%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:41:58 PM UTC 2026
% Result : Unsatisfiable 0.96s 1.21s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 147
% Number of leaves : 246
% Syntax : Number of clauses : 891 ( 450 unt; 0 nHn; 503 RR)
% Number of literals : 1545 (1544 equ; 656 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 1203 ( 34 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_wajsberg_lemma,negated_conjecture,
implies(not(x),not(y)) != implies(y,x) ).
cnf(refute_0_0,plain,
implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(implies(Y,implies(not(Y),not(X_101))),implies(not(Y),not(X_101))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(not(Y),not(X_101))))]]) ).
cnf(refute_0_1,plain,
implies(implies(X,implies(X_16,X_17)),implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(X_16,X_17))),bind(Z,$fot(implies(implies(X_17,X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_2,plain,
implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_3,plain,
( implies(implies(X,implies(X_16,X_17)),implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != truth
| implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))) != truth
| implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_4,plain,
( implies(implies(X,implies(X_16,X_17)),implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != truth
| implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),truth) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),truth) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) = implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))))]]) ).
cnf(refute_0_7,plain,
implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),
introduced(tautology,[refl,[$fot(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))))]]) ).
cnf(refute_0_8,plain,
( implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))))
| implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) != implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))
| implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))))) ),[1,1],$fot(implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_9,plain,
( implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) != implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))
| implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) = implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))
| implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != truth
| implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),truth) ),[0],$fot(implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))))]]) ).
cnf(refute_0_12,plain,
( implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) != truth
| implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(implies(X,implies(X_16,X_17)),implies(X,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_16,X_17)),implies(truth,implies(X,implies(implies(X_17,X_18),implies(X_16,X_18))))),truth) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(implies(X_17,implies(X_16,X_17)),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth,
inference(subst,[],[refute_0_13:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_15,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(implies(implies(X_18,truth),truth))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_16,plain,
implies(implies(X,X),X) = implies(implies(X,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(X))]]) ).
cnf(refute_0_17,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_18,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_19,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(truth,X_2) != X_2
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) ),[0,0],$fot(X_2)]]) ).
cnf(refute_0_20,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_23,plain,
( implies(X,X) != implies(implies(X,truth),truth)
| implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) ),[1,0],$fot(implies(implies(X,truth),truth))]]) ).
cnf(refute_0_24,plain,
( implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
inference(resolve,[$cnf( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X),
inference(resolve,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) )],[refute_0_16,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(implies(X_18,X_18),X_18) = implies(implies(implies(X_18,truth),truth),X_18),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_27,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_28,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_29,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( implies(implies(X_18,X_18),X_18) != implies(implies(implies(X_18,truth),truth),X_18)
| implies(implies(implies(X_18,truth),truth),X_18) = implies(implies(X_18,X_18),X_18) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(implies(X_18,X_18),X_18))),bind(Y0,$fot(implies(implies(implies(X_18,truth),truth),X_18)))]]) ).
cnf(refute_0_31,plain,
implies(implies(implies(X_18,truth),truth),X_18) = implies(implies(X_18,X_18),X_18),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(implies(X_18,truth),truth),X_18)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) != truth
| implies(implies(implies(X_18,truth),truth),X_18) != implies(implies(X_18,X_18),X_18)
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))),truth) ),[0,1,0],$fot(implies(implies(X_18,X_18),X_18))]]) ).
cnf(refute_0_33,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,truth),truth),X_18),implies(implies(X_18,X_18),X_18)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))),truth) )],[refute_0_15,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(truth,X_18) = X_18,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_36,plain,
implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),bind(Y,$fot(truth)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_37,plain,
implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_38,plain,
implies(X_4,X_4) = implies(implies(X_4,truth),truth),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_39,plain,
( implies(X_4,X_4) != implies(implies(X_4,truth),truth)
| implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) ),[0,1],$fot(implies(implies(X_4,truth),truth))]]) ).
cnf(refute_0_40,plain,
( implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_4,X_4),implies(implies(X_4,truth),truth)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) = truth,
inference(subst,[],[refute_0_41:[bind(X_4,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_43,plain,
implies(implies(not(X_4),not(truth)),implies(truth,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_44,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_45,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(truth,X_4) != X_4
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_46,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(implies(not(X_4),not(truth)),X_4) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(implies(not(truth),not(truth)),truth) = truth,
inference(subst,[],[refute_0_47:[bind(X_4,$fot(truth))]]) ).
cnf(refute_0_49,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
| implies(implies(not(truth),not(truth)),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_50,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),truth),truth) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) )],[refute_0_42,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_53,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))]]) ).
cnf(refute_0_54,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
| implies(truth,truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_55,plain,
( implies(truth,truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(not(implies(not(truth),not(truth)))))]]) ).
cnf(refute_0_58,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))]]) ).
cnf(refute_0_59,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))
| implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) ),[1,0],$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).
cnf(refute_0_60,plain,
( implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_63,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_29,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))),bind(Y0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))),bind(Z0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)))]]) ).
cnf(refute_0_65,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_56,refute_0_65]) ).
cnf(refute_0_67,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) ),[0],$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth))]]) ).
cnf(refute_0_68,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) )],[refute_0_51,refute_0_68]) ).
cnf(refute_0_70,plain,
( implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) != truth
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_71,plain,
( implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != truth
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),truth) )],[refute_0_36,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_74,plain,
implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_5)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_75,plain,
implies(not(X_5),not(X_5)) = implies(implies(not(X_5),truth),truth),
inference(subst,[],[refute_0_21:[bind(X_2,$fot(not(X_5)))]]) ).
cnf(refute_0_76,plain,
( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
| implies(not(X_5),not(X_5)) != implies(implies(not(X_5),truth),truth)
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) ),[0,0],$fot(implies(implies(not(X_5),truth),truth))]]) ).
cnf(refute_0_77,plain,
( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_5),not(X_5)),implies(implies(not(X_5),truth),truth)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
inference(subst,[],[refute_0_78:[bind(X_5,$fot(truth))]]) ).
cnf(refute_0_80,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_81,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( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_73,refute_0_81]) ).
cnf(refute_0_83,plain,
( implies(X_2,X_2) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,truth),truth) = implies(X_2,X_2) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(X_2,X_2))),bind(Y0,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_84,plain,
implies(implies(X_2,truth),truth) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),implies(implies(X_2,truth),truth)) )],[refute_0_21,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_84:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_86,plain,
implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).
cnf(refute_0_87,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).
cnf(refute_0_88,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_89,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( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_63:[bind(X0,$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_92,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( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_85,refute_0_92]) ).
cnf(refute_0_94,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).
cnf(refute_0_95,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_82,refute_0_95]) ).
cnf(refute_0_97,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),truth),truth) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(truth),truth),truth))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_98,plain,
( implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_85,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(implies(not(truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_96,refute_0_98]) ).
cnf(refute_0_100,plain,
not(implies(not(truth),not(truth))) = not(implies(not(truth),not(truth))),
introduced(tautology,[refl,[$fot(not(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_101,plain,
( implies(not(truth),not(truth)) != truth
| not(implies(not(truth),not(truth))) != not(implies(not(truth),not(truth)))
| not(implies(not(truth),not(truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_102,plain,
( implies(not(truth),not(truth)) != truth
| not(implies(not(truth),not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
not(implies(not(truth),not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_96,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(not(implies(not(truth),not(truth))),truth) = implies(not(implies(not(truth),not(truth))),truth),
introduced(tautology,[refl,[$fot(implies(not(implies(not(truth),not(truth))),truth))]]) ).
cnf(refute_0_105,plain,
( implies(not(implies(not(truth),not(truth))),truth) != implies(not(implies(not(truth),not(truth))),truth)
| not(implies(not(truth),not(truth))) != not(truth)
| implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_106,plain,
( not(implies(not(truth),not(truth))) != not(truth)
| implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(truth)) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).
cnf(refute_0_109,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).
cnf(refute_0_110,plain,
( implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(truth),truth)) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(not(truth),truth),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_113,plain,
( implies(implies(not(truth),truth),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),truth) )],[refute_0_99,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))]]) ).
cnf(refute_0_116,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = implies(truth,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_117,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = implies(truth,X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = implies(truth,X_18),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) != implies(truth,X_18)
| implies(truth,X_18) != X_18
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = X_18 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),bind(Y0,$fot(implies(truth,X_18))),bind(Z0,$fot(X_18))]]) ).
cnf(refute_0_120,plain,
( implies(truth,X_18) != X_18
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = X_18 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18),implies(truth,X_18)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) = X_18,
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_35,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),
introduced(tautology,[refl,[$fot(implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)))]]) ).
cnf(refute_0_123,plain,
( implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) != X_18
| implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_124,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18) != X_18
| implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18) ),
inference(resolve,[$cnf( $equal(implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18),X_18) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)))]]) ).
cnf(refute_0_127,plain,
( implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))
| implies(truth,X_18) != X_18
| implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_128,plain,
( implies(truth,X_18) != X_18
| implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_35,refute_0_128]) ).
cnf(refute_0_130,plain,
( implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,X_18)
| implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))
| implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)))),bind(Y0,$fot(implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)))),bind(Z0,$fot(implies(X_18,X_18)))]]) ).
cnf(refute_0_131,plain,
( implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,X_18)
| implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) = implies(X_18,X_18),
inference(resolve,[$cnf( $equal(implies(X_18,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(X_18,X_18)) )],[refute_0_125,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))))]]) ).
cnf(refute_0_134,plain,
( implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,X_18)
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = implies(X_18,X_18) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))))),bind(Y0,$fot(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)))),bind(Z0,$fot(implies(X_18,X_18)))]]) ).
cnf(refute_0_135,plain,
( implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)) != implies(X_18,X_18)
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = implies(X_18,X_18) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) = implies(X_18,X_18),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18)),implies(X_18,X_18)) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
( implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != implies(X_18,X_18)
| implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != truth
| implies(X_18,X_18) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),truth) ),[0],$fot(implies(X_18,X_18))]]) ).
cnf(refute_0_138,plain,
( implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))) != truth
| implies(X_18,X_18) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),implies(X_18,X_18)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(X_18,X_18) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_18),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_18))),truth) )],[refute_0_72,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(implies(X_18,X_18),X_18) = implies(implies(X_18,X_18),X_18),
introduced(tautology,[refl,[$fot(implies(implies(X_18,X_18),X_18))]]) ).
cnf(refute_0_141,plain,
( implies(X_18,X_18) != truth
| implies(implies(X_18,X_18),X_18) != implies(implies(X_18,X_18),X_18)
| implies(implies(X_18,X_18),X_18) = implies(truth,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(X_18,X_18),X_18)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_142,plain,
( implies(X_18,X_18) != truth
| implies(implies(X_18,X_18),X_18) = implies(truth,X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(X_18,X_18),X_18)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(X_18,X_18),X_18) = implies(truth,X_18),
inference(resolve,[$cnf( $equal(implies(X_18,X_18),truth) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(implies(X_18,X_18),X_18) != implies(truth,X_18)
| implies(truth,X_18) != X_18
| implies(implies(X_18,X_18),X_18) = X_18 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(X_18,X_18),X_18))),bind(Y0,$fot(implies(truth,X_18))),bind(Z0,$fot(X_18))]]) ).
cnf(refute_0_145,plain,
( implies(truth,X_18) != X_18
| implies(implies(X_18,X_18),X_18) = X_18 ),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(truth,X_18)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(implies(X_18,X_18),X_18) = X_18,
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_35,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))]]) ).
cnf(refute_0_148,plain,
( implies(implies(X_18,X_18),X_18) != X_18
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_149,plain,
( implies(implies(X_18,X_18),X_18) != X_18
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),X_18) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_152,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) ),[1,1],$fot(implies(X_18,implies(X_16,X_18)))]]) ).
cnf(refute_0_153,plain,
( implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(X_18,implies(X_16,X_18))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18)))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),truth) ),[0],$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_156,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),truth) )],[refute_0_34,refute_0_156]) ).
cnf(refute_0_158,plain,
implies(truth,implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_159,plain,
implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(X_17)),bind(Z,$fot(implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_160,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_161,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
| implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_41,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) )],[refute_0_159,refute_0_161]) ).
cnf(refute_0_163,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_164,plain,
implies(not(X_4),not(X_4)) = truth,
inference(subst,[],[refute_0_139:[bind(X_18,$fot(not(X_4)))]]) ).
cnf(refute_0_165,plain,
implies(implies(not(X_4),not(X_4)),X_17) = implies(implies(not(X_4),not(X_4)),X_17),
introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_17))]]) ).
cnf(refute_0_166,plain,
( implies(implies(not(X_4),not(X_4)),X_17) != implies(implies(not(X_4),not(X_4)),X_17)
| implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_17) = implies(truth,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(not(X_4),not(X_4)),X_17)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_167,plain,
( implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_17) = implies(truth,X_17) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(not(X_4),not(X_4)),X_17)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(not(X_4),not(X_4)),X_17) = implies(truth,X_17),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(implies(not(X_4),not(X_4)),X_17) != implies(truth,X_17)
| implies(truth,X_17) != X_17
| implies(implies(not(X_4),not(X_4)),X_17) = X_17 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_17))),bind(Y0,$fot(implies(truth,X_17))),bind(Z0,$fot(X_17))]]) ).
cnf(refute_0_170,plain,
( implies(truth,X_17) != X_17
| implies(implies(not(X_4),not(X_4)),X_17) = X_17 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_17),implies(truth,X_17)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(not(X_4),not(X_4)),X_17) = X_17,
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_163,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_173,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))
| implies(implies(not(X_4),not(X_4)),X_17) != X_17
| implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_174,plain,
( implies(implies(not(X_4),not(X_4)),X_17) != X_17
| implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_17),X_17) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))
| implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_177,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_17),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_162,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(X_9,truth),truth))),bind(Y,$fot(implies(not(X_9),not(X_9))))]]) ).
cnf(refute_0_180,plain,
implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)) = truth,
inference(subst,[],[refute_0_41:[bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_181,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))
| implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)) != truth
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_182,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),truth) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(truth,implies(implies(X_9,truth),truth)) = implies(implies(X_9,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_185,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(truth,implies(implies(X_9,truth),truth))
| implies(truth,implies(implies(X_9,truth),truth)) != implies(implies(X_9,truth),truth)
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) ),[0],$fot(implies(truth,implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_186,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(truth,implies(implies(X_9,truth),truth))
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(truth,implies(implies(X_9,truth),truth))) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(implies(implies(X_4,truth),truth))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_189,plain,
( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_190,plain,
( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != truth
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_41,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),truth) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
implies(implies(not(X_4),not(X_4)),X_18) = implies(implies(not(X_4),not(X_4)),X_18),
introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_18))]]) ).
cnf(refute_0_193,plain,
( implies(implies(not(X_4),not(X_4)),X_18) != implies(implies(not(X_4),not(X_4)),X_18)
| implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_18) = implies(truth,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_18),implies(implies(not(X_4),not(X_4)),X_18)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_194,plain,
( implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_18) = implies(truth,X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_18),implies(implies(not(X_4),not(X_4)),X_18)) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
implies(implies(not(X_4),not(X_4)),X_18) = implies(truth,X_18),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_164,refute_0_194]) ).
cnf(refute_0_196,plain,
( implies(implies(not(X_4),not(X_4)),X_18) != implies(truth,X_18)
| implies(truth,X_18) != X_18
| implies(implies(not(X_4),not(X_4)),X_18) = X_18 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_18))),bind(Y0,$fot(implies(truth,X_18))),bind(Z0,$fot(X_18))]]) ).
cnf(refute_0_197,plain,
( implies(truth,X_18) != X_18
| implies(implies(not(X_4),not(X_4)),X_18) = X_18 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_18),implies(truth,X_18)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(implies(not(X_4),not(X_4)),X_18) = X_18,
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_35,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) = implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)))]]) ).
cnf(refute_0_200,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) != implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))
| implies(implies(not(X_4),not(X_4)),X_18) != X_18
| implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) ),[1,1],$fot(X_18)]]) ).
cnf(refute_0_201,plain,
( implies(implies(not(X_4),not(X_4)),X_18) != X_18
| implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_18),X_18) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))))]]) ).
cnf(refute_0_204,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) != implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))))),bind(Y0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)))),bind(Z0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)))]]) ).
cnf(refute_0_205,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)) != implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) = implies(implies(implies(implies(X_4,truth),truth),X_18),X_18),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18)),implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != truth
| implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),truth) ),[0],$fot(implies(implies(implies(implies(X_4,truth),truth),X_18),X_18))]]) ).
cnf(refute_0_208,plain,
( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))) != truth
| implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),implies(implies(implies(implies(X_4,truth),truth),X_18),X_18)) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(implies(implies(implies(X_4,truth),truth),X_18),X_18) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_18),implies(implies(not(X_4),not(X_4)),X_18))),truth) )],[refute_0_191,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = truth,
inference(subst,[],[refute_0_209:[bind(X_18,$fot(implies(not(X_9),not(X_9)))),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_211,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(X_9,truth),truth)
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != truth
| truth = implies(implies(X_9,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_212,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(X_9,truth),truth)
| truth = implies(implies(X_9,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),truth) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
truth = implies(implies(X_9,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) )],[refute_0_187,refute_0_212]) ).
cnf(refute_0_214,plain,
( truth != implies(implies(X_9,truth),truth)
| implies(implies(X_9,truth),truth) = truth ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_215,plain,
implies(implies(X_9,truth),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(X_9,truth),truth)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(implies(X_17,truth),truth) = truth,
inference(subst,[],[refute_0_215:[bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_217,plain,
implies(implies(X_4,truth),truth) = truth,
inference(subst,[],[refute_0_215:[bind(X_9,$fot(X_4))]]) ).
cnf(refute_0_218,plain,
implies(X_17,implies(implies(X_4,truth),truth)) = implies(X_17,implies(implies(X_4,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_17,implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_219,plain,
( implies(X_17,implies(implies(X_4,truth),truth)) != implies(X_17,implies(implies(X_4,truth),truth))
| implies(implies(X_4,truth),truth) != truth
| implies(X_17,implies(implies(X_4,truth),truth)) = implies(X_17,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(implies(X_4,truth),truth)),implies(X_17,implies(implies(X_4,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_220,plain,
( implies(implies(X_4,truth),truth) != truth
| implies(X_17,implies(implies(X_4,truth),truth)) = implies(X_17,truth) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_4,truth),truth)),implies(X_17,implies(implies(X_4,truth),truth))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
implies(X_17,implies(implies(X_4,truth),truth)) = implies(X_17,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_4,truth),truth),truth) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_17,implies(implies(X_4,truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))]]) ).
cnf(refute_0_223,plain,
( implies(X_17,implies(implies(X_4,truth),truth)) != implies(X_17,truth)
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_17,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) ),[1,0],$fot(implies(X_17,truth))]]) ).
cnf(refute_0_224,plain,
( implies(X_17,implies(implies(X_4,truth),truth)) != implies(X_17,truth)
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_17,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth),implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_17,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_4,truth),truth)),implies(X_17,truth)) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_17,truth),truth)
| implies(implies(X_17,truth),truth) != truth
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))),bind(Y0,$fot(implies(implies(X_17,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_227,plain,
( implies(implies(X_17,truth),truth) != truth
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth),implies(implies(X_17,truth),truth)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_17,truth),truth),truth) )],[refute_0_216,refute_0_227]) ).
cnf(refute_0_229,plain,
implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),
introduced(tautology,[refl,[$fot(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_230,plain,
( implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))
| implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) != truth
| implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_231,plain,
( implies(implies(X_17,implies(implies(X_4,truth),truth)),truth) != truth
| implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,truth) ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) = implies(X_17,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(implies(X_4,truth),truth)),truth),truth) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != implies(X_17,truth)
| implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_17,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_17,truth))]]) ).
cnf(refute_0_234,plain,
( implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_17,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),implies(X_17,truth)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(X_17,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_17,implies(implies(X_17,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_178,refute_0_234]) ).
cnf(refute_0_236,plain,
implies(X_16,truth) = truth,
inference(subst,[],[refute_0_235:[bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_237,plain,
implies(implies(X_18,truth),truth) = truth,
inference(subst,[],[refute_0_235:[bind(X_17,$fot(implies(X_18,truth)))]]) ).
cnf(refute_0_238,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,implies(implies(X_18,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_16,implies(implies(X_18,truth),truth)))]]) ).
cnf(refute_0_239,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != implies(X_16,implies(implies(X_18,truth),truth))
| implies(implies(X_18,truth),truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,implies(implies(X_18,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_240,plain,
( implies(implies(X_18,truth),truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth) ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,implies(implies(X_18,truth),truth))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_18,truth),truth),truth) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != implies(X_16,truth)
| implies(X_16,truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(X_16,implies(implies(X_18,truth),truth)))),bind(Y0,$fot(implies(X_16,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_243,plain,
( implies(X_16,truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,truth)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(X_16,truth),truth) )],[refute_0_236,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_246,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) != implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18)))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_247,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18)))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),truth) )],[refute_0_244,refute_0_247]) ).
cnf(refute_0_249,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) != implies(truth,implies(X_18,implies(X_16,X_18)))
| implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(X_16,implies(implies(X_18,truth),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_250,plain,
( implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),implies(truth,implies(X_18,implies(X_16,X_18)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_18,implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_158,refute_0_250]) ).
cnf(refute_0_252,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),truth) ),[0],$fot(implies(X_18,implies(X_16,X_18)))]]) ).
cnf(refute_0_253,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(X_18,implies(X_16,X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_18,implies(X_16,X_18))),truth) )],[refute_0_157,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(X_17,implies(X_16,X_17)) = truth,
inference(subst,[],[refute_0_254:[bind(X_18,$fot(X_17))]]) ).
cnf(refute_0_256,plain,
( implies(X_17,implies(X_16,X_17)) != truth
| implies(implies(X_17,implies(X_16,X_17)),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) != truth
| implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,implies(X_16,X_17)),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_257,plain,
( implies(implies(X_17,implies(X_16,X_17)),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) != truth
| implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth ),
inference(resolve,[$cnf( $equal(implies(X_17,implies(X_16,X_17)),truth) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_17,implies(X_16,X_17)),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))),truth) )],[refute_0_14,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) = implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))))]]) ).
cnf(refute_0_260,plain,
( implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) != implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))
| implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) != truth
| implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))),truth) ),[0],$fot(implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_261,plain,
( implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) != truth
| implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))),implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_17,implies(implies(X_17,X_18),implies(X_16,X_18)))),truth) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(X_99,implies(implies(X_99,not(truth)),implies(X_98,not(truth)))) = truth,
inference(subst,[],[refute_0_262:[bind(X_16,$fot(X_98)),bind(X_17,$fot(X_99)),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_264,plain,
implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(not(X_63))))),bind(Y,$fot(implies(X_63,not(truth))))]]) ).
cnf(refute_0_265,plain,
implies(implies(not(not(not(not(X_62)))),not(truth)),not(not(not(X_62)))) = truth,
inference(subst,[],[refute_0_47:[bind(X_4,$fot(not(not(not(X_62)))))]]) ).
cnf(refute_0_266,plain,
implies(implies(not(not(not(not(Y)))),Y),Y) = implies(implies(Y,not(not(not(not(Y))))),not(not(not(not(Y))))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(not(not(Y))))))]]) ).
cnf(refute_0_267,plain,
implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_268,plain,
( implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) != truth
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_269,plain,
( implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) != truth
| implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))),truth) )],[refute_0_267,refute_0_269]) ).
cnf(refute_0_271,plain,
implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) = implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))))]]) ).
cnf(refute_0_272,plain,
( implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) != implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))
| implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) != truth
| implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))),truth) ),[0],$fot(implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18)))]]) ).
cnf(refute_0_273,plain,
( implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) != truth
| implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))),implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(Y,X),X_18),implies(implies(not(X),not(Y)),X_18))),truth) )],[refute_0_270,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(implies(implies(X_42,X_43),X_43),implies(implies(not(X_43),not(X_42)),X_43)) = truth,
inference(subst,[],[refute_0_274:[bind(X,$fot(X_43)),bind(Y,$fot(X_42)),bind(X_18,$fot(X_43))]]) ).
cnf(refute_0_276,plain,
implies(implies(X_43,X_42),X_42) = implies(implies(X_42,X_43),X_43),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_43)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_277,plain,
( implies(implies(X_43,X_42),X_42) != implies(implies(X_42,X_43),X_43)
| implies(implies(X_42,X_43),X_43) = implies(implies(X_43,X_42),X_42) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(implies(X_43,X_42),X_42))),bind(Y0,$fot(implies(implies(X_42,X_43),X_43)))]]) ).
cnf(refute_0_278,plain,
implies(implies(X_42,X_43),X_43) = implies(implies(X_43,X_42),X_42),
inference(resolve,[$cnf( $equal(implies(implies(X_43,X_42),X_42),implies(implies(X_42,X_43),X_43)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
( implies(implies(X_42,X_43),X_43) != implies(implies(X_43,X_42),X_42)
| implies(implies(implies(X_42,X_43),X_43),implies(implies(not(X_43),not(X_42)),X_43)) != truth
| implies(implies(implies(X_43,X_42),X_42),implies(implies(not(X_43),not(X_42)),X_43)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_42,X_43),X_43),implies(implies(not(X_43),not(X_42)),X_43)),truth) ),[0,0],$fot(implies(implies(X_43,X_42),X_42))]]) ).
cnf(refute_0_280,plain,
( implies(implies(implies(X_42,X_43),X_43),implies(implies(not(X_43),not(X_42)),X_43)) != truth
| implies(implies(implies(X_43,X_42),X_42),implies(implies(not(X_43),not(X_42)),X_43)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_42,X_43),X_43),implies(implies(X_43,X_42),X_42)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
implies(implies(implies(X_43,X_42),X_42),implies(implies(not(X_43),not(X_42)),X_43)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_42,X_43),X_43),implies(implies(not(X_43),not(X_42)),X_43)),truth) )],[refute_0_275,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(implies(implies(not(not(not(not(X_42)))),X_42),X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = truth,
inference(subst,[],[refute_0_281:[bind(X_43,$fot(not(not(not(not(X_42))))))]]) ).
cnf(refute_0_283,plain,
implies(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) = truth,
inference(subst,[],[refute_0_274:[bind(X,$fot(not(truth))),bind(Y,$fot(not(implies(not(not(truth)),not(not(X_43)))))),bind(X_18,$fot(X_43))]]) ).
cnf(refute_0_284,plain,
implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_17),not(truth)))),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_285,plain,
implies(implies(not(X_17),not(truth)),X_17) = truth,
inference(subst,[],[refute_0_47:[bind(X_4,$fot(X_17))]]) ).
cnf(refute_0_286,plain,
( implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(not(X_17),not(truth)),X_17) != truth
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth ),
introduced(tautology,[equality,[$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_287,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( $equal(implies(implies(not(X_17),not(truth)),X_17),truth) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_284,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))))]]) ).
cnf(refute_0_290,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_291,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( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(implies(implies(not(not(truth)),not(not(X_37))),X_37),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) = truth,
inference(subst,[],[refute_0_292:[bind(X_17,$fot(implies(not(not(truth)),not(not(X_37))))),bind(X_18,$fot(X_37))]]) ).
cnf(refute_0_294,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(implies(not(X_18),not(truth)))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_295,plain,
implies(implies(not(X_18),not(truth)),X_18) = truth,
inference(subst,[],[refute_0_47:[bind(X_4,$fot(X_18))]]) ).
cnf(refute_0_296,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) != truth
| implies(implies(not(X_18),not(truth)),X_18) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_297,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_18),not(truth)),X_18),truth) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))),truth) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(truth,implies(X_16,X_18)) = implies(X_16,X_18),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_16,X_18)))]]) ).
cnf(refute_0_300,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))))]]) ).
cnf(refute_0_301,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))
| implies(truth,implies(X_16,X_18)) != implies(X_16,X_18)
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))) ),[1,1],$fot(implies(X_16,X_18))]]) ).
cnf(refute_0_302,plain,
( implies(truth,implies(X_16,X_18)) != implies(X_16,X_18)
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_16,X_18)),implies(X_16,X_18)) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18))
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),truth) ),[0],$fot(implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)))]]) ).
cnf(refute_0_305,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18))) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),truth) )],[refute_0_298,refute_0_305]) ).
cnf(refute_0_307,plain,
implies(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),implies(implies(not(not(truth)),not(not(X_21))),X_21)) = truth,
inference(subst,[],[refute_0_306:[bind(X_16,$fot(implies(not(not(truth)),not(not(X_21))))),bind(X_18,$fot(X_21))]]) ).
cnf(refute_0_308,plain,
implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_21)))]]) ).
cnf(refute_0_309,plain,
( implies(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),implies(implies(not(not(truth)),not(not(X_21))),X_21)) != truth
| implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),implies(implies(not(not(truth)),not(not(X_21))),X_21)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_310,plain,
( implies(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),implies(implies(not(not(truth)),not(not(X_21))),X_21)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),truth) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_21))),implies(not(X_21),not(truth))),implies(implies(not(not(truth)),not(not(X_21))),X_21)),truth) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) = implies(implies(not(not(truth)),not(not(X_21))),X_21),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_21))),X_21)))]]) ).
cnf(refute_0_313,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) != implies(implies(not(not(truth)),not(not(X_21))),X_21)
| implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) != truth
| implies(implies(not(not(truth)),not(not(X_21))),X_21) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_21))),X_21))]]) ).
cnf(refute_0_314,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)) != truth
| implies(implies(not(not(truth)),not(not(X_21))),X_21) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)),implies(implies(not(not(truth)),not(not(X_21))),X_21)) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(implies(not(not(truth)),not(not(X_21))),X_21) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_21))),X_21)),truth) )],[refute_0_311,refute_0_314]) ).
cnf(refute_0_316,plain,
implies(implies(not(not(truth)),not(not(X_37))),X_37) = truth,
inference(subst,[],[refute_0_315:[bind(X_21,$fot(X_37))]]) ).
cnf(refute_0_317,plain,
( implies(implies(implies(not(not(truth)),not(not(X_37))),X_37),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) != truth
| implies(implies(not(not(truth)),not(not(X_37))),X_37) != truth
| implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_37))),X_37),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_318,plain,
( implies(implies(implies(not(not(truth)),not(not(X_37))),X_37),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) != truth
| implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_37))),X_37),truth) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_37))),X_37),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)),truth) )],[refute_0_293,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) = implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)))]]) ).
cnf(refute_0_321,plain,
( implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) != implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)
| implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) != truth
| implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)),truth) ),[0],$fot(implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37))]]) ).
cnf(refute_0_322,plain,
( implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) != truth
| implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)),implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(implies(not(not(truth)),not(not(X_37)))),not(truth)),X_37)),truth) )],[refute_0_319,refute_0_322]) ).
cnf(refute_0_324,plain,
implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43) = truth,
inference(subst,[],[refute_0_323:[bind(X_37,$fot(X_43))]]) ).
cnf(refute_0_325,plain,
( implies(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) != truth
| implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_326,plain,
( implies(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),truth) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(not(truth)),not(not(X_43)))),not(truth)),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)),truth) )],[refute_0_283,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) = implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)))]]) ).
cnf(refute_0_329,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) != implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)
| implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) != truth
| implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43))]]) ).
cnf(refute_0_330,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) != truth
| implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)),truth) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(truth,not(not(not(not(X_43))))) = not(not(not(not(X_43)))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(not(X_43))))))]]) ).
cnf(refute_0_333,plain,
implies(truth,not(not(X_43))) = not(not(X_43)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_43))))]]) ).
cnf(refute_0_334,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(not(not(truth)),not(truth)))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_335,plain,
implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_306:[bind(X_16,$fot(not(not(truth)))),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_336,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))
| implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) ),[0],$fot(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_337,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))) )],[refute_0_334,refute_0_337]) ).
cnf(refute_0_339,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_340,plain,
implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(implies(Y,X_4)))]]) ).
cnf(refute_0_341,plain,
implies(implies(X_4,Y),Y) = implies(implies(Y,X_4),X_4),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_342,plain,
( implies(implies(X_4,Y),Y) != implies(implies(Y,X_4),X_4)
| implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(implies(X_4,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_4),X_4)))]]) ).
cnf(refute_0_343,plain,
implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_4,Y),Y),implies(implies(Y,X_4),X_4)) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
( implies(implies(Y,X_4),X_4) != implies(implies(X_4,Y),Y)
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) ),[0,1],$fot(implies(implies(X_4,Y),Y))]]) ).
cnf(refute_0_345,plain,
( implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_4),X_4),implies(implies(X_4,Y),Y)) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) )],[refute_0_340,refute_0_345]) ).
cnf(refute_0_347,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_1,X_23),X_23),X_23),X_23)) = truth,
inference(subst,[],[refute_0_346:[bind(Y,$fot(X_23)),bind(X_4,$fot(implies(implies(X_1,X_23),X_23)))]]) ).
cnf(refute_0_348,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X_1,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_1,X)))]]) ).
cnf(refute_0_349,plain,
implies(implies(X_1,X),X) = implies(implies(X,X_1),X_1),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_1)),bind(Y,$fot(X))]]) ).
cnf(refute_0_350,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X_1,X),X) != implies(implies(X,X_1),X_1)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) ),[1,0],$fot(implies(implies(X,X_1),X_1))]]) ).
cnf(refute_0_351,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1,X),X),implies(implies(X,X_1),X_1)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) ),[0],$fot(implies(implies(implies(X_1,X),X),X))]]) ).
cnf(refute_0_354,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_348,refute_0_353]) ).
cnf(refute_0_355,plain,
implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) )],[refute_0_352,refute_0_354]) ).
cnf(refute_0_356,plain,
implies(implies(implies(X_1,X_23),X_23),X_23) = implies(implies(implies(X_23,X_1),X_1),X_23),
inference(subst,[],[refute_0_355:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_357,plain,
( implies(implies(implies(X_1,X_23),X_23),X_23) != implies(implies(implies(X_23,X_1),X_1),X_23)
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_1,X_23),X_23),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_1,X_23),X_23),X_23),X_23)),truth) ),[0,1,0],$fot(implies(implies(implies(X_23,X_1),X_1),X_23))]]) ).
cnf(refute_0_358,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_1,X_23),X_23),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,X_23),X_23),X_23),implies(implies(implies(X_23,X_1),X_1),X_23)) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_1,X_23),X_23),X_23),X_23)),truth) )],[refute_0_347,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(X_23,implies(implies(X_1,X_23),X_23)) = truth,
inference(subst,[],[refute_0_254:[bind(X_16,$fot(implies(X_1,X_23))),bind(X_18,$fot(X_23))]]) ).
cnf(refute_0_361,plain,
not(implies(X_23,implies(implies(X_1,X_23),X_23))) = not(implies(X_23,implies(implies(X_1,X_23),X_23))),
introduced(tautology,[refl,[$fot(not(implies(X_23,implies(implies(X_1,X_23),X_23))))]]) ).
cnf(refute_0_362,plain,
( implies(X_23,implies(implies(X_1,X_23),X_23)) != truth
| not(implies(X_23,implies(implies(X_1,X_23),X_23))) != not(implies(X_23,implies(implies(X_1,X_23),X_23)))
| not(implies(X_23,implies(implies(X_1,X_23),X_23))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_23,implies(implies(X_1,X_23),X_23))),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_363,plain,
( implies(X_23,implies(implies(X_1,X_23),X_23)) != truth
| not(implies(X_23,implies(implies(X_1,X_23),X_23))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_23,implies(implies(X_1,X_23),X_23))),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
not(implies(X_23,implies(implies(X_1,X_23),X_23))) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_23,implies(implies(X_1,X_23),X_23)),truth) )],[refute_0_360,refute_0_363]) ).
cnf(refute_0_365,plain,
implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) = implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),
introduced(tautology,[refl,[$fot(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))))]]) ).
cnf(refute_0_366,plain,
( implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) != implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23))))
| not(implies(X_23,implies(implies(X_1,X_23),X_23))) != not(truth)
| implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) = implies(not(implies(implies(X_1,X_23),X_23)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_367,plain,
( not(implies(X_23,implies(implies(X_1,X_23),X_23))) != not(truth)
| implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) = implies(not(implies(implies(X_1,X_23),X_23)),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23))))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) = implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(X_23,implies(implies(X_1,X_23),X_23))),not(truth)) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)))]]) ).
cnf(refute_0_370,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))
| implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) != implies(not(implies(implies(X_1,X_23),X_23)),not(truth))
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))) ),[1,0],$fot(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)))]]) ).
cnf(refute_0_371,plain,
( implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))) != implies(not(implies(implies(X_1,X_23),X_23)),not(truth))
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(not(implies(implies(X_1,X_23),X_23)),not(truth))) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),truth) ),[0],$fot(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)))]]) ).
cnf(refute_0_374,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(implies(X_23,implies(implies(X_1,X_23),X_23)))),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),truth) )],[refute_0_359,refute_0_374]) ).
cnf(refute_0_376,plain,
implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(implies(Y,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(Y,X_26),X_26)))]]) ).
cnf(refute_0_377,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_378,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) != truth
| implies(truth,X_18) != X_18
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))),truth) ),[0,1,1],$fot(X_18)]]) ).
cnf(refute_0_379,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) != truth
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_35,refute_0_378]) ).
cnf(refute_0_380,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))),truth) )],[refute_0_377,refute_0_379]) ).
cnf(refute_0_381,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)))]]) ).
cnf(refute_0_382,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))
| implies(truth,X_17) != X_17
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_383,plain,
( implies(truth,X_17) != X_17
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_163,refute_0_383]) ).
cnf(refute_0_385,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != implies(X_17,implies(implies(X_17,X_18),X_18))
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != truth
| implies(X_17,implies(implies(X_17,X_18),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),truth) ),[0],$fot(implies(X_17,implies(implies(X_17,X_18),X_18)))]]) ).
cnf(refute_0_386,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != truth
| implies(X_17,implies(implies(X_17,X_18),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(X_17,implies(implies(X_17,X_18),X_18))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
implies(X_17,implies(implies(X_17,X_18),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),truth) )],[refute_0_380,refute_0_386]) ).
cnf(refute_0_388,plain,
implies(Y,implies(implies(Y,X_26),X_26)) = truth,
inference(subst,[],[refute_0_387:[bind(X_17,$fot(Y)),bind(X_18,$fot(X_26))]]) ).
cnf(refute_0_389,plain,
( implies(Y,implies(implies(Y,X_26),X_26)) != truth
| implies(implies(implies(implies(Y,X_26),X_26),Y),Y) != implies(implies(Y,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26))
| implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(truth,implies(implies(Y,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_26),X_26),Y),Y),implies(implies(Y,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_390,plain,
( implies(implies(implies(implies(Y,X_26),X_26),Y),Y) != implies(implies(Y,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26))
| implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(truth,implies(implies(Y,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(Y,X_26),X_26)),truth) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(truth,implies(implies(Y,X_26),X_26)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_26),X_26),Y),Y),implies(implies(Y,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26))) )],[refute_0_376,refute_0_390]) ).
cnf(refute_0_392,plain,
implies(truth,implies(implies(Y,X_26),X_26)) = implies(implies(Y,X_26),X_26),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(Y,X_26),X_26)))]]) ).
cnf(refute_0_393,plain,
( implies(implies(implies(implies(Y,X_26),X_26),Y),Y) != implies(truth,implies(implies(Y,X_26),X_26))
| implies(truth,implies(implies(Y,X_26),X_26)) != implies(implies(Y,X_26),X_26)
| implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(implies(Y,X_26),X_26) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(Y,X_26),X_26),Y),Y),implies(implies(Y,X_26),X_26)) ),[0],$fot(implies(truth,implies(implies(Y,X_26),X_26)))]]) ).
cnf(refute_0_394,plain,
( implies(implies(implies(implies(Y,X_26),X_26),Y),Y) != implies(truth,implies(implies(Y,X_26),X_26))
| implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(implies(Y,X_26),X_26) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(Y,X_26),X_26)),implies(implies(Y,X_26),X_26)) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
implies(implies(implies(implies(Y,X_26),X_26),Y),Y) = implies(implies(Y,X_26),X_26),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_26),X_26),Y),Y),implies(truth,implies(implies(Y,X_26),X_26))) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23) = implies(implies(X_23,X_1),X_1),
inference(subst,[],[refute_0_395:[bind(Y,$fot(X_23)),bind(X_26,$fot(X_1))]]) ).
cnf(refute_0_397,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)))]]) ).
cnf(refute_0_398,plain,
( implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23) != implies(implies(X_23,X_1),X_1)
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))) ),[1,1],$fot(implies(implies(X_23,X_1),X_1))]]) ).
cnf(refute_0_399,plain,
( implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23) != implies(implies(X_23,X_1),X_1)
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) = implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23),implies(implies(X_23,X_1),X_1)) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1))
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),truth) ),[0],$fot(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)))]]) ).
cnf(refute_0_402,plain,
( implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)) != truth
| implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1))) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(X_23,X_1),X_1)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_1,X_23),X_23)),not(truth)),implies(implies(implies(implies(X_23,X_1),X_1),X_23),X_23)),truth) )],[refute_0_375,refute_0_402]) ).
cnf(refute_0_404,plain,
implies(implies(not(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = truth,
inference(subst,[],[refute_0_403:[bind(X_1,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth))))),bind(X_23,$fot(not(not(truth))))]]) ).
cnf(refute_0_405,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| implies(implies(not(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != truth
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),truth) ),[0,0,0,0,0],$fot(truth)]]) ).
cnf(refute_0_406,plain,
( implies(implies(not(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != truth
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) )],[refute_0_338,refute_0_405]) ).
cnf(refute_0_407,plain,
implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),truth) )],[refute_0_404,refute_0_406]) ).
cnf(refute_0_408,plain,
implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(implies(X_32,X_31),X_31),X_32))),bind(Y,$fot(implies(X_31,X_32)))]]) ).
cnf(refute_0_409,plain,
implies(implies(Y,X_26),implies(implies(implies(Y,X_26),X_26),X_26)) = truth,
inference(subst,[],[refute_0_387:[bind(X_17,$fot(implies(Y,X_26))),bind(X_18,$fot(X_26))]]) ).
cnf(refute_0_410,plain,
implies(implies(X_26,Y),Y) = implies(implies(Y,X_26),X_26),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_411,plain,
( implies(implies(X_26,Y),Y) != implies(implies(Y,X_26),X_26)
| implies(implies(Y,X_26),X_26) = implies(implies(X_26,Y),Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(implies(X_26,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_26),X_26)))]]) ).
cnf(refute_0_412,plain,
implies(implies(Y,X_26),X_26) = implies(implies(X_26,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_26,Y),Y),implies(implies(Y,X_26),X_26)) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
( implies(implies(Y,X_26),X_26) != implies(implies(X_26,Y),Y)
| implies(implies(Y,X_26),implies(implies(implies(Y,X_26),X_26),X_26)) != truth
| implies(implies(Y,X_26),implies(implies(implies(X_26,Y),Y),X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,X_26),implies(implies(implies(Y,X_26),X_26),X_26)),truth) ),[0,1,0],$fot(implies(implies(X_26,Y),Y))]]) ).
cnf(refute_0_414,plain,
( implies(implies(Y,X_26),implies(implies(implies(Y,X_26),X_26),X_26)) != truth
| implies(implies(Y,X_26),implies(implies(implies(X_26,Y),Y),X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_26),X_26),implies(implies(X_26,Y),Y)) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
implies(implies(Y,X_26),implies(implies(implies(X_26,Y),Y),X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(Y,X_26),implies(implies(implies(Y,X_26),X_26),X_26)),truth) )],[refute_0_409,refute_0_414]) ).
cnf(refute_0_416,plain,
implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)) = truth,
inference(subst,[],[refute_0_415:[bind(Y,$fot(X_31)),bind(X_26,$fot(X_32))]]) ).
cnf(refute_0_417,plain,
( implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)) != truth
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_418,plain,
( implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),truth) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(implies(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32))) )],[refute_0_408,refute_0_418]) ).
cnf(refute_0_420,plain,
implies(truth,implies(X_31,X_32)) = implies(X_31,X_32),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_31,X_32)))]]) ).
cnf(refute_0_421,plain,
implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) = implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)),
inference(subst,[],[refute_0_355:[bind(X,$fot(implies(X_15,X_1)))]]) ).
cnf(refute_0_422,plain,
implies(implies(implies(X_15,X_1),X_1),X_1) = implies(implies(implies(X_1,X_15),X_15),X_1),
inference(subst,[],[refute_0_355:[bind(X,$fot(X_1)),bind(X_1,$fot(X_15))]]) ).
cnf(refute_0_423,plain,
( implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) != implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))
| implies(implies(implies(X_15,X_1),X_1),X_1) != implies(implies(implies(X_1,X_15),X_15),X_1)
| implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)),implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))) ),[1,0],$fot(implies(implies(implies(X_1,X_15),X_15),X_1))]]) ).
cnf(refute_0_424,plain,
( implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) != implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))
| implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_15,X_1),X_1),X_1),implies(implies(implies(X_1,X_15),X_15),X_1)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)),implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))) )],[refute_0_421,refute_0_424]) ).
cnf(refute_0_426,plain,
( implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) != implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))
| implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) != implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))
| implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)),implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))) ),[0],$fot(implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)))]]) ).
cnf(refute_0_427,plain,
( implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)) != implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))
| implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)),implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1))) )],[refute_0_421,refute_0_426]) ).
cnf(refute_0_428,plain,
implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_15,X_1)),implies(X_15,X_1)),implies(X_15,X_1)),implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))) )],[refute_0_425,refute_0_427]) ).
cnf(refute_0_429,plain,
implies(implies(X,implies(implies(X,X_26),X_26)),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(X,X_26),X_26)))]]) ).
cnf(refute_0_430,plain,
implies(X,implies(implies(X,X_26),X_26)) = truth,
inference(subst,[],[refute_0_387:[bind(X_17,$fot(X)),bind(X_18,$fot(X_26))]]) ).
cnf(refute_0_431,plain,
( implies(X,implies(implies(X,X_26),X_26)) != truth
| implies(implies(X,implies(implies(X,X_26),X_26)),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X,X_26),X_26)),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_432,plain,
( implies(implies(X,implies(implies(X,X_26),X_26)),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,X_26),X_26)),truth) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X,X_26),X_26)),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))),truth) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) = implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))))]]) ).
cnf(refute_0_435,plain,
( implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) != implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))
| implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z)))]]) ).
cnf(refute_0_436,plain,
( implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))),implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_26),X_26),Z),implies(X,Z))),truth) )],[refute_0_433,refute_0_436]) ).
cnf(refute_0_438,plain,
implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) = truth,
inference(subst,[],[refute_0_437:[bind(X,$fot(X_15)),bind(Z,$fot(X_1)),bind(X_26,$fot(X_1))]]) ).
cnf(refute_0_439,plain,
( implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) != implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))
| implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) != truth
| truth = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)),implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))) ),[0],$fot(truth)]]) ).
cnf(refute_0_440,plain,
( implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)) != implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))
| truth = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)),truth) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
truth = implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_15,X_1),X_1),X_1),implies(X_15,X_1)),implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))) )],[refute_0_428,refute_0_440]) ).
cnf(refute_0_442,plain,
( truth != implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))
| implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) = truth ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))))]]) ).
cnf(refute_0_443,plain,
implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(implies(implies(X_1,X_15),X_15),X_1),implies(X_15,X_1))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)) = truth,
inference(subst,[],[refute_0_443:[bind(X_1,$fot(X_32)),bind(X_15,$fot(X_31))]]) ).
cnf(refute_0_445,plain,
implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)))]]) ).
cnf(refute_0_446,plain,
( implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)) != truth
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32))
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(X_31,X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_447,plain,
( implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)) != truth
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(X_31,X_32)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(truth,implies(X_31,X_32)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),truth) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(truth,implies(X_31,X_32))
| implies(truth,implies(X_31,X_32)) != implies(X_31,X_32)
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(X_31,X_32) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)))),bind(Y0,$fot(implies(truth,implies(X_31,X_32)))),bind(Z0,$fot(implies(X_31,X_32)))]]) ).
cnf(refute_0_450,plain,
( implies(truth,implies(X_31,X_32)) != implies(X_31,X_32)
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(X_31,X_32) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(truth,implies(X_31,X_32))) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) = implies(X_31,X_32),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_31,X_32)),implies(X_31,X_32)) )],[refute_0_420,refute_0_450]) ).
cnf(refute_0_452,plain,
( implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(X_31,X_32)
| implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(X_31,X_32) = implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))) ),[0],$fot(implies(X_31,X_32))]]) ).
cnf(refute_0_453,plain,
( implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(X_31,X_32) = implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(X_31,X_32)) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) = implies(implies(implies(X_32,X_31),X_31),X_32),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(X_32,X_31),X_31),X_32)))]]) ).
cnf(refute_0_455,plain,
( implies(X_31,X_32) != implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)) != implies(implies(implies(X_32,X_31),X_31),X_32)
| implies(X_31,X_32) = implies(implies(implies(X_32,X_31),X_31),X_32) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)) ),[0],$fot(implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)))]]) ).
cnf(refute_0_456,plain,
( implies(X_31,X_32) != implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(X_31,X_32) = implies(implies(implies(X_32,X_31),X_31),X_32) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32)),implies(implies(implies(X_32,X_31),X_31),X_32)) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
( implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)) != implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))
| implies(X_31,X_32) = implies(implies(implies(X_32,X_31),X_31),X_32) ),
inference(resolve,[$cnf( $equal(implies(X_31,X_32),implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
implies(X_31,X_32) = implies(implies(implies(X_32,X_31),X_31),X_32),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_32,X_31),X_31),X_32),implies(X_31,X_32)),implies(X_31,X_32)),implies(truth,implies(implies(implies(X_32,X_31),X_31),X_32))) )],[refute_0_419,refute_0_457]) ).
cnf(refute_0_459,plain,
( implies(X_31,X_32) != implies(implies(implies(X_32,X_31),X_31),X_32)
| implies(implies(implies(X_32,X_31),X_31),X_32) = implies(X_31,X_32) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(X_31,X_32))),bind(Y0,$fot(implies(implies(implies(X_32,X_31),X_31),X_32)))]]) ).
cnf(refute_0_460,plain,
implies(implies(implies(X_32,X_31),X_31),X_32) = implies(X_31,X_32),
inference(resolve,[$cnf( $equal(implies(X_31,X_32),implies(implies(implies(X_32,X_31),X_31),X_32)) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
implies(implies(implies(X,X_1),X_1),X) = implies(X_1,X),
inference(subst,[],[refute_0_460:[bind(X_31,$fot(X_1)),bind(X_32,$fot(X))]]) ).
cnf(refute_0_462,plain,
( implies(implies(implies(X,X_1),X_1),X) != implies(X_1,X)
| implies(implies(implies(X_1,X),X),X) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(implies(X_1,X),X),X) = implies(X_1,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,X),X),X),implies(implies(implies(X,X_1),X_1),X)) ),[1],$fot(implies(X_1,X))]]) ).
cnf(refute_0_463,plain,
( implies(implies(implies(X_1,X),X),X) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(implies(X_1,X),X),X) = implies(X_1,X) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,X_1),X_1),X),implies(X_1,X)) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
implies(implies(implies(X_1,X),X),X) = implies(X_1,X),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,X),X),X),implies(implies(implies(X,X_1),X_1),X)) )],[refute_0_355,refute_0_463]) ).
cnf(refute_0_465,plain,
implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))),
inference(subst,[],[refute_0_464:[bind(X,$fot(not(not(truth)))),bind(X_1,$fot(implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_466,plain,
implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_412:[bind(Y,$fot(not(not(truth)))),bind(X_26,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_467,plain,
( implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))
| implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))),bind(Y0,$fot(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))))),bind(Z0,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_468,plain,
( implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth)))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) )],[refute_0_465,refute_0_468]) ).
cnf(refute_0_470,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))))]]) ).
cnf(refute_0_471,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))
| implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))) ),[1,1],$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth))))]]) ).
cnf(refute_0_472,plain,
( implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) )],[refute_0_469,refute_0_472]) ).
cnf(refute_0_474,plain,
not(implies(truth,not(not(truth)))) = not(implies(truth,not(not(truth)))),
introduced(tautology,[refl,[$fot(not(implies(truth,not(not(truth)))))]]) ).
cnf(refute_0_475,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| not(implies(truth,not(not(truth)))) != not(implies(truth,not(not(truth))))
| not(implies(truth,not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(truth,not(not(truth)))),not(implies(truth,not(not(truth))))) ),[1,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_476,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| not(implies(truth,not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(not(implies(truth,not(not(truth)))),not(implies(truth,not(not(truth))))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
not(implies(truth,not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_339,refute_0_476]) ).
cnf(refute_0_478,plain,
implies(not(implies(truth,not(not(truth)))),not(truth)) = implies(not(implies(truth,not(not(truth)))),not(truth)),
introduced(tautology,[refl,[$fot(implies(not(implies(truth,not(not(truth)))),not(truth)))]]) ).
cnf(refute_0_479,plain,
( implies(not(implies(truth,not(not(truth)))),not(truth)) != implies(not(implies(truth,not(not(truth)))),not(truth))
| not(implies(truth,not(not(truth)))) != not(not(not(truth)))
| implies(not(implies(truth,not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(not(implies(truth,not(not(truth)))),not(truth))) ),[1,0],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_480,plain,
( not(implies(truth,not(not(truth)))) != not(not(not(truth)))
| implies(not(implies(truth,not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(not(implies(truth,not(not(truth)))),not(truth))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
implies(not(implies(truth,not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(truth,not(not(truth)))),not(not(not(truth)))) )],[refute_0_477,refute_0_480]) ).
cnf(refute_0_482,plain,
implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))))]]) ).
cnf(refute_0_483,plain,
( implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))
| implies(not(implies(truth,not(not(truth)))),not(truth)) != implies(not(not(not(truth))),not(truth))
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))) ),[1,0],$fot(implies(not(not(not(truth))),not(truth)))]]) ).
cnf(refute_0_484,plain,
( implies(not(implies(truth,not(not(truth)))),not(truth)) != implies(not(not(not(truth))),not(truth))
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),
inference(resolve,[$cnf( $equal(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(not(not(not(truth))),not(truth))) )],[refute_0_481,refute_0_484]) ).
cnf(refute_0_486,plain,
( implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))))),bind(Y0,$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))))),bind(Z0,$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))))]]) ).
cnf(refute_0_487,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) )],[refute_0_473,refute_0_487]) ).
cnf(refute_0_489,plain,
( implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))
| implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != truth
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),truth) ),[0],$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_490,plain,
( implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) != truth
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(truth,not(not(truth)))),not(truth)),implies(implies(not(not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth))))),truth) )],[refute_0_407,refute_0_490]) ).
cnf(refute_0_492,plain,
implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_493,plain,
implies(implies(implies(not(not(truth)),not(not(X_43))),X_43),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) = truth,
inference(subst,[],[refute_0_274:[bind(X,$fot(not(not(X_43)))),bind(Y,$fot(not(not(truth)))),bind(X_18,$fot(X_43))]]) ).
cnf(refute_0_494,plain,
implies(implies(not(not(truth)),not(not(X_43))),X_43) = truth,
inference(subst,[],[refute_0_315:[bind(X_21,$fot(X_43))]]) ).
cnf(refute_0_495,plain,
( implies(implies(implies(not(not(truth)),not(not(X_43))),X_43),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) != truth
| implies(implies(not(not(truth)),not(not(X_43))),X_43) != truth
| implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_43))),X_43),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_496,plain,
( implies(implies(implies(not(not(truth)),not(not(X_43))),X_43),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) != truth
| implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_43))),X_43),truth) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_43))),X_43),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)),truth) )],[refute_0_493,refute_0_496]) ).
cnf(refute_0_498,plain,
implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) = implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)))]]) ).
cnf(refute_0_499,plain,
( implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) != implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)
| implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) != truth
| implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)),truth) ),[0],$fot(implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43))]]) ).
cnf(refute_0_500,plain,
( implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) != truth
| implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)),implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(X_43))),not(not(not(truth)))),X_43)),truth) )],[refute_0_497,refute_0_500]) ).
cnf(refute_0_502,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(truth)) = truth,
inference(subst,[],[refute_0_501:[bind(X_43,$fot(not(truth)))]]) ).
cnf(refute_0_503,plain,
implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(not(truth))))),bind(Y,$fot(implies(not(not(not(not(truth)))),not(not(not(truth))))))]]) ).
cnf(refute_0_504,plain,
implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) = truth,
inference(subst,[],[refute_0_281:[bind(X_42,$fot(not(not(truth)))),bind(X_43,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_505,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) = truth,
inference(subst,[],[refute_0_281:[bind(X_42,$fot(not(truth))),bind(X_43,$fot(not(not(truth))))]]) ).
cnf(refute_0_506,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_47:[bind(X_4,$fot(not(truth)))]]) ).
cnf(refute_0_507,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_508,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) != truth
| implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(truth)),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))),truth) )],[refute_0_505,refute_0_508]) ).
cnf(refute_0_510,plain,
implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) = implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_511,plain,
( implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) != implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))
| implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))),truth) ),[0],$fot(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_512,plain,
( implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))),implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth)))),truth) )],[refute_0_509,refute_0_512]) ).
cnf(refute_0_514,plain,
( implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != truth
| implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_515,plain,
( implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) != truth
| implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),truth) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))),truth) )],[refute_0_504,refute_0_515]) ).
cnf(refute_0_517,plain,
implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) = implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))))]]) ).
cnf(refute_0_518,plain,
( implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) != implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))
| implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) != truth
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))),truth) ),[0],$fot(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))))]]) ).
cnf(refute_0_519,plain,
( implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) != truth
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))),implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))),truth) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_522,plain,
( implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),truth) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(truth,not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_503,refute_0_522]) ).
cnf(refute_0_524,plain,
implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = implies(not(not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[refute_0_464:[bind(X,$fot(not(not(not(truth))))),bind(X_1,$fot(not(not(not(not(truth))))))]]) ).
cnf(refute_0_525,plain,
( implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != implies(not(not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(not(not(not(not(truth)))),not(not(not(truth)))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))))),bind(Y0,$fot(implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))))),bind(Z0,$fot(implies(not(not(not(not(truth)))),not(not(not(truth))))))]]) ).
cnf(refute_0_526,plain,
( implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != implies(not(not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(not(not(not(not(truth)))),not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_503,refute_0_525]) ).
cnf(refute_0_527,plain,
implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) = implies(not(not(not(not(truth)))),not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_524,refute_0_526]) ).
cnf(refute_0_528,plain,
( implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(not(not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(truth,not(not(not(truth))))
| implies(not(not(not(not(truth)))),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(truth,not(not(not(truth))))) ),[0],$fot(implies(not(not(not(not(truth)))),not(not(not(truth)))))]]) ).
cnf(refute_0_529,plain,
( implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(truth,not(not(not(truth))))
| implies(not(not(not(not(truth)))),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_531,plain,
( implies(not(not(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(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) ),[0],$fot(implies(truth,not(not(not(truth)))))]]) ).
cnf(refute_0_532,plain,
( implies(not(not(not(not(truth)))),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(not(not(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
( implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))) != implies(truth,not(not(not(truth))))
| implies(not(not(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(truth,not(not(not(truth))))) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
implies(not(not(not(not(truth)))),not(not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(not(not(not(not(truth)))),not(not(not(truth))))),implies(truth,not(not(not(truth))))) )],[refute_0_523,refute_0_533]) ).
cnf(refute_0_535,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(truth)) != truth
| implies(not(not(not(not(truth)))),not(not(not(truth)))) != not(not(not(truth)))
| implies(not(not(not(truth))),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(truth)),truth) ),[0,0],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_536,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(truth)) != truth
| implies(not(not(not(truth))),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(truth)),truth) )],[refute_0_502,refute_0_536]) ).
cnf(refute_0_538,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_539,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))
| implies(not(not(not(truth))),not(truth)) != truth
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_540,plain,
( implies(not(not(not(truth))),not(truth)) != truth
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth))))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(truth)),truth) )],[refute_0_537,refute_0_540]) ).
cnf(refute_0_542,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth))))
| implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))))),bind(Y0,$fot(implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))))),bind(Z0,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_543,plain,
( implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth))))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = implies(implies(not(not(truth)),not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) )],[refute_0_492,refute_0_543]) ).
cnf(refute_0_545,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != implies(implies(not(not(truth)),not(truth)),not(not(truth)))
| implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != truth
| implies(implies(not(not(truth)),not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),truth) ),[0],$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth))))]]) ).
cnf(refute_0_546,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != truth
| implies(implies(not(not(truth)),not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
implies(implies(not(not(truth)),not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),truth) )],[refute_0_491,refute_0_546]) ).
cnf(refute_0_548,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_549,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))
| implies(implies(not(not(truth)),not(truth)),not(not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_550,plain,
( implies(implies(not(not(truth)),not(truth)),not(not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(not(truth))),truth) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_553,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_339,refute_0_553]) ).
cnf(refute_0_555,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_556,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) )],[refute_0_338,refute_0_556]) ).
cnf(refute_0_558,plain,
implies(not(not(truth)),not(not(X_43))) = implies(not(not(truth)),not(not(X_43))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_43))))]]) ).
cnf(refute_0_559,plain,
( implies(not(not(truth)),not(not(X_43))) != implies(not(not(truth)),not(not(X_43)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_43))) = implies(truth,not(not(X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_43))),implies(not(not(truth)),not(not(X_43)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_560,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_43))) = implies(truth,not(not(X_43))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_43))),implies(not(not(truth)),not(not(X_43)))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
implies(not(not(truth)),not(not(X_43))) = implies(truth,not(not(X_43))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
( implies(not(not(truth)),not(not(X_43))) != implies(truth,not(not(X_43)))
| implies(truth,not(not(X_43))) != not(not(X_43))
| implies(not(not(truth)),not(not(X_43))) = not(not(X_43)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(not(not(truth)),not(not(X_43))))),bind(Y0,$fot(implies(truth,not(not(X_43))))),bind(Z0,$fot(not(not(X_43))))]]) ).
cnf(refute_0_563,plain,
( implies(truth,not(not(X_43))) != not(not(X_43))
| implies(not(not(truth)),not(not(X_43))) = not(not(X_43)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_43))),implies(truth,not(not(X_43)))) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
implies(not(not(truth)),not(not(X_43))) = not(not(X_43)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_43))),not(not(X_43))) )],[refute_0_333,refute_0_563]) ).
cnf(refute_0_565,plain,
not(implies(not(not(truth)),not(not(X_43)))) = not(implies(not(not(truth)),not(not(X_43)))),
introduced(tautology,[refl,[$fot(not(implies(not(not(truth)),not(not(X_43)))))]]) ).
cnf(refute_0_566,plain,
( implies(not(not(truth)),not(not(X_43))) != not(not(X_43))
| not(implies(not(not(truth)),not(not(X_43)))) != not(implies(not(not(truth)),not(not(X_43))))
| not(implies(not(not(truth)),not(not(X_43)))) = not(not(not(X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(truth)),not(not(X_43)))),not(implies(not(not(truth)),not(not(X_43))))) ),[1,0],$fot(not(not(X_43)))]]) ).
cnf(refute_0_567,plain,
( implies(not(not(truth)),not(not(X_43))) != not(not(X_43))
| not(implies(not(not(truth)),not(not(X_43)))) = not(not(not(X_43))) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(X_43)))),not(implies(not(not(truth)),not(not(X_43))))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
not(implies(not(not(truth)),not(not(X_43)))) = not(not(not(X_43))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_43))),not(not(X_43))) )],[refute_0_564,refute_0_567]) ).
cnf(refute_0_569,plain,
not(not(implies(not(not(truth)),not(not(X_43))))) = not(not(implies(not(not(truth)),not(not(X_43))))),
introduced(tautology,[refl,[$fot(not(not(implies(not(not(truth)),not(not(X_43))))))]]) ).
cnf(refute_0_570,plain,
( not(implies(not(not(truth)),not(not(X_43)))) != not(not(not(X_43)))
| not(not(implies(not(not(truth)),not(not(X_43))))) != not(not(implies(not(not(truth)),not(not(X_43)))))
| not(not(implies(not(not(truth)),not(not(X_43))))) = not(not(not(not(X_43)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(not(not(truth)),not(not(X_43))))),not(not(implies(not(not(truth)),not(not(X_43)))))) ),[1,0],$fot(not(not(not(X_43))))]]) ).
cnf(refute_0_571,plain,
( not(implies(not(not(truth)),not(not(X_43)))) != not(not(not(X_43)))
| not(not(implies(not(not(truth)),not(not(X_43))))) = not(not(not(not(X_43)))) ),
inference(resolve,[$cnf( $equal(not(not(implies(not(not(truth)),not(not(X_43))))),not(not(implies(not(not(truth)),not(not(X_43)))))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
not(not(implies(not(not(truth)),not(not(X_43))))) = not(not(not(not(X_43)))),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(X_43)))),not(not(not(X_43)))) )],[refute_0_568,refute_0_571]) ).
cnf(refute_0_573,plain,
implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))),
introduced(tautology,[refl,[$fot(implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))))]]) ).
cnf(refute_0_574,plain,
( implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(truth,not(not(implies(not(not(truth)),not(not(X_43))))))
| not(not(implies(not(not(truth)),not(not(X_43))))) != not(not(not(not(X_43))))
| implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))),implies(truth,not(not(implies(not(not(truth)),not(not(X_43))))))) ),[1,1],$fot(not(not(not(not(X_43)))))]]) ).
cnf(refute_0_575,plain,
( not(not(implies(not(not(truth)),not(not(X_43))))) != not(not(not(not(X_43))))
| implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))),implies(truth,not(not(implies(not(not(truth)),not(not(X_43))))))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))),
inference(resolve,[$cnf( $equal(not(not(implies(not(not(truth)),not(not(X_43))))),not(not(not(not(X_43))))) )],[refute_0_572,refute_0_575]) ).
cnf(refute_0_577,plain,
implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))))]]) ).
cnf(refute_0_578,plain,
( implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43))))))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43))))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_579,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43))))))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_557,refute_0_579]) ).
cnf(refute_0_581,plain,
( implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(truth,not(not(implies(not(not(truth)),not(not(X_43))))))
| implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(truth,not(not(not(not(X_43)))))
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))))),bind(Y0,$fot(implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))))),bind(Z0,$fot(implies(truth,not(not(not(not(X_43)))))))]]) ).
cnf(refute_0_582,plain,
( implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(truth,not(not(not(not(X_43)))))
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),implies(truth,not(not(implies(not(not(truth)),not(not(X_43))))))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = implies(truth,not(not(not(not(X_43))))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(implies(not(not(truth)),not(not(X_43)))))),implies(truth,not(not(not(not(X_43)))))) )],[refute_0_576,refute_0_582]) ).
cnf(refute_0_584,plain,
( implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) != implies(truth,not(not(not(not(X_43)))))
| implies(truth,not(not(not(not(X_43))))) != not(not(not(not(X_43))))
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = not(not(not(not(X_43)))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))))),bind(Y0,$fot(implies(truth,not(not(not(not(X_43))))))),bind(Z0,$fot(not(not(not(not(X_43))))))]]) ).
cnf(refute_0_585,plain,
( implies(truth,not(not(not(not(X_43))))) != not(not(not(not(X_43))))
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = not(not(not(not(X_43)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),implies(truth,not(not(not(not(X_43)))))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) = not(not(not(not(X_43)))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(not(X_43))))),not(not(not(not(X_43))))) )],[refute_0_332,refute_0_585]) ).
cnf(refute_0_587,plain,
implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43))]]) ).
cnf(refute_0_588,plain,
( implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) != implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)
| implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) != not(not(not(not(X_43))))
| implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = implies(not(not(not(not(X_43)))),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) ),[1,0],$fot(not(not(not(not(X_43)))))]]) ).
cnf(refute_0_589,plain,
( implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))) != not(not(not(not(X_43))))
| implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = implies(not(not(not(not(X_43)))),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43)) )],[refute_0_587,refute_0_588]) ).
cnf(refute_0_590,plain,
implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) = implies(not(not(not(not(X_43)))),X_43),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),not(not(not(not(X_43))))) )],[refute_0_586,refute_0_589]) ).
cnf(refute_0_591,plain,
( implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) != implies(not(not(not(not(X_43)))),X_43)
| implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) != truth
| implies(not(not(not(not(X_43)))),X_43) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),truth) ),[0],$fot(implies(not(not(not(not(X_43)))),X_43))]]) ).
cnf(refute_0_592,plain,
( implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43) != truth
| implies(not(not(not(not(X_43)))),X_43) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),implies(not(not(not(not(X_43)))),X_43)) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
implies(not(not(not(not(X_43)))),X_43) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(implies(not(not(truth)),not(not(X_43)))))),X_43),truth) )],[refute_0_331,refute_0_592]) ).
cnf(refute_0_594,plain,
implies(not(not(not(not(X_42)))),X_42) = truth,
inference(subst,[],[refute_0_593:[bind(X_43,$fot(X_42))]]) ).
cnf(refute_0_595,plain,
( implies(implies(implies(not(not(not(not(X_42)))),X_42),X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != truth
| implies(not(not(not(not(X_42)))),X_42) != truth
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(not(not(X_42)))),X_42),X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_596,plain,
( implies(implies(implies(not(not(not(not(X_42)))),X_42),X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != truth
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(X_42)))),X_42),truth) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(not(not(X_42)))),X_42),X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),truth) )],[refute_0_282,refute_0_596]) ).
cnf(refute_0_598,plain,
implies(truth,not(not(not(not(X_42))))) = not(not(not(not(X_42)))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(not(X_42))))))]]) ).
cnf(refute_0_599,plain,
implies(not(not(not(not(not(X_42))))),not(X_42)) = truth,
inference(subst,[],[refute_0_593:[bind(X_43,$fot(not(X_42)))]]) ).
cnf(refute_0_600,plain,
implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))]]) ).
cnf(refute_0_601,plain,
( implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) != implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))
| implies(not(not(not(not(not(X_42))))),not(X_42)) != truth
| implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = implies(truth,not(not(not(not(X_42))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_602,plain,
( implies(not(not(not(not(not(X_42))))),not(X_42)) != truth
| implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = implies(truth,not(not(not(not(X_42))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) )],[refute_0_600,refute_0_601]) ).
cnf(refute_0_603,plain,
implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = implies(truth,not(not(not(not(X_42))))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(X_42))))),not(X_42)),truth) )],[refute_0_599,refute_0_602]) ).
cnf(refute_0_604,plain,
( implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) != implies(truth,not(not(not(not(X_42)))))
| implies(truth,not(not(not(not(X_42))))) != not(not(not(not(X_42))))
| implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = not(not(not(not(X_42)))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))),bind(Y0,$fot(implies(truth,not(not(not(not(X_42))))))),bind(Z0,$fot(not(not(not(not(X_42))))))]]) ).
cnf(refute_0_605,plain,
( implies(truth,not(not(not(not(X_42))))) != not(not(not(not(X_42))))
| implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = not(not(not(not(X_42)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))),implies(truth,not(not(not(not(X_42)))))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) = not(not(not(not(X_42)))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(not(X_42))))),not(not(not(not(X_42))))) )],[refute_0_598,refute_0_605]) ).
cnf(refute_0_607,plain,
implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),
introduced(tautology,[refl,[$fot(implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))))]]) ).
cnf(refute_0_608,plain,
( implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))
| implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) != not(not(not(not(X_42))))
| implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))) ),[1,1],$fot(not(not(not(not(X_42)))))]]) ).
cnf(refute_0_609,plain,
( implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))) != not(not(not(not(X_42))))
| implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))) ),
inference(resolve,[$cnf( $equal(implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))),not(not(not(not(X_42))))) )],[refute_0_606,refute_0_609]) ).
cnf(refute_0_611,plain,
implies(truth,X_42) = X_42,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_612,plain,
implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))))]]) ).
cnf(refute_0_613,plain,
( implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))
| implies(truth,X_42) != X_42
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))) ),[1,0],$fot(X_42)]]) ).
cnf(refute_0_614,plain,
( implies(truth,X_42) != X_42
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),
inference(resolve,[$cnf( $equal(implies(truth,X_42),X_42) )],[refute_0_611,refute_0_614]) ).
cnf(refute_0_616,plain,
( implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(X_42,not(not(not(not(X_42)))))
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))))),bind(Y0,$fot(implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))))),bind(Z0,$fot(implies(X_42,not(not(not(not(X_42)))))))]]) ).
cnf(refute_0_617,plain,
( implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(X_42,not(not(not(not(X_42)))))
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42))))))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) = implies(X_42,not(not(not(not(X_42))))),
inference(resolve,[$cnf( $equal(implies(X_42,implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(X_42,not(not(not(not(X_42)))))) )],[refute_0_610,refute_0_617]) ).
cnf(refute_0_619,plain,
( implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != implies(X_42,not(not(not(not(X_42)))))
| implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != truth
| implies(X_42,not(not(not(not(X_42))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),truth) ),[0],$fot(implies(X_42,not(not(not(not(X_42))))))]]) ).
cnf(refute_0_620,plain,
( implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))) != truth
| implies(X_42,not(not(not(not(X_42))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),implies(X_42,not(not(not(not(X_42)))))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
implies(X_42,not(not(not(not(X_42))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_42),implies(implies(not(not(not(not(not(X_42))))),not(X_42)),not(not(not(not(X_42)))))),truth) )],[refute_0_597,refute_0_620]) ).
cnf(refute_0_622,plain,
implies(Y,not(not(not(not(Y))))) = truth,
inference(subst,[],[refute_0_621:[bind(X_42,$fot(Y))]]) ).
cnf(refute_0_623,plain,
( implies(Y,not(not(not(not(Y))))) != truth
| implies(implies(not(not(not(not(Y)))),Y),Y) != implies(implies(Y,not(not(not(not(Y))))),not(not(not(not(Y)))))
| implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,not(not(not(not(Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(implies(Y,not(not(not(not(Y))))),not(not(not(not(Y)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_624,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != implies(implies(Y,not(not(not(not(Y))))),not(not(not(not(Y)))))
| implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,not(not(not(not(Y))))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(not(not(not(Y))))),truth) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,not(not(not(not(Y))))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(implies(Y,not(not(not(not(Y))))),not(not(not(not(Y)))))) )],[refute_0_266,refute_0_624]) ).
cnf(refute_0_626,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_627,plain,
implies(not(not(not(not(Y)))),Y) = truth,
inference(subst,[],[refute_0_593:[bind(X_43,$fot(Y))]]) ).
cnf(refute_0_628,plain,
implies(implies(not(not(not(not(Y)))),Y),Y) = implies(implies(not(not(not(not(Y)))),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(not(Y)))),Y),Y))]]) ).
cnf(refute_0_629,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != implies(implies(not(not(not(not(Y)))),Y),Y)
| implies(not(not(not(not(Y)))),Y) != truth
| implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(implies(not(not(not(not(Y)))),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_630,plain,
( implies(not(not(not(not(Y)))),Y) != truth
| implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(implies(not(not(not(not(Y)))),Y),Y)) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
implies(implies(not(not(not(not(Y)))),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(Y)))),Y),truth) )],[refute_0_627,refute_0_630]) ).
cnf(refute_0_632,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(not(not(Y)))),Y),Y) = Y ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(not(not(Y)))),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_633,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(not(not(Y)))),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(truth,Y)) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
implies(implies(not(not(not(not(Y)))),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_626,refute_0_633]) ).
cnf(refute_0_635,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != Y
| implies(implies(not(not(not(not(Y)))),Y),Y) != implies(truth,not(not(not(not(Y)))))
| Y = implies(truth,not(not(not(not(Y))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(truth,not(not(not(not(Y)))))) ),[0],$fot(Y)]]) ).
cnf(refute_0_636,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != implies(truth,not(not(not(not(Y)))))
| Y = implies(truth,not(not(not(not(Y))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),Y) )],[refute_0_634,refute_0_635]) ).
cnf(refute_0_637,plain,
implies(truth,not(not(not(not(Y))))) = not(not(not(not(Y)))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(not(Y))))))]]) ).
cnf(refute_0_638,plain,
( Y != implies(truth,not(not(not(not(Y)))))
| implies(truth,not(not(not(not(Y))))) != not(not(not(not(Y))))
| Y = not(not(not(not(Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(not(not(Y))))) ),[0],$fot(implies(truth,not(not(not(not(Y))))))]]) ).
cnf(refute_0_639,plain,
( Y != implies(truth,not(not(not(not(Y)))))
| Y = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(not(Y))))),not(not(not(not(Y))))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
( implies(implies(not(not(not(not(Y)))),Y),Y) != implies(truth,not(not(not(not(Y)))))
| Y = not(not(not(not(Y)))) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(not(not(Y)))))) )],[refute_0_636,refute_0_639]) ).
cnf(refute_0_641,plain,
Y = not(not(not(not(Y)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(Y)))),Y),Y),implies(truth,not(not(not(not(Y)))))) )],[refute_0_625,refute_0_640]) ).
cnf(refute_0_642,plain,
X_62 = not(not(not(not(X_62)))),
inference(subst,[],[refute_0_641:[bind(Y,$fot(X_62))]]) ).
cnf(refute_0_643,plain,
( X_62 != not(not(not(not(X_62))))
| not(not(not(not(X_62)))) = X_62 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(X_62)),bind(Y0,$fot(not(not(not(not(X_62))))))]]) ).
cnf(refute_0_644,plain,
not(not(not(not(X_62)))) = X_62,
inference(resolve,[$cnf( $equal(X_62,not(not(not(not(X_62))))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
( implies(implies(not(not(not(not(X_62)))),not(truth)),not(not(not(X_62)))) != truth
| not(not(not(not(X_62)))) != X_62
| implies(implies(X_62,not(truth)),not(not(not(X_62)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(X_62)))),not(truth)),not(not(not(X_62)))),truth) ),[0,0,0],$fot(X_62)]]) ).
cnf(refute_0_646,plain,
( implies(implies(not(not(not(not(X_62)))),not(truth)),not(not(not(X_62)))) != truth
| implies(implies(X_62,not(truth)),not(not(not(X_62)))) = truth ),
inference(resolve,[$cnf( $equal(not(not(not(not(X_62)))),X_62) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
implies(implies(X_62,not(truth)),not(not(not(X_62)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(X_62)))),not(truth)),not(not(not(X_62)))),truth) )],[refute_0_265,refute_0_646]) ).
cnf(refute_0_648,plain,
implies(implies(X_63,not(truth)),not(not(not(X_63)))) = truth,
inference(subst,[],[refute_0_647:[bind(X_62,$fot(X_63))]]) ).
cnf(refute_0_649,plain,
( implies(implies(X_63,not(truth)),not(not(not(X_63)))) != truth
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63))))
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,not(not(not(X_63)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_650,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63))))
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,not(not(not(X_63)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_63,not(truth)),not(not(not(X_63)))),truth) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,not(not(not(X_63)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63))))) )],[refute_0_264,refute_0_650]) ).
cnf(refute_0_652,plain,
implies(truth,implies(X_63,not(truth))) = implies(X_63,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_63,not(truth))))]]) ).
cnf(refute_0_653,plain,
implies(implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = truth,
inference(subst,[],[refute_0_281:[bind(X_42,$fot(not(not(not(X_63))))),bind(X_43,$fot(implies(X_63,not(truth))))]]) ).
cnf(refute_0_654,plain,
( implies(implies(X_63,not(truth)),not(not(not(X_63)))) != truth
| implies(implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != truth
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_655,plain,
( implies(implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != truth
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_63,not(truth)),not(not(not(X_63)))),truth) )],[refute_0_648,refute_0_654]) ).
cnf(refute_0_656,plain,
implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_63,not(truth)),not(not(not(X_63)))),not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),truth) )],[refute_0_653,refute_0_655]) ).
cnf(refute_0_657,plain,
implies(implies(not(not(truth)),not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = truth,
inference(subst,[],[refute_0_346:[bind(X_4,$fot(not(truth)))]]) ).
cnf(refute_0_658,plain,
( implies(implies(not(not(truth)),not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_659,plain,
( implies(implies(not(not(truth)),not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != truth
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_557,refute_0_658]) ).
cnf(refute_0_660,plain,
implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),truth) )],[refute_0_657,refute_0_659]) ).
cnf(refute_0_661,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),not(not(truth))),X_43)) = truth,
inference(subst,[],[refute_0_281:[bind(X_42,$fot(not(truth)))]]) ).
cnf(refute_0_662,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),not(not(truth))),X_43)) != truth
| not(not(truth)) != truth
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),not(not(truth))),X_43)),truth) ),[0,1,0,1],$fot(truth)]]) ).
cnf(refute_0_663,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),not(not(truth))),X_43)) != truth
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_557,refute_0_662]) ).
cnf(refute_0_664,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),not(not(truth))),X_43)),truth) )],[refute_0_661,refute_0_663]) ).
cnf(refute_0_665,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),X_43) = implies(not(truth),X_43),
inference(subst,[],[refute_0_460:[bind(X_31,$fot(not(truth))),bind(X_32,$fot(X_43))]]) ).
cnf(refute_0_666,plain,
implies(truth,X_43) = X_43,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_43))]]) ).
cnf(refute_0_667,plain,
implies(not(X_43),truth) = truth,
inference(subst,[],[refute_0_235:[bind(X_17,$fot(not(X_43)))]]) ).
cnf(refute_0_668,plain,
implies(implies(not(X_43),truth),X_43) = implies(implies(not(X_43),truth),X_43),
introduced(tautology,[refl,[$fot(implies(implies(not(X_43),truth),X_43))]]) ).
cnf(refute_0_669,plain,
( implies(implies(not(X_43),truth),X_43) != implies(implies(not(X_43),truth),X_43)
| implies(not(X_43),truth) != truth
| implies(implies(not(X_43),truth),X_43) = implies(truth,X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_43),truth),X_43),implies(implies(not(X_43),truth),X_43)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_670,plain,
( implies(not(X_43),truth) != truth
| implies(implies(not(X_43),truth),X_43) = implies(truth,X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_43),truth),X_43),implies(implies(not(X_43),truth),X_43)) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
implies(implies(not(X_43),truth),X_43) = implies(truth,X_43),
inference(resolve,[$cnf( $equal(implies(not(X_43),truth),truth) )],[refute_0_667,refute_0_670]) ).
cnf(refute_0_672,plain,
( implies(implies(not(X_43),truth),X_43) != implies(truth,X_43)
| implies(truth,X_43) != X_43
| implies(implies(not(X_43),truth),X_43) = X_43 ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(X_43),truth),X_43))),bind(Y0,$fot(implies(truth,X_43))),bind(Z0,$fot(X_43))]]) ).
cnf(refute_0_673,plain,
( implies(truth,X_43) != X_43
| implies(implies(not(X_43),truth),X_43) = X_43 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_43),truth),X_43),implies(truth,X_43)) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
implies(implies(not(X_43),truth),X_43) = X_43,
inference(resolve,[$cnf( $equal(implies(truth,X_43),X_43) )],[refute_0_666,refute_0_673]) ).
cnf(refute_0_675,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)))]]) ).
cnf(refute_0_676,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) != implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43))
| implies(implies(not(X_43),truth),X_43) != X_43
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(implies(implies(X_43,not(truth)),not(truth)),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43))) ),[1,1],$fot(X_43)]]) ).
cnf(refute_0_677,plain,
( implies(implies(not(X_43),truth),X_43) != X_43
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(implies(implies(X_43,not(truth)),not(truth)),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(implies(implies(X_43,not(truth)),not(truth)),X_43),
inference(resolve,[$cnf( $equal(implies(implies(not(X_43),truth),X_43),X_43) )],[refute_0_674,refute_0_677]) ).
cnf(refute_0_679,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),X_43) != implies(not(truth),X_43)
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) != implies(implies(implies(X_43,not(truth)),not(truth)),X_43)
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(not(truth),X_43) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)))),bind(Y0,$fot(implies(implies(implies(X_43,not(truth)),not(truth)),X_43))),bind(Z0,$fot(implies(not(truth),X_43)))]]) ).
cnf(refute_0_680,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),X_43) != implies(not(truth),X_43)
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(not(truth),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),implies(implies(implies(X_43,not(truth)),not(truth)),X_43)) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) = implies(not(truth),X_43),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),X_43),implies(not(truth),X_43)) )],[refute_0_665,refute_0_680]) ).
cnf(refute_0_682,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) != implies(not(truth),X_43)
| implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) != truth
| implies(not(truth),X_43) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),truth) ),[0],$fot(implies(not(truth),X_43))]]) ).
cnf(refute_0_683,plain,
( implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)) != truth
| implies(not(truth),X_43) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),implies(not(truth),X_43)) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
implies(not(truth),X_43) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_43,not(truth)),not(truth)),implies(implies(not(X_43),truth),X_43)),truth) )],[refute_0_664,refute_0_683]) ).
cnf(refute_0_685,plain,
implies(not(truth),Y) = truth,
inference(subst,[],[refute_0_684:[bind(X_43,$fot(Y))]]) ).
cnf(refute_0_686,plain,
implies(implies(not(truth),Y),Y) = implies(implies(not(truth),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),Y),Y))]]) ).
cnf(refute_0_687,plain,
( implies(implies(not(truth),Y),Y) != implies(implies(not(truth),Y),Y)
| implies(not(truth),Y) != truth
| implies(implies(not(truth),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(not(truth),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_688,plain,
( implies(not(truth),Y) != truth
| implies(implies(not(truth),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(not(truth),Y),Y)) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
implies(implies(not(truth),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(truth),Y),truth) )],[refute_0_685,refute_0_688]) ).
cnf(refute_0_690,plain,
( implies(implies(not(truth),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(truth),Y),Y) = Y ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(truth),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_691,plain,
( implies(truth,Y) != Y
| implies(implies(not(truth),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(truth,Y)) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
implies(implies(not(truth),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_626,refute_0_691]) ).
cnf(refute_0_693,plain,
implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)),
introduced(tautology,[refl,[$fot(implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)))]]) ).
cnf(refute_0_694,plain,
( implies(implies(not(truth),Y),Y) != Y
| implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) != implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y))
| implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)),implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y))) ),[1,1],$fot(Y)]]) ).
cnf(refute_0_695,plain,
( implies(implies(not(truth),Y),Y) != Y
| implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y) ),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)),implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y))) )],[refute_0_693,refute_0_694]) ).
cnf(refute_0_696,plain,
implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),Y) )],[refute_0_692,refute_0_695]) ).
cnf(refute_0_697,plain,
implies(truth,not(implies(Y,not(truth)))) = not(implies(Y,not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(implies(Y,not(truth)))))]]) ).
cnf(refute_0_698,plain,
implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)))]]) ).
cnf(refute_0_699,plain,
( implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y))
| implies(truth,not(implies(Y,not(truth)))) != not(implies(Y,not(truth)))
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y))) ),[1,0],$fot(not(implies(Y,not(truth))))]]) ).
cnf(refute_0_700,plain,
( implies(truth,not(implies(Y,not(truth)))) != not(implies(Y,not(truth)))
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(Y,not(truth)))),not(implies(Y,not(truth)))) )],[refute_0_697,refute_0_700]) ).
cnf(refute_0_702,plain,
( implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y))
| implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) != implies(not(implies(Y,not(truth))),Y)
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)))),bind(Y0,$fot(implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)))),bind(Z0,$fot(implies(not(implies(Y,not(truth))),Y)))]]) ).
cnf(refute_0_703,plain,
( implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)) != implies(not(implies(Y,not(truth))),Y)
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) = implies(not(implies(Y,not(truth))),Y),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,not(truth))),implies(implies(not(truth),Y),Y)),implies(not(implies(Y,not(truth))),Y)) )],[refute_0_696,refute_0_703]) ).
cnf(refute_0_705,plain,
( implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != implies(not(implies(Y,not(truth))),Y)
| implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != truth
| implies(not(implies(Y,not(truth))),Y) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),truth) ),[0],$fot(implies(not(implies(Y,not(truth))),Y))]]) ).
cnf(refute_0_706,plain,
( implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)) != truth
| implies(not(implies(Y,not(truth))),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),implies(not(implies(Y,not(truth))),Y)) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
implies(not(implies(Y,not(truth))),Y) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(Y,not(truth)))),implies(implies(not(truth),Y),Y)),truth) )],[refute_0_660,refute_0_706]) ).
cnf(refute_0_708,plain,
implies(not(implies(X_63,not(truth))),X_63) = truth,
inference(subst,[],[refute_0_707:[bind(Y,$fot(X_63))]]) ).
cnf(refute_0_709,plain,
( Y != not(not(not(not(Y))))
| not(not(not(not(Y)))) = Y ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(not(not(Y))))))]]) ).
cnf(refute_0_710,plain,
not(not(not(not(Y)))) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(not(not(Y))))) )],[refute_0_641,refute_0_709]) ).
cnf(refute_0_711,plain,
not(not(not(not(X_63)))) = X_63,
inference(subst,[],[refute_0_710:[bind(Y,$fot(X_63))]]) ).
cnf(refute_0_712,plain,
implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),
introduced(tautology,[refl,[$fot(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))))]]) ).
cnf(refute_0_713,plain,
( implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) != implies(not(implies(X_63,not(truth))),not(not(not(not(X_63)))))
| not(not(not(not(X_63)))) != X_63
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = implies(not(implies(X_63,not(truth))),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(not(implies(X_63,not(truth))),not(not(not(not(X_63)))))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_714,plain,
( not(not(not(not(X_63)))) != X_63
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = implies(not(implies(X_63,not(truth))),X_63) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(not(implies(X_63,not(truth))),not(not(not(not(X_63)))))) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = implies(not(implies(X_63,not(truth))),X_63),
inference(resolve,[$cnf( $equal(not(not(not(not(X_63)))),X_63) )],[refute_0_711,refute_0_714]) ).
cnf(refute_0_716,plain,
( implies(not(implies(X_63,not(truth))),X_63) != truth
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) != implies(not(implies(X_63,not(truth))),X_63)
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = truth ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))))),bind(Y0,$fot(implies(not(implies(X_63,not(truth))),X_63))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_717,plain,
( implies(not(implies(X_63,not(truth))),X_63) != truth
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(not(implies(X_63,not(truth))),X_63)) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(implies(X_63,not(truth))),X_63),truth) )],[refute_0_708,refute_0_717]) ).
cnf(refute_0_719,plain,
implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))]]) ).
cnf(refute_0_720,plain,
( implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) != implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))
| implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) != truth
| implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_721,plain,
( implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))) != truth
| implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) )],[refute_0_719,refute_0_720]) ).
cnf(refute_0_722,plain,
implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))),
inference(resolve,[$cnf( $equal(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),truth) )],[refute_0_718,refute_0_721]) ).
cnf(refute_0_723,plain,
( implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) != implies(truth,implies(X_63,not(truth)))
| implies(truth,implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(X_63,not(truth)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))),bind(Y0,$fot(implies(truth,implies(X_63,not(truth))))),bind(Z0,$fot(implies(X_63,not(truth))))]]) ).
cnf(refute_0_724,plain,
( implies(truth,implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(X_63,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))),implies(truth,implies(X_63,not(truth)))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) = implies(X_63,not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_63,not(truth))),implies(X_63,not(truth))) )],[refute_0_652,refute_0_724]) ).
cnf(refute_0_726,plain,
implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),
introduced(tautology,[refl,[$fot(implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))))]]) ).
cnf(refute_0_727,plain,
( implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))
| implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))) ),[1,1],$fot(implies(X_63,not(truth)))]]) ).
cnf(refute_0_728,plain,
( implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))),implies(X_63,not(truth))) )],[refute_0_725,refute_0_728]) ).
cnf(refute_0_730,plain,
implies(truth,not(not(not(X_63)))) = not(not(not(X_63))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(X_63)))))]]) ).
cnf(refute_0_731,plain,
implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))))]]) ).
cnf(refute_0_732,plain,
( implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))
| implies(truth,not(not(not(X_63)))) != not(not(not(X_63)))
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))) ),[1,0],$fot(not(not(not(X_63))))]]) ).
cnf(refute_0_733,plain,
( implies(truth,not(not(not(X_63)))) != not(not(not(X_63)))
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(X_63)))),not(not(not(X_63)))) )],[refute_0_730,refute_0_733]) ).
cnf(refute_0_735,plain,
( implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))
| implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(not(not(not(X_63))),implies(X_63,not(truth)))
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))))),bind(Y0,$fot(implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))))),bind(Z0,$fot(implies(not(not(not(X_63))),implies(X_63,not(truth)))))]]) ).
cnf(refute_0_736,plain,
( implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(not(not(not(X_63))),implies(X_63,not(truth)))
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth))))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) = implies(not(not(not(X_63))),implies(X_63,not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_63))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(not(not(not(X_63))),implies(X_63,not(truth)))) )],[refute_0_729,refute_0_736]) ).
cnf(refute_0_738,plain,
( implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != implies(not(not(not(X_63))),implies(X_63,not(truth)))
| implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != truth
| implies(not(not(not(X_63))),implies(X_63,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),truth) ),[0],$fot(implies(not(not(not(X_63))),implies(X_63,not(truth))))]]) ).
cnf(refute_0_739,plain,
( implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))) != truth
| implies(not(not(not(X_63))),implies(X_63,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),implies(not(not(not(X_63))),implies(X_63,not(truth)))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
implies(not(not(not(X_63))),implies(X_63,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(not(X_63)))),implies(implies(not(implies(X_63,not(truth))),not(not(not(not(X_63))))),implies(X_63,not(truth)))),truth) )],[refute_0_656,refute_0_739]) ).
cnf(refute_0_741,plain,
implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))))]]) ).
cnf(refute_0_742,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth)))
| implies(not(not(not(X_63))),implies(X_63,not(truth))) != truth
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_743,plain,
( implies(not(not(not(X_63))),implies(X_63,not(truth))) != truth
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth)))) )],[refute_0_741,refute_0_742]) ).
cnf(refute_0_744,plain,
implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(truth,implies(X_63,not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_63))),implies(X_63,not(truth))),truth) )],[refute_0_740,refute_0_743]) ).
cnf(refute_0_745,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(truth,implies(X_63,not(truth)))
| implies(truth,implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(X_63,not(truth)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))))),bind(Y0,$fot(implies(truth,implies(X_63,not(truth))))),bind(Z0,$fot(implies(X_63,not(truth))))]]) ).
cnf(refute_0_746,plain,
( implies(truth,implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(X_63,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(truth,implies(X_63,not(truth)))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) = implies(X_63,not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_63,not(truth))),implies(X_63,not(truth))) )],[refute_0_652,refute_0_746]) ).
cnf(refute_0_748,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(X_63,not(truth))
| implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(truth,not(not(not(X_63))))
| implies(X_63,not(truth)) = implies(truth,not(not(not(X_63)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(truth,not(not(not(X_63))))) ),[0],$fot(implies(X_63,not(truth)))]]) ).
cnf(refute_0_749,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(truth,not(not(not(X_63))))
| implies(X_63,not(truth)) = implies(truth,not(not(not(X_63)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(X_63,not(truth))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
( implies(X_63,not(truth)) != implies(truth,not(not(not(X_63))))
| implies(truth,not(not(not(X_63)))) != not(not(not(X_63)))
| implies(X_63,not(truth)) = not(not(not(X_63))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_63,not(truth)),not(not(not(X_63)))) ),[0],$fot(implies(truth,not(not(not(X_63)))))]]) ).
cnf(refute_0_751,plain,
( implies(X_63,not(truth)) != implies(truth,not(not(not(X_63))))
| implies(X_63,not(truth)) = not(not(not(X_63))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(X_63)))),not(not(not(X_63)))) )],[refute_0_730,refute_0_750]) ).
cnf(refute_0_752,plain,
( implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))) != implies(truth,not(not(not(X_63))))
| implies(X_63,not(truth)) = not(not(not(X_63))) ),
inference(resolve,[$cnf( $equal(implies(X_63,not(truth)),implies(truth,not(not(not(X_63))))) )],[refute_0_749,refute_0_751]) ).
cnf(refute_0_753,plain,
implies(X_63,not(truth)) = not(not(not(X_63))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(X_63))),implies(X_63,not(truth))),implies(X_63,not(truth))),implies(truth,not(not(not(X_63))))) )],[refute_0_651,refute_0_752]) ).
cnf(refute_0_754,plain,
implies(implies(X,not(truth)),not(truth)) = implies(implies(not(truth),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_755,plain,
implies(not(truth),X) = truth,
inference(subst,[],[refute_0_684:[bind(X_43,$fot(X))]]) ).
cnf(refute_0_756,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(not(truth),X) != truth
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_757,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( $equal(implies(not(truth),X),truth) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
implies(implies(X,not(truth)),not(truth)) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) )],[refute_0_754,refute_0_757]) ).
cnf(refute_0_759,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(truth,X) != X
| implies(implies(X,not(truth)),not(truth)) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,not(truth)),not(truth)),X) ),[0],$fot(implies(truth,X))]]) ).
cnf(refute_0_760,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(implies(X,not(truth)),not(truth)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_759]) ).
cnf(refute_0_761,plain,
implies(implies(X,not(truth)),not(truth)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) )],[refute_0_758,refute_0_760]) ).
cnf(refute_0_762,plain,
not(not(not(not(X)))) = X,
inference(subst,[],[refute_0_710:[bind(Y,$fot(X))]]) ).
cnf(refute_0_763,plain,
implies(X,not(truth)) = not(not(not(X))),
inference(subst,[],[refute_0_753:[bind(X_63,$fot(X))]]) ).
cnf(refute_0_764,plain,
not(implies(X,not(truth))) = not(implies(X,not(truth))),
introduced(tautology,[refl,[$fot(not(implies(X,not(truth))))]]) ).
cnf(refute_0_765,plain,
( implies(X,not(truth)) != not(not(not(X)))
| not(implies(X,not(truth))) != not(implies(X,not(truth)))
| not(implies(X,not(truth))) = not(not(not(not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) ),[1,0],$fot(not(not(not(X))))]]) ).
cnf(refute_0_766,plain,
( implies(X,not(truth)) != not(not(not(X)))
| not(implies(X,not(truth))) = not(not(not(not(X)))) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
not(implies(X,not(truth))) = not(not(not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X,not(truth)),not(not(not(X)))) )],[refute_0_763,refute_0_766]) ).
cnf(refute_0_768,plain,
( not(implies(X,not(truth))) != not(not(not(not(X))))
| not(not(not(not(X)))) != X
| not(implies(X,not(truth))) = X ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(not(implies(X,not(truth))))),bind(Y0,$fot(not(not(not(not(X)))))),bind(Z0,$fot(X))]]) ).
cnf(refute_0_769,plain,
( not(not(not(not(X)))) != X
| not(implies(X,not(truth))) = X ),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(not(not(not(X))))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
not(implies(X,not(truth))) = X,
inference(resolve,[$cnf( $equal(not(not(not(not(X)))),X) )],[refute_0_762,refute_0_769]) ).
cnf(refute_0_771,plain,
not(not(implies(X,not(truth)))) = not(not(implies(X,not(truth)))),
introduced(tautology,[refl,[$fot(not(not(implies(X,not(truth)))))]]) ).
cnf(refute_0_772,plain,
( not(implies(X,not(truth))) != X
| not(not(implies(X,not(truth)))) != not(not(implies(X,not(truth))))
| not(not(implies(X,not(truth)))) = not(X) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(implies(X,not(truth)))),not(not(implies(X,not(truth))))) ),[1,0],$fot(X)]]) ).
cnf(refute_0_773,plain,
( not(implies(X,not(truth))) != X
| not(not(implies(X,not(truth)))) = not(X) ),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(truth)))),not(not(implies(X,not(truth))))) )],[refute_0_771,refute_0_772]) ).
cnf(refute_0_774,plain,
not(not(implies(X,not(truth)))) = not(X),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),X) )],[refute_0_770,refute_0_773]) ).
cnf(refute_0_775,plain,
not(not(not(implies(X,not(truth))))) = not(not(not(implies(X,not(truth))))),
introduced(tautology,[refl,[$fot(not(not(not(implies(X,not(truth))))))]]) ).
cnf(refute_0_776,plain,
( not(not(implies(X,not(truth)))) != not(X)
| not(not(not(implies(X,not(truth))))) != not(not(not(implies(X,not(truth)))))
| not(not(not(implies(X,not(truth))))) = not(not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(implies(X,not(truth))))),not(not(not(implies(X,not(truth)))))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_777,plain,
( not(not(implies(X,not(truth)))) != not(X)
| not(not(not(implies(X,not(truth))))) = not(not(X)) ),
inference(resolve,[$cnf( $equal(not(not(not(implies(X,not(truth))))),not(not(not(implies(X,not(truth)))))) )],[refute_0_775,refute_0_776]) ).
cnf(refute_0_778,plain,
not(not(not(implies(X,not(truth))))) = not(not(X)),
inference(resolve,[$cnf( $equal(not(not(implies(X,not(truth)))),not(X)) )],[refute_0_774,refute_0_777]) ).
cnf(refute_0_779,plain,
implies(implies(X,not(truth)),not(truth)) = not(not(not(implies(X,not(truth))))),
inference(subst,[],[refute_0_753:[bind(X_63,$fot(implies(X,not(truth))))]]) ).
cnf(refute_0_780,plain,
( implies(implies(X,not(truth)),not(truth)) != not(not(not(implies(X,not(truth)))))
| not(not(not(implies(X,not(truth))))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(X,not(truth)),not(truth)))),bind(Y0,$fot(not(not(not(implies(X,not(truth))))))),bind(Z0,$fot(not(not(X))))]]) ).
cnf(refute_0_781,plain,
( not(not(not(implies(X,not(truth))))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(not(not(implies(X,not(truth)))))) )],[refute_0_779,refute_0_780]) ).
cnf(refute_0_782,plain,
implies(implies(X,not(truth)),not(truth)) = not(not(X)),
inference(resolve,[$cnf( $equal(not(not(not(implies(X,not(truth))))),not(not(X))) )],[refute_0_778,refute_0_781]) ).
cnf(refute_0_783,plain,
( implies(implies(X,not(truth)),not(truth)) != X
| implies(implies(X,not(truth)),not(truth)) != not(not(X))
| not(not(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),X) ),[0],$fot(not(not(X)))]]) ).
cnf(refute_0_784,plain,
( implies(implies(X,not(truth)),not(truth)) != X
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(not(X))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),X) )],[refute_0_761,refute_0_784]) ).
cnf(refute_0_786,plain,
not(not(not(X_63))) = not(X_63),
inference(subst,[],[refute_0_785:[bind(X,$fot(not(X_63)))]]) ).
cnf(refute_0_787,plain,
( implies(X_63,not(truth)) != not(not(not(X_63)))
| not(not(not(X_63))) != not(X_63)
| implies(X_63,not(truth)) = not(X_63) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_63,not(truth)),not(X_63)) ),[0],$fot(not(not(not(X_63))))]]) ).
cnf(refute_0_788,plain,
( implies(X_63,not(truth)) != not(not(not(X_63)))
| implies(X_63,not(truth)) = not(X_63) ),
inference(resolve,[$cnf( $equal(not(not(not(X_63))),not(X_63)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
implies(X_63,not(truth)) = not(X_63),
inference(resolve,[$cnf( $equal(implies(X_63,not(truth)),not(not(not(X_63)))) )],[refute_0_753,refute_0_788]) ).
cnf(refute_0_790,plain,
implies(X_98,not(truth)) = not(X_98),
inference(subst,[],[refute_0_789:[bind(X_63,$fot(X_98))]]) ).
cnf(refute_0_791,plain,
( implies(X_98,not(truth)) != not(X_98)
| implies(X_99,implies(implies(X_99,not(truth)),implies(X_98,not(truth)))) != truth
| implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),implies(X_98,not(truth)))),truth) ),[0,1,1],$fot(not(X_98))]]) ).
cnf(refute_0_792,plain,
( implies(X_99,implies(implies(X_99,not(truth)),implies(X_98,not(truth)))) != truth
| implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = truth ),
inference(resolve,[$cnf( $equal(implies(X_98,not(truth)),not(X_98)) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = truth,
inference(resolve,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),implies(X_98,not(truth)))),truth) )],[refute_0_263,refute_0_792]) ).
cnf(refute_0_794,plain,
implies(X_99,not(truth)) = not(X_99),
inference(subst,[],[refute_0_789:[bind(X_63,$fot(X_99))]]) ).
cnf(refute_0_795,plain,
implies(implies(X_99,not(truth)),not(X_98)) = implies(implies(X_99,not(truth)),not(X_98)),
introduced(tautology,[refl,[$fot(implies(implies(X_99,not(truth)),not(X_98)))]]) ).
cnf(refute_0_796,plain,
( implies(X_99,not(truth)) != not(X_99)
| implies(implies(X_99,not(truth)),not(X_98)) != implies(implies(X_99,not(truth)),not(X_98))
| implies(implies(X_99,not(truth)),not(X_98)) = implies(not(X_99),not(X_98)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_99,not(truth)),not(X_98)),implies(implies(X_99,not(truth)),not(X_98))) ),[1,0],$fot(not(X_99))]]) ).
cnf(refute_0_797,plain,
( implies(X_99,not(truth)) != not(X_99)
| implies(implies(X_99,not(truth)),not(X_98)) = implies(not(X_99),not(X_98)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_99,not(truth)),not(X_98)),implies(implies(X_99,not(truth)),not(X_98))) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
implies(implies(X_99,not(truth)),not(X_98)) = implies(not(X_99),not(X_98)),
inference(resolve,[$cnf( $equal(implies(X_99,not(truth)),not(X_99)) )],[refute_0_794,refute_0_797]) ).
cnf(refute_0_799,plain,
implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),
introduced(tautology,[refl,[$fot(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))))]]) ).
cnf(refute_0_800,plain,
( implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) != implies(X_99,implies(implies(X_99,not(truth)),not(X_98)))
| implies(implies(X_99,not(truth)),not(X_98)) != implies(not(X_99),not(X_98))
| implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = implies(X_99,implies(not(X_99),not(X_98))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),implies(X_99,implies(implies(X_99,not(truth)),not(X_98)))) ),[1,1],$fot(implies(not(X_99),not(X_98)))]]) ).
cnf(refute_0_801,plain,
( implies(implies(X_99,not(truth)),not(X_98)) != implies(not(X_99),not(X_98))
| implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = implies(X_99,implies(not(X_99),not(X_98))) ),
inference(resolve,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),implies(X_99,implies(implies(X_99,not(truth)),not(X_98)))) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) = implies(X_99,implies(not(X_99),not(X_98))),
inference(resolve,[$cnf( $equal(implies(implies(X_99,not(truth)),not(X_98)),implies(not(X_99),not(X_98))) )],[refute_0_798,refute_0_801]) ).
cnf(refute_0_803,plain,
( implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) != implies(X_99,implies(not(X_99),not(X_98)))
| implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) != truth
| implies(X_99,implies(not(X_99),not(X_98))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),truth) ),[0],$fot(implies(X_99,implies(not(X_99),not(X_98))))]]) ).
cnf(refute_0_804,plain,
( implies(X_99,implies(implies(X_99,not(truth)),not(X_98))) != truth
| implies(X_99,implies(not(X_99),not(X_98))) = truth ),
inference(resolve,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),implies(X_99,implies(not(X_99),not(X_98)))) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
implies(X_99,implies(not(X_99),not(X_98))) = truth,
inference(resolve,[$cnf( $equal(implies(X_99,implies(implies(X_99,not(truth)),not(X_98))),truth) )],[refute_0_793,refute_0_804]) ).
cnf(refute_0_806,plain,
implies(Y,implies(not(Y),not(X_101))) = truth,
inference(subst,[],[refute_0_805:[bind(X_98,$fot(X_101)),bind(X_99,$fot(Y))]]) ).
cnf(refute_0_807,plain,
( implies(Y,implies(not(Y),not(X_101))) != truth
| implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(implies(Y,implies(not(Y),not(X_101))),implies(not(Y),not(X_101)))
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(truth,implies(not(Y),not(X_101))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(implies(Y,implies(not(Y),not(X_101))),implies(not(Y),not(X_101)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_808,plain,
( implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(implies(Y,implies(not(Y),not(X_101))),implies(not(Y),not(X_101)))
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(truth,implies(not(Y),not(X_101))) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(not(Y),not(X_101))),truth) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(truth,implies(not(Y),not(X_101))),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(implies(Y,implies(not(Y),not(X_101))),implies(not(Y),not(X_101)))) )],[refute_0_0,refute_0_808]) ).
cnf(refute_0_810,plain,
implies(implies(implies(X_101,Y),Y),Y) = implies(X_101,Y),
inference(subst,[],[refute_0_464:[bind(X,$fot(Y)),bind(X_1,$fot(X_101))]]) ).
cnf(refute_0_811,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(not(X_41),not(X_42)),X_43))),bind(Y,$fot(implies(implies(X_42,X_41),X_43)))]]) ).
cnf(refute_0_812,plain,
implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)) = truth,
inference(subst,[],[refute_0_274:[bind(X,$fot(X_41)),bind(Y,$fot(X_42)),bind(X_18,$fot(X_43))]]) ).
cnf(refute_0_813,plain,
( implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)) != truth
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43))
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(not(X_41),not(X_42)),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_814,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43))
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(not(X_41),not(X_42)),X_43)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),truth) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(not(X_41),not(X_42)),X_43)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43))) )],[refute_0_811,refute_0_814]) ).
cnf(refute_0_816,plain,
implies(truth,implies(implies(not(X_41),not(X_42)),X_43)) = implies(implies(not(X_41),not(X_42)),X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(X_41),not(X_42)),X_43)))]]) ).
cnf(refute_0_817,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(truth,implies(implies(not(X_41),not(X_42)),X_43))
| implies(truth,implies(implies(not(X_41),not(X_42)),X_43)) != implies(implies(not(X_41),not(X_42)),X_43)
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(not(X_41),not(X_42)),X_43) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(not(X_41),not(X_42)),X_43)) ),[0],$fot(implies(truth,implies(implies(not(X_41),not(X_42)),X_43)))]]) ).
cnf(refute_0_818,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(truth,implies(implies(not(X_41),not(X_42)),X_43))
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(not(X_41),not(X_42)),X_43) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X_41),not(X_42)),X_43)),implies(implies(not(X_41),not(X_42)),X_43)) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(not(X_41),not(X_42)),X_43),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(truth,implies(implies(not(X_41),not(X_42)),X_43))) )],[refute_0_815,refute_0_818]) ).
cnf(refute_0_820,plain,
implies(truth,implies(implies(X_42,X_41),X_43)) = implies(implies(X_42,X_41),X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_42,X_41),X_43)))]]) ).
cnf(refute_0_821,plain,
implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(X_16,X_17))),bind(Y,$fot(implies(implies(X_17,X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_822,plain,
( implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))) != truth
| implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) != truth
| implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_823,plain,
( implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) != truth
| implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),truth) )],[refute_0_2,refute_0_822]) ).
cnf(refute_0_824,plain,
implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_16,X_17),implies(implies(X_17,X_18),implies(X_16,X_18))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))),truth) )],[refute_0_821,refute_0_823]) ).
cnf(refute_0_825,plain,
implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) = implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))))]]) ).
cnf(refute_0_826,plain,
( implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) != implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))
| implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) != truth
| implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))),truth) ),[0],$fot(implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z)))]]) ).
cnf(refute_0_827,plain,
( implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) != truth
| implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))),implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_17,X_18),implies(X_16,X_18)),Z),implies(implies(X_16,X_17),Z))),truth) )],[refute_0_824,refute_0_827]) ).
cnf(refute_0_829,plain,
implies(implies(implies(implies(X_80,not(truth)),implies(X_79,not(truth))),X_78),implies(implies(X_79,X_80),X_78)) = truth,
inference(subst,[],[refute_0_828:[bind(Z,$fot(X_78)),bind(X_16,$fot(X_79)),bind(X_17,$fot(X_80)),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_830,plain,
implies(X_79,not(truth)) = not(X_79),
inference(subst,[],[refute_0_789:[bind(X_63,$fot(X_79))]]) ).
cnf(refute_0_831,plain,
( implies(X_79,not(truth)) != not(X_79)
| implies(implies(implies(implies(X_80,not(truth)),implies(X_79,not(truth))),X_78),implies(implies(X_79,X_80),X_78)) != truth
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),implies(X_79,not(truth))),X_78),implies(implies(X_79,X_80),X_78)),truth) ),[0,0,0,1],$fot(not(X_79))]]) ).
cnf(refute_0_832,plain,
( implies(implies(implies(implies(X_80,not(truth)),implies(X_79,not(truth))),X_78),implies(implies(X_79,X_80),X_78)) != truth
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_79,not(truth)),not(X_79)) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),implies(X_79,not(truth))),X_78),implies(implies(X_79,X_80),X_78)),truth) )],[refute_0_829,refute_0_832]) ).
cnf(refute_0_834,plain,
implies(X_80,not(truth)) = not(X_80),
inference(subst,[],[refute_0_789:[bind(X_63,$fot(X_80))]]) ).
cnf(refute_0_835,plain,
implies(implies(X_80,not(truth)),not(X_79)) = implies(implies(X_80,not(truth)),not(X_79)),
introduced(tautology,[refl,[$fot(implies(implies(X_80,not(truth)),not(X_79)))]]) ).
cnf(refute_0_836,plain,
( implies(X_80,not(truth)) != not(X_80)
| implies(implies(X_80,not(truth)),not(X_79)) != implies(implies(X_80,not(truth)),not(X_79))
| implies(implies(X_80,not(truth)),not(X_79)) = implies(not(X_80),not(X_79)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_80,not(truth)),not(X_79)),implies(implies(X_80,not(truth)),not(X_79))) ),[1,0],$fot(not(X_80))]]) ).
cnf(refute_0_837,plain,
( implies(X_80,not(truth)) != not(X_80)
| implies(implies(X_80,not(truth)),not(X_79)) = implies(not(X_80),not(X_79)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_80,not(truth)),not(X_79)),implies(implies(X_80,not(truth)),not(X_79))) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
implies(implies(X_80,not(truth)),not(X_79)) = implies(not(X_80),not(X_79)),
inference(resolve,[$cnf( $equal(implies(X_80,not(truth)),not(X_80)) )],[refute_0_834,refute_0_837]) ).
cnf(refute_0_839,plain,
implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) = implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78))]]) ).
cnf(refute_0_840,plain,
( implies(implies(X_80,not(truth)),not(X_79)) != implies(not(X_80),not(X_79))
| implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) != implies(implies(implies(X_80,not(truth)),not(X_79)),X_78)
| implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) = implies(implies(not(X_80),not(X_79)),X_78) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(implies(X_80,not(truth)),not(X_79)),X_78)) ),[1,0],$fot(implies(not(X_80),not(X_79)))]]) ).
cnf(refute_0_841,plain,
( implies(implies(X_80,not(truth)),not(X_79)) != implies(not(X_80),not(X_79))
| implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) = implies(implies(not(X_80),not(X_79)),X_78) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(implies(X_80,not(truth)),not(X_79)),X_78)) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) = implies(implies(not(X_80),not(X_79)),X_78),
inference(resolve,[$cnf( $equal(implies(implies(X_80,not(truth)),not(X_79)),implies(not(X_80),not(X_79))) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)))]]) ).
cnf(refute_0_844,plain,
( implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) != implies(implies(not(X_80),not(X_79)),X_78)
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) != implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78))
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78))) ),[1,0],$fot(implies(implies(not(X_80),not(X_79)),X_78))]]) ).
cnf(refute_0_845,plain,
( implies(implies(implies(X_80,not(truth)),not(X_79)),X_78) != implies(implies(not(X_80),not(X_79)),X_78)
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(not(X_80),not(X_79)),X_78)) )],[refute_0_842,refute_0_845]) ).
cnf(refute_0_847,plain,
( implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) != implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78))
| implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) != truth
| implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),truth) ),[0],$fot(implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)))]]) ).
cnf(refute_0_848,plain,
( implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) != truth
| implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
implies(implies(implies(not(X_80),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_80,not(truth)),not(X_79)),X_78),implies(implies(X_79,X_80),X_78)),truth) )],[refute_0_833,refute_0_848]) ).
cnf(refute_0_850,plain,
implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)) = truth,
inference(subst,[],[refute_0_849:[bind(X_78,$fot(X_43)),bind(X_79,$fot(X_42)),bind(X_80,$fot(X_41))]]) ).
cnf(refute_0_851,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)))]]) ).
cnf(refute_0_852,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43))
| implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)) != truth
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(X_42,X_41),X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_853,plain,
( implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)) != truth
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(X_42,X_41),X_43)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43))) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(truth,implies(implies(X_42,X_41),X_43)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),truth) )],[refute_0_850,refute_0_853]) ).
cnf(refute_0_855,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(truth,implies(implies(X_42,X_41),X_43))
| implies(truth,implies(implies(X_42,X_41),X_43)) != implies(implies(X_42,X_41),X_43)
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(X_42,X_41),X_43) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)))),bind(Y0,$fot(implies(truth,implies(implies(X_42,X_41),X_43)))),bind(Z0,$fot(implies(implies(X_42,X_41),X_43)))]]) ).
cnf(refute_0_856,plain,
( implies(truth,implies(implies(X_42,X_41),X_43)) != implies(implies(X_42,X_41),X_43)
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(X_42,X_41),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(truth,implies(implies(X_42,X_41),X_43))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) = implies(implies(X_42,X_41),X_43),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) )],[refute_0_820,refute_0_856]) ).
cnf(refute_0_858,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(X_42,X_41),X_43)
| implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(not(X_41),not(X_42)),X_43)
| implies(implies(X_42,X_41),X_43) = implies(implies(not(X_41),not(X_42)),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(not(X_41),not(X_42)),X_43)) ),[0],$fot(implies(implies(X_42,X_41),X_43))]]) ).
cnf(refute_0_859,plain,
( implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) != implies(implies(not(X_41),not(X_42)),X_43)
| implies(implies(X_42,X_41),X_43) = implies(implies(not(X_41),not(X_42)),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)) )],[refute_0_857,refute_0_858]) ).
cnf(refute_0_860,plain,
implies(implies(X_42,X_41),X_43) = implies(implies(not(X_41),not(X_42)),X_43),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_41),not(X_42)),X_43),implies(implies(X_42,X_41),X_43)),implies(implies(X_42,X_41),X_43)),implies(implies(not(X_41),not(X_42)),X_43)) )],[refute_0_819,refute_0_859]) ).
cnf(refute_0_861,plain,
( implies(implies(X_42,X_41),X_43) != implies(implies(not(X_41),not(X_42)),X_43)
| implies(implies(not(X_41),not(X_42)),X_43) = implies(implies(X_42,X_41),X_43) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(implies(X_42,X_41),X_43))),bind(Y0,$fot(implies(implies(not(X_41),not(X_42)),X_43)))]]) ).
cnf(refute_0_862,plain,
implies(implies(not(X_41),not(X_42)),X_43) = implies(implies(X_42,X_41),X_43),
inference(resolve,[$cnf( $equal(implies(implies(X_42,X_41),X_43),implies(implies(not(X_41),not(X_42)),X_43)) )],[refute_0_860,refute_0_861]) ).
cnf(refute_0_863,plain,
implies(implies(not(Y),not(X_101)),Y) = implies(implies(X_101,Y),Y),
inference(subst,[],[refute_0_862:[bind(X_41,$fot(Y)),bind(X_42,$fot(X_101)),bind(X_43,$fot(Y))]]) ).
cnf(refute_0_864,plain,
implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(implies(implies(not(Y),not(X_101)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(Y),not(X_101)),Y),Y))]]) ).
cnf(refute_0_865,plain,
( implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(implies(implies(not(Y),not(X_101)),Y),Y)
| implies(implies(not(Y),not(X_101)),Y) != implies(implies(X_101,Y),Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(implies(implies(X_101,Y),Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(implies(implies(not(Y),not(X_101)),Y),Y)) ),[1,0],$fot(implies(implies(X_101,Y),Y))]]) ).
cnf(refute_0_866,plain,
( implies(implies(not(Y),not(X_101)),Y) != implies(implies(X_101,Y),Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(implies(implies(X_101,Y),Y),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(implies(implies(not(Y),not(X_101)),Y),Y)) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(implies(implies(X_101,Y),Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X_101)),Y),implies(implies(X_101,Y),Y)) )],[refute_0_863,refute_0_866]) ).
cnf(refute_0_868,plain,
( implies(implies(implies(X_101,Y),Y),Y) != implies(X_101,Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(implies(implies(X_101,Y),Y),Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(X_101,Y) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(implies(implies(implies(not(Y),not(X_101)),Y),Y))),bind(Y0,$fot(implies(implies(implies(X_101,Y),Y),Y))),bind(Z0,$fot(implies(X_101,Y)))]]) ).
cnf(refute_0_869,plain,
( implies(implies(implies(X_101,Y),Y),Y) != implies(X_101,Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(X_101,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(implies(implies(X_101,Y),Y),Y)) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
implies(implies(implies(not(Y),not(X_101)),Y),Y) = implies(X_101,Y),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_101,Y),Y),Y),implies(X_101,Y)) )],[refute_0_810,refute_0_869]) ).
cnf(refute_0_871,plain,
( implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(X_101,Y)
| implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(truth,implies(not(Y),not(X_101)))
| implies(X_101,Y) = implies(truth,implies(not(Y),not(X_101))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(truth,implies(not(Y),not(X_101)))) ),[0],$fot(implies(X_101,Y))]]) ).
cnf(refute_0_872,plain,
( implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(truth,implies(not(Y),not(X_101)))
| implies(X_101,Y) = implies(truth,implies(not(Y),not(X_101))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(X_101,Y)) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
implies(truth,implies(not(Y),not(X_101))) = implies(not(Y),not(X_101)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(Y),not(X_101))))]]) ).
cnf(refute_0_874,plain,
( implies(X_101,Y) != implies(truth,implies(not(Y),not(X_101)))
| implies(truth,implies(not(Y),not(X_101))) != implies(not(Y),not(X_101))
| implies(X_101,Y) = implies(not(Y),not(X_101)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_101,Y),implies(not(Y),not(X_101))) ),[0],$fot(implies(truth,implies(not(Y),not(X_101))))]]) ).
cnf(refute_0_875,plain,
( implies(X_101,Y) != implies(truth,implies(not(Y),not(X_101)))
| implies(X_101,Y) = implies(not(Y),not(X_101)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(Y),not(X_101))),implies(not(Y),not(X_101))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
( implies(implies(implies(not(Y),not(X_101)),Y),Y) != implies(truth,implies(not(Y),not(X_101)))
| implies(X_101,Y) = implies(not(Y),not(X_101)) ),
inference(resolve,[$cnf( $equal(implies(X_101,Y),implies(truth,implies(not(Y),not(X_101)))) )],[refute_0_872,refute_0_875]) ).
cnf(refute_0_877,plain,
implies(X_101,Y) = implies(not(Y),not(X_101)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(Y),not(X_101)),Y),Y),implies(truth,implies(not(Y),not(X_101)))) )],[refute_0_809,refute_0_876]) ).
cnf(refute_0_878,plain,
( implies(X_101,Y) != implies(not(Y),not(X_101))
| implies(not(Y),not(X_101)) = implies(X_101,Y) ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(implies(X_101,Y))),bind(Y0,$fot(implies(not(Y),not(X_101))))]]) ).
cnf(refute_0_879,plain,
implies(not(Y),not(X_101)) = implies(X_101,Y),
inference(resolve,[$cnf( $equal(implies(X_101,Y),implies(not(Y),not(X_101))) )],[refute_0_877,refute_0_878]) ).
cnf(refute_0_880,plain,
implies(not(x),not(y)) = implies(y,x),
inference(subst,[],[refute_0_879:[bind(Y,$fot(x)),bind(X_101,$fot(y))]]) ).
cnf(refute_0_881,plain,
( implies(not(x),not(y)) != implies(y,x)
| implies(y,x) != implies(y,x)
| implies(not(x),not(y)) = implies(y,x) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(x),not(y)),implies(y,x)) ),[0],$fot(implies(y,x))]]) ).
cnf(refute_0_882,plain,
( implies(y,x) != implies(y,x)
| implies(not(x),not(y)) = implies(y,x) ),
inference(resolve,[$cnf( $equal(implies(not(x),not(y)),implies(y,x)) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
implies(y,x) != implies(y,x),
inference(resolve,[$cnf( $equal(implies(not(x),not(y)),implies(y,x)) )],[refute_0_882,prove_wajsberg_lemma]) ).
cnf(refute_0_884,plain,
implies(y,x) = implies(y,x),
introduced(tautology,[refl,[$fot(implies(y,x))]]) ).
cnf(refute_0_885,plain,
$false,
inference(resolve,[$cnf( $equal(implies(y,x),implies(y,x)) )],[refute_0_884,refute_0_883]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL141-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.10/0.36 % Computer : n010.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 6 01:00:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.96/1.21 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.96/1.21
% 0.96/1.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.06/1.34
%------------------------------------------------------------------------------