%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL113-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:41:54 PM UTC 2026
% Result : Unsatisfiable 0.22s 0.48s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 98
% Number of leaves : 108
% Syntax : Number of clauses : 403 ( 204 unt; 0 nHn; 257 RR)
% Number of literals : 700 ( 699 equ; 299 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 379 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_mv_33,negated_conjecture,
implies(implies(not(x),y),implies(not(y),x)) != truth ).
cnf(refute_0_0,plain,
implies(implies(not(X),not(not(X_38))),implies(not(X_38),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(not(X_38)))]]) ).
cnf(refute_0_1,plain,
implies(implies(X,not(truth)),not(truth)) = implies(implies(not(truth),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_2,plain,
implies(implies(not(X),not(not(truth))),implies(not(truth),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_3,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_4,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_5,plain,
implies(implies(X,implies(X_9,X)),implies(X_9,X)) = implies(implies(implies(X_9,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_9,X)))]]) ).
cnf(refute_0_6,plain,
implies(implies(X_9,X),X) = implies(implies(X,X_9),X_9),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_9)),bind(Y,$fot(X))]]) ).
cnf(refute_0_7,plain,
( implies(implies(X,implies(X_9,X)),implies(X_9,X)) != implies(implies(implies(X_9,X),X),X)
| implies(implies(X_9,X),X) != implies(implies(X,X_9),X_9)
| implies(implies(X,implies(X_9,X)),implies(X_9,X)) = implies(implies(implies(X,X_9),X_9),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_9,X)),implies(X_9,X)),implies(implies(implies(X_9,X),X),X)) ),[1,0],$fot(implies(implies(X,X_9),X_9))]]) ).
cnf(refute_0_8,plain,
( implies(implies(X,implies(X_9,X)),implies(X_9,X)) != implies(implies(implies(X_9,X),X),X)
| implies(implies(X,implies(X_9,X)),implies(X_9,X)) = implies(implies(implies(X,X_9),X_9),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,X),X),implies(implies(X,X_9),X_9)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(implies(X,implies(X_9,X)),implies(X_9,X)) = implies(implies(implies(X,X_9),X_9),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_9,X)),implies(X_9,X)),implies(implies(implies(X_9,X),X),X)) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(implies(X,implies(X_9,X)),implies(X_9,X)) != implies(implies(implies(X,X_9),X_9),X)
| implies(implies(X,implies(X_9,X)),implies(X_9,X)) != implies(implies(implies(X_9,X),X),X)
| implies(implies(implies(X_9,X),X),X) = implies(implies(implies(X,X_9),X_9),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_9,X)),implies(X_9,X)),implies(implies(implies(X,X_9),X_9),X)) ),[0],$fot(implies(implies(implies(X_9,X),X),X))]]) ).
cnf(refute_0_11,plain,
( implies(implies(X,implies(X_9,X)),implies(X_9,X)) != implies(implies(implies(X,X_9),X_9),X)
| implies(implies(implies(X_9,X),X),X) = implies(implies(implies(X,X_9),X_9),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_9,X)),implies(X_9,X)),implies(implies(implies(X_9,X),X),X)) )],[refute_0_5,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(implies(implies(X_9,X),X),X) = implies(implies(implies(X,X_9),X_9),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_9,X)),implies(X_9,X)),implies(implies(implies(X,X_9),X_9),X)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(implies(implies(X_33,Y),Y),Y) = implies(implies(Y,implies(X_33,Y)),implies(X_33,Y)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_33,Y)))]]) ).
cnf(refute_0_14,plain,
implies(implies(X_16,truth),implies(implies(truth,X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(truth)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_15,plain,
implies(truth,X_18) = X_18,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_16,plain,
( implies(implies(X_16,truth),implies(implies(truth,X_18),implies(X_16,X_18))) != truth
| implies(truth,X_18) != X_18
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,truth),implies(implies(truth,X_18),implies(X_16,X_18))),truth) ),[0,1,0],$fot(X_18)]]) ).
cnf(refute_0_17,plain,
( implies(implies(X_16,truth),implies(implies(truth,X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),implies(implies(truth,X_18),implies(X_16,X_18))),truth) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(truth,implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_20,plain,
implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),implies(implies(implies(not(Y),truth),truth),implies(Y,Y)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(Y),truth),truth))),bind(Y,$fot(X_17)),bind(Z,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_21,plain,
implies(implies(not(Y),not(Y)),implies(Y,Y)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(Y))]]) ).
cnf(refute_0_22,plain,
implies(implies(truth,X_10),X_10) = implies(implies(X_10,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_23,plain,
implies(truth,X_10) = X_10,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_10))]]) ).
cnf(refute_0_24,plain,
( implies(implies(truth,X_10),X_10) != implies(implies(X_10,truth),truth)
| implies(truth,X_10) != X_10
| implies(X_10,X_10) = implies(implies(X_10,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_10),X_10),implies(implies(X_10,truth),truth)) ),[0,0],$fot(X_10)]]) ).
cnf(refute_0_25,plain,
( implies(implies(truth,X_10),X_10) != implies(implies(X_10,truth),truth)
| implies(X_10,X_10) = implies(implies(X_10,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_10),X_10) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(X_10,X_10) = implies(implies(X_10,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_10),X_10),implies(implies(X_10,truth),truth)) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(not(Y),not(Y)) = implies(implies(not(Y),truth),truth),
inference(subst,[],[refute_0_26:[bind(X_10,$fot(not(Y)))]]) ).
cnf(refute_0_28,plain,
( implies(implies(not(Y),not(Y)),implies(Y,Y)) != truth
| implies(not(Y),not(Y)) != implies(implies(not(Y),truth),truth)
| implies(implies(implies(not(Y),truth),truth),implies(Y,Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),not(Y)),implies(Y,Y)),truth) ),[0,0],$fot(implies(implies(not(Y),truth),truth))]]) ).
cnf(refute_0_29,plain,
( implies(implies(not(Y),not(Y)),implies(Y,Y)) != truth
| implies(implies(implies(not(Y),truth),truth),implies(Y,Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(Y),not(Y)),implies(implies(not(Y),truth),truth)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(implies(implies(not(Y),truth),truth),implies(Y,Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(Y)),implies(Y,Y)),truth) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
( implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),implies(implies(implies(not(Y),truth),truth),implies(Y,Y)))) != truth
| implies(implies(implies(not(Y),truth),truth),implies(Y,Y)) != truth
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),implies(implies(implies(not(Y),truth),truth),implies(Y,Y)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_32,plain,
( implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),implies(implies(implies(not(Y),truth),truth),implies(Y,Y)))) != truth
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),truth),truth),implies(Y,Y)),truth) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),implies(implies(implies(not(Y),truth),truth),implies(Y,Y)))),truth) )],[refute_0_20,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(implies(not(X),not(X)),implies(X,X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(X))]]) ).
cnf(refute_0_35,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(subst,[],[refute_0_26:[bind(X_10,$fot(X))]]) ).
cnf(refute_0_36,plain,
( implies(X,X) != implies(implies(X,truth),truth)
| implies(implies(not(X),not(X)),implies(X,X)) != truth
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(X)),implies(X,X)),truth) ),[0,1],$fot(implies(implies(X,truth),truth))]]) ).
cnf(refute_0_37,plain,
( implies(implies(not(X),not(X)),implies(X,X)) != truth
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(X)),implies(X,X)),truth) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(truth,implies(implies(X,truth),truth)) = implies(implies(X,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X,truth),truth)))]]) ).
cnf(refute_0_40,plain,
implies(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_41,plain,
implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),implies(implies(not(X_1),not(X_2)),implies(X_2,X_1))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(implies(X_2,X_1))),bind(Y,$fot(implies(not(X_1),not(X_2))))]]) ).
cnf(refute_0_42,plain,
implies(implies(not(X_1),not(X_2)),implies(X_2,X_1)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_1)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_43,plain,
( implies(implies(not(X_1),not(X_2)),implies(X_2,X_1)) != truth
| implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),implies(implies(not(X_1),not(X_2)),implies(X_2,X_1))) != truth
| implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),implies(implies(not(X_1),not(X_2)),implies(X_2,X_1))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_44,plain,
( implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),implies(implies(not(X_1),not(X_2)),implies(X_2,X_1))) != truth
| implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_1),not(X_2)),implies(X_2,X_1)),truth) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_2,X_1)),not(implies(not(X_1),not(X_2)))),implies(implies(not(X_1),not(X_2)),implies(X_2,X_1))),truth) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(not(truth)),not(not(truth))))),truth) = truth,
inference(subst,[],[refute_0_45:[bind(X_1,$fot(not(truth))),bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_47,plain,
implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_48,plain,
implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
inference(subst,[],[refute_0_30:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_49,plain,
( implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) != truth
| implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_50,plain,
( implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_53,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( implies(X_10,X_10) != implies(implies(X_10,truth),truth)
| implies(implies(X_10,truth),truth) = implies(X_10,X_10) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(implies(X_10,X_10))),bind(Y0,$fot(implies(implies(X_10,truth),truth)))]]) ).
cnf(refute_0_56,plain,
implies(implies(X_10,truth),truth) = implies(X_10,X_10),
inference(resolve,[$cnf( $equal(implies(X_10,X_10),implies(implies(X_10,truth),truth)) )],[refute_0_26,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_56:[bind(X_10,$fot(not(truth)))]]) ).
cnf(refute_0_58,plain,
implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).
cnf(refute_0_59,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).
cnf(refute_0_60,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(truth,implies(not(truth),truth)),truth)
| implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).
cnf(refute_0_61,plain,
( implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_64,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_54,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(truth,implies(not(truth),truth)),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_66,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_57,refute_0_66]) ).
cnf(refute_0_68,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).
cnf(refute_0_69,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_51,refute_0_69]) ).
cnf(refute_0_71,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(not(truth)),not(not(truth))))),truth) != truth
| implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(not(truth)),not(not(truth))))),truth),truth) ),[0,0,0,0],$fot(truth)]]) ).
cnf(refute_0_72,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(not(truth)),not(not(truth))))),truth) != truth
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(not(truth)),not(not(truth))))),truth),truth) )],[refute_0_46,refute_0_72]) ).
cnf(refute_0_74,plain,
( implies(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != truth
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_75,plain,
( implies(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),truth) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),truth) )],[refute_0_40,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(truth,Z) = Z,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_78,plain,
implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),
introduced(tautology,[refl,[$fot(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)))]]) ).
cnf(refute_0_79,plain,
( implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) ),[1,0],$fot(Z)]]) ).
cnf(refute_0_80,plain,
( implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))))]]) ).
cnf(refute_0_83,plain,
( implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))))),bind(Y0,$fot(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)))),bind(Z0,$fot(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))))]]) ).
cnf(refute_0_84,plain,
( implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != truth
| implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),truth) ),[0],$fot(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)))]]) ).
cnf(refute_0_87,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) != truth
| implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),truth) )],[refute_0_76,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(implies(not(X),not(implies(X_9,X))),implies(implies(X_9,X),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(implies(X_9,X)))]]) ).
cnf(refute_0_90,plain,
( implies(implies(X_9,X),X) != implies(implies(X,X_9),X_9)
| implies(implies(not(X),not(implies(X_9,X))),implies(implies(X_9,X),X)) != truth
| implies(implies(not(X),not(implies(X_9,X))),implies(implies(X,X_9),X_9)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(implies(X_9,X))),implies(implies(X_9,X),X)),truth) ),[0,1],$fot(implies(implies(X,X_9),X_9))]]) ).
cnf(refute_0_91,plain,
( implies(implies(not(X),not(implies(X_9,X))),implies(implies(X_9,X),X)) != truth
| implies(implies(not(X),not(implies(X_9,X))),implies(implies(X,X_9),X_9)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_9,X),X),implies(implies(X,X_9),X_9)) )],[refute_0_6,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(implies(not(X),not(implies(X_9,X))),implies(implies(X,X_9),X_9)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(implies(X_9,X))),implies(implies(X_9,X),X)),truth) )],[refute_0_89,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(not(truth),not(implies(not(not(truth)),truth))),implies(implies(truth,not(not(truth))),not(not(truth)))) = truth,
inference(subst,[],[refute_0_92:[bind(X,$fot(truth)),bind(X_9,$fot(not(not(truth))))]]) ).
cnf(refute_0_94,plain,
implies(implies(X_16,not(not(X_16))),implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(not(not(X_16)))),bind(Z,$fot(not(X_16)))]]) ).
cnf(refute_0_95,plain,
implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(X_16))),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_96,plain,
( implies(implies(X_16,not(not(X_16))),implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16)))) != truth
| implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16))) != truth
| implies(implies(X_16,not(not(X_16))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,not(not(X_16))),implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_97,plain,
( implies(implies(X_16,not(not(X_16))),implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16)))) != truth
| implies(implies(X_16,not(not(X_16))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16))),truth) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(implies(X_16,not(not(X_16))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,not(not(X_16))),implies(implies(not(not(X_16)),not(X_16)),implies(X_16,not(X_16)))),truth) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(implies(truth,not(not(truth))),truth) = truth,
inference(subst,[],[refute_0_98:[bind(X_16,$fot(truth))]]) ).
cnf(refute_0_100,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_101,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(not(truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) ),[0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_102,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(not(not(truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(not(not(truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) )],[refute_0_99,refute_0_102]) ).
cnf(refute_0_104,plain,
( implies(implies(not(truth),not(implies(not(not(truth)),truth))),implies(implies(truth,not(not(truth))),not(not(truth)))) != truth
| implies(not(not(truth)),truth) != truth
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),truth))),implies(implies(truth,not(not(truth))),not(not(truth)))),truth) ),[0,0,1,0],$fot(truth)]]) ).
cnf(refute_0_105,plain,
( implies(implies(not(truth),not(implies(not(not(truth)),truth))),implies(implies(truth,not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),truth),truth) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),truth))),implies(implies(truth,not(not(truth))),not(not(truth)))),truth) )],[refute_0_93,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(truth,implies(not(not(truth)),not(not(truth)))) = implies(not(not(truth)),not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_108,plain,
implies(implies(not(not(truth)),truth),truth) = implies(not(not(truth)),not(not(truth))),
inference(subst,[],[refute_0_56:[bind(X_10,$fot(not(not(truth))))]]) ).
cnf(refute_0_109,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) = implies(implies(X,Y),Y) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(implies(implies(X,Y),Y))),bind(Y0,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_110,plain,
implies(implies(Y,X),X) = implies(implies(X,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),truth),truth),
inference(subst,[],[refute_0_110:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_112,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(truth,not(not(truth))),not(not(truth))))),bind(Y0,$fot(implies(implies(not(not(truth)),truth),truth))),bind(Z0,$fot(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_113,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),truth),truth),implies(not(not(truth)),not(not(truth)))) )],[refute_0_108,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))),
introduced(tautology,[refl,[$fot(implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_116,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(not(not(truth)),not(not(truth)))
| implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(truth,implies(implies(truth,not(not(truth))),not(not(truth))))
| implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))),implies(truth,implies(implies(truth,not(not(truth))),not(not(truth))))) ),[1,1],$fot(implies(not(not(truth)),not(not(truth))))]]) ).
cnf(refute_0_117,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(not(not(truth)),not(not(truth)))
| implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))),implies(truth,implies(implies(truth,not(not(truth))),not(not(truth))))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_120,plain,
( implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth))))
| implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_121,plain,
( implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth))))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_70,refute_0_121]) ).
cnf(refute_0_123,plain,
( implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(truth,implies(implies(truth,not(not(truth))),not(not(truth))))
| implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(truth,implies(not(not(truth)),not(not(truth))))
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))))),bind(Y0,$fot(implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))))),bind(Z0,$fot(implies(truth,implies(not(not(truth)),not(not(truth))))))]]) ).
cnf(refute_0_124,plain,
( implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(truth,implies(not(not(truth)),not(not(truth))))
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),implies(truth,implies(implies(truth,not(not(truth))),not(not(truth))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(truth,implies(not(not(truth)),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,not(not(truth))),not(not(truth)))),implies(truth,implies(not(not(truth)),not(not(truth))))) )],[refute_0_118,refute_0_124]) ).
cnf(refute_0_126,plain,
( implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(truth,implies(not(not(truth)),not(not(truth))))
| implies(truth,implies(not(not(truth)),not(not(truth)))) != implies(not(not(truth)),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(not(not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))))),bind(Y0,$fot(implies(truth,implies(not(not(truth)),not(not(truth)))))),bind(Z0,$fot(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_127,plain,
( implies(truth,implies(not(not(truth)),not(not(truth)))) != implies(not(not(truth)),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(not(not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),implies(truth,implies(not(not(truth)),not(not(truth))))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) = implies(not(not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(not(truth)),not(not(truth)))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_107,refute_0_127]) ).
cnf(refute_0_129,plain,
( implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != implies(not(not(truth)),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != truth
| implies(not(not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),truth) ),[0],$fot(implies(not(not(truth)),not(not(truth))))]]) ).
cnf(refute_0_130,plain,
( implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))) != truth
| implies(not(not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(truth,not(not(truth))),not(not(truth)))),truth) )],[refute_0_106,refute_0_130]) ).
cnf(refute_0_132,plain,
not(implies(not(not(truth)),not(not(truth)))) = not(implies(not(not(truth)),not(not(truth)))),
introduced(tautology,[refl,[$fot(not(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_133,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| not(implies(not(not(truth)),not(not(truth)))) != not(implies(not(not(truth)),not(not(truth))))
| not(implies(not(not(truth)),not(not(truth)))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(truth)),not(not(truth)))),not(implies(not(not(truth)),not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_134,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| not(implies(not(not(truth)),not(not(truth)))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(truth)))),not(implies(not(not(truth)),not(not(truth))))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
not(implies(not(not(truth)),not(not(truth)))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))))]]) ).
cnf(refute_0_137,plain,
( implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) != implies(not(truth),not(implies(not(not(truth)),not(not(truth)))))
| not(implies(not(not(truth)),not(not(truth)))) != not(truth)
| implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),implies(not(truth),not(implies(not(not(truth)),not(not(truth)))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_138,plain,
( not(implies(not(not(truth)),not(not(truth)))) != not(truth)
| implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),implies(not(truth),not(implies(not(not(truth)),not(not(truth)))))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(truth)))),not(truth)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_141,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),implies(not(truth),not(truth))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_70,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))]]) ).
cnf(refute_0_144,plain,
( implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) != implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)
| implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) != truth
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = implies(truth,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_145,plain,
( implies(not(truth),not(implies(not(not(truth)),not(not(truth))))) != truth
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = implies(truth,Z) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z),implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = implies(truth,Z),
inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),truth) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) != implies(truth,Z)
| implies(truth,Z) != Z
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = Z ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))),bind(Y0,$fot(implies(truth,Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_148,plain,
( implies(truth,Z) != Z
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = Z ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z),implies(truth,Z)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) = Z,
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_77,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),
introduced(tautology,[refl,[$fot(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)))]]) ).
cnf(refute_0_151,plain,
( implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))
| implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) != Z
| implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_152,plain,
( implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z) != Z
| implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,Z) ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) = implies(Z,Z),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z),Z) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
( implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != implies(Z,Z)
| implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != truth
| implies(Z,Z) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),truth) ),[0],$fot(implies(Z,Z))]]) ).
cnf(refute_0_155,plain,
( implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)) != truth
| implies(Z,Z) = truth ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),implies(Z,Z)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(Z,Z) = truth,
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(truth),not(implies(not(not(truth)),not(not(truth))))),Z)),truth) )],[refute_0_88,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(not(X),not(X)) = truth,
inference(subst,[],[refute_0_156:[bind(Z,$fot(not(X)))]]) ).
cnf(refute_0_158,plain,
implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)))]]) ).
cnf(refute_0_159,plain,
( implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) != implies(implies(not(X),not(X)),implies(implies(X,truth),truth))
| implies(not(X),not(X)) != truth
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(truth,implies(implies(X,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),implies(implies(not(X),not(X)),implies(implies(X,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_160,plain,
( implies(not(X),not(X)) != truth
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(truth,implies(implies(X,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),implies(implies(not(X),not(X)),implies(implies(X,truth),truth))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(truth,implies(implies(X,truth),truth)),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),truth) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
( implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) != implies(truth,implies(implies(X,truth),truth))
| implies(truth,implies(implies(X,truth),truth)) != implies(implies(X,truth),truth)
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(implies(X,truth),truth) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)))),bind(Y0,$fot(implies(truth,implies(implies(X,truth),truth)))),bind(Z0,$fot(implies(implies(X,truth),truth)))]]) ).
cnf(refute_0_163,plain,
( implies(truth,implies(implies(X,truth),truth)) != implies(implies(X,truth),truth)
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(implies(X,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),implies(truth,implies(implies(X,truth),truth))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) = implies(implies(X,truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X,truth),truth)),implies(implies(X,truth),truth)) )],[refute_0_39,refute_0_163]) ).
cnf(refute_0_165,plain,
( implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) != implies(implies(X,truth),truth)
| implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) != truth
| implies(implies(X,truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),truth) ),[0],$fot(implies(implies(X,truth),truth))]]) ).
cnf(refute_0_166,plain,
( implies(implies(not(X),not(X)),implies(implies(X,truth),truth)) != truth
| implies(implies(X,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),implies(implies(X,truth),truth)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(implies(X,truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(X)),implies(implies(X,truth),truth)),truth) )],[refute_0_38,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(X_17,truth),truth) = truth,
inference(subst,[],[refute_0_167:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_169,plain,
implies(Y,Y) = truth,
inference(subst,[],[refute_0_156:[bind(Z,$fot(Y))]]) ).
cnf(refute_0_170,plain,
implies(X_17,implies(Y,Y)) = implies(X_17,implies(Y,Y)),
introduced(tautology,[refl,[$fot(implies(X_17,implies(Y,Y)))]]) ).
cnf(refute_0_171,plain,
( implies(Y,Y) != truth
| implies(X_17,implies(Y,Y)) != implies(X_17,implies(Y,Y))
| implies(X_17,implies(Y,Y)) = implies(X_17,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(Y,Y)),implies(X_17,implies(Y,Y))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_172,plain,
( implies(Y,Y) != truth
| implies(X_17,implies(Y,Y)) = implies(X_17,truth) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(Y,Y)),implies(X_17,implies(Y,Y))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
implies(X_17,implies(Y,Y)) = implies(X_17,truth),
inference(resolve,[$cnf( $equal(implies(Y,Y),truth) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(implies(X_17,implies(Y,Y)),truth) = implies(implies(X_17,implies(Y,Y)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_17,implies(Y,Y)),truth))]]) ).
cnf(refute_0_175,plain,
( implies(X_17,implies(Y,Y)) != implies(X_17,truth)
| implies(implies(X_17,implies(Y,Y)),truth) != implies(implies(X_17,implies(Y,Y)),truth)
| implies(implies(X_17,implies(Y,Y)),truth) = implies(implies(X_17,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,implies(Y,Y)),truth),implies(implies(X_17,implies(Y,Y)),truth)) ),[1,0],$fot(implies(X_17,truth))]]) ).
cnf(refute_0_176,plain,
( implies(X_17,implies(Y,Y)) != implies(X_17,truth)
| implies(implies(X_17,implies(Y,Y)),truth) = implies(implies(X_17,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(Y,Y)),truth),implies(implies(X_17,implies(Y,Y)),truth)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
implies(implies(X_17,implies(Y,Y)),truth) = implies(implies(X_17,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_17,implies(Y,Y)),implies(X_17,truth)) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
( implies(implies(X_17,implies(Y,Y)),truth) != implies(implies(X_17,truth),truth)
| implies(implies(X_17,truth),truth) != truth
| implies(implies(X_17,implies(Y,Y)),truth) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X_17,implies(Y,Y)),truth))),bind(Y0,$fot(implies(implies(X_17,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_179,plain,
( implies(implies(X_17,truth),truth) != truth
| implies(implies(X_17,implies(Y,Y)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(Y,Y)),truth),implies(implies(X_17,truth),truth)) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(implies(X_17,implies(Y,Y)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_17,truth),truth),truth) )],[refute_0_168,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)),
introduced(tautology,[refl,[$fot(implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)))]]) ).
cnf(refute_0_182,plain,
( implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) != implies(X_17,implies(implies(X_17,implies(Y,Y)),truth))
| implies(implies(X_17,implies(Y,Y)),truth) != truth
| implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)),implies(X_17,implies(implies(X_17,implies(Y,Y)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_183,plain,
( implies(implies(X_17,implies(Y,Y)),truth) != truth
| implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)),implies(X_17,implies(implies(X_17,implies(Y,Y)),truth))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(Y,Y)),truth),truth) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_186,plain,
implies(implies(not(Y),truth),truth) = truth,
inference(subst,[],[refute_0_167:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_187,plain,
implies(implies(implies(not(Y),truth),truth),X_17) = implies(implies(implies(not(Y),truth),truth),X_17),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(Y),truth),truth),X_17))]]) ).
cnf(refute_0_188,plain,
( implies(implies(implies(not(Y),truth),truth),X_17) != implies(implies(implies(not(Y),truth),truth),X_17)
| implies(implies(not(Y),truth),truth) != truth
| implies(implies(implies(not(Y),truth),truth),X_17) = implies(truth,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(implies(not(Y),truth),truth),X_17)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_189,plain,
( implies(implies(not(Y),truth),truth) != truth
| implies(implies(implies(not(Y),truth),truth),X_17) = implies(truth,X_17) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(implies(not(Y),truth),truth),X_17)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(implies(implies(not(Y),truth),truth),X_17) = implies(truth,X_17),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),truth),truth),truth) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
( implies(implies(implies(not(Y),truth),truth),X_17) != implies(truth,X_17)
| implies(truth,X_17) != X_17
| implies(implies(implies(not(Y),truth),truth),X_17) = X_17 ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(not(Y),truth),truth),X_17))),bind(Y0,$fot(implies(truth,X_17))),bind(Z0,$fot(X_17))]]) ).
cnf(refute_0_192,plain,
( implies(truth,X_17) != X_17
| implies(implies(implies(not(Y),truth),truth),X_17) = X_17 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),truth),truth),X_17),implies(truth,X_17)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(implies(not(Y),truth),truth),X_17) = X_17,
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_185,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)))]]) ).
cnf(refute_0_195,plain,
( implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) != implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth))
| implies(implies(implies(not(Y),truth),truth),X_17) != X_17
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth))) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_196,plain,
( implies(implies(implies(not(Y),truth),truth),X_17) != X_17
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),truth),truth),X_17),X_17) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) != implies(X_17,truth)
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) != implies(X_17,implies(implies(X_17,implies(Y,Y)),truth))
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)))),bind(Y0,$fot(implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)))),bind(Z0,$fot(implies(X_17,truth)))]]) ).
cnf(refute_0_199,plain,
( implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)) != implies(X_17,truth)
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),implies(X_17,implies(implies(X_17,implies(Y,Y)),truth))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) = implies(X_17,truth),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(Y,Y)),truth)),implies(X_17,truth)) )],[refute_0_184,refute_0_199]) ).
cnf(refute_0_201,plain,
( implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) != implies(X_17,truth)
| implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) != truth
| implies(X_17,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),truth) ),[0],$fot(implies(X_17,truth))]]) ).
cnf(refute_0_202,plain,
( implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)) != truth
| implies(X_17,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),implies(X_17,truth)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(X_17,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(Y),truth),truth),X_17),implies(implies(X_17,implies(Y,Y)),truth)),truth) )],[refute_0_33,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(X_16,truth) = truth,
inference(subst,[],[refute_0_203:[bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_205,plain,
implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_206,plain,
( implies(X_16,truth) != truth
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) != implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18)))
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_207,plain,
( implies(X_16,truth) != truth
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18)))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(X_16,truth),truth) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) != implies(truth,implies(X_18,implies(X_16,X_18)))
| implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))))),bind(Y0,$fot(implies(truth,implies(X_18,implies(X_16,X_18))))),bind(Z0,$fot(implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_210,plain,
( implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),implies(truth,implies(X_18,implies(X_16,X_18)))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_18,implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_19,refute_0_210]) ).
cnf(refute_0_212,plain,
( implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),truth) ),[0],$fot(implies(X_18,implies(X_16,X_18)))]]) ).
cnf(refute_0_213,plain,
( implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(X_18,implies(X_16,X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),implies(X_18,implies(X_16,X_18))),truth) )],[refute_0_18,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(Y,implies(X_33,Y)) = truth,
inference(subst,[],[refute_0_214:[bind(X_16,$fot(X_33)),bind(X_18,$fot(Y))]]) ).
cnf(refute_0_216,plain,
( implies(Y,implies(X_33,Y)) != truth
| implies(implies(implies(X_33,Y),Y),Y) != implies(implies(Y,implies(X_33,Y)),implies(X_33,Y))
| implies(implies(implies(X_33,Y),Y),Y) = implies(truth,implies(X_33,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_33,Y),Y),Y),implies(implies(Y,implies(X_33,Y)),implies(X_33,Y))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_217,plain,
( implies(implies(implies(X_33,Y),Y),Y) != implies(implies(Y,implies(X_33,Y)),implies(X_33,Y))
| implies(implies(implies(X_33,Y),Y),Y) = implies(truth,implies(X_33,Y)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(X_33,Y)),truth) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
implies(implies(implies(X_33,Y),Y),Y) = implies(truth,implies(X_33,Y)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,Y),Y),Y),implies(implies(Y,implies(X_33,Y)),implies(X_33,Y))) )],[refute_0_13,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(truth,implies(X_33,Y)) = implies(X_33,Y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_33,Y)))]]) ).
cnf(refute_0_220,plain,
( implies(implies(implies(X_33,Y),Y),Y) != implies(truth,implies(X_33,Y))
| implies(truth,implies(X_33,Y)) != implies(X_33,Y)
| implies(implies(implies(X_33,Y),Y),Y) = implies(X_33,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_33,Y),Y),Y),implies(X_33,Y)) ),[0],$fot(implies(truth,implies(X_33,Y)))]]) ).
cnf(refute_0_221,plain,
( implies(implies(implies(X_33,Y),Y),Y) != implies(truth,implies(X_33,Y))
| implies(implies(implies(X_33,Y),Y),Y) = implies(X_33,Y) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_33,Y)),implies(X_33,Y)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(implies(implies(X_33,Y),Y),Y) = implies(X_33,Y),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,Y),Y),Y),implies(truth,implies(X_33,Y))) )],[refute_0_218,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(implies(implies(X_9,X),X),X) = implies(X_9,X),
inference(subst,[],[refute_0_222:[bind(Y,$fot(X)),bind(X_33,$fot(X_9))]]) ).
cnf(refute_0_224,plain,
( implies(implies(implies(X_9,X),X),X) != implies(X_9,X)
| implies(implies(implies(X_9,X),X),X) != implies(implies(implies(X,X_9),X_9),X)
| implies(X_9,X) = implies(implies(implies(X,X_9),X_9),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_9,X),X),X),implies(implies(implies(X,X_9),X_9),X)) ),[0],$fot(implies(X_9,X))]]) ).
cnf(refute_0_225,plain,
( implies(implies(implies(X_9,X),X),X) != implies(implies(implies(X,X_9),X_9),X)
| implies(X_9,X) = implies(implies(implies(X,X_9),X_9),X) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_9,X),X),X),implies(X_9,X)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(X_9,X) = implies(implies(implies(X,X_9),X_9),X),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_9,X),X),X),implies(implies(implies(X,X_9),X_9),X)) )],[refute_0_12,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth)))),
inference(subst,[],[refute_0_226:[bind(X,$fot(not(not(not(truth))))),bind(X_9,$fot(not(not(truth))))]]) ).
cnf(refute_0_228,plain,
implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_229,plain,
implies(not(truth),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))),
inference(subst,[],[refute_0_226:[bind(X,$fot(not(not(truth)))),bind(X_9,$fot(not(truth)))]]) ).
cnf(refute_0_230,plain,
implies(implies(not(X_1),not(truth)),implies(truth,X_1)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_231,plain,
implies(truth,X_1) = X_1,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_232,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(truth,X_1) != X_1
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) ),[0,1],$fot(X_1)]]) ).
cnf(refute_0_233,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_1),X_1) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
implies(implies(not(X_1),not(truth)),X_1) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_234:[bind(X_1,$fot(not(truth)))]]) ).
cnf(refute_0_236,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_237,plain,
( implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) )],[refute_0_229,refute_0_237]) ).
cnf(refute_0_239,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(truth),not(not(truth))),not(not(truth))) ),[0],$fot(implies(truth,not(not(truth))))]]) ).
cnf(refute_0_240,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_100,refute_0_239]) ).
cnf(refute_0_241,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_238,refute_0_240]) ).
cnf(refute_0_242,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_243,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_228,refute_0_243]) ).
cnf(refute_0_245,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != truth
| implies(not(not(truth)),not(not(not(truth)))) != implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_246,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),truth) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))) )],[refute_0_227,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_249,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(truth,not(not(not(truth)))) != not(not(not(truth)))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) ),[0],$fot(implies(truth,not(not(not(truth)))))]]) ).
cnf(refute_0_250,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(truth,not(not(not(truth))))) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) != truth
| implies(not(not(truth)),not(not(not(truth)))) != not(not(not(truth)))
| implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),truth) ),[0,0],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_253,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) != truth
| implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_4,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(not(not(truth)),not(truth)) = implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)),
inference(subst,[],[refute_0_226:[bind(X,$fot(not(truth))),bind(X_9,$fot(not(not(truth))))]]) ).
cnf(refute_0_256,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))) ),[1,0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_257,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_241,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))) )],[refute_0_255,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(truth,not(truth)) = not(truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_260,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(truth))),not(truth)))]]) ).
cnf(refute_0_261,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_262,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_131,refute_0_262]) ).
cnf(refute_0_264,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != implies(truth,not(truth))
| implies(truth,not(truth)) != not(truth)
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(not(truth)),not(not(truth))),not(truth)))),bind(Y0,$fot(implies(truth,not(truth)))),bind(Z0,$fot(not(truth)))]]) ).
cnf(refute_0_265,plain,
( implies(truth,not(truth)) != not(truth)
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(truth,not(truth))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(truth,not(truth)),not(truth)) )],[refute_0_259,refute_0_265]) ).
cnf(refute_0_267,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != not(truth)
| implies(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) ),[1],$fot(not(truth))]]) ).
cnf(refute_0_268,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),not(truth)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) )],[refute_0_258,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),
introduced(tautology,[refl,[$fot(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_271,plain,
( implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) != implies(not(not(not(truth))),implies(not(not(truth)),not(truth)))
| implies(not(not(truth)),not(truth)) != not(truth)
| implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),implies(not(not(not(truth))),implies(not(not(truth)),not(truth)))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_272,plain,
( implies(not(not(truth)),not(truth)) != not(truth)
| implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),implies(not(not(not(truth))),implies(not(not(truth)),not(truth)))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),not(truth)) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
( implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) != implies(not(not(not(truth))),not(truth))
| implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) != truth
| implies(not(not(not(truth))),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),truth) ),[0],$fot(implies(not(not(not(truth))),not(truth)))]]) ).
cnf(refute_0_275,plain,
( implies(not(not(not(truth))),implies(not(not(truth)),not(truth))) != truth
| implies(not(not(not(truth))),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),implies(not(not(not(truth))),not(truth))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_254,refute_0_275]) ).
cnf(refute_0_277,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(not(not(not(truth))),not(truth)) != truth
| implies(truth,implies(truth,not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_278,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(truth,implies(truth,not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(truth)),truth) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(truth,implies(truth,not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),truth) )],[refute_0_3,refute_0_278]) ).
cnf(refute_0_280,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(truth,not(not(truth)))))]]) ).
cnf(refute_0_281,plain,
( implies(truth,implies(truth,not(not(truth)))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) = not(not(truth)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,implies(truth,not(not(truth)))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_282,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),implies(truth,not(not(truth)))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(truth,implies(truth,not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_100,refute_0_282]) ).
cnf(refute_0_284,plain,
( implies(truth,implies(truth,not(not(truth)))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_285,plain,
( implies(truth,implies(truth,not(not(truth)))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),not(not(truth))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),truth) )],[refute_0_279,refute_0_285]) ).
cnf(refute_0_287,plain,
( implies(implies(not(X),not(not(truth))),implies(not(truth),X)) != truth
| not(not(truth)) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(not(truth))),implies(not(truth),X)),truth) ),[0,0,1],$fot(truth)]]) ).
cnf(refute_0_288,plain,
( implies(implies(not(X),not(not(truth))),implies(not(truth),X)) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(not(truth))),implies(not(truth),X)),truth) )],[refute_0_2,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(truth,implies(not(truth),X)) = implies(not(truth),X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_291,plain,
implies(not(X),truth) = truth,
inference(subst,[],[refute_0_203:[bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_292,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(implies(not(X),truth),implies(not(truth),X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),implies(not(truth),X)))]]) ).
cnf(refute_0_293,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(implies(not(X),truth),implies(not(truth),X))
| implies(not(X),truth) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(implies(not(X),truth),implies(not(truth),X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_294,plain,
( implies(not(X),truth) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(implies(not(X),truth),implies(not(truth),X))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)),
inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(truth,implies(not(truth),X))
| implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(X),truth),implies(not(truth),X)))),bind(Y0,$fot(implies(truth,implies(not(truth),X)))),bind(Z0,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_297,plain,
( implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(truth,implies(not(truth),X))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_290,refute_0_297]) ).
cnf(refute_0_299,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),truth) ),[0],$fot(implies(not(truth),X))]]) ).
cnf(refute_0_300,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
implies(not(truth),X) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),truth) )],[refute_0_289,refute_0_300]) ).
cnf(refute_0_302,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(not(truth),X) != truth
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_303,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(not(truth),X),truth) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(implies(X,not(truth)),not(truth)) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) )],[refute_0_1,refute_0_303]) ).
cnf(refute_0_305,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(not(truth),not(X_26)),not(X_26)))),bind(Y,$fot(implies(X_26,not(truth))))]]) ).
cnf(refute_0_306,plain,
implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_17),not(truth)))),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_307,plain,
implies(implies(not(X_17),not(truth)),X_17) = truth,
inference(subst,[],[refute_0_234:[bind(X_1,$fot(X_17))]]) ).
cnf(refute_0_308,plain,
( implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(not(X_17),not(truth)),X_17) != truth
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_309,plain,
( implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_17),not(truth)),X_17),truth) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))))]]) ).
cnf(refute_0_312,plain,
( implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) ),[0],$fot(implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)))]]) ).
cnf(refute_0_313,plain,
( implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(implies(X_20,not(truth)),implies(implies(not(X_20),not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_314:[bind(X_17,$fot(X_20)),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_316,plain,
implies(implies(not(truth),not(X_20)),not(X_20)) = implies(implies(not(X_20),not(truth)),not(truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_20)))]]) ).
cnf(refute_0_317,plain,
( implies(implies(not(truth),not(X_20)),not(X_20)) != implies(implies(not(X_20),not(truth)),not(truth))
| implies(implies(not(X_20),not(truth)),not(truth)) = implies(implies(not(truth),not(X_20)),not(X_20)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(implies(implies(not(truth),not(X_20)),not(X_20)))),bind(Y0,$fot(implies(implies(not(X_20),not(truth)),not(truth))))]]) ).
cnf(refute_0_318,plain,
implies(implies(not(X_20),not(truth)),not(truth)) = implies(implies(not(truth),not(X_20)),not(X_20)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_20)),not(X_20)),implies(implies(not(X_20),not(truth)),not(truth))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( implies(implies(X_20,not(truth)),implies(implies(not(X_20),not(truth)),not(truth))) != truth
| implies(implies(not(X_20),not(truth)),not(truth)) != implies(implies(not(truth),not(X_20)),not(X_20))
| implies(implies(X_20,not(truth)),implies(implies(not(truth),not(X_20)),not(X_20))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_20,not(truth)),implies(implies(not(X_20),not(truth)),not(truth))),truth) ),[0,1],$fot(implies(implies(not(truth),not(X_20)),not(X_20)))]]) ).
cnf(refute_0_320,plain,
( implies(implies(X_20,not(truth)),implies(implies(not(X_20),not(truth)),not(truth))) != truth
| implies(implies(X_20,not(truth)),implies(implies(not(truth),not(X_20)),not(X_20))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_20),not(truth)),not(truth)),implies(implies(not(truth),not(X_20)),not(X_20))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
implies(implies(X_20,not(truth)),implies(implies(not(truth),not(X_20)),not(X_20))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_20,not(truth)),implies(implies(not(X_20),not(truth)),not(truth))),truth) )],[refute_0_315,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))) = truth,
inference(subst,[],[refute_0_321:[bind(X_20,$fot(X_26))]]) ).
cnf(refute_0_323,plain,
( implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))) != truth
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26)))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_324,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26)))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),truth) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26)))) )],[refute_0_305,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))) = implies(implies(not(truth),not(X_26)),not(X_26)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(truth),not(X_26)),not(X_26))))]]) ).
cnf(refute_0_327,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(truth,implies(implies(not(truth),not(X_26)),not(X_26)))
| implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(implies(not(truth),not(X_26)),not(X_26)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(not(truth),not(X_26)),not(X_26))) ),[0],$fot(implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))))]]) ).
cnf(refute_0_328,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(truth,implies(implies(not(truth),not(X_26)),not(X_26)))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(implies(not(truth),not(X_26)),not(X_26)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),not(X_26)),not(X_26))),implies(implies(not(truth),not(X_26)),not(X_26))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(implies(not(truth),not(X_26)),not(X_26)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(truth,implies(implies(not(truth),not(X_26)),not(X_26)))) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
implies(truth,implies(X_26,not(truth))) = implies(X_26,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_26,not(truth))))]]) ).
cnf(refute_0_331,plain,
implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_332,plain,
( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_333,plain,
( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_286,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) )],[refute_0_331,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(truth,not(Y)) = not(Y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_336,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(implies(truth,not(Y)),implies(Y,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(Y)),implies(Y,not(truth))))]]) ).
cnf(refute_0_337,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(implies(truth,not(Y)),implies(Y,not(truth)))
| implies(truth,not(Y)) != not(Y)
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_338,plain,
( implies(truth,not(Y)) != not(Y)
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(Y)),not(Y)) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(not(Y),implies(Y,not(truth)))
| implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) ),[0],$fot(implies(not(Y),implies(Y,not(truth))))]]) ).
cnf(refute_0_341,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(not(Y),implies(Y,not(truth)))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
implies(not(Y),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) )],[refute_0_334,refute_0_341]) ).
cnf(refute_0_343,plain,
implies(not(X_26),implies(X_26,not(truth))) = truth,
inference(subst,[],[refute_0_342:[bind(Y,$fot(X_26))]]) ).
cnf(refute_0_344,plain,
implies(truth,not(X_26)) = not(X_26),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_26)))]]) ).
cnf(refute_0_345,plain,
implies(not(truth),not(X_26)) = truth,
inference(subst,[],[refute_0_301:[bind(X,$fot(not(X_26)))]]) ).
cnf(refute_0_346,plain,
implies(implies(not(truth),not(X_26)),not(X_26)) = implies(implies(not(truth),not(X_26)),not(X_26)),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(X_26)),not(X_26)))]]) ).
cnf(refute_0_347,plain,
( implies(implies(not(truth),not(X_26)),not(X_26)) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(not(truth),not(X_26)) != truth
| implies(implies(not(truth),not(X_26)),not(X_26)) = implies(truth,not(X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(X_26)),not(X_26)),implies(implies(not(truth),not(X_26)),not(X_26))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_348,plain,
( implies(not(truth),not(X_26)) != truth
| implies(implies(not(truth),not(X_26)),not(X_26)) = implies(truth,not(X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_26)),not(X_26)),implies(implies(not(truth),not(X_26)),not(X_26))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
implies(implies(not(truth),not(X_26)),not(X_26)) = implies(truth,not(X_26)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(X_26)),truth) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
( implies(implies(not(truth),not(X_26)),not(X_26)) != implies(truth,not(X_26))
| implies(truth,not(X_26)) != not(X_26)
| implies(implies(not(truth),not(X_26)),not(X_26)) = not(X_26) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(truth),not(X_26)),not(X_26)))),bind(Y0,$fot(implies(truth,not(X_26)))),bind(Z0,$fot(not(X_26)))]]) ).
cnf(refute_0_351,plain,
( implies(truth,not(X_26)) != not(X_26)
| implies(implies(not(truth),not(X_26)),not(X_26)) = not(X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_26)),not(X_26)),implies(truth,not(X_26))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(implies(not(truth),not(X_26)),not(X_26)) = not(X_26),
inference(resolve,[$cnf( $equal(implies(truth,not(X_26)),not(X_26)) )],[refute_0_344,refute_0_351]) ).
cnf(refute_0_353,plain,
implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))))]]) ).
cnf(refute_0_354,plain,
( implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) != implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth)))
| implies(implies(not(truth),not(X_26)),not(X_26)) != not(X_26)
| implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = implies(not(X_26),implies(X_26,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth)))) ),[1,0],$fot(not(X_26))]]) ).
cnf(refute_0_355,plain,
( implies(implies(not(truth),not(X_26)),not(X_26)) != not(X_26)
| implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = implies(not(X_26),implies(X_26,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = implies(not(X_26),implies(X_26,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_26)),not(X_26)),not(X_26)) )],[refute_0_352,refute_0_355]) ).
cnf(refute_0_357,plain,
( implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) != implies(not(X_26),implies(X_26,not(truth)))
| implies(not(X_26),implies(X_26,not(truth))) != truth
| implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))))),bind(Y0,$fot(implies(not(X_26),implies(X_26,not(truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_358,plain,
( implies(not(X_26),implies(X_26,not(truth))) != truth
| implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(not(X_26),implies(X_26,not(truth)))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_26),implies(X_26,not(truth))),truth) )],[refute_0_343,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))))]]) ).
cnf(refute_0_361,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth)))
| implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) != truth
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(X_26,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_362,plain,
( implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))) != truth
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(X_26,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(truth,implies(X_26,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),truth) )],[refute_0_359,refute_0_362]) ).
cnf(refute_0_364,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(truth,implies(X_26,not(truth)))
| implies(truth,implies(X_26,not(truth))) != implies(X_26,not(truth))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(X_26,not(truth)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))))),bind(Y0,$fot(implies(truth,implies(X_26,not(truth))))),bind(Z0,$fot(implies(X_26,not(truth))))]]) ).
cnf(refute_0_365,plain,
( implies(truth,implies(X_26,not(truth))) != implies(X_26,not(truth))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(X_26,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(truth,implies(X_26,not(truth)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) = implies(X_26,not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_26,not(truth))),implies(X_26,not(truth))) )],[refute_0_330,refute_0_365]) ).
cnf(refute_0_367,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(X_26,not(truth))
| implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(X_26,not(truth)) = implies(implies(not(truth),not(X_26)),not(X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(not(truth),not(X_26)),not(X_26))) ),[0],$fot(implies(X_26,not(truth)))]]) ).
cnf(refute_0_368,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(X_26,not(truth)) = implies(implies(not(truth),not(X_26)),not(X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(X_26,not(truth))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
( implies(X_26,not(truth)) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(implies(not(truth),not(X_26)),not(X_26)) != not(X_26)
| implies(X_26,not(truth)) = not(X_26) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_26,not(truth)),not(X_26)) ),[0],$fot(implies(implies(not(truth),not(X_26)),not(X_26)))]]) ).
cnf(refute_0_370,plain,
( implies(X_26,not(truth)) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(X_26,not(truth)) = not(X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_26)),not(X_26)),not(X_26)) )],[refute_0_352,refute_0_369]) ).
cnf(refute_0_371,plain,
( implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))) != implies(implies(not(truth),not(X_26)),not(X_26))
| implies(X_26,not(truth)) = not(X_26) ),
inference(resolve,[$cnf( $equal(implies(X_26,not(truth)),implies(implies(not(truth),not(X_26)),not(X_26))) )],[refute_0_368,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(X_26,not(truth)) = not(X_26),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_26)),not(X_26)),implies(X_26,not(truth))),implies(X_26,not(truth))),implies(implies(not(truth),not(X_26)),not(X_26))) )],[refute_0_329,refute_0_371]) ).
cnf(refute_0_373,plain,
implies(X,not(truth)) = not(X),
inference(subst,[],[refute_0_372:[bind(X_26,$fot(X))]]) ).
cnf(refute_0_374,plain,
not(implies(X,not(truth))) = not(implies(X,not(truth))),
introduced(tautology,[refl,[$fot(not(implies(X,not(truth))))]]) ).
cnf(refute_0_375,plain,
( implies(X,not(truth)) != not(X)
| not(implies(X,not(truth))) != not(implies(X,not(truth)))
| not(implies(X,not(truth))) = not(not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_376,plain,
( implies(X,not(truth)) != not(X)
| not(implies(X,not(truth))) = not(not(X)) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
not(implies(X,not(truth))) = not(not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(truth)),not(X)) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
implies(implies(X,not(truth)),not(truth)) = not(implies(X,not(truth))),
inference(subst,[],[refute_0_372:[bind(X_26,$fot(implies(X,not(truth))))]]) ).
cnf(refute_0_379,plain,
( implies(implies(X,not(truth)),not(truth)) != not(implies(X,not(truth)))
| not(implies(X,not(truth))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X,not(truth)),not(truth)))),bind(Y0,$fot(not(implies(X,not(truth))))),bind(Z0,$fot(not(not(X))))]]) ).
cnf(refute_0_380,plain,
( not(implies(X,not(truth))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(implies(X,not(truth)))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
implies(implies(X,not(truth)),not(truth)) = not(not(X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(not(X))) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(implies(X,not(truth)),not(truth)) != not(not(X))
| not(not(X)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) ),[0],$fot(not(not(X)))]]) ).
cnf(refute_0_383,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| not(not(X)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(not(X))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
( implies(truth,X) != X
| not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(not(not(X)),implies(truth,X)) ),[1],$fot(X)]]) ).
cnf(refute_0_385,plain,
( not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_384]) ).
cnf(refute_0_386,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(not(not(X)),implies(truth,X)) )],[refute_0_383,refute_0_385]) ).
cnf(refute_0_387,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) )],[refute_0_304,refute_0_386]) ).
cnf(refute_0_388,plain,
not(not(X_38)) = X_38,
inference(subst,[],[refute_0_387:[bind(X,$fot(X_38))]]) ).
cnf(refute_0_389,plain,
( implies(implies(not(X),not(not(X_38))),implies(not(X_38),X)) != truth
| not(not(X_38)) != X_38
| implies(implies(not(X),X_38),implies(not(X_38),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(not(X_38))),implies(not(X_38),X)),truth) ),[0,0,1],$fot(X_38)]]) ).
cnf(refute_0_390,plain,
( implies(implies(not(X),not(not(X_38))),implies(not(X_38),X)) != truth
| implies(implies(not(X),X_38),implies(not(X_38),X)) = truth ),
inference(resolve,[$cnf( $equal(not(not(X_38)),X_38) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
implies(implies(not(X),X_38),implies(not(X_38),X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(not(X_38))),implies(not(X_38),X)),truth) )],[refute_0_0,refute_0_390]) ).
cnf(refute_0_392,plain,
implies(implies(not(x),y),implies(not(y),x)) = truth,
inference(subst,[],[refute_0_391:[bind(X,$fot(x)),bind(X_38,$fot(y))]]) ).
cnf(refute_0_393,plain,
( implies(implies(not(x),y),implies(not(y),x)) != truth
| truth != truth
| implies(implies(not(x),y),implies(not(y),x)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(not(x),y),implies(not(y),x)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_394,plain,
( truth != truth
| implies(implies(not(x),y),implies(not(y),x)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(x),y),implies(not(y),x)),truth) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(implies(not(x),y),implies(not(y),x)),truth) )],[refute_0_394,prove_mv_33]) ).
cnf(refute_0_396,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_397,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_396,refute_0_395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL113-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.07/0.34 % Computer : n029.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 4 20:17:24 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.48
% 0.22/0.48 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.53
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