( $equal(not(not(implies(implies(X_381,X_18),X_381))),implies(implies(X_381,X_18),X_381)) )],[refute_0_970,refute_0_977]) ).
cnf(refute_0_979,plain,
implies(not(X_381),not(implies(X_381,X_18))) = not(and_star(not(X_381),implies(X_381,X_18))),
inference(subst,[],[refute_0_300:[bind(X_17,$fot(not(X_381))),bind(X_6,$fot(implies(X_381,X_18)))]]) ).
cnf(refute_0_980,plain,
( implies(not(X_381),not(implies(X_381,X_18))) != not(and_star(not(X_381),implies(X_381,X_18)))
| not(and_star(not(X_381),implies(X_381,X_18))) != implies(implies(X_381,X_18),X_381)
| implies(not(X_381),not(implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(X_381),not(implies(X_381,X_18))))),bind(Y0,$fot(not(and_star(not(X_381),implies(X_381,X_18))))),bind(Z0,$fot(implies(implies(X_381,X_18),X_381)))]]) ).
cnf(refute_0_981,plain,
( not(and_star(not(X_381),implies(X_381,X_18))) != implies(implies(X_381,X_18),X_381)
| implies(not(X_381),not(implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381) ),
inference(resolve,[$cnf( $equal(implies(not(X_381),not(implies(X_381,X_18))),not(and_star(not(X_381),implies(X_381,X_18)))) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
implies(not(X_381),not(implies(X_381,X_18))) = implies(implies(X_381,X_18),X_381),
inference(resolve,[$cnf( $equal(not(and_star(not(X_381),implies(X_381,X_18))),implies(implies(X_381,X_18),X_381)) )],[refute_0_978,refute_0_981]) ).
cnf(refute_0_983,plain,
implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))),
introduced(tautology,[refl,[$fot(implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))))]]) ).
cnf(refute_0_984,plain,
( implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) != implies(X_18,implies(not(X_381),not(implies(X_381,X_18))))
| implies(not(X_381),not(implies(X_381,X_18))) != implies(implies(X_381,X_18),X_381)
| implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))),implies(X_18,implies(not(X_381),not(implies(X_381,X_18))))) ),[1,1],$fot(implies(implies(X_381,X_18),X_381))]]) ).
cnf(refute_0_985,plain,
( implies(not(X_381),not(implies(X_381,X_18))) != implies(implies(X_381,X_18),X_381)
| implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)) ),
inference(resolve,[$cnf( $equal(implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))),implies(X_18,implies(not(X_381),not(implies(X_381,X_18))))) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)),
inference(resolve,[$cnf( $equal(implies(not(X_381),not(implies(X_381,X_18))),implies(implies(X_381,X_18),X_381)) )],[refute_0_982,refute_0_985]) ).
cnf(refute_0_987,plain,
implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),
introduced(tautology,[refl,[$fot(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))))]]) ).
cnf(refute_0_988,plain,
( implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18))))
| not(not(X_18)) != X_18
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18))))) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_989,plain,
( not(not(X_18)) != X_18
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18))))) )],[refute_0_987,refute_0_988]) ).
cnf(refute_0_990,plain,
implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))),
inference(resolve,[$cnf( $equal(not(not(X_18)),X_18) )],[refute_0_455,refute_0_989]) ).
cnf(refute_0_991,plain,
( implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) != implies(X_18,implies(implies(X_381,X_18),X_381))
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(X_18,implies(not(X_381),not(implies(X_381,X_18))))
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))))),bind(Y0,$fot(implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))))),bind(Z0,$fot(implies(X_18,implies(implies(X_381,X_18),X_381))))]]) ).
cnf(refute_0_992,plain,
( implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))) != implies(X_18,implies(implies(X_381,X_18),X_381))
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(X_18,implies(not(X_381),not(implies(X_381,X_18))))) )],[refute_0_990,refute_0_991]) ).
cnf(refute_0_993,plain,
implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) = implies(X_18,implies(implies(X_381,X_18),X_381)),
inference(resolve,[$cnf( $equal(implies(X_18,implies(not(X_381),not(implies(X_381,X_18)))),implies(X_18,implies(implies(X_381,X_18),X_381))) )],[refute_0_986,refute_0_992]) ).
cnf(refute_0_994,plain,
( implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(X_18,implies(implies(X_381,X_18),X_381))
| implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(not(not(X_18)),X_381)
| implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(not(not(X_18)),X_381) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(not(not(X_18)),X_381)) ),[0],$fot(implies(X_18,implies(implies(X_381,X_18),X_381)))]]) ).
cnf(refute_0_995,plain,
( implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(not(not(X_18)),X_381)
| implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(not(not(X_18)),X_381) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(X_18,implies(implies(X_381,X_18),X_381))) )],[refute_0_993,refute_0_994]) ).
cnf(refute_0_996,plain,
implies(not(not(X_18)),X_381) = implies(not(not(X_18)),X_381),
introduced(tautology,[refl,[$fot(implies(not(not(X_18)),X_381))]]) ).
cnf(refute_0_997,plain,
( implies(not(not(X_18)),X_381) != implies(not(not(X_18)),X_381)
| not(not(X_18)) != X_18
| implies(not(not(X_18)),X_381) = implies(X_18,X_381) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_18)),X_381),implies(not(not(X_18)),X_381)) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_998,plain,
( not(not(X_18)) != X_18
| implies(not(not(X_18)),X_381) = implies(X_18,X_381) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),X_381),implies(not(not(X_18)),X_381)) )],[refute_0_996,refute_0_997]) ).
cnf(refute_0_999,plain,
implies(not(not(X_18)),X_381) = implies(X_18,X_381),
inference(resolve,[$cnf( $equal(not(not(X_18)),X_18) )],[refute_0_455,refute_0_998]) ).
cnf(refute_0_1000,plain,
( implies(X_18,implies(implies(X_381,X_18),X_381)) != implies(not(not(X_18)),X_381)
| implies(not(not(X_18)),X_381) != implies(X_18,X_381)
| implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(X_18,X_381) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_18,implies(implies(X_381,X_18),X_381)),implies(X_18,X_381)) ),[0],$fot(implies(not(not(X_18)),X_381))]]) ).
cnf(refute_0_1001,plain,
( implies(X_18,implies(implies(X_381,X_18),X_381)) != implies(not(not(X_18)),X_381)
| implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(X_18,X_381) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),X_381),implies(X_18,X_381)) )],[refute_0_999,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))) != implies(not(not(X_18)),X_381)
| implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(X_18,X_381) ),
inference(resolve,[$cnf( $equal(implies(X_18,implies(implies(X_381,X_18),X_381)),implies(not(not(X_18)),X_381)) )],[refute_0_995,refute_0_1001]) ).
cnf(refute_0_1003,plain,
implies(X_18,implies(implies(X_381,X_18),X_381)) = implies(X_18,X_381),
inference(resolve,[$cnf( $equal(implies(not(not(X_18)),implies(not(X_381),not(implies(X_381,X_18)))),implies(not(not(X_18)),X_381)) )],[refute_0_969,refute_0_1002]) ).
cnf(refute_0_1004,plain,
implies(b,implies(implies(a,b),a)) = implies(b,a),
inference(subst,[],[refute_0_1003:[bind(X_18,$fot(b)),bind(X_381,$fot(a))]]) ).
cnf(refute_0_1005,plain,
implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(b,implies(implies(a,b),a)),a),
introduced(tautology,[refl,[$fot(implies(implies(b,implies(implies(a,b),a)),a))]]) ).
cnf(refute_0_1006,plain,
( implies(b,implies(implies(a,b),a)) != implies(b,a)
| implies(implies(b,implies(implies(a,b),a)),a) != implies(implies(b,implies(implies(a,b),a)),a)
| implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(b,a),a) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(b,implies(implies(a,b),a)),a),implies(implies(b,implies(implies(a,b),a)),a)) ),[1,0],$fot(implies(b,a))]]) ).
cnf(refute_0_1007,plain,
( implies(b,implies(implies(a,b),a)) != implies(b,a)
| implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(b,a),a) ),
inference(resolve,[$cnf( $equal(implies(implies(b,implies(implies(a,b),a)),a),implies(implies(b,implies(implies(a,b),a)),a)) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(b,a),a),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(a,b),a)),implies(b,a)) )],[refute_0_1004,refute_0_1007]) ).
cnf(refute_0_1009,plain,
( implies(implies(b,a),a) != implies(implies(a,b),b)
| implies(implies(b,implies(implies(a,b),a)),a) != implies(implies(b,a),a)
| implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(a,b),b) ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(implies(b,implies(implies(a,b),a)),a))),bind(Y0,$fot(implies(implies(b,a),a))),bind(Z0,$fot(implies(implies(a,b),b)))]]) ).
cnf(refute_0_1010,plain,
( implies(implies(b,a),a) != implies(implies(a,b),b)
| implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(a,b),b) ),
inference(resolve,[$cnf( $equal(implies(implies(b,implies(implies(a,b),a)),a),implies(implies(b,a),a)) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
implies(implies(b,implies(implies(a,b),a)),a) = implies(implies(a,b),b),
inference(resolve,[$cnf( $equal(implies(implies(b,a),a),implies(implies(a,b),b)) )],[refute_0_585,refute_0_1010]) ).
cnf(refute_0_1012,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
introduced(tautology,[refl,[$fot(implies(b,implies(implies(b,implies(implies(a,b),a)),a)))]]) ).
cnf(refute_0_1013,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(b,implies(implies(a,b),a)),a) != implies(implies(a,b),b)
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(b,implies(implies(a,b),b)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) ),[1,1],$fot(implies(implies(a,b),b))]]) ).
cnf(refute_0_1014,plain,
( implies(implies(b,implies(implies(a,b),a)),a) != implies(implies(a,b),b)
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(b,implies(implies(a,b),b)) ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(b,implies(implies(a,b),b)),
inference(resolve,[$cnf( $equal(implies(implies(b,implies(implies(a,b),a)),a),implies(implies(a,b),b)) )],[refute_0_1011,refute_0_1014]) ).
cnf(refute_0_1016,plain,
( implies(b,implies(implies(a,b),b)) != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != implies(b,implies(implies(a,b),b))
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
inference(subst,[],[refute_0_31:[bind(X0,$fot(implies(b,implies(implies(b,implies(implies(a,b),a)),a)))),bind(Y0,$fot(implies(b,implies(implies(a,b),b)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_1017,plain,
( implies(b,implies(implies(a,b),b)) != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(b,implies(implies(a,b),b))) )],[refute_0_1015,refute_0_1016]) ).
cnf(refute_0_1018,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth,
inference(resolve,[$cnf( $equal(implies(b,implies(implies(a,b),b)),truth) )],[refute_0_230,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth
| truth != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_1020,plain,
( truth != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),truth) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),truth) )],[refute_0_1020,refute_0_153]) ).
cnf(refute_0_1022,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_1023,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_1022,refute_0_1021]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL109-6 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.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 : Mon Jul 4 04:15:51 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 194.10/194.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 194.10/194.28
% 194.10/194.28 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 194.21/194.40
%------------------------------------------------------------------------------