TSTP Solution File: LCL109-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:33 EDT 2022
% Result : Unsatisfiable 66.00s 66.17s
% Output : CNFRefutation 66.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 280
% Syntax : Number of clauses : 1157 ( 590 unt; 0 nHn; 570 RR)
% Number of literals : 1976 (1975 equ; 823 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 2690 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(lemma_1,axiom,
implies(X,X) = truth ).
cnf(lemma_3,axiom,
implies(X,truth) = truth ).
cnf(lemma_4,axiom,
implies(X,implies(Y,X)) = truth ).
cnf(lemma_5,axiom,
( implies(X,Y) != implies(Y,Z)
| implies(X,Z) = truth ) ).
cnf(lemma_6,axiom,
implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = truth ).
cnf(lemma_7,axiom,
implies(X,implies(Y,Z)) = implies(Y,implies(X,Z)) ).
cnf(lemma_8,axiom,
implies(X,not(truth)) = not(X) ).
cnf(lemma_9,axiom,
not(not(X)) = X ).
cnf(lemma_10,axiom,
implies(not(X),not(Y)) = implies(Y,X) ).
cnf(prove_wajsberg_mv_4,negated_conjecture,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != truth ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( implies(X,implies(Y,Z)) != implies(Y,implies(X,Z))
| implies(Y,implies(X,Z)) = implies(X,implies(Y,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(Y,Z)))),bind(Y0,$fot(implies(Y,implies(X,Z))))]]) ).
cnf(refute_0_4,plain,
implies(Y,implies(X,Z)) = implies(X,implies(Y,Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(Y,Z)),implies(Y,implies(X,Z))) )],[lemma_7,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(implies(a,b),implies(b,a)) = implies(b,implies(implies(a,b),a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(b)),bind(Y,$fot(implies(a,b))),bind(Z,$fot(a))]]) ).
cnf(refute_0_6,plain,
implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(implies(a,b),implies(b,a)),a),
introduced(tautology,[refl,[$fot(implies(implies(implies(a,b),implies(b,a)),a))]]) ).
cnf(refute_0_7,plain,
( implies(implies(a,b),implies(b,a)) != implies(b,implies(implies(a,b),a))
| implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(implies(a,b),implies(b,a)),a)
| implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(implies(a,b),implies(b,a)),a)) ),[1,0],$fot(implies(b,implies(implies(a,b),a)))]]) ).
cnf(refute_0_8,plain,
( implies(implies(a,b),implies(b,a)) != implies(b,implies(implies(a,b),a))
| implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(implies(a,b),implies(b,a)),a)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(implies(implies(a,b),implies(b,a)),a) = implies(implies(b,implies(implies(a,b),a)),a),
inference(resolve,[$cnf( $equal(implies(implies(a,b),implies(b,a)),implies(b,implies(implies(a,b),a))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(implies(a,b),implies(b,a)),a)),
introduced(tautology,[refl,[$fot(implies(b,implies(implies(implies(a,b),implies(b,a)),a)))]]) ).
cnf(refute_0_11,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(implies(a,b),implies(b,a)),a))
| implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(b,implies(implies(a,b),a)),a)
| implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) ),[1,1],$fot(implies(implies(b,implies(implies(a,b),a)),a))]]) ).
cnf(refute_0_12,plain,
( implies(implies(implies(a,b),implies(b,a)),a) != implies(implies(b,implies(implies(a,b),a)),a)
| implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(b,implies(implies(implies(a,b),implies(b,a)),a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),a),implies(implies(b,implies(implies(a,b),a)),a)) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(implies(a,b),implies(b,a)),a)),
inference(subst,[],[refute_0_4:[bind(X,$fot(b)),bind(Y,$fot(implies(implies(a,b),implies(b,a)))),bind(Z,$fot(a))]]) ).
cnf(refute_0_15,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_15]) ).
cnf(refute_0_17,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != implies(b,implies(implies(implies(a,b),implies(b,a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(a,b),implies(b,a)),implies(b,a)))),bind(Y0,$fot(implies(b,implies(implies(implies(a,b),implies(b,a)),a)))),bind(Z0,$fot(implies(b,implies(implies(b,implies(implies(a,b),a)),a))))]]) ).
cnf(refute_0_18,plain,
( implies(b,implies(implies(implies(a,b),implies(b,a)),a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(implies(a,b),implies(b,a)),a))) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = implies(b,implies(implies(b,implies(implies(a,b),a)),a)),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(implies(a,b),implies(b,a)),a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) != implies(b,implies(implies(b,implies(implies(a,b),a)),a))
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) ),[1],$fot(truth)]]) ).
cnf(refute_0_21,plain,
( implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth
| implies(implies(implies(a,b),implies(b,a)),implies(b,a)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),implies(b,implies(implies(b,implies(implies(a,b),a)),a))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(a,b),implies(b,a)),implies(b,a)),truth) )],[refute_0_21,prove_wajsberg_mv_4]) ).
cnf(refute_0_23,plain,
implies(not(X_7),not(not(X))) = implies(not(X),X_7),
inference(subst,[],[lemma_10:[bind(X,$fot(X_7)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_24,plain,
( implies(not(X_7),not(not(X))) != implies(not(X),X_7)
| not(not(X)) != X
| implies(not(X_7),X) = implies(not(X),X_7) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_7),not(not(X))),implies(not(X),X_7)) ),[0,1],$fot(X)]]) ).
cnf(refute_0_25,plain,
( implies(not(X_7),not(not(X))) != implies(not(X),X_7)
| implies(not(X_7),X) = implies(not(X),X_7) ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[lemma_9,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(not(X_7),X) = implies(not(X),X_7),
inference(resolve,[$cnf( $equal(implies(not(X_7),not(not(X))),implies(not(X),X_7)) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(not(implies(X_30,X_31)),X) = implies(not(X),implies(X_30,X_31)),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_28,plain,
implies(not(X),implies(X_30,X_31)) = implies(X_30,implies(not(X),X_31)),
inference(subst,[],[lemma_7:[bind(X,$fot(not(X))),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_29,plain,
( implies(not(X),implies(X_30,X_31)) != implies(X_30,implies(not(X),X_31))
| implies(not(implies(X_30,X_31)),X) != implies(not(X),implies(X_30,X_31))
| implies(not(implies(X_30,X_31)),X) = implies(X_30,implies(not(X),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_30,X_31)),X),implies(not(X),implies(X_30,X_31))) ),[1],$fot(implies(X_30,implies(not(X),X_31)))]]) ).
cnf(refute_0_30,plain,
( implies(not(implies(X_30,X_31)),X) != implies(not(X),implies(X_30,X_31))
| implies(not(implies(X_30,X_31)),X) = implies(X_30,implies(not(X),X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(X_30,X_31)),implies(X_30,implies(not(X),X_31))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(not(implies(X_30,X_31)),X) = implies(X_30,implies(not(X),X_31)),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),X),implies(not(X),implies(X_30,X_31))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)),
inference(subst,[],[refute_0_31:[bind(X,$fot(not(implies(X_178,not(not(implies(X_30,X_31)))))))]]) ).
cnf(refute_0_33,plain,
implies(implies(X,not(X_51)),not(X_51)) = implies(implies(not(X_51),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(X_51)))]]) ).
cnf(refute_0_34,plain,
implies(implies(X_35,not(X)),not(X)) = implies(implies(not(X),X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_35,plain,
implies(not(not(X)),not(X_8)) = implies(X_8,not(X)),
inference(subst,[],[lemma_10:[bind(X,$fot(not(X))),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_36,plain,
( implies(not(not(X)),not(X_8)) != implies(X_8,not(X))
| not(not(X)) != X
| implies(X,not(X_8)) = implies(X_8,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X)),not(X_8)),implies(X_8,not(X))) ),[0,0],$fot(X)]]) ).
cnf(refute_0_37,plain,
( implies(not(not(X)),not(X_8)) != implies(X_8,not(X))
| implies(X,not(X_8)) = implies(X_8,not(X)) ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[lemma_9,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(X,not(X_8)) = implies(X_8,not(X)),
inference(resolve,[$cnf( $equal(implies(not(not(X)),not(X_8)),implies(X_8,not(X))) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(X,not(X_35)) = implies(X_35,not(X)),
inference(subst,[],[refute_0_38:[bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_40,plain,
( implies(X,not(X_35)) != implies(X_35,not(X))
| implies(X_35,not(X)) = implies(X,not(X_35)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(X_35)))),bind(Y0,$fot(implies(X_35,not(X))))]]) ).
cnf(refute_0_41,plain,
implies(X_35,not(X)) = implies(X,not(X_35)),
inference(resolve,[$cnf( $equal(implies(X,not(X_35)),implies(X_35,not(X))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( implies(X_35,not(X)) != implies(X,not(X_35))
| implies(implies(X_35,not(X)),not(X)) != implies(implies(not(X),X_35),X_35)
| implies(implies(X,not(X_35)),not(X)) = implies(implies(not(X),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,not(X)),not(X)),implies(implies(not(X),X_35),X_35)) ),[0,0],$fot(implies(X,not(X_35)))]]) ).
cnf(refute_0_43,plain,
( implies(implies(X_35,not(X)),not(X)) != implies(implies(not(X),X_35),X_35)
| implies(implies(X,not(X_35)),not(X)) = implies(implies(not(X),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(X_35,not(X)),implies(X,not(X_35))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(X,not(X_35)),not(X)) = implies(implies(not(X),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,not(X)),not(X)),implies(implies(not(X),X_35),X_35)) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
( implies(X,not(X_8)) != implies(X_8,not(X))
| implies(X_8,not(X)) = implies(X,not(X_8)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(X_8)))),bind(Y0,$fot(implies(X_8,not(X))))]]) ).
cnf(refute_0_46,plain,
implies(X_8,not(X)) = implies(X,not(X_8)),
inference(resolve,[$cnf( $equal(implies(X,not(X_8)),implies(X_8,not(X))) )],[refute_0_38,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(implies(X,not(X_35)),not(X)) = implies(X,not(implies(X,not(X_35)))),
inference(subst,[],[refute_0_46:[bind(X_8,$fot(implies(X,not(X_35))))]]) ).
cnf(refute_0_48,plain,
( implies(implies(X,not(X_35)),not(X)) != implies(X,not(implies(X,not(X_35))))
| implies(implies(X,not(X_35)),not(X)) != implies(implies(not(X),X_35),X_35)
| implies(X,not(implies(X,not(X_35)))) = implies(implies(not(X),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(X_35)),not(X)),implies(implies(not(X),X_35),X_35)) ),[0],$fot(implies(X,not(implies(X,not(X_35)))))]]) ).
cnf(refute_0_49,plain,
( implies(implies(X,not(X_35)),not(X)) != implies(implies(not(X),X_35),X_35)
| implies(X,not(implies(X,not(X_35)))) = implies(implies(not(X),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_35)),not(X)),implies(X,not(implies(X,not(X_35))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(X,not(implies(X,not(X_35)))) = implies(implies(not(X),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_35)),not(X)),implies(implies(not(X),X_35),X_35)) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(X_51,not(implies(X_51,not(X)))) = implies(implies(not(X_51),X),X),
inference(subst,[],[refute_0_50:[bind(X,$fot(X_51)),bind(X_35,$fot(X))]]) ).
cnf(refute_0_52,plain,
( implies(X_51,not(implies(X_51,not(X)))) != implies(implies(not(X_51),X),X)
| implies(implies(not(X_51),X),X) = implies(X_51,not(implies(X_51,not(X)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_51,not(implies(X_51,not(X)))))),bind(Y0,$fot(implies(implies(not(X_51),X),X)))]]) ).
cnf(refute_0_53,plain,
implies(implies(not(X_51),X),X) = implies(X_51,not(implies(X_51,not(X)))),
inference(resolve,[$cnf( $equal(implies(X_51,not(implies(X_51,not(X)))),implies(implies(not(X_51),X),X)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( implies(implies(X,not(X_51)),not(X_51)) != implies(implies(not(X_51),X),X)
| implies(implies(not(X_51),X),X) != implies(X_51,not(implies(X_51,not(X))))
| implies(implies(X,not(X_51)),not(X_51)) = implies(X_51,not(implies(X_51,not(X)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,not(X_51)),not(X_51)),implies(X_51,not(implies(X_51,not(X))))) ),[0],$fot(implies(implies(not(X_51),X),X))]]) ).
cnf(refute_0_55,plain,
( implies(implies(X,not(X_51)),not(X_51)) != implies(implies(not(X_51),X),X)
| implies(implies(X,not(X_51)),not(X_51)) = implies(X_51,not(implies(X_51,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_51),X),X),implies(X_51,not(implies(X_51,not(X))))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(implies(X,not(X_51)),not(X_51)) = implies(X_51,not(implies(X_51,not(X)))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_51)),not(X_51)),implies(implies(not(X_51),X),X)) )],[refute_0_33,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(X,not(X_51)),not(X_51)) = implies(X_51,not(implies(X,not(X_51)))),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_51)),bind(X_8,$fot(implies(X,not(X_51))))]]) ).
cnf(refute_0_58,plain,
( implies(implies(X,not(X_51)),not(X_51)) != implies(X_51,not(implies(X,not(X_51))))
| implies(implies(X,not(X_51)),not(X_51)) != implies(X_51,not(implies(X_51,not(X))))
| implies(X_51,not(implies(X,not(X_51)))) = implies(X_51,not(implies(X_51,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(X_51)),not(X_51)),implies(X_51,not(implies(X_51,not(X))))) ),[0],$fot(implies(X_51,not(implies(X,not(X_51)))))]]) ).
cnf(refute_0_59,plain,
( implies(implies(X,not(X_51)),not(X_51)) != implies(X_51,not(implies(X_51,not(X))))
| implies(X_51,not(implies(X,not(X_51)))) = implies(X_51,not(implies(X_51,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_51)),not(X_51)),implies(X_51,not(implies(X,not(X_51))))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(X_51,not(implies(X,not(X_51)))) = implies(X_51,not(implies(X_51,not(X)))),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_51)),not(X_51)),implies(X_51,not(implies(X_51,not(X))))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),
inference(subst,[],[refute_0_60:[bind(X,$fot(X_178)),bind(X_51,$fot(not(implies(X_30,X_31))))]]) ).
cnf(refute_0_62,plain,
( implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178))))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))),implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))) ),[0],$fot(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))))]]) ).
cnf(refute_0_63,plain,
( implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))),implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178))))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(X_178,not(not(implies(X_30,X_31)))))),implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))) )],[refute_0_32,refute_0_63]) ).
cnf(refute_0_65,plain,
not(not(X_178)) = X_178,
inference(subst,[],[lemma_9:[bind(X,$fot(X_178))]]) ).
cnf(refute_0_66,plain,
implies(not(not(X_178)),X_31) = implies(not(not(X_178)),X_31),
introduced(tautology,[refl,[$fot(implies(not(not(X_178)),X_31))]]) ).
cnf(refute_0_67,plain,
( implies(not(not(X_178)),X_31) != implies(not(not(X_178)),X_31)
| not(not(X_178)) != X_178
| implies(not(not(X_178)),X_31) = implies(X_178,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_178)),X_31),implies(not(not(X_178)),X_31)) ),[1,0],$fot(X_178)]]) ).
cnf(refute_0_68,plain,
( not(not(X_178)) != X_178
| implies(not(not(X_178)),X_31) = implies(X_178,X_31) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_178)),X_31),implies(not(not(X_178)),X_31)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(not(not(X_178)),X_31) = implies(X_178,X_31),
inference(resolve,[$cnf( $equal(not(not(X_178)),X_178) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(X_30,implies(not(not(X_178)),X_31)) = implies(X_30,implies(not(not(X_178)),X_31)),
introduced(tautology,[refl,[$fot(implies(X_30,implies(not(not(X_178)),X_31)))]]) ).
cnf(refute_0_71,plain,
( implies(X_30,implies(not(not(X_178)),X_31)) != implies(X_30,implies(not(not(X_178)),X_31))
| implies(not(not(X_178)),X_31) != implies(X_178,X_31)
| implies(X_30,implies(not(not(X_178)),X_31)) = implies(X_30,implies(X_178,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,implies(not(not(X_178)),X_31)),implies(X_30,implies(not(not(X_178)),X_31))) ),[1,1],$fot(implies(X_178,X_31))]]) ).
cnf(refute_0_72,plain,
( implies(not(not(X_178)),X_31) != implies(X_178,X_31)
| implies(X_30,implies(not(not(X_178)),X_31)) = implies(X_30,implies(X_178,X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(not(X_178)),X_31)),implies(X_30,implies(not(not(X_178)),X_31))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(X_30,implies(not(not(X_178)),X_31)) = implies(X_30,implies(X_178,X_31)),
inference(resolve,[$cnf( $equal(implies(not(not(X_178)),X_31),implies(X_178,X_31)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(not(implies(X_30,X_31)),not(X_178)) = implies(X_30,implies(not(not(X_178)),X_31)),
inference(subst,[],[refute_0_31:[bind(X,$fot(not(X_178)))]]) ).
cnf(refute_0_75,plain,
( implies(X_30,implies(not(not(X_178)),X_31)) != implies(X_30,implies(X_178,X_31))
| implies(not(implies(X_30,X_31)),not(X_178)) != implies(X_30,implies(not(not(X_178)),X_31))
| implies(not(implies(X_30,X_31)),not(X_178)) = implies(X_30,implies(X_178,X_31)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(X_30,X_31)),not(X_178)))),bind(Y0,$fot(implies(X_30,implies(not(not(X_178)),X_31)))),bind(Z0,$fot(implies(X_30,implies(X_178,X_31))))]]) ).
cnf(refute_0_76,plain,
( implies(X_30,implies(not(not(X_178)),X_31)) != implies(X_30,implies(X_178,X_31))
| implies(not(implies(X_30,X_31)),not(X_178)) = implies(X_30,implies(X_178,X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(X_178)),implies(X_30,implies(not(not(X_178)),X_31))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(not(implies(X_30,X_31)),not(X_178)) = implies(X_30,implies(X_178,X_31)),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(not(X_178)),X_31)),implies(X_30,implies(X_178,X_31))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) = implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31))]]) ).
cnf(refute_0_79,plain,
( implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) != implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31)
| implies(not(implies(X_30,X_31)),not(X_178)) != implies(X_30,implies(X_178,X_31))
| implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) = implies(implies(X_30,implies(X_178,X_31)),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31),implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31)) ),[1,0],$fot(implies(X_30,implies(X_178,X_31)))]]) ).
cnf(refute_0_80,plain,
( implies(not(implies(X_30,X_31)),not(X_178)) != implies(X_30,implies(X_178,X_31))
| implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) = implies(implies(X_30,implies(X_178,X_31)),X_31) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31),implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) = implies(implies(X_30,implies(X_178,X_31)),X_31),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(X_178)),implies(X_30,implies(X_178,X_31))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31),
inference(subst,[],[lemma_10:[bind(X,$fot(X_31)),bind(Y,$fot(implies(not(implies(X_30,X_31)),not(X_178))))]]) ).
cnf(refute_0_83,plain,
( implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) != implies(implies(X_30,implies(X_178,X_31)),X_31)
| implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31)
| implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(implies(X_30,implies(X_178,X_31)),X_31) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))),bind(Y0,$fot(implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31))),bind(Z0,$fot(implies(implies(X_30,implies(X_178,X_31)),X_31)))]]) ).
cnf(refute_0_84,plain,
( implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31) != implies(implies(X_30,implies(X_178,X_31)),X_31)
| implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(implies(X_30,implies(X_178,X_31)),X_31) ),
inference(resolve,[$cnf( $equal(implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(implies(X_30,implies(X_178,X_31)),X_31),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_30,X_31)),not(X_178)),X_31),implies(implies(X_30,implies(X_178,X_31)),X_31)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) = implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),
introduced(tautology,[refl,[$fot(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))))]]) ).
cnf(refute_0_87,plain,
( implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) != implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))
| implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(implies(X_30,implies(X_178,X_31)),X_31)
| implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))) ),[1,1],$fot(implies(implies(X_30,implies(X_178,X_31)),X_31))]]) ).
cnf(refute_0_88,plain,
( implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(implies(X_30,implies(X_178,X_31)),X_31)
| implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(implies(X_30,implies(X_178,X_31)),X_31)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(X_29,implies(not(X),not(Y))) = implies(not(X),implies(X_29,not(Y))),
inference(subst,[],[lemma_7:[bind(X,$fot(X_29)),bind(Y,$fot(not(X))),bind(Z,$fot(not(Y)))]]) ).
cnf(refute_0_91,plain,
( implies(X_29,implies(not(X),not(Y))) != implies(not(X),implies(X_29,not(Y)))
| implies(not(X),not(Y)) != implies(Y,X)
| implies(X_29,implies(Y,X)) = implies(not(X),implies(X_29,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,implies(not(X),not(Y))),implies(not(X),implies(X_29,not(Y)))) ),[0,1],$fot(implies(Y,X))]]) ).
cnf(refute_0_92,plain,
( implies(X_29,implies(not(X),not(Y))) != implies(not(X),implies(X_29,not(Y)))
| implies(X_29,implies(Y,X)) = implies(not(X),implies(X_29,not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),implies(Y,X)) )],[lemma_10,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(X_29,implies(Y,X)) = implies(not(X),implies(X_29,not(Y))),
inference(resolve,[$cnf( $equal(implies(X_29,implies(not(X),not(Y))),implies(not(X),implies(X_29,not(Y)))) )],[refute_0_90,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(X_177,implies(not(X),X_175)) = implies(not(X_175),implies(X_177,not(not(X)))),
inference(subst,[],[refute_0_93:[bind(X,$fot(X_175)),bind(Y,$fot(not(X))),bind(X_29,$fot(X_177))]]) ).
cnf(refute_0_95,plain,
implies(not(X_175),X) = implies(not(X),X_175),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_175))]]) ).
cnf(refute_0_96,plain,
( implies(not(X_175),X) != implies(not(X),X_175)
| implies(not(X),X_175) = implies(not(X_175),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_175),X))),bind(Y0,$fot(implies(not(X),X_175)))]]) ).
cnf(refute_0_97,plain,
implies(not(X),X_175) = implies(not(X_175),X),
inference(resolve,[$cnf( $equal(implies(not(X_175),X),implies(not(X),X_175)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( implies(X_177,implies(not(X),X_175)) != implies(not(X_175),implies(X_177,not(not(X))))
| implies(not(X),X_175) != implies(not(X_175),X)
| implies(X_177,implies(not(X_175),X)) = implies(not(X_175),implies(X_177,not(not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_177,implies(not(X),X_175)),implies(not(X_175),implies(X_177,not(not(X))))) ),[0,1],$fot(implies(not(X_175),X))]]) ).
cnf(refute_0_99,plain,
( implies(X_177,implies(not(X),X_175)) != implies(not(X_175),implies(X_177,not(not(X))))
| implies(X_177,implies(not(X_175),X)) = implies(not(X_175),implies(X_177,not(not(X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_175),implies(not(X_175),X)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(X_177,implies(not(X_175),X)) = implies(not(X_175),implies(X_177,not(not(X)))),
inference(resolve,[$cnf( $equal(implies(X_177,implies(not(X),X_175)),implies(not(X_175),implies(X_177,not(not(X))))) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
( implies(X_29,implies(Y,X)) != implies(not(X),implies(X_29,not(Y)))
| implies(not(X),implies(X_29,not(Y))) = implies(X_29,implies(Y,X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_29,implies(Y,X)))),bind(Y0,$fot(implies(not(X),implies(X_29,not(Y)))))]]) ).
cnf(refute_0_102,plain,
implies(not(X),implies(X_29,not(Y))) = implies(X_29,implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(X_29,implies(Y,X)),implies(not(X),implies(X_29,not(Y)))) )],[refute_0_93,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(not(X_175),implies(X_177,not(not(X)))) = implies(X_177,implies(not(X),X_175)),
inference(subst,[],[refute_0_102:[bind(X,$fot(X_175)),bind(Y,$fot(not(X))),bind(X_29,$fot(X_177))]]) ).
cnf(refute_0_104,plain,
( implies(X_177,implies(not(X_175),X)) != implies(not(X_175),implies(X_177,not(not(X))))
| implies(not(X_175),implies(X_177,not(not(X)))) != implies(X_177,implies(not(X),X_175))
| implies(X_177,implies(not(X_175),X)) = implies(X_177,implies(not(X),X_175)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_177,implies(not(X_175),X)),implies(X_177,implies(not(X),X_175))) ),[0],$fot(implies(not(X_175),implies(X_177,not(not(X)))))]]) ).
cnf(refute_0_105,plain,
( implies(X_177,implies(not(X_175),X)) != implies(not(X_175),implies(X_177,not(not(X))))
| implies(X_177,implies(not(X_175),X)) = implies(X_177,implies(not(X),X_175)) ),
inference(resolve,[$cnf( $equal(implies(not(X_175),implies(X_177,not(not(X)))),implies(X_177,implies(not(X),X_175))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(X_177,implies(not(X_175),X)) = implies(X_177,implies(not(X),X_175)),
inference(resolve,[$cnf( $equal(implies(X_177,implies(not(X_175),X)),implies(not(X_175),implies(X_177,not(not(X))))) )],[refute_0_100,refute_0_105]) ).
cnf(refute_0_107,plain,
( implies(X_177,implies(not(X_175),X)) != implies(X_177,implies(not(X),X_175))
| implies(X_177,implies(not(X),X_175)) = implies(X_177,implies(not(X_175),X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_177,implies(not(X_175),X)))),bind(Y0,$fot(implies(X_177,implies(not(X),X_175))))]]) ).
cnf(refute_0_108,plain,
implies(X_177,implies(not(X),X_175)) = implies(X_177,implies(not(X_175),X)),
inference(resolve,[$cnf( $equal(implies(X_177,implies(not(X_175),X)),implies(X_177,implies(not(X),X_175))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)) = implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),
inference(subst,[],[refute_0_108:[bind(X,$fot(not(implies(not(implies(X_30,X_31)),not(X_178))))),bind(X_175,$fot(X_31)),bind(X_177,$fot(X_30))]]) ).
cnf(refute_0_110,plain,
implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)),
inference(subst,[],[refute_0_31:[bind(X,$fot(not(implies(not(implies(X_30,X_31)),not(X_178)))))]]) ).
cnf(refute_0_111,plain,
( implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)) != implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))))),bind(Y0,$fot(implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)))),bind(Z0,$fot(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))))]]) ).
cnf(refute_0_112,plain,
( implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)) != implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(not(implies(not(implies(X_30,X_31)),not(X_178)))),X_31)),implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) != implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))))),bind(Y0,$fot(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))))),bind(Z0,$fot(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))))]]) ).
cnf(refute_0_115,plain,
( implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))) != implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178)))))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(not(implies(X_30,X_31)),not(X_178))))),implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))) )],[refute_0_89,refute_0_115]) ).
cnf(refute_0_117,plain,
( implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))
| implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))) ),[0],$fot(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)))]]) ).
cnf(refute_0_118,plain,
( implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
not(not(implies(X_30,X_31))) = implies(X_30,X_31),
inference(subst,[],[lemma_9:[bind(X,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_120,plain,
implies(X_178,not(not(implies(X_30,X_31)))) = implies(X_178,not(not(implies(X_30,X_31)))),
introduced(tautology,[refl,[$fot(implies(X_178,not(not(implies(X_30,X_31)))))]]) ).
cnf(refute_0_121,plain,
( implies(X_178,not(not(implies(X_30,X_31)))) != implies(X_178,not(not(implies(X_30,X_31))))
| not(not(implies(X_30,X_31))) != implies(X_30,X_31)
| implies(X_178,not(not(implies(X_30,X_31)))) = implies(X_178,implies(X_30,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_178,not(not(implies(X_30,X_31)))),implies(X_178,not(not(implies(X_30,X_31))))) ),[1,1],$fot(implies(X_30,X_31))]]) ).
cnf(refute_0_122,plain,
( not(not(implies(X_30,X_31))) != implies(X_30,X_31)
| implies(X_178,not(not(implies(X_30,X_31)))) = implies(X_178,implies(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_178,not(not(implies(X_30,X_31)))),implies(X_178,not(not(implies(X_30,X_31))))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(X_178,not(not(implies(X_30,X_31)))) = implies(X_178,implies(X_30,X_31)),
inference(resolve,[$cnf( $equal(not(not(implies(X_30,X_31))),implies(X_30,X_31)) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) = implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31),
introduced(tautology,[refl,[$fot(implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31))]]) ).
cnf(refute_0_125,plain,
( implies(X_178,not(not(implies(X_30,X_31)))) != implies(X_178,implies(X_30,X_31))
| implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) != implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31)
| implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) = implies(implies(X_178,implies(X_30,X_31)),X_31) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31),implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31)) ),[1,0],$fot(implies(X_178,implies(X_30,X_31)))]]) ).
cnf(refute_0_126,plain,
( implies(X_178,not(not(implies(X_30,X_31)))) != implies(X_178,implies(X_30,X_31))
| implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) = implies(implies(X_178,implies(X_30,X_31)),X_31) ),
inference(resolve,[$cnf( $equal(implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31),implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) = implies(implies(X_178,implies(X_30,X_31)),X_31),
inference(resolve,[$cnf( $equal(implies(X_178,not(not(implies(X_30,X_31)))),implies(X_178,implies(X_30,X_31))) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31),
inference(subst,[],[lemma_10:[bind(X,$fot(X_31)),bind(Y,$fot(implies(X_178,not(not(implies(X_30,X_31))))))]]) ).
cnf(refute_0_129,plain,
( implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) != implies(implies(X_178,implies(X_30,X_31)),X_31)
| implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31)
| implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(implies(X_178,implies(X_30,X_31)),X_31) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))),bind(Y0,$fot(implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31))),bind(Z0,$fot(implies(implies(X_178,implies(X_30,X_31)),X_31)))]]) ).
cnf(refute_0_130,plain,
( implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31) != implies(implies(X_178,implies(X_30,X_31)),X_31)
| implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(implies(X_178,implies(X_30,X_31)),X_31) ),
inference(resolve,[$cnf( $equal(implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))),implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) = implies(implies(X_178,implies(X_30,X_31)),X_31),
inference(resolve,[$cnf( $equal(implies(implies(X_178,not(not(implies(X_30,X_31)))),X_31),implies(implies(X_178,implies(X_30,X_31)),X_31)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) = implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))),
introduced(tautology,[refl,[$fot(implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))))]]) ).
cnf(refute_0_133,plain,
( implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) != implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))
| implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(implies(X_178,implies(X_30,X_31)),X_31)
| implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))),implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))) ),[1,1],$fot(implies(implies(X_178,implies(X_30,X_31)),X_31))]]) ).
cnf(refute_0_134,plain,
( implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))) != implies(implies(X_178,implies(X_30,X_31)),X_31)
| implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))),implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))),implies(implies(X_178,implies(X_30,X_31)),X_31)) )],[refute_0_131,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) = implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))),
inference(subst,[],[refute_0_108:[bind(X,$fot(not(implies(X_178,not(not(implies(X_30,X_31))))))),bind(X_175,$fot(X_31)),bind(X_177,$fot(X_30))]]) ).
cnf(refute_0_137,plain,
( implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) != implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))
| implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) != implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))
| implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)))),bind(Y0,$fot(implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))))),bind(Z0,$fot(implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))))]]) ).
cnf(refute_0_138,plain,
( implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))) != implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))
| implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)),implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31)))))))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(X_31),not(implies(X_178,not(not(implies(X_30,X_31))))))),implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
( implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)) != implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))
| implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))) ),[0],$fot(implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)))]]) ).
cnf(refute_0_141,plain,
( implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31)),implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
( implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))) != implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))
| implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))) )],[refute_0_118,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) = implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(not(implies(X_30,X_31)),not(implies(not(implies(X_30,X_31)),not(X_178)))),implies(X_30,implies(not(not(implies(X_178,not(not(implies(X_30,X_31)))))),X_31))) )],[refute_0_64,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) != implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))
| implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)))),bind(Y0,$fot(implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))))]]) ).
cnf(refute_0_145,plain,
implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31)) = implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),
inference(resolve,[$cnf( $equal(implies(X_30,implies(implies(X_30,implies(X_178,X_31)),X_31)),implies(X_30,implies(implies(X_178,implies(X_30,X_31)),X_31))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(a,implies(implies(implies(b,a),implies(a,b)),b)) = implies(a,implies(implies(a,implies(implies(b,a),b)),b)),
inference(subst,[],[refute_0_145:[bind(X_178,$fot(implies(b,a))),bind(X_30,$fot(a)),bind(X_31,$fot(b))]]) ).
cnf(refute_0_147,plain,
implies(X,implies(implies(X_35,implies(X,Z)),Z)) = implies(implies(X_35,implies(X,Z)),implies(X,Z)),
inference(subst,[],[lemma_7:[bind(Y,$fot(implies(X_35,implies(X,Z))))]]) ).
cnf(refute_0_148,plain,
implies(implies(X_35,implies(X,Z)),implies(X,Z)) = implies(implies(implies(X,Z),X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35)),bind(Y,$fot(implies(X,Z)))]]) ).
cnf(refute_0_149,plain,
( implies(X,implies(implies(X_35,implies(X,Z)),Z)) != implies(implies(X_35,implies(X,Z)),implies(X,Z))
| implies(implies(X_35,implies(X,Z)),implies(X,Z)) != implies(implies(implies(X,Z),X_35),X_35)
| implies(X,implies(implies(X_35,implies(X,Z)),Z)) = implies(implies(implies(X,Z),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,implies(implies(X_35,implies(X,Z)),Z)),implies(implies(implies(X,Z),X_35),X_35)) ),[0],$fot(implies(implies(X_35,implies(X,Z)),implies(X,Z)))]]) ).
cnf(refute_0_150,plain,
( implies(X,implies(implies(X_35,implies(X,Z)),Z)) != implies(implies(X_35,implies(X,Z)),implies(X,Z))
| implies(X,implies(implies(X_35,implies(X,Z)),Z)) = implies(implies(implies(X,Z),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(X,Z)),implies(X,Z)),implies(implies(implies(X,Z),X_35),X_35)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
implies(X,implies(implies(X_35,implies(X,Z)),Z)) = implies(implies(implies(X,Z),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X_35,implies(X,Z)),Z)),implies(implies(X_35,implies(X,Z)),implies(X,Z))) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(implies(implies(X_284,X_285),implies(X,Z)),implies(X,Z)),
inference(subst,[],[refute_0_151:[bind(X,$fot(X_284)),bind(Z,$fot(X_285)),bind(X_35,$fot(implies(X,Z)))]]) ).
cnf(refute_0_153,plain,
implies(X,implies(implies(X_284,X_285),Z)) = implies(implies(X_284,X_285),implies(X,Z)),
inference(subst,[],[lemma_7:[bind(Y,$fot(implies(X_284,X_285)))]]) ).
cnf(refute_0_154,plain,
( implies(X,implies(implies(X_284,X_285),Z)) != implies(implies(X_284,X_285),implies(X,Z))
| implies(implies(X_284,X_285),implies(X,Z)) = implies(X,implies(implies(X_284,X_285),Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(implies(X_284,X_285),Z)))),bind(Y0,$fot(implies(implies(X_284,X_285),implies(X,Z))))]]) ).
cnf(refute_0_155,plain,
implies(implies(X_284,X_285),implies(X,Z)) = implies(X,implies(implies(X_284,X_285),Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X_284,X_285),Z)),implies(implies(X_284,X_285),implies(X,Z))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
( implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) != implies(implies(implies(X_284,X_285),implies(X,Z)),implies(X,Z))
| implies(implies(X_284,X_285),implies(X,Z)) != implies(X,implies(implies(X_284,X_285),Z))
| implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),implies(implies(implies(X_284,X_285),implies(X,Z)),implies(X,Z))) ),[1,0],$fot(implies(X,implies(implies(X_284,X_285),Z)))]]) ).
cnf(refute_0_157,plain,
( implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) != implies(implies(implies(X_284,X_285),implies(X,Z)),implies(X,Z))
| implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_284,X_285),implies(X,Z)),implies(X,implies(implies(X_284,X_285),Z))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),implies(implies(implies(X_284,X_285),implies(X,Z)),implies(X,Z))) )],[refute_0_152,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(implies(X,implies(implies(X_284,X_285),Z))))]]) ).
cnf(refute_0_160,plain,
( implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) != implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z))
| implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)) != implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))
| implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))) ),[0],$fot(implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)))]]) ).
cnf(refute_0_161,plain,
( implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) != implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z))
| implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z)),implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) = implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),implies(implies(X,implies(implies(X_284,X_285),Z)),implies(X,Z))) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
( implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) != implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))
| implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)) = implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)))),bind(Y0,$fot(implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))))]]) ).
cnf(refute_0_164,plain,
implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z)) = implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),
inference(resolve,[$cnf( $equal(implies(X_284,implies(implies(implies(X,Z),implies(X_284,X_285)),X_285)),implies(X,implies(implies(X,implies(implies(X_284,X_285),Z)),Z))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(a,implies(implies(implies(b,a),implies(a,b)),b)),
inference(subst,[],[refute_0_164:[bind(X,$fot(b)),bind(Z,$fot(a)),bind(X_284,$fot(a)),bind(X_285,$fot(b))]]) ).
cnf(refute_0_166,plain,
( implies(a,implies(implies(implies(b,a),implies(a,b)),b)) != implies(a,implies(implies(a,implies(implies(b,a),b)),b))
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != implies(a,implies(implies(implies(b,a),implies(a,b)),b))
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(a,implies(implies(a,implies(implies(b,a),b)),b)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(b,implies(implies(b,implies(implies(a,b),a)),a)))),bind(Y0,$fot(implies(a,implies(implies(implies(b,a),implies(a,b)),b)))),bind(Z0,$fot(implies(a,implies(implies(a,implies(implies(b,a),b)),b))))]]) ).
cnf(refute_0_167,plain,
( implies(a,implies(implies(implies(b,a),implies(a,b)),b)) != implies(a,implies(implies(a,implies(implies(b,a),b)),b))
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(a,implies(implies(a,implies(implies(b,a),b)),b)) ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(a,implies(implies(implies(b,a),implies(a,b)),b))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = implies(a,implies(implies(a,implies(implies(b,a),b)),b)),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(implies(b,a),implies(a,b)),b)),implies(a,implies(implies(a,implies(implies(b,a),b)),b))) )],[refute_0_146,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) != implies(a,implies(implies(a,implies(implies(b,a),b)),b))
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(a,implies(implies(a,implies(implies(b,a),b)),b))) ),[1],$fot(truth)]]) ).
cnf(refute_0_170,plain,
( implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != truth
| implies(b,implies(implies(b,implies(implies(a,b),a)),a)) = truth ),
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),implies(a,implies(implies(a,implies(implies(b,a),b)),b))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != truth,
inference(resolve,[$cnf( $equal(implies(b,implies(implies(b,implies(implies(a,b),a)),a)),truth) )],[refute_0_170,refute_0_22]) ).
cnf(refute_0_172,plain,
implies(implies(not(X),not(Y)),X) = implies(implies(not(X),not(Y)),X),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),X))]]) ).
cnf(refute_0_173,plain,
( implies(implies(not(X),not(Y)),X) != implies(implies(not(X),not(Y)),X)
| implies(not(X),not(Y)) != implies(Y,X)
| implies(implies(not(X),not(Y)),X) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),X),implies(implies(not(X),not(Y)),X)) ),[1,0],$fot(implies(Y,X))]]) ).
cnf(refute_0_174,plain,
( implies(not(X),not(Y)) != implies(Y,X)
| implies(implies(not(X),not(Y)),X) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),X),implies(implies(not(X),not(Y)),X)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(not(X),not(Y)),X) = implies(implies(Y,X),X),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),implies(Y,X)) )],[lemma_10,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(Y,implies(implies(not(X),not(Y)),X)) = implies(Y,implies(implies(not(X),not(Y)),X)),
introduced(tautology,[refl,[$fot(implies(Y,implies(implies(not(X),not(Y)),X)))]]) ).
cnf(refute_0_177,plain,
( implies(Y,implies(implies(not(X),not(Y)),X)) != implies(Y,implies(implies(not(X),not(Y)),X))
| implies(implies(not(X),not(Y)),X) != implies(implies(Y,X),X)
| implies(Y,implies(implies(not(X),not(Y)),X)) = implies(Y,implies(implies(Y,X),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(implies(not(X),not(Y)),X)),implies(Y,implies(implies(not(X),not(Y)),X))) ),[1,1],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_178,plain,
( implies(implies(not(X),not(Y)),X) != implies(implies(Y,X),X)
| implies(Y,implies(implies(not(X),not(Y)),X)) = implies(Y,implies(implies(Y,X),X)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(not(X),not(Y)),X)),implies(Y,implies(implies(not(X),not(Y)),X))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(Y,implies(implies(not(X),not(Y)),X)) = implies(Y,implies(implies(Y,X),X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),X),implies(implies(Y,X),X)) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(Y,implies(implies(not(X),not(Y)),X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_181,plain,
( implies(Y,implies(implies(not(X),not(Y)),X)) != implies(Y,implies(implies(Y,X),X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != implies(Y,implies(implies(not(X),not(Y)),X))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(Y,implies(implies(Y,X),X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X),not(Y)),implies(Y,X)))),bind(Y0,$fot(implies(Y,implies(implies(not(X),not(Y)),X)))),bind(Z0,$fot(implies(Y,implies(implies(Y,X),X))))]]) ).
cnf(refute_0_182,plain,
( implies(Y,implies(implies(not(X),not(Y)),X)) != implies(Y,implies(implies(Y,X),X))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(Y,implies(implies(Y,X),X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,implies(implies(not(X),not(Y)),X))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(Y,implies(implies(Y,X),X)),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(not(X),not(Y)),X)),implies(Y,implies(implies(Y,X),X))) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(Y,implies(implies(Y,X),X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(Y,implies(implies(Y,X),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) ),[0],$fot(implies(Y,implies(implies(Y,X),X)))]]) ).
cnf(refute_0_185,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(Y,implies(implies(Y,X),X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,implies(implies(Y,X),X))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(Y,implies(implies(Y,X),X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(a,implies(implies(a,b),b)) = truth,
inference(subst,[],[refute_0_186:[bind(X,$fot(b)),bind(Y,$fot(a))]]) ).
cnf(refute_0_188,plain,
implies(implies(not(X),not(Y)),not(Y)) = implies(implies(not(Y),not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_189,plain,
( implies(implies(not(X),not(Y)),not(Y)) != implies(implies(not(Y),not(X)),not(X))
| implies(not(X),not(Y)) != implies(Y,X)
| implies(implies(Y,X),not(Y)) = implies(implies(not(Y),not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),not(Y)),implies(implies(not(Y),not(X)),not(X))) ),[0,0],$fot(implies(Y,X))]]) ).
cnf(refute_0_190,plain,
( implies(implies(not(X),not(Y)),not(Y)) != implies(implies(not(Y),not(X)),not(X))
| implies(implies(Y,X),not(Y)) = implies(implies(not(Y),not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),implies(Y,X)) )],[lemma_10,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(implies(Y,X),not(Y)) = implies(implies(not(Y),not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),not(Y)),implies(implies(not(Y),not(X)),not(X))) )],[refute_0_188,refute_0_190]) ).
cnf(refute_0_192,plain,
implies(implies(Y,X),not(Y)) = implies(Y,not(implies(Y,X))),
inference(subst,[],[refute_0_46:[bind(X,$fot(Y)),bind(X_8,$fot(implies(Y,X)))]]) ).
cnf(refute_0_193,plain,
( implies(implies(Y,X),not(Y)) != implies(Y,not(implies(Y,X)))
| implies(implies(Y,X),not(Y)) != implies(implies(not(Y),not(X)),not(X))
| implies(Y,not(implies(Y,X))) = implies(implies(not(Y),not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,X),not(Y)),implies(implies(not(Y),not(X)),not(X))) ),[0],$fot(implies(Y,not(implies(Y,X))))]]) ).
cnf(refute_0_194,plain,
( implies(implies(Y,X),not(Y)) != implies(implies(not(Y),not(X)),not(X))
| implies(Y,not(implies(Y,X))) = implies(implies(not(Y),not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),not(Y)),implies(Y,not(implies(Y,X)))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
implies(not(Y),not(X)) = implies(X,Y),
inference(subst,[],[lemma_10:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_196,plain,
not(implies(not(Y),not(X))) = not(implies(not(Y),not(X))),
introduced(tautology,[refl,[$fot(not(implies(not(Y),not(X))))]]) ).
cnf(refute_0_197,plain,
( implies(not(Y),not(X)) != implies(X,Y)
| not(implies(not(Y),not(X))) != not(implies(not(Y),not(X)))
| not(implies(not(Y),not(X))) = not(implies(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(Y),not(X))),not(implies(not(Y),not(X)))) ),[1,0],$fot(implies(X,Y))]]) ).
cnf(refute_0_198,plain,
( implies(not(Y),not(X)) != implies(X,Y)
| not(implies(not(Y),not(X))) = not(implies(X,Y)) ),
inference(resolve,[$cnf( $equal(not(implies(not(Y),not(X))),not(implies(not(Y),not(X)))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
not(implies(not(Y),not(X))) = not(implies(X,Y)),
inference(resolve,[$cnf( $equal(implies(not(Y),not(X)),implies(X,Y)) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(X,not(implies(not(Y),not(X)))) = implies(X,not(implies(not(Y),not(X)))),
introduced(tautology,[refl,[$fot(implies(X,not(implies(not(Y),not(X)))))]]) ).
cnf(refute_0_201,plain,
( implies(X,not(implies(not(Y),not(X)))) != implies(X,not(implies(not(Y),not(X))))
| not(implies(not(Y),not(X))) != not(implies(X,Y))
| implies(X,not(implies(not(Y),not(X)))) = implies(X,not(implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(not(Y),not(X)))),implies(X,not(implies(not(Y),not(X))))) ),[1,1],$fot(not(implies(X,Y)))]]) ).
cnf(refute_0_202,plain,
( not(implies(not(Y),not(X))) != not(implies(X,Y))
| implies(X,not(implies(not(Y),not(X)))) = implies(X,not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(not(Y),not(X)))),implies(X,not(implies(not(Y),not(X))))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(X,not(implies(not(Y),not(X)))) = implies(X,not(implies(X,Y))),
inference(resolve,[$cnf( $equal(not(implies(not(Y),not(X))),not(implies(X,Y))) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(not(Y),not(X)),not(X)) = implies(X,not(implies(not(Y),not(X)))),
inference(subst,[],[refute_0_46:[bind(X_8,$fot(implies(not(Y),not(X))))]]) ).
cnf(refute_0_205,plain,
( implies(X,not(implies(not(Y),not(X)))) != implies(X,not(implies(X,Y)))
| implies(implies(not(Y),not(X)),not(X)) != implies(X,not(implies(not(Y),not(X))))
| implies(implies(not(Y),not(X)),not(X)) = implies(X,not(implies(X,Y))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(Y),not(X)),not(X)))),bind(Y0,$fot(implies(X,not(implies(not(Y),not(X)))))),bind(Z0,$fot(implies(X,not(implies(X,Y)))))]]) ).
cnf(refute_0_206,plain,
( implies(X,not(implies(not(Y),not(X)))) != implies(X,not(implies(X,Y)))
| implies(implies(not(Y),not(X)),not(X)) = implies(X,not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),not(X)),implies(X,not(implies(not(Y),not(X))))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(implies(not(Y),not(X)),not(X)) = implies(X,not(implies(X,Y))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(not(Y),not(X)))),implies(X,not(implies(X,Y)))) )],[refute_0_203,refute_0_206]) ).
cnf(refute_0_208,plain,
( implies(Y,not(implies(Y,X))) != implies(implies(not(Y),not(X)),not(X))
| implies(implies(not(Y),not(X)),not(X)) != implies(X,not(implies(X,Y)))
| implies(Y,not(implies(Y,X))) = implies(X,not(implies(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(Y,not(implies(Y,X))),implies(X,not(implies(X,Y)))) ),[0],$fot(implies(implies(not(Y),not(X)),not(X)))]]) ).
cnf(refute_0_209,plain,
( implies(Y,not(implies(Y,X))) != implies(implies(not(Y),not(X)),not(X))
| implies(Y,not(implies(Y,X))) = implies(X,not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(X)),not(X)),implies(X,not(implies(X,Y)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
( implies(implies(Y,X),not(Y)) != implies(implies(not(Y),not(X)),not(X))
| implies(Y,not(implies(Y,X))) = implies(X,not(implies(X,Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,X))),implies(implies(not(Y),not(X)),not(X))) )],[refute_0_194,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(Y,not(implies(Y,X))) = implies(X,not(implies(X,Y))),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),not(Y)),implies(implies(not(Y),not(X)),not(X))) )],[refute_0_191,refute_0_210]) ).
cnf(refute_0_212,plain,
implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) = implies(X,not(implies(X,not(implies(X,X_40))))),
inference(subst,[],[refute_0_211:[bind(Y,$fot(not(implies(X,X_40))))]]) ).
cnf(refute_0_213,plain,
implies(X,not(implies(X,X_40))) = implies(X_40,not(implies(X_40,X))),
inference(subst,[],[refute_0_211:[bind(X,$fot(X_40)),bind(Y,$fot(X))]]) ).
cnf(refute_0_214,plain,
( implies(X,not(implies(X,X_40))) != implies(X_40,not(implies(X_40,X)))
| implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) != implies(X,not(implies(X,not(implies(X,X_40)))))
| implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))),implies(X,not(implies(X,not(implies(X,X_40)))))) ),[1,1,0],$fot(implies(X_40,not(implies(X_40,X))))]]) ).
cnf(refute_0_215,plain,
( implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) != implies(X,not(implies(X,not(implies(X,X_40)))))
| implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,X_40))),implies(X_40,not(implies(X_40,X)))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) = implies(X,not(implies(X_40,not(implies(X_40,X))))),
inference(resolve,[$cnf( $equal(implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))),implies(X,not(implies(X,not(implies(X,X_40)))))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
( implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) != implies(X,not(implies(X,not(implies(X,X_40)))))
| implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) != implies(X,not(implies(X_40,not(implies(X_40,X)))))
| implies(X,not(implies(X,not(implies(X,X_40))))) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))),implies(X,not(implies(X_40,not(implies(X_40,X)))))) ),[0],$fot(implies(X,not(implies(X,not(implies(X,X_40))))))]]) ).
cnf(refute_0_218,plain,
( implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))) != implies(X,not(implies(X_40,not(implies(X_40,X)))))
| implies(X,not(implies(X,not(implies(X,X_40))))) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))),implies(X,not(implies(X,not(implies(X,X_40)))))) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(X,not(implies(X,not(implies(X,X_40))))) = implies(X,not(implies(X_40,not(implies(X_40,X))))),
inference(resolve,[$cnf( $equal(implies(not(implies(X,X_40)),not(implies(not(implies(X,X_40)),X))),implies(X,not(implies(X_40,not(implies(X_40,X)))))) )],[refute_0_216,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(implies(implies(not(not(X)),X_43),not(X)),not(X)),
inference(subst,[],[refute_0_38:[bind(X_8,$fot(implies(implies(not(not(X)),X_43),not(X))))]]) ).
cnf(refute_0_221,plain,
implies(implies(X_35,implies(not(X_35),X_7)),implies(not(X_35),X_7)) = implies(implies(implies(not(X_35),X_7),X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35)),bind(Y,$fot(implies(not(X_35),X_7)))]]) ).
cnf(refute_0_222,plain,
implies(not(X_8),implies(not(X_7),not(X_8))) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(not(X_8))),bind(Y,$fot(not(X_7)))]]) ).
cnf(refute_0_223,plain,
implies(not(X_7),not(X_8)) = implies(X_8,X_7),
inference(subst,[],[lemma_10:[bind(X,$fot(X_7)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_224,plain,
( implies(not(X_7),not(X_8)) != implies(X_8,X_7)
| implies(not(X_8),implies(not(X_7),not(X_8))) != truth
| implies(not(X_8),implies(X_8,X_7)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_8),implies(not(X_7),not(X_8))),truth) ),[0,1],$fot(implies(X_8,X_7))]]) ).
cnf(refute_0_225,plain,
( implies(not(X_8),implies(not(X_7),not(X_8))) != truth
| implies(not(X_8),implies(X_8,X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_7),not(X_8)),implies(X_8,X_7)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(not(X_8),implies(X_8,X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_8),implies(not(X_7),not(X_8))),truth) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(not(X_8),implies(X_8,X_7)) = implies(X_8,implies(not(X_8),X_7)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_8)),bind(Y,$fot(not(X_8))),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_228,plain,
( implies(not(X_8),implies(X_8,X_7)) != implies(X_8,implies(not(X_8),X_7))
| implies(not(X_8),implies(X_8,X_7)) != truth
| implies(X_8,implies(not(X_8),X_7)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_8),implies(X_8,X_7)),truth) ),[0],$fot(implies(X_8,implies(not(X_8),X_7)))]]) ).
cnf(refute_0_229,plain,
( implies(not(X_8),implies(X_8,X_7)) != truth
| implies(X_8,implies(not(X_8),X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_8),implies(X_8,X_7)),implies(X_8,implies(not(X_8),X_7))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(X_8,implies(not(X_8),X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_8),implies(X_8,X_7)),truth) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(X_35,implies(not(X_35),X_7)) = truth,
inference(subst,[],[refute_0_230:[bind(X_8,$fot(X_35))]]) ).
cnf(refute_0_232,plain,
( implies(X_35,implies(not(X_35),X_7)) != truth
| implies(implies(X_35,implies(not(X_35),X_7)),implies(not(X_35),X_7)) != implies(implies(implies(not(X_35),X_7),X_35),X_35)
| implies(truth,implies(not(X_35),X_7)) = implies(implies(implies(not(X_35),X_7),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_7)),implies(not(X_35),X_7)),implies(implies(implies(not(X_35),X_7),X_35),X_35)) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_233,plain,
( implies(implies(X_35,implies(not(X_35),X_7)),implies(not(X_35),X_7)) != implies(implies(implies(not(X_35),X_7),X_35),X_35)
| implies(truth,implies(not(X_35),X_7)) = implies(implies(implies(not(X_35),X_7),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(X_35,implies(not(X_35),X_7)),truth) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
implies(truth,implies(not(X_35),X_7)) = implies(implies(implies(not(X_35),X_7),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_7)),implies(not(X_35),X_7)),implies(implies(implies(not(X_35),X_7),X_35),X_35)) )],[refute_0_221,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(truth,implies(not(X_35),X_7)) = implies(not(X_35),X_7),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X_35),X_7)))]]) ).
cnf(refute_0_236,plain,
( implies(truth,implies(not(X_35),X_7)) != implies(implies(implies(not(X_35),X_7),X_35),X_35)
| implies(truth,implies(not(X_35),X_7)) != implies(not(X_35),X_7)
| implies(not(X_35),X_7) = implies(implies(implies(not(X_35),X_7),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(X_35),X_7)),implies(implies(implies(not(X_35),X_7),X_35),X_35)) ),[0],$fot(implies(not(X_35),X_7))]]) ).
cnf(refute_0_237,plain,
( implies(truth,implies(not(X_35),X_7)) != implies(implies(implies(not(X_35),X_7),X_35),X_35)
| implies(not(X_35),X_7) = implies(implies(implies(not(X_35),X_7),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_35),X_7)),implies(not(X_35),X_7)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(not(X_35),X_7) = implies(implies(implies(not(X_35),X_7),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_35),X_7)),implies(implies(implies(not(X_35),X_7),X_35),X_35)) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(not(not(X)),X_43) = implies(implies(implies(not(not(X)),X_43),not(X)),not(X)),
inference(subst,[],[refute_0_238:[bind(X_35,$fot(not(X))),bind(X_7,$fot(X_43))]]) ).
cnf(refute_0_240,plain,
( implies(not(not(X)),X_43) != implies(implies(implies(not(not(X)),X_43),not(X)),not(X))
| implies(implies(implies(not(not(X)),X_43),not(X)),not(X)) = implies(not(not(X)),X_43) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(not(X)),X_43))),bind(Y0,$fot(implies(implies(implies(not(not(X)),X_43),not(X)),not(X))))]]) ).
cnf(refute_0_241,plain,
implies(implies(implies(not(not(X)),X_43),not(X)),not(X)) = implies(not(not(X)),X_43),
inference(resolve,[$cnf( $equal(implies(not(not(X)),X_43),implies(implies(implies(not(not(X)),X_43),not(X)),not(X))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(implies(implies(not(not(X)),X_43),not(X)),not(X))
| implies(implies(implies(not(not(X)),X_43),not(X)),not(X)) != implies(not(not(X)),X_43)
| implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(not(not(X)),X_43) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(not(not(X)),X_43)) ),[0],$fot(implies(implies(implies(not(not(X)),X_43),not(X)),not(X)))]]) ).
cnf(refute_0_243,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(implies(implies(not(not(X)),X_43),not(X)),not(X))
| implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(not(not(X)),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(X)),X_43),not(X)),not(X)),implies(not(not(X)),X_43)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(not(not(X)),X_43),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(implies(implies(not(not(X)),X_43),not(X)),not(X))) )],[refute_0_220,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(not(not(X)),X_43) = implies(not(not(X)),X_43),
introduced(tautology,[refl,[$fot(implies(not(not(X)),X_43))]]) ).
cnf(refute_0_246,plain,
( implies(not(not(X)),X_43) != implies(not(not(X)),X_43)
| not(not(X)) != X
| implies(not(not(X)),X_43) = implies(X,X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X)),X_43),implies(not(not(X)),X_43)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_247,plain,
( not(not(X)) != X
| implies(not(not(X)),X_43) = implies(X,X_43) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),X_43),implies(not(not(X)),X_43)) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(not(not(X)),X_43) = implies(X,X_43),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[lemma_9,refute_0_247]) ).
cnf(refute_0_249,plain,
not(implies(not(not(X)),X_43)) = not(implies(not(not(X)),X_43)),
introduced(tautology,[refl,[$fot(not(implies(not(not(X)),X_43)))]]) ).
cnf(refute_0_250,plain,
( implies(not(not(X)),X_43) != implies(X,X_43)
| not(implies(not(not(X)),X_43)) != not(implies(not(not(X)),X_43))
| not(implies(not(not(X)),X_43)) = not(implies(X,X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(X)),X_43)),not(implies(not(not(X)),X_43))) ),[1,0],$fot(implies(X,X_43))]]) ).
cnf(refute_0_251,plain,
( implies(not(not(X)),X_43) != implies(X,X_43)
| not(implies(not(not(X)),X_43)) = not(implies(X,X_43)) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(X)),X_43)),not(implies(not(not(X)),X_43))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
not(implies(not(not(X)),X_43)) = not(implies(X,X_43)),
inference(resolve,[$cnf( $equal(implies(not(not(X)),X_43),implies(X,X_43)) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
implies(X,not(implies(not(not(X)),X_43))) = implies(X,not(implies(not(not(X)),X_43))),
introduced(tautology,[refl,[$fot(implies(X,not(implies(not(not(X)),X_43))))]]) ).
cnf(refute_0_254,plain,
( implies(X,not(implies(not(not(X)),X_43))) != implies(X,not(implies(not(not(X)),X_43)))
| not(implies(not(not(X)),X_43)) != not(implies(X,X_43))
| implies(X,not(implies(not(not(X)),X_43))) = implies(X,not(implies(X,X_43))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(not(not(X)),X_43))),implies(X,not(implies(not(not(X)),X_43)))) ),[1,1],$fot(not(implies(X,X_43)))]]) ).
cnf(refute_0_255,plain,
( not(implies(not(not(X)),X_43)) != not(implies(X,X_43))
| implies(X,not(implies(not(not(X)),X_43))) = implies(X,not(implies(X,X_43))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(not(not(X)),X_43))),implies(X,not(implies(not(not(X)),X_43)))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
implies(X,not(implies(not(not(X)),X_43))) = implies(X,not(implies(X,X_43))),
inference(resolve,[$cnf( $equal(not(implies(not(not(X)),X_43)),not(implies(X,X_43))) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(implies(not(not(X)),X_43),not(X)) = implies(X,not(implies(not(not(X)),X_43))),
inference(subst,[],[refute_0_46:[bind(X_8,$fot(implies(not(not(X)),X_43)))]]) ).
cnf(refute_0_258,plain,
( implies(X,not(implies(not(not(X)),X_43))) != implies(X,not(implies(X,X_43)))
| implies(implies(not(not(X)),X_43),not(X)) != implies(X,not(implies(not(not(X)),X_43)))
| implies(implies(not(not(X)),X_43),not(X)) = implies(X,not(implies(X,X_43))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(not(X)),X_43),not(X)))),bind(Y0,$fot(implies(X,not(implies(not(not(X)),X_43))))),bind(Z0,$fot(implies(X,not(implies(X,X_43)))))]]) ).
cnf(refute_0_259,plain,
( implies(X,not(implies(not(not(X)),X_43))) != implies(X,not(implies(X,X_43)))
| implies(implies(not(not(X)),X_43),not(X)) = implies(X,not(implies(X,X_43))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X)),X_43),not(X)),implies(X,not(implies(not(not(X)),X_43)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
implies(implies(not(not(X)),X_43),not(X)) = implies(X,not(implies(X,X_43))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(not(not(X)),X_43))),implies(X,not(implies(X,X_43)))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
not(implies(implies(not(not(X)),X_43),not(X))) = not(implies(implies(not(not(X)),X_43),not(X))),
introduced(tautology,[refl,[$fot(not(implies(implies(not(not(X)),X_43),not(X))))]]) ).
cnf(refute_0_262,plain,
( implies(implies(not(not(X)),X_43),not(X)) != implies(X,not(implies(X,X_43)))
| not(implies(implies(not(not(X)),X_43),not(X))) != not(implies(implies(not(not(X)),X_43),not(X)))
| not(implies(implies(not(not(X)),X_43),not(X))) = not(implies(X,not(implies(X,X_43)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(not(X)),X_43),not(X))),not(implies(implies(not(not(X)),X_43),not(X)))) ),[1,0],$fot(implies(X,not(implies(X,X_43))))]]) ).
cnf(refute_0_263,plain,
( implies(implies(not(not(X)),X_43),not(X)) != implies(X,not(implies(X,X_43)))
| not(implies(implies(not(not(X)),X_43),not(X))) = not(implies(X,not(implies(X,X_43)))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(not(X)),X_43),not(X))),not(implies(implies(not(not(X)),X_43),not(X)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
not(implies(implies(not(not(X)),X_43),not(X))) = not(implies(X,not(implies(X,X_43)))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X)),X_43),not(X)),implies(X,not(implies(X,X_43)))) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),
introduced(tautology,[refl,[$fot(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))))]]) ).
cnf(refute_0_266,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(X,not(implies(implies(not(not(X)),X_43),not(X))))
| not(implies(implies(not(not(X)),X_43),not(X))) != not(implies(X,not(implies(X,X_43))))
| implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(X,not(implies(X,not(implies(X,X_43))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(X,not(implies(implies(not(not(X)),X_43),not(X))))) ),[1,1],$fot(not(implies(X,not(implies(X,X_43)))))]]) ).
cnf(refute_0_267,plain,
( not(implies(implies(not(not(X)),X_43),not(X))) != not(implies(X,not(implies(X,X_43))))
| implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(X,not(implies(X,not(implies(X,X_43))))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(X,not(implies(implies(not(not(X)),X_43),not(X))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) = implies(X,not(implies(X,not(implies(X,X_43))))),
inference(resolve,[$cnf( $equal(not(implies(implies(not(not(X)),X_43),not(X))),not(implies(X,not(implies(X,X_43))))) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(X,not(implies(X,not(implies(X,X_43)))))
| implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(not(not(X)),X_43)
| implies(X,not(implies(X,not(implies(X,X_43))))) = implies(not(not(X)),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(not(not(X)),X_43)) ),[0],$fot(implies(X,not(implies(X,not(implies(X,X_43))))))]]) ).
cnf(refute_0_270,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(not(not(X)),X_43)
| implies(X,not(implies(X,not(implies(X,X_43))))) = implies(not(not(X)),X_43) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(X,not(implies(X,not(implies(X,X_43)))))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
( implies(X,not(implies(X,not(implies(X,X_43))))) != implies(not(not(X)),X_43)
| implies(not(not(X)),X_43) != implies(X,X_43)
| implies(X,not(implies(X,not(implies(X,X_43))))) = implies(X,X_43) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(implies(X,not(implies(X,X_43))))),implies(X,X_43)) ),[0],$fot(implies(not(not(X)),X_43))]]) ).
cnf(refute_0_272,plain,
( implies(X,not(implies(X,not(implies(X,X_43))))) != implies(not(not(X)),X_43)
| implies(X,not(implies(X,not(implies(X,X_43))))) = implies(X,X_43) ),
inference(resolve,[$cnf( $equal(implies(not(not(X)),X_43),implies(X,X_43)) )],[refute_0_248,refute_0_271]) ).
cnf(refute_0_273,plain,
( implies(X,not(implies(implies(not(not(X)),X_43),not(X)))) != implies(not(not(X)),X_43)
| implies(X,not(implies(X,not(implies(X,X_43))))) = implies(X,X_43) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(implies(X,X_43))))),implies(not(not(X)),X_43)) )],[refute_0_270,refute_0_272]) ).
cnf(refute_0_274,plain,
implies(X,not(implies(X,not(implies(X,X_43))))) = implies(X,X_43),
inference(resolve,[$cnf( $equal(implies(X,not(implies(implies(not(not(X)),X_43),not(X)))),implies(not(not(X)),X_43)) )],[refute_0_244,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(X,not(implies(X,not(implies(X,X_40))))) = implies(X,X_40),
inference(subst,[],[refute_0_274:[bind(X_43,$fot(X_40))]]) ).
cnf(refute_0_276,plain,
( implies(X,not(implies(X,not(implies(X,X_40))))) != implies(X,X_40)
| implies(X,not(implies(X,not(implies(X,X_40))))) != implies(X,not(implies(X_40,not(implies(X_40,X)))))
| implies(X,X_40) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,not(implies(X,not(implies(X,X_40))))),implies(X,not(implies(X_40,not(implies(X_40,X)))))) ),[0],$fot(implies(X,X_40))]]) ).
cnf(refute_0_277,plain,
( implies(X,not(implies(X,not(implies(X,X_40))))) != implies(X,not(implies(X_40,not(implies(X_40,X)))))
| implies(X,X_40) = implies(X,not(implies(X_40,not(implies(X_40,X))))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(implies(X,X_40))))),implies(X,X_40)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(X,X_40) = implies(X,not(implies(X_40,not(implies(X_40,X))))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(implies(X,X_40))))),implies(X,not(implies(X_40,not(implies(X_40,X)))))) )],[refute_0_219,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(implies(X_40,X_348),X_40) = implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,implies(X_40,X_348)))))),
inference(subst,[],[refute_0_278:[bind(X,$fot(implies(X_40,X_348)))]]) ).
cnf(refute_0_280,plain,
implies(not(not(Y)),implies(Y,X)) = implies(not(X),implies(not(not(Y)),not(Y))),
inference(subst,[],[refute_0_93:[bind(X_29,$fot(not(not(Y))))]]) ).
cnf(refute_0_281,plain,
implies(implies(not(implies(Y,X_40)),Y),Y) = implies(implies(Y,not(implies(Y,X_40))),not(implies(Y,X_40))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(implies(Y,X_40))))]]) ).
cnf(refute_0_282,plain,
implies(Y,not(implies(Y,X_40))) = implies(X_40,not(implies(X_40,Y))),
inference(subst,[],[refute_0_211:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_283,plain,
( implies(Y,not(implies(Y,X_40))) != implies(X_40,not(implies(X_40,Y)))
| implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(Y,not(implies(Y,X_40))),not(implies(Y,X_40)))
| implies(implies(not(implies(Y,X_40)),Y),Y) = implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(Y,not(implies(Y,X_40))),not(implies(Y,X_40)))) ),[1,0],$fot(implies(X_40,not(implies(X_40,Y))))]]) ).
cnf(refute_0_284,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(Y,not(implies(Y,X_40))),not(implies(Y,X_40)))
| implies(implies(not(implies(Y,X_40)),Y),Y) = implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,X_40))),implies(X_40,not(implies(X_40,Y)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
implies(implies(not(implies(Y,X_40)),Y),Y) = implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(Y,not(implies(Y,X_40))),not(implies(Y,X_40)))) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_287,plain,
implies(Y,implies(not(Y),X_40)) = truth,
inference(subst,[],[refute_0_230:[bind(X_7,$fot(X_40)),bind(X_8,$fot(Y))]]) ).
cnf(refute_0_288,plain,
implies(not(implies(Y,X_40)),Y) = implies(Y,implies(not(Y),X_40)),
inference(subst,[],[refute_0_31:[bind(X,$fot(Y)),bind(X_30,$fot(Y)),bind(X_31,$fot(X_40))]]) ).
cnf(refute_0_289,plain,
( implies(Y,implies(not(Y),X_40)) != truth
| implies(not(implies(Y,X_40)),Y) != implies(Y,implies(not(Y),X_40))
| implies(not(implies(Y,X_40)),Y) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(Y,X_40)),Y))),bind(Y0,$fot(implies(Y,implies(not(Y),X_40)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_290,plain,
( implies(Y,implies(not(Y),X_40)) != truth
| implies(not(implies(Y,X_40)),Y) = truth ),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,X_40)),Y),implies(Y,implies(not(Y),X_40))) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
implies(not(implies(Y,X_40)),Y) = truth,
inference(resolve,[$cnf( $equal(implies(Y,implies(not(Y),X_40)),truth) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(implies(not(implies(Y,X_40)),Y),Y) = implies(implies(not(implies(Y,X_40)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(Y,X_40)),Y),Y))]]) ).
cnf(refute_0_293,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(not(implies(Y,X_40)),Y),Y)
| implies(not(implies(Y,X_40)),Y) != truth
| implies(implies(not(implies(Y,X_40)),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(not(implies(Y,X_40)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_294,plain,
( implies(not(implies(Y,X_40)),Y) != truth
| implies(implies(not(implies(Y,X_40)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(not(implies(Y,X_40)),Y),Y)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(implies(not(implies(Y,X_40)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,X_40)),Y),truth) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(implies(Y,X_40)),Y),Y) = Y ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(implies(Y,X_40)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_297,plain,
( implies(truth,Y) != Y
| implies(implies(not(implies(Y,X_40)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(truth,Y)) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
implies(implies(not(implies(Y,X_40)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_286,refute_0_297]) ).
cnf(refute_0_299,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != Y
| implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))
| Y = implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_300,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))
| Y = implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),Y) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) = implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y))))),
inference(subst,[],[refute_0_46:[bind(X,$fot(implies(Y,X_40))),bind(X_8,$fot(implies(X_40,not(implies(X_40,Y)))))]]) ).
cnf(refute_0_302,plain,
( Y != implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))
| implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))) != implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y)))))
| Y = implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y)))))) ),[0],$fot(implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))))]]) ).
cnf(refute_0_303,plain,
( Y != implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))
| Y = implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y))))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40))),implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y)))))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(implies(not(implies(Y,X_40)),Y),Y) != implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))
| Y = implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y))))) ),
inference(resolve,[$cnf( $equal(Y,implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
Y = implies(implies(Y,X_40),not(implies(X_40,not(implies(X_40,Y))))),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_40)),Y),Y),implies(implies(X_40,not(implies(X_40,Y))),not(implies(Y,X_40)))) )],[refute_0_285,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(not(X_40),X_40) = implies(implies(implies(not(X_40),X_40),X_40),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))),
inference(subst,[],[refute_0_305:[bind(Y,$fot(implies(not(X_40),X_40)))]]) ).
cnf(refute_0_307,plain,
implies(implies(Z,X),implies(Z,Y)) = implies(Z,implies(implies(Z,X),Y)),
inference(subst,[],[refute_0_4:[bind(X,$fot(Z)),bind(Y,$fot(implies(Z,X))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_308,plain,
implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),
introduced(tautology,[refl,[$fot(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))))]]) ).
cnf(refute_0_309,plain,
( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) != implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y)))
| implies(implies(Z,X),implies(Z,Y)) != implies(Z,implies(implies(Z,X),Y))
| implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y)))) ),[1,1],$fot(implies(Z,implies(implies(Z,X),Y)))]]) ).
cnf(refute_0_310,plain,
( implies(implies(Z,X),implies(Z,Y)) != implies(Z,implies(implies(Z,X),Y))
| implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y)))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) = implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))),
inference(resolve,[$cnf( $equal(implies(implies(Z,X),implies(Z,Y)),implies(Z,implies(implies(Z,X),Y))) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) != implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y)))
| implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) != truth
| implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),truth) ),[0],$fot(implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))))]]) ).
cnf(refute_0_313,plain,
( implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))) != truth
| implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y)))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(implies(X,Y),implies(Z,implies(implies(Z,X),Y))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Z,X),implies(Z,Y))),truth) )],[lemma_6,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(implies(not(X),X_33),implies(X_34,implies(implies(X_34,not(X)),X_33))) = truth,
inference(subst,[],[refute_0_314:[bind(X,$fot(not(X))),bind(Y,$fot(X_33)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_316,plain,
implies(not(X_33),X) = implies(not(X),X_33),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_33))]]) ).
cnf(refute_0_317,plain,
( implies(not(X_33),X) != implies(not(X),X_33)
| implies(not(X),X_33) = implies(not(X_33),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_33),X))),bind(Y0,$fot(implies(not(X),X_33)))]]) ).
cnf(refute_0_318,plain,
implies(not(X),X_33) = implies(not(X_33),X),
inference(resolve,[$cnf( $equal(implies(not(X_33),X),implies(not(X),X_33)) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
( implies(implies(not(X),X_33),implies(X_34,implies(implies(X_34,not(X)),X_33))) != truth
| implies(not(X),X_33) != implies(not(X_33),X)
| implies(implies(not(X_33),X),implies(X_34,implies(implies(X_34,not(X)),X_33))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_33),implies(X_34,implies(implies(X_34,not(X)),X_33))),truth) ),[0,0],$fot(implies(not(X_33),X))]]) ).
cnf(refute_0_320,plain,
( implies(implies(not(X),X_33),implies(X_34,implies(implies(X_34,not(X)),X_33))) != truth
| implies(implies(not(X_33),X),implies(X_34,implies(implies(X_34,not(X)),X_33))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),X_33),implies(not(X_33),X)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
implies(implies(not(X_33),X),implies(X_34,implies(implies(X_34,not(X)),X_33))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_33),implies(X_34,implies(implies(X_34,not(X)),X_33))),truth) )],[refute_0_315,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(implies(not(X_116),implies(Y,not(X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) = truth,
inference(subst,[],[refute_0_321:[bind(X,$fot(implies(Y,not(X_116)))),bind(X_33,$fot(X_116)),bind(X_34,$fot(X_117))]]) ).
cnf(refute_0_323,plain,
implies(not(X_116),implies(Y,not(X_116))) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(not(X_116)))]]) ).
cnf(refute_0_324,plain,
( implies(implies(not(X_116),implies(Y,not(X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) != truth
| implies(not(X_116),implies(Y,not(X_116))) != truth
| implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_116),implies(Y,not(X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_325,plain,
( implies(implies(not(X_116),implies(Y,not(X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) != truth
| implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_116),implies(Y,not(X_116))),truth) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),implies(Y,not(X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))),truth) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) = implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))))]]) ).
cnf(refute_0_328,plain,
( implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) != implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))
| implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) != truth
| implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))),truth) ),[0],$fot(implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116)))]]) ).
cnf(refute_0_329,plain,
( implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) != truth
| implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))),implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_117,implies(implies(X_117,not(implies(Y,not(X_116)))),X_116))),truth) )],[refute_0_326,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(implies(not(X_116),not(not(X_116))),implies(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),X_116)) = truth,
inference(subst,[],[refute_0_330:[bind(Y,$fot(not(not(X_116)))),bind(X_117,$fot(implies(not(X_116),not(not(X_116)))))]]) ).
cnf(refute_0_332,plain,
( implies(implies(not(X_340),Y),X_340) != implies(X_340,X_341)
| implies(implies(not(X_340),Y),X_341) = truth ),
inference(subst,[],[lemma_5:[bind(X,$fot(implies(not(X_340),Y))),bind(Y,$fot(X_340)),bind(Z,$fot(X_341))]]) ).
cnf(refute_0_333,plain,
implies(not(X_42),not(implies(not(X_42),Y))) = implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42),
inference(subst,[],[refute_0_238:[bind(X_35,$fot(X_42)),bind(X_7,$fot(not(implies(not(X_42),Y))))]]) ).
cnf(refute_0_334,plain,
implies(Y,not(implies(Y,not(X_42)))) = implies(not(X_42),not(implies(not(X_42),Y))),
inference(subst,[],[refute_0_211:[bind(X,$fot(not(X_42)))]]) ).
cnf(refute_0_335,plain,
( implies(Y,not(implies(Y,not(X_42)))) != implies(not(X_42),not(implies(not(X_42),Y)))
| implies(not(X_42),not(implies(not(X_42),Y))) = implies(Y,not(implies(Y,not(X_42)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(Y,not(implies(Y,not(X_42)))))),bind(Y0,$fot(implies(not(X_42),not(implies(not(X_42),Y)))))]]) ).
cnf(refute_0_336,plain,
implies(not(X_42),not(implies(not(X_42),Y))) = implies(Y,not(implies(Y,not(X_42)))),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(X_42)))),implies(not(X_42),not(implies(not(X_42),Y)))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
( implies(not(X_42),not(implies(not(X_42),Y))) != implies(Y,not(implies(Y,not(X_42))))
| implies(not(X_42),not(implies(not(X_42),Y))) != implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)
| implies(Y,not(implies(Y,not(X_42)))) = implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_42),not(implies(not(X_42),Y))),implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)) ),[0],$fot(implies(Y,not(implies(Y,not(X_42)))))]]) ).
cnf(refute_0_338,plain,
( implies(not(X_42),not(implies(not(X_42),Y))) != implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)
| implies(Y,not(implies(Y,not(X_42)))) = implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) ),
inference(resolve,[$cnf( $equal(implies(not(X_42),not(implies(not(X_42),Y))),implies(Y,not(implies(Y,not(X_42))))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
implies(Y,not(implies(Y,not(X_42)))) = implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42),
inference(resolve,[$cnf( $equal(implies(not(X_42),not(implies(not(X_42),Y))),implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)) )],[refute_0_333,refute_0_338]) ).
cnf(refute_0_340,plain,
implies(not(X_42),not(implies(not(X_42),Y))) = implies(implies(not(X_42),Y),X_42),
inference(subst,[],[lemma_10:[bind(X,$fot(X_42)),bind(Y,$fot(implies(not(X_42),Y)))]]) ).
cnf(refute_0_341,plain,
( implies(not(X_35),X_7) != implies(implies(implies(not(X_35),X_7),X_35),X_35)
| implies(implies(implies(not(X_35),X_7),X_35),X_35) = implies(not(X_35),X_7) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_35),X_7))),bind(Y0,$fot(implies(implies(implies(not(X_35),X_7),X_35),X_35)))]]) ).
cnf(refute_0_342,plain,
implies(implies(implies(not(X_35),X_7),X_35),X_35) = implies(not(X_35),X_7),
inference(resolve,[$cnf( $equal(implies(not(X_35),X_7),implies(implies(implies(not(X_35),X_7),X_35),X_35)) )],[refute_0_238,refute_0_341]) ).
cnf(refute_0_343,plain,
implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) = implies(not(X_42),not(implies(not(X_42),Y))),
inference(subst,[],[refute_0_342:[bind(X_35,$fot(X_42)),bind(X_7,$fot(not(implies(not(X_42),Y))))]]) ).
cnf(refute_0_344,plain,
( implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) != implies(not(X_42),not(implies(not(X_42),Y)))
| implies(not(X_42),not(implies(not(X_42),Y))) != implies(implies(not(X_42),Y),X_42)
| implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) = implies(implies(not(X_42),Y),X_42) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42))),bind(Y0,$fot(implies(not(X_42),not(implies(not(X_42),Y))))),bind(Z0,$fot(implies(implies(not(X_42),Y),X_42)))]]) ).
cnf(refute_0_345,plain,
( implies(not(X_42),not(implies(not(X_42),Y))) != implies(implies(not(X_42),Y),X_42)
| implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) = implies(implies(not(X_42),Y),X_42) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42),implies(not(X_42),not(implies(not(X_42),Y)))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) = implies(implies(not(X_42),Y),X_42),
inference(resolve,[$cnf( $equal(implies(not(X_42),not(implies(not(X_42),Y))),implies(implies(not(X_42),Y),X_42)) )],[refute_0_340,refute_0_345]) ).
cnf(refute_0_347,plain,
( implies(Y,not(implies(Y,not(X_42)))) != implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)
| implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42) != implies(implies(not(X_42),Y),X_42)
| implies(Y,not(implies(Y,not(X_42)))) = implies(implies(not(X_42),Y),X_42) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(Y,not(implies(Y,not(X_42)))),implies(implies(not(X_42),Y),X_42)) ),[0],$fot(implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42))]]) ).
cnf(refute_0_348,plain,
( implies(Y,not(implies(Y,not(X_42)))) != implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)
| implies(Y,not(implies(Y,not(X_42)))) = implies(implies(not(X_42),Y),X_42) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42),implies(implies(not(X_42),Y),X_42)) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
implies(Y,not(implies(Y,not(X_42)))) = implies(implies(not(X_42),Y),X_42),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(X_42)))),implies(implies(implies(not(X_42),not(implies(not(X_42),Y))),X_42),X_42)) )],[refute_0_339,refute_0_348]) ).
cnf(refute_0_350,plain,
implies(Y,not(implies(Y,not(X_340)))) = implies(implies(not(X_340),Y),X_340),
inference(subst,[],[refute_0_349:[bind(X_42,$fot(X_340))]]) ).
cnf(refute_0_351,plain,
( implies(Y,not(implies(Y,not(X_340)))) != implies(implies(not(X_340),Y),X_340)
| implies(implies(not(X_340),Y),X_340) = implies(Y,not(implies(Y,not(X_340)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(Y,not(implies(Y,not(X_340)))))),bind(Y0,$fot(implies(implies(not(X_340),Y),X_340)))]]) ).
cnf(refute_0_352,plain,
implies(implies(not(X_340),Y),X_340) = implies(Y,not(implies(Y,not(X_340)))),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(X_340)))),implies(implies(not(X_340),Y),X_340)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( implies(Y,not(implies(Y,not(X_340)))) != implies(X_340,X_341)
| implies(implies(not(X_340),Y),X_340) != implies(Y,not(implies(Y,not(X_340))))
| implies(implies(not(X_340),Y),X_340) = implies(X_340,X_341) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_340),Y),X_340),implies(Y,not(implies(Y,not(X_340))))) ),[1],$fot(implies(X_340,X_341))]]) ).
cnf(refute_0_354,plain,
( implies(Y,not(implies(Y,not(X_340)))) != implies(X_340,X_341)
| implies(implies(not(X_340),Y),X_340) = implies(X_340,X_341) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_340),Y),X_340),implies(Y,not(implies(Y,not(X_340))))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
( implies(Y,not(implies(Y,not(X_340)))) != implies(X_340,X_341)
| implies(implies(not(X_340),Y),X_341) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_340),Y),X_340),implies(X_340,X_341)) )],[refute_0_354,refute_0_332]) ).
cnf(refute_0_356,plain,
( implies(X_340,not(implies(X_340,not(X_340)))) != implies(X_340,not(implies(X_340,not(X_340))))
| implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) = truth ),
inference(subst,[],[refute_0_355:[bind(Y,$fot(X_340)),bind(X_341,$fot(not(implies(X_340,not(X_340)))))]]) ).
cnf(refute_0_357,plain,
implies(X_340,not(implies(X_340,not(X_340)))) = implies(X_340,not(implies(X_340,not(X_340)))),
introduced(tautology,[refl,[$fot(implies(X_340,not(implies(X_340,not(X_340)))))]]) ).
cnf(refute_0_358,plain,
implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) = truth,
inference(resolve,[$cnf( $equal(implies(X_340,not(implies(X_340,not(X_340)))),implies(X_340,not(implies(X_340,not(X_340))))) )],[refute_0_357,refute_0_356]) ).
cnf(refute_0_359,plain,
implies(implies(X_170,not(X_171)),not(X_8)) = implies(X_8,not(implies(X_170,not(X_171)))),
inference(subst,[],[refute_0_38:[bind(X,$fot(implies(X_170,not(X_171))))]]) ).
cnf(refute_0_360,plain,
not(implies(X_119,not(X_42))) = implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(X_119,not(implies(X_119,not(X_42)))))))),
inference(subst,[],[refute_0_305:[bind(Y,$fot(not(implies(X_119,not(X_42))))),bind(X_40,$fot(X_119))]]) ).
cnf(refute_0_361,plain,
implies(X_119,not(implies(X_119,not(X_42)))) = implies(implies(not(X_42),X_119),X_42),
inference(subst,[],[refute_0_349:[bind(Y,$fot(X_119))]]) ).
cnf(refute_0_362,plain,
( implies(X_119,not(implies(X_119,not(X_42)))) != implies(implies(not(X_42),X_119),X_42)
| not(implies(X_119,not(X_42))) != implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(X_119,not(implies(X_119,not(X_42))))))))
| not(implies(X_119,not(X_42))) = implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_119,not(X_42))),implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(X_119,not(implies(X_119,not(X_42))))))))) ),[1,1,0,1,0],$fot(implies(implies(not(X_42),X_119),X_42))]]) ).
cnf(refute_0_363,plain,
( not(implies(X_119,not(X_42))) != implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(X_119,not(implies(X_119,not(X_42))))))))
| not(implies(X_119,not(X_42))) = implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) ),
inference(resolve,[$cnf( $equal(implies(X_119,not(implies(X_119,not(X_42)))),implies(implies(not(X_42),X_119),X_42)) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
not(implies(X_119,not(X_42))) = implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),
inference(resolve,[$cnf( $equal(not(implies(X_119,not(X_42))),implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(X_119,not(implies(X_119,not(X_42))))))))) )],[refute_0_360,refute_0_363]) ).
cnf(refute_0_365,plain,
implies(truth,not(implies(X_42,not(X_119)))) = not(implies(X_42,not(X_119))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(implies(X_42,not(X_119)))))]]) ).
cnf(refute_0_366,plain,
implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X,not(implies(X,not(implies(X_50,not(X)))))),
inference(subst,[],[refute_0_211:[bind(Y,$fot(not(implies(X_50,not(X)))))]]) ).
cnf(refute_0_367,plain,
implies(implies(not(X),X_36),X_36) = implies(implies(X_36,not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(X_36))]]) ).
cnf(refute_0_368,plain,
implies(not(X_36),X) = implies(not(X),X_36),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_36))]]) ).
cnf(refute_0_369,plain,
( implies(not(X_36),X) != implies(not(X),X_36)
| implies(not(X),X_36) = implies(not(X_36),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_36),X))),bind(Y0,$fot(implies(not(X),X_36)))]]) ).
cnf(refute_0_370,plain,
implies(not(X),X_36) = implies(not(X_36),X),
inference(resolve,[$cnf( $equal(implies(not(X_36),X),implies(not(X),X_36)) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
( implies(implies(not(X),X_36),X_36) != implies(implies(X_36,not(X)),not(X))
| implies(not(X),X_36) != implies(not(X_36),X)
| implies(implies(not(X_36),X),X_36) = implies(implies(X_36,not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_36),X_36),implies(implies(X_36,not(X)),not(X))) ),[0,0],$fot(implies(not(X_36),X))]]) ).
cnf(refute_0_372,plain,
( implies(implies(not(X),X_36),X_36) != implies(implies(X_36,not(X)),not(X))
| implies(implies(not(X_36),X),X_36) = implies(implies(X_36,not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_36),implies(not(X_36),X)) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
implies(implies(not(X_36),X),X_36) = implies(implies(X_36,not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_36),X_36),implies(implies(X_36,not(X)),not(X))) )],[refute_0_367,refute_0_372]) ).
cnf(refute_0_374,plain,
implies(implies(X_36,not(X)),not(X)) = implies(X,not(implies(X_36,not(X)))),
inference(subst,[],[refute_0_46:[bind(X_8,$fot(implies(X_36,not(X))))]]) ).
cnf(refute_0_375,plain,
( implies(implies(X_36,not(X)),not(X)) != implies(X,not(implies(X_36,not(X))))
| implies(implies(not(X_36),X),X_36) != implies(implies(X_36,not(X)),not(X))
| implies(implies(not(X_36),X),X_36) = implies(X,not(implies(X_36,not(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_36),X),X_36),implies(implies(X_36,not(X)),not(X))) ),[1],$fot(implies(X,not(implies(X_36,not(X)))))]]) ).
cnf(refute_0_376,plain,
( implies(implies(not(X_36),X),X_36) != implies(implies(X_36,not(X)),not(X))
| implies(implies(not(X_36),X),X_36) = implies(X,not(implies(X_36,not(X)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_36,not(X)),not(X)),implies(X,not(implies(X_36,not(X))))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
implies(implies(not(X_36),X),X_36) = implies(X,not(implies(X_36,not(X)))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_36),X),X_36),implies(implies(X_36,not(X)),not(X))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
implies(implies(not(X_50),X),X_50) = implies(X,not(implies(X_50,not(X)))),
inference(subst,[],[refute_0_377:[bind(X_36,$fot(X_50))]]) ).
cnf(refute_0_379,plain,
( implies(implies(not(X_50),X),X_50) != implies(X,not(implies(X_50,not(X))))
| implies(X,not(implies(X_50,not(X)))) = implies(implies(not(X_50),X),X_50) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_50),X),X_50))),bind(Y0,$fot(implies(X,not(implies(X_50,not(X))))))]]) ).
cnf(refute_0_380,plain,
implies(X,not(implies(X_50,not(X)))) = implies(implies(not(X_50),X),X_50),
inference(resolve,[$cnf( $equal(implies(implies(not(X_50),X),X_50),implies(X,not(implies(X_50,not(X))))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
( implies(X,not(implies(X_50,not(X)))) != implies(implies(not(X_50),X),X_50)
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X,not(implies(X,not(implies(X_50,not(X))))))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X,not(implies(implies(not(X_50),X),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X,not(implies(X,not(implies(X_50,not(X))))))) ),[1,1,0],$fot(implies(implies(not(X_50),X),X_50))]]) ).
cnf(refute_0_382,plain,
( implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X,not(implies(X,not(implies(X_50,not(X))))))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X,not(implies(implies(not(X_50),X),X_50))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X_50,not(X)))),implies(implies(not(X_50),X),X_50)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X,not(implies(implies(not(X_50),X),X_50))),
inference(resolve,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X,not(implies(X,not(implies(X_50,not(X))))))) )],[refute_0_366,refute_0_382]) ).
cnf(refute_0_384,plain,
implies(X,not(implies(X_35,not(X)))) = implies(implies(X_35,not(X)),not(X)),
inference(subst,[],[refute_0_38:[bind(X_8,$fot(implies(X_35,not(X))))]]) ).
cnf(refute_0_385,plain,
( implies(X,not(implies(X_35,not(X)))) != implies(implies(X_35,not(X)),not(X))
| implies(implies(X_35,not(X)),not(X)) != implies(implies(not(X),X_35),X_35)
| implies(X,not(implies(X_35,not(X)))) = implies(implies(not(X),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,not(implies(X_35,not(X)))),implies(implies(not(X),X_35),X_35)) ),[0],$fot(implies(implies(X_35,not(X)),not(X)))]]) ).
cnf(refute_0_386,plain,
( implies(X,not(implies(X_35,not(X)))) != implies(implies(X_35,not(X)),not(X))
| implies(X,not(implies(X_35,not(X)))) = implies(implies(not(X),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,not(X)),not(X)),implies(implies(not(X),X_35),X_35)) )],[refute_0_34,refute_0_385]) ).
cnf(refute_0_387,plain,
implies(X,not(implies(X_35,not(X)))) = implies(implies(not(X),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X_35,not(X)))),implies(implies(X_35,not(X)),not(X))) )],[refute_0_384,refute_0_386]) ).
cnf(refute_0_388,plain,
implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(implies(not(X_47),implies(Y,not(X_47))),implies(Y,not(X_47))),
inference(subst,[],[refute_0_387:[bind(X,$fot(X_47)),bind(X_35,$fot(implies(Y,not(X_47))))]]) ).
cnf(refute_0_389,plain,
implies(not(X_47),implies(Y,not(X_47))) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(not(X_47)))]]) ).
cnf(refute_0_390,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(implies(not(X_47),implies(Y,not(X_47))),implies(Y,not(X_47)))
| implies(not(X_47),implies(Y,not(X_47))) != truth
| implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(truth,implies(Y,not(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(implies(not(X_47),implies(Y,not(X_47))),implies(Y,not(X_47)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_391,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(implies(not(X_47),implies(Y,not(X_47))),implies(Y,not(X_47)))
| implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(truth,implies(Y,not(X_47))) ),
inference(resolve,[$cnf( $equal(implies(not(X_47),implies(Y,not(X_47))),truth) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(truth,implies(Y,not(X_47))),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(implies(not(X_47),implies(Y,not(X_47))),implies(Y,not(X_47)))) )],[refute_0_388,refute_0_391]) ).
cnf(refute_0_393,plain,
implies(implies(Y,not(X_47)),not(X_47)) = implies(X_47,not(implies(Y,not(X_47)))),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_47)),bind(X_8,$fot(implies(Y,not(X_47))))]]) ).
cnf(refute_0_394,plain,
not(implies(implies(Y,not(X_47)),not(X_47))) = not(implies(implies(Y,not(X_47)),not(X_47))),
introduced(tautology,[refl,[$fot(not(implies(implies(Y,not(X_47)),not(X_47))))]]) ).
cnf(refute_0_395,plain,
( implies(implies(Y,not(X_47)),not(X_47)) != implies(X_47,not(implies(Y,not(X_47))))
| not(implies(implies(Y,not(X_47)),not(X_47))) != not(implies(implies(Y,not(X_47)),not(X_47)))
| not(implies(implies(Y,not(X_47)),not(X_47))) = not(implies(X_47,not(implies(Y,not(X_47))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(Y,not(X_47)),not(X_47))),not(implies(implies(Y,not(X_47)),not(X_47)))) ),[1,0],$fot(implies(X_47,not(implies(Y,not(X_47)))))]]) ).
cnf(refute_0_396,plain,
( implies(implies(Y,not(X_47)),not(X_47)) != implies(X_47,not(implies(Y,not(X_47))))
| not(implies(implies(Y,not(X_47)),not(X_47))) = not(implies(X_47,not(implies(Y,not(X_47))))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(Y,not(X_47)),not(X_47))),not(implies(implies(Y,not(X_47)),not(X_47)))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
not(implies(implies(Y,not(X_47)),not(X_47))) = not(implies(X_47,not(implies(Y,not(X_47))))),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(X_47)),not(X_47)),implies(X_47,not(implies(Y,not(X_47))))) )],[refute_0_393,refute_0_396]) ).
cnf(refute_0_398,plain,
implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),
introduced(tautology,[refl,[$fot(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))))]]) ).
cnf(refute_0_399,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47))))
| not(implies(implies(Y,not(X_47)),not(X_47))) != not(implies(X_47,not(implies(Y,not(X_47)))))
| implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47))))) ),[1,1],$fot(not(implies(X_47,not(implies(Y,not(X_47))))))]]) ).
cnf(refute_0_400,plain,
( not(implies(implies(Y,not(X_47)),not(X_47))) != not(implies(X_47,not(implies(Y,not(X_47)))))
| implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) ),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47))))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) = implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))),
inference(resolve,[$cnf( $equal(not(implies(implies(Y,not(X_47)),not(X_47))),not(implies(X_47,not(implies(Y,not(X_47)))))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(X_47,not(implies(X_47,not(implies(Y,not(X_47))))))
| implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(truth,implies(Y,not(X_47)))
| implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(truth,implies(Y,not(X_47))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(truth,implies(Y,not(X_47)))) ),[0],$fot(implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))))]]) ).
cnf(refute_0_403,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(truth,implies(Y,not(X_47)))
| implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(truth,implies(Y,not(X_47))) ),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(X_47,not(implies(X_47,not(implies(Y,not(X_47))))))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
implies(truth,implies(Y,not(X_47))) = implies(Y,not(X_47)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(X_47))))]]) ).
cnf(refute_0_405,plain,
( implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) != implies(truth,implies(Y,not(X_47)))
| implies(truth,implies(Y,not(X_47))) != implies(Y,not(X_47))
| implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(Y,not(X_47)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))),implies(Y,not(X_47))) ),[0],$fot(implies(truth,implies(Y,not(X_47))))]]) ).
cnf(refute_0_406,plain,
( implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) != implies(truth,implies(Y,not(X_47)))
| implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(Y,not(X_47)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(X_47))),implies(Y,not(X_47))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
( implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))) != implies(truth,implies(Y,not(X_47)))
| implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(Y,not(X_47)) ),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))),implies(truth,implies(Y,not(X_47)))) )],[refute_0_403,refute_0_406]) ).
cnf(refute_0_408,plain,
implies(X_47,not(implies(X_47,not(implies(Y,not(X_47)))))) = implies(Y,not(X_47)),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(implies(Y,not(X_47)),not(X_47)))),implies(truth,implies(Y,not(X_47)))) )],[refute_0_392,refute_0_407]) ).
cnf(refute_0_409,plain,
implies(X,not(implies(X,not(implies(X_50,not(X)))))) = implies(X_50,not(X)),
inference(subst,[],[refute_0_408:[bind(Y,$fot(X_50)),bind(X_47,$fot(X))]]) ).
cnf(refute_0_410,plain,
( implies(X,not(implies(X,not(implies(X_50,not(X)))))) != implies(X_50,not(X))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X,not(implies(X,not(implies(X_50,not(X))))))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X_50,not(X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))))),bind(Y0,$fot(implies(X,not(implies(X,not(implies(X_50,not(X)))))))),bind(Z0,$fot(implies(X_50,not(X))))]]) ).
cnf(refute_0_411,plain,
( implies(X,not(implies(X,not(implies(X_50,not(X)))))) != implies(X_50,not(X))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X_50,not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X,not(implies(X,not(implies(X_50,not(X))))))) )],[refute_0_366,refute_0_410]) ).
cnf(refute_0_412,plain,
implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) = implies(X_50,not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(implies(X_50,not(X)))))),implies(X_50,not(X))) )],[refute_0_409,refute_0_411]) ).
cnf(refute_0_413,plain,
( implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X,not(implies(implies(not(X_50),X),X_50)))
| implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X_50,not(X))
| implies(X_50,not(X)) = implies(X,not(implies(implies(not(X_50),X),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X,not(implies(implies(not(X_50),X),X_50)))) ),[0],$fot(implies(X_50,not(X)))]]) ).
cnf(refute_0_414,plain,
( implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))) != implies(X,not(implies(implies(not(X_50),X),X_50)))
| implies(X_50,not(X)) = implies(X,not(implies(implies(not(X_50),X),X_50))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X_50,not(X))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
implies(X_50,not(X)) = implies(X,not(implies(implies(not(X_50),X),X_50))),
inference(resolve,[$cnf( $equal(implies(not(implies(X_50,not(X))),not(implies(not(implies(X_50,not(X))),X))),implies(X,not(implies(implies(not(X_50),X),X_50)))) )],[refute_0_383,refute_0_414]) ).
cnf(refute_0_416,plain,
( implies(X_50,not(X)) != implies(X,not(implies(implies(not(X_50),X),X_50)))
| implies(X,not(implies(implies(not(X_50),X),X_50))) = implies(X_50,not(X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_50,not(X)))),bind(Y0,$fot(implies(X,not(implies(implies(not(X_50),X),X_50)))))]]) ).
cnf(refute_0_417,plain,
implies(X,not(implies(implies(not(X_50),X),X_50))) = implies(X_50,not(X)),
inference(resolve,[$cnf( $equal(implies(X_50,not(X)),implies(X,not(implies(implies(not(X_50),X),X_50)))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
implies(X_119,not(implies(implies(not(X_42),X_119),X_42))) = implies(X_42,not(X_119)),
inference(subst,[],[refute_0_417:[bind(X,$fot(X_119)),bind(X_50,$fot(X_42))]]) ).
cnf(refute_0_419,plain,
not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) = not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))),
introduced(tautology,[refl,[$fot(not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))]]) ).
cnf(refute_0_420,plain,
( implies(X_119,not(implies(implies(not(X_42),X_119),X_42))) != implies(X_42,not(X_119))
| not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) != not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))
| not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) = not(implies(X_42,not(X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) ),[1,0],$fot(implies(X_42,not(X_119)))]]) ).
cnf(refute_0_421,plain,
( implies(X_119,not(implies(implies(not(X_42),X_119),X_42))) != implies(X_42,not(X_119))
| not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) = not(implies(X_42,not(X_119))) ),
inference(resolve,[$cnf( $equal(not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) = not(implies(X_42,not(X_119))),
inference(resolve,[$cnf( $equal(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))),implies(X_42,not(X_119))) )],[refute_0_418,refute_0_421]) ).
cnf(refute_0_423,plain,
implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),
introduced(tautology,[refl,[$fot(implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))]]) ).
cnf(refute_0_424,plain,
( implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) != not(implies(X_42,not(X_119)))
| implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) ),[1,1],$fot(not(implies(X_42,not(X_119))))]]) ).
cnf(refute_0_425,plain,
( not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))) != not(implies(X_42,not(X_119)))
| implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) )],[refute_0_423,refute_0_424]) ).
cnf(refute_0_426,plain,
implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))),
inference(resolve,[$cnf( $equal(not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))),not(implies(X_42,not(X_119)))) )],[refute_0_422,refute_0_425]) ).
cnf(refute_0_427,plain,
implies(X_119,implies(X_42,X_119)) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(X_119)),bind(Y,$fot(X_42))]]) ).
cnf(refute_0_428,plain,
not(not(X_119)) = X_119,
inference(subst,[],[lemma_9:[bind(X,$fot(X_119))]]) ).
cnf(refute_0_429,plain,
implies(X_42,not(not(X_119))) = implies(X_42,not(not(X_119))),
introduced(tautology,[refl,[$fot(implies(X_42,not(not(X_119))))]]) ).
cnf(refute_0_430,plain,
( implies(X_42,not(not(X_119))) != implies(X_42,not(not(X_119)))
| not(not(X_119)) != X_119
| implies(X_42,not(not(X_119))) = implies(X_42,X_119) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_42,not(not(X_119))),implies(X_42,not(not(X_119)))) ),[1,1],$fot(X_119)]]) ).
cnf(refute_0_431,plain,
( not(not(X_119)) != X_119
| implies(X_42,not(not(X_119))) = implies(X_42,X_119) ),
inference(resolve,[$cnf( $equal(implies(X_42,not(not(X_119))),implies(X_42,not(not(X_119)))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
implies(X_42,not(not(X_119))) = implies(X_42,X_119),
inference(resolve,[$cnf( $equal(not(not(X_119)),X_119) )],[refute_0_428,refute_0_431]) ).
cnf(refute_0_433,plain,
implies(X_119,implies(X_42,not(not(X_119)))) = implies(X_119,implies(X_42,not(not(X_119)))),
introduced(tautology,[refl,[$fot(implies(X_119,implies(X_42,not(not(X_119)))))]]) ).
cnf(refute_0_434,plain,
( implies(X_119,implies(X_42,not(not(X_119)))) != implies(X_119,implies(X_42,not(not(X_119))))
| implies(X_42,not(not(X_119))) != implies(X_42,X_119)
| implies(X_119,implies(X_42,not(not(X_119)))) = implies(X_119,implies(X_42,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_119,implies(X_42,not(not(X_119)))),implies(X_119,implies(X_42,not(not(X_119))))) ),[1,1],$fot(implies(X_42,X_119))]]) ).
cnf(refute_0_435,plain,
( implies(X_42,not(not(X_119))) != implies(X_42,X_119)
| implies(X_119,implies(X_42,not(not(X_119)))) = implies(X_119,implies(X_42,X_119)) ),
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_42,not(not(X_119)))),implies(X_119,implies(X_42,not(not(X_119))))) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
implies(X_119,implies(X_42,not(not(X_119)))) = implies(X_119,implies(X_42,X_119)),
inference(resolve,[$cnf( $equal(implies(X_42,not(not(X_119))),implies(X_42,X_119)) )],[refute_0_432,refute_0_435]) ).
cnf(refute_0_437,plain,
( implies(X_119,implies(X_42,X_119)) != truth
| implies(X_119,implies(X_42,not(not(X_119)))) != implies(X_119,implies(X_42,X_119))
| implies(X_119,implies(X_42,not(not(X_119)))) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_119,implies(X_42,not(not(X_119)))))),bind(Y0,$fot(implies(X_119,implies(X_42,X_119)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_438,plain,
( implies(X_119,implies(X_42,X_119)) != truth
| implies(X_119,implies(X_42,not(not(X_119)))) = truth ),
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_42,not(not(X_119)))),implies(X_119,implies(X_42,X_119))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
implies(X_119,implies(X_42,not(not(X_119)))) = truth,
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_42,X_119)),truth) )],[refute_0_427,refute_0_438]) ).
cnf(refute_0_440,plain,
implies(X_29,implies(X_30,not(X))) = implies(X_30,implies(X_29,not(X))),
inference(subst,[],[lemma_7:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(not(X)))]]) ).
cnf(refute_0_441,plain,
implies(X,not(X_30)) = implies(X_30,not(X)),
inference(subst,[],[refute_0_38:[bind(X_8,$fot(X_30))]]) ).
cnf(refute_0_442,plain,
( implies(X,not(X_30)) != implies(X_30,not(X))
| implies(X_30,not(X)) = implies(X,not(X_30)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(X_30)))),bind(Y0,$fot(implies(X_30,not(X))))]]) ).
cnf(refute_0_443,plain,
implies(X_30,not(X)) = implies(X,not(X_30)),
inference(resolve,[$cnf( $equal(implies(X,not(X_30)),implies(X_30,not(X))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( implies(X_29,implies(X_30,not(X))) != implies(X_30,implies(X_29,not(X)))
| implies(X_30,not(X)) != implies(X,not(X_30))
| implies(X_29,implies(X,not(X_30))) = implies(X_30,implies(X_29,not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,implies(X_30,not(X))),implies(X_30,implies(X_29,not(X)))) ),[0,1],$fot(implies(X,not(X_30)))]]) ).
cnf(refute_0_445,plain,
( implies(X_29,implies(X_30,not(X))) != implies(X_30,implies(X_29,not(X)))
| implies(X_29,implies(X,not(X_30))) = implies(X_30,implies(X_29,not(X))) ),
inference(resolve,[$cnf( $equal(implies(X_30,not(X)),implies(X,not(X_30))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
implies(X_29,implies(X,not(X_30))) = implies(X_30,implies(X_29,not(X))),
inference(resolve,[$cnf( $equal(implies(X_29,implies(X_30,not(X))),implies(X_30,implies(X_29,not(X)))) )],[refute_0_440,refute_0_445]) ).
cnf(refute_0_447,plain,
implies(X_93,implies(X_92,not(Y))) = implies(Y,implies(X_93,not(X_92))),
inference(subst,[],[refute_0_446:[bind(X,$fot(X_92)),bind(X_29,$fot(X_93)),bind(X_30,$fot(Y))]]) ).
cnf(refute_0_448,plain,
( implies(X_93,implies(X_92,not(Y))) != implies(Y,implies(X_93,not(X_92)))
| implies(Y,implies(X_93,not(X_92))) = implies(X_93,implies(X_92,not(Y))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_93,implies(X_92,not(Y))))),bind(Y0,$fot(implies(Y,implies(X_93,not(X_92)))))]]) ).
cnf(refute_0_449,plain,
implies(Y,implies(X_93,not(X_92))) = implies(X_93,implies(X_92,not(Y))),
inference(resolve,[$cnf( $equal(implies(X_93,implies(X_92,not(Y))),implies(Y,implies(X_93,not(X_92)))) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
implies(not(X_119),implies(X_119,not(X_42))) = implies(X_119,implies(X_42,not(not(X_119)))),
inference(subst,[],[refute_0_449:[bind(Y,$fot(not(X_119))),bind(X_92,$fot(X_42)),bind(X_93,$fot(X_119))]]) ).
cnf(refute_0_451,plain,
( implies(X_119,implies(X_42,not(not(X_119)))) != truth
| implies(not(X_119),implies(X_119,not(X_42))) != implies(X_119,implies(X_42,not(not(X_119))))
| implies(not(X_119),implies(X_119,not(X_42))) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(X_119),implies(X_119,not(X_42))))),bind(Y0,$fot(implies(X_119,implies(X_42,not(not(X_119)))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_452,plain,
( implies(X_119,implies(X_42,not(not(X_119)))) != truth
| implies(not(X_119),implies(X_119,not(X_42))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_119),implies(X_119,not(X_42))),implies(X_119,implies(X_42,not(not(X_119))))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
implies(not(X_119),implies(X_119,not(X_42))) = truth,
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_42,not(not(X_119)))),truth) )],[refute_0_439,refute_0_452]) ).
cnf(refute_0_454,plain,
implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))]]) ).
cnf(refute_0_455,plain,
( implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| implies(not(X_119),implies(X_119,not(X_42))) != truth
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_456,plain,
( implies(not(X_119),implies(X_119,not(X_42))) != truth
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),
inference(resolve,[$cnf( $equal(implies(not(X_119),implies(X_119,not(X_42))),truth) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
( implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(truth,not(implies(X_42,not(X_119))))
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))),bind(Y0,$fot(implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))),bind(Z0,$fot(implies(truth,not(implies(X_42,not(X_119))))))]]) ).
cnf(refute_0_459,plain,
( implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(truth,not(implies(X_42,not(X_119))))
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(truth,not(implies(X_42,not(X_119)))),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(truth,not(implies(X_42,not(X_119))))) )],[refute_0_426,refute_0_459]) ).
cnf(refute_0_461,plain,
( implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(truth,not(implies(X_42,not(X_119))))
| implies(truth,not(implies(X_42,not(X_119)))) != not(implies(X_42,not(X_119)))
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))),bind(Y0,$fot(implies(truth,not(implies(X_42,not(X_119)))))),bind(Z0,$fot(not(implies(X_42,not(X_119)))))]]) ).
cnf(refute_0_462,plain,
( implies(truth,not(implies(X_42,not(X_119)))) != not(implies(X_42,not(X_119)))
| implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(truth,not(implies(X_42,not(X_119))))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X_42,not(X_119)))),not(implies(X_42,not(X_119)))) )],[refute_0_365,refute_0_462]) ).
cnf(refute_0_464,plain,
implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(implies(implies(Y,X_35),X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35)),bind(Y,$fot(implies(Y,X_35)))]]) ).
cnf(refute_0_465,plain,
implies(implies(X_35,Y),Y) = implies(implies(Y,X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_466,plain,
( implies(implies(X_35,Y),Y) != implies(implies(Y,X_35),X_35)
| implies(implies(Y,X_35),X_35) = implies(implies(X_35,Y),Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_35,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_35),X_35)))]]) ).
cnf(refute_0_467,plain,
implies(implies(Y,X_35),X_35) = implies(implies(X_35,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_35,Y),Y),implies(implies(Y,X_35),X_35)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( implies(implies(Y,X_35),X_35) != implies(implies(X_35,Y),Y)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(implies(implies(X_35,Y),Y),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) ),[1,0],$fot(implies(implies(X_35,Y),Y))]]) ).
cnf(refute_0_469,plain,
( implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(implies(implies(X_35,Y),Y),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_35),X_35),implies(implies(X_35,Y),Y)) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(implies(implies(X_35,Y),Y),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) )],[refute_0_464,refute_0_469]) ).
cnf(refute_0_471,plain,
implies(X_35,implies(Y,X_35)) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_472,plain,
( implies(X_35,implies(Y,X_35)) != truth
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(truth,implies(Y,X_35)) = implies(implies(implies(Y,X_35),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_473,plain,
( implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(truth,implies(Y,X_35)) = implies(implies(implies(Y,X_35),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(X_35,implies(Y,X_35)),truth) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
implies(truth,implies(Y,X_35)) = implies(implies(implies(Y,X_35),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) )],[refute_0_464,refute_0_473]) ).
cnf(refute_0_475,plain,
implies(truth,implies(Y,X_35)) = implies(Y,X_35),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,X_35)))]]) ).
cnf(refute_0_476,plain,
( implies(truth,implies(Y,X_35)) != implies(Y,X_35)
| implies(truth,implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(Y,X_35) = implies(implies(implies(Y,X_35),X_35),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) ),[0],$fot(implies(Y,X_35))]]) ).
cnf(refute_0_477,plain,
( implies(truth,implies(Y,X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(Y,X_35) = implies(implies(implies(Y,X_35),X_35),X_35) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,X_35)),implies(Y,X_35)) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
implies(Y,X_35) = implies(implies(implies(Y,X_35),X_35),X_35),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( implies(Y,X_35) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(implies(implies(Y,X_35),X_35),X_35) = implies(Y,X_35) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(Y,X_35))),bind(Y0,$fot(implies(implies(implies(Y,X_35),X_35),X_35)))]]) ).
cnf(refute_0_480,plain,
implies(implies(implies(Y,X_35),X_35),X_35) = implies(Y,X_35),
inference(resolve,[$cnf( $equal(implies(Y,X_35),implies(implies(implies(Y,X_35),X_35),X_35)) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) = implies(implies(implies(Y,X_35),X_35),X_35),
inference(subst,[],[refute_0_151:[bind(X,$fot(Y)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_482,plain,
( implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) != implies(implies(implies(Y,X_35),X_35),X_35)
| implies(implies(implies(Y,X_35),X_35),X_35) != implies(Y,X_35)
| implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) = implies(Y,X_35) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)))),bind(Y0,$fot(implies(implies(implies(Y,X_35),X_35),X_35))),bind(Z0,$fot(implies(Y,X_35)))]]) ).
cnf(refute_0_483,plain,
( implies(implies(implies(Y,X_35),X_35),X_35) != implies(Y,X_35)
| implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) = implies(Y,X_35) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)),implies(implies(implies(Y,X_35),X_35),X_35)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) = implies(Y,X_35),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_35),X_35),X_35),implies(Y,X_35)) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(implies(X_35,implies(Y,X_35)))),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_486,plain,
( implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) != implies(Y,X_35)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35))
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(Y,X_35) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)))),bind(Y0,$fot(implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)))),bind(Z0,$fot(implies(Y,X_35)))]]) ).
cnf(refute_0_487,plain,
( implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)) != implies(Y,X_35)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(Y,X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) = implies(Y,X_35),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(X_35,implies(Y,X_35)),X_35)),implies(Y,X_35)) )],[refute_0_484,refute_0_487]) ).
cnf(refute_0_489,plain,
( implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(Y,X_35)
| implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(X_35,Y),Y),X_35)
| implies(Y,X_35) = implies(implies(implies(X_35,Y),Y),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(X_35,Y),Y),X_35)) ),[0],$fot(implies(Y,X_35))]]) ).
cnf(refute_0_490,plain,
( implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)) != implies(implies(implies(X_35,Y),Y),X_35)
| implies(Y,X_35) = implies(implies(implies(X_35,Y),Y),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(Y,X_35)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
implies(Y,X_35) = implies(implies(implies(X_35,Y),Y),X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(Y,X_35)),implies(Y,X_35)),implies(implies(implies(X_35,Y),Y),X_35)) )],[refute_0_470,refute_0_490]) ).
cnf(refute_0_492,plain,
implies(implies(not(X_85),X_83),X_35) = implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35),
inference(subst,[],[refute_0_491:[bind(Y,$fot(implies(not(X_85),X_83)))]]) ).
cnf(refute_0_493,plain,
implies(X_29,implies(not(X),X_31)) = implies(not(X),implies(X_29,X_31)),
inference(subst,[],[lemma_7:[bind(X,$fot(X_29)),bind(Y,$fot(not(X))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_494,plain,
implies(not(X_31),X) = implies(not(X),X_31),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_31))]]) ).
cnf(refute_0_495,plain,
( implies(not(X_31),X) != implies(not(X),X_31)
| implies(not(X),X_31) = implies(not(X_31),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_31),X))),bind(Y0,$fot(implies(not(X),X_31)))]]) ).
cnf(refute_0_496,plain,
implies(not(X),X_31) = implies(not(X_31),X),
inference(resolve,[$cnf( $equal(implies(not(X_31),X),implies(not(X),X_31)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
( implies(X_29,implies(not(X),X_31)) != implies(not(X),implies(X_29,X_31))
| implies(not(X),X_31) != implies(not(X_31),X)
| implies(X_29,implies(not(X_31),X)) = implies(not(X),implies(X_29,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,implies(not(X),X_31)),implies(not(X),implies(X_29,X_31))) ),[0,1],$fot(implies(not(X_31),X))]]) ).
cnf(refute_0_498,plain,
( implies(X_29,implies(not(X),X_31)) != implies(not(X),implies(X_29,X_31))
| implies(X_29,implies(not(X_31),X)) = implies(not(X),implies(X_29,X_31)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_31),implies(not(X_31),X)) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
implies(X_29,implies(not(X_31),X)) = implies(not(X),implies(X_29,X_31)),
inference(resolve,[$cnf( $equal(implies(X_29,implies(not(X),X_31)),implies(not(X),implies(X_29,X_31))) )],[refute_0_493,refute_0_498]) ).
cnf(refute_0_500,plain,
implies(X_35,implies(not(X_85),X_83)) = implies(not(X_83),implies(X_35,X_85)),
inference(subst,[],[refute_0_499:[bind(X,$fot(X_83)),bind(X_29,$fot(X_35)),bind(X_31,$fot(X_85))]]) ).
cnf(refute_0_501,plain,
( implies(X_35,implies(not(X_85),X_83)) != implies(not(X_83),implies(X_35,X_85))
| implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)) ),[1,0,0],$fot(implies(not(X_83),implies(X_35,X_85)))]]) ).
cnf(refute_0_502,plain,
( implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) ),
inference(resolve,[$cnf( $equal(implies(X_35,implies(not(X_85),X_83)),implies(not(X_83),implies(X_35,X_85))) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
implies(implies(not(X_85),X_83),X_35) = implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)) )],[refute_0_492,refute_0_502]) ).
cnf(refute_0_504,plain,
implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)) = implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),
inference(subst,[],[refute_0_499:[bind(X,$fot(X_83)),bind(X_29,$fot(implies(X_35,implies(not(X_85),X_83)))),bind(X_31,$fot(X_85))]]) ).
cnf(refute_0_505,plain,
( implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)) != implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85))
| implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)) ),[1,0],$fot(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)))]]) ).
cnf(refute_0_506,plain,
( implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(X_35,implies(not(X_85),X_83)),implies(not(X_85),X_83)),X_35)) )],[refute_0_492,refute_0_506]) ).
cnf(refute_0_508,plain,
( implies(implies(not(X_85),X_83),X_35) != implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35)
| implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35) = implies(implies(not(X_85),X_83),X_35) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_85),X_83),X_35))),bind(Y0,$fot(implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35)))]]) ).
cnf(refute_0_509,plain,
implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35) = implies(implies(not(X_85),X_83),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(not(X_83),implies(implies(X_35,implies(not(X_85),X_83)),X_85)),X_35)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35) = implies(implies(not(X_83),X_85),X_35),
inference(subst,[],[refute_0_509:[bind(X_83,$fot(X_85)),bind(X_85,$fot(X_83))]]) ).
cnf(refute_0_511,plain,
implies(not(implies(X_35,X_85)),X_83) = implies(X_35,implies(not(X_83),X_85)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_83)),bind(X_30,$fot(X_35)),bind(X_31,$fot(X_85))]]) ).
cnf(refute_0_512,plain,
implies(implies(not(implies(X_35,X_85)),X_83),X_83) = implies(implies(not(implies(X_35,X_85)),X_83),X_83),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(X_35,X_85)),X_83),X_83))]]) ).
cnf(refute_0_513,plain,
( implies(implies(not(implies(X_35,X_85)),X_83),X_83) != implies(implies(not(implies(X_35,X_85)),X_83),X_83)
| implies(not(implies(X_35,X_85)),X_83) != implies(X_35,implies(not(X_83),X_85))
| implies(implies(not(implies(X_35,X_85)),X_83),X_83) = implies(implies(X_35,implies(not(X_83),X_85)),X_83) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(X_35,X_85)),X_83),X_83),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) ),[1,0],$fot(implies(X_35,implies(not(X_83),X_85)))]]) ).
cnf(refute_0_514,plain,
( implies(not(implies(X_35,X_85)),X_83) != implies(X_35,implies(not(X_83),X_85))
| implies(implies(not(implies(X_35,X_85)),X_83),X_83) = implies(implies(X_35,implies(not(X_83),X_85)),X_83) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_35,X_85)),X_83),X_83),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
implies(implies(not(implies(X_35,X_85)),X_83),X_83) = implies(implies(X_35,implies(not(X_83),X_85)),X_83),
inference(resolve,[$cnf( $equal(implies(not(implies(X_35,X_85)),X_83),implies(X_35,implies(not(X_83),X_85))) )],[refute_0_511,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) = implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)),
introduced(tautology,[refl,[$fot(implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)))]]) ).
cnf(refute_0_517,plain,
( implies(implies(not(implies(X_35,X_85)),X_83),X_83) != implies(implies(X_35,implies(not(X_83),X_85)),X_83)
| implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) != implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83))
| implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)),implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83))) ),[1,1],$fot(implies(implies(X_35,implies(not(X_83),X_85)),X_83))]]) ).
cnf(refute_0_518,plain,
( implies(implies(not(implies(X_35,X_85)),X_83),X_83) != implies(implies(X_35,implies(not(X_83),X_85)),X_83)
| implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)) ),
inference(resolve,[$cnf( $equal(implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)),implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_35,X_85)),X_83),X_83),implies(implies(X_35,implies(not(X_83),X_85)),X_83)) )],[refute_0_515,refute_0_518]) ).
cnf(refute_0_520,plain,
implies(implies(not(Z),X_64),implies(Y,Z)) = implies(Y,implies(implies(not(Z),X_64),Z)),
inference(subst,[],[lemma_7:[bind(X,$fot(implies(not(Z),X_64)))]]) ).
cnf(refute_0_521,plain,
implies(implies(not(X),X_63),X_63) = implies(implies(implies(implies(not(X),X_63),X_63),X_63),X_63),
inference(subst,[],[refute_0_478:[bind(Y,$fot(implies(not(X),X_63))),bind(X_35,$fot(X_63))]]) ).
cnf(refute_0_522,plain,
implies(X,not(implies(X,not(X_63)))) = implies(implies(not(X),X_63),X_63),
inference(subst,[],[refute_0_50:[bind(X_35,$fot(X_63))]]) ).
cnf(refute_0_523,plain,
( implies(X,not(implies(X,not(X_63)))) != implies(implies(not(X),X_63),X_63)
| implies(implies(not(X),X_63),X_63) = implies(X,not(implies(X,not(X_63)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(implies(X,not(X_63)))))),bind(Y0,$fot(implies(implies(not(X),X_63),X_63)))]]) ).
cnf(refute_0_524,plain,
implies(implies(not(X),X_63),X_63) = implies(X,not(implies(X,not(X_63)))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X_63)))),implies(implies(not(X),X_63),X_63)) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
( implies(implies(not(X),X_63),X_63) != implies(X,not(implies(X,not(X_63))))
| implies(implies(not(X),X_63),X_63) != implies(implies(implies(implies(not(X),X_63),X_63),X_63),X_63)
| implies(implies(not(X),X_63),X_63) = implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_63),X_63),implies(implies(implies(implies(not(X),X_63),X_63),X_63),X_63)) ),[1,0,0],$fot(implies(X,not(implies(X,not(X_63)))))]]) ).
cnf(refute_0_526,plain,
( implies(implies(not(X),X_63),X_63) != implies(implies(implies(implies(not(X),X_63),X_63),X_63),X_63)
| implies(implies(not(X),X_63),X_63) = implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_63),X_63),implies(X,not(implies(X,not(X_63))))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
implies(implies(not(X),X_63),X_63) = implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_63),X_63),implies(implies(implies(implies(not(X),X_63),X_63),X_63),X_63)) )],[refute_0_521,refute_0_526]) ).
cnf(refute_0_528,plain,
implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))),
inference(subst,[],[refute_0_377:[bind(X,$fot(not(implies(not(X_50),Y)))),bind(X_36,$fot(X_50))]]) ).
cnf(refute_0_529,plain,
implies(Y,not(implies(Y,not(X_50)))) = implies(not(X_50),not(implies(not(X_50),Y))),
inference(subst,[],[refute_0_211:[bind(X,$fot(not(X_50)))]]) ).
cnf(refute_0_530,plain,
( implies(Y,not(implies(Y,not(X_50)))) != implies(not(X_50),not(implies(not(X_50),Y)))
| implies(not(X_50),not(implies(not(X_50),Y))) = implies(Y,not(implies(Y,not(X_50)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(Y,not(implies(Y,not(X_50)))))),bind(Y0,$fot(implies(not(X_50),not(implies(not(X_50),Y)))))]]) ).
cnf(refute_0_531,plain,
implies(not(X_50),not(implies(not(X_50),Y))) = implies(Y,not(implies(Y,not(X_50)))),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(X_50)))),implies(not(X_50),not(implies(not(X_50),Y)))) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
( implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))
| implies(not(X_50),not(implies(not(X_50),Y))) != implies(Y,not(implies(Y,not(X_50))))
| implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))) ),[0,0],$fot(implies(Y,not(implies(Y,not(X_50)))))]]) ).
cnf(refute_0_533,plain,
( implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))
| implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) ),
inference(resolve,[$cnf( $equal(implies(not(X_50),not(implies(not(X_50),Y))),implies(Y,not(implies(Y,not(X_50))))) )],[refute_0_531,refute_0_532]) ).
cnf(refute_0_534,plain,
implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))) )],[refute_0_528,refute_0_533]) ).
cnf(refute_0_535,plain,
implies(implies(implies(not(X_50),Y),X_50),X_50) = implies(not(X_50),Y),
inference(subst,[],[refute_0_342:[bind(X_35,$fot(X_50)),bind(X_7,$fot(Y))]]) ).
cnf(refute_0_536,plain,
implies(not(X_50),not(implies(not(X_50),Y))) = implies(implies(not(X_50),Y),X_50),
inference(subst,[],[lemma_10:[bind(X,$fot(X_50)),bind(Y,$fot(implies(not(X_50),Y)))]]) ).
cnf(refute_0_537,plain,
implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),
introduced(tautology,[refl,[$fot(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50))]]) ).
cnf(refute_0_538,plain,
( implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50)
| implies(not(X_50),not(implies(not(X_50),Y))) != implies(implies(not(X_50),Y),X_50)
| implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(implies(implies(not(X_50),Y),X_50),X_50) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50)) ),[1,0],$fot(implies(implies(not(X_50),Y),X_50))]]) ).
cnf(refute_0_539,plain,
( implies(not(X_50),not(implies(not(X_50),Y))) != implies(implies(not(X_50),Y),X_50)
| implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(implies(implies(not(X_50),Y),X_50),X_50) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50)) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(implies(implies(not(X_50),Y),X_50),X_50),
inference(resolve,[$cnf( $equal(implies(not(X_50),not(implies(not(X_50),Y))),implies(implies(not(X_50),Y),X_50)) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
( implies(implies(implies(not(X_50),Y),X_50),X_50) != implies(not(X_50),Y)
| implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(implies(implies(not(X_50),Y),X_50),X_50)
| implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(not(X_50),Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50))),bind(Y0,$fot(implies(implies(implies(not(X_50),Y),X_50),X_50))),bind(Z0,$fot(implies(not(X_50),Y)))]]) ).
cnf(refute_0_542,plain,
( implies(implies(implies(not(X_50),Y),X_50),X_50) != implies(not(X_50),Y)
| implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(not(X_50),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(implies(implies(not(X_50),Y),X_50),X_50)) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) = implies(not(X_50),Y),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_50),Y),X_50),X_50),implies(not(X_50),Y)) )],[refute_0_535,refute_0_542]) ).
cnf(refute_0_544,plain,
implies(X_47,not(implies(X_48,not(X_47)))) = implies(implies(not(X_47),X_48),X_48),
inference(subst,[],[refute_0_387:[bind(X,$fot(X_47)),bind(X_35,$fot(X_48))]]) ).
cnf(refute_0_545,plain,
implies(not(X_48),X_47) = implies(not(X_47),X_48),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_47)),bind(X_7,$fot(X_48))]]) ).
cnf(refute_0_546,plain,
( implies(not(X_48),X_47) != implies(not(X_47),X_48)
| implies(not(X_47),X_48) = implies(not(X_48),X_47) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_48),X_47))),bind(Y0,$fot(implies(not(X_47),X_48)))]]) ).
cnf(refute_0_547,plain,
implies(not(X_47),X_48) = implies(not(X_48),X_47),
inference(resolve,[$cnf( $equal(implies(not(X_48),X_47),implies(not(X_47),X_48)) )],[refute_0_545,refute_0_546]) ).
cnf(refute_0_548,plain,
( implies(X_47,not(implies(X_48,not(X_47)))) != implies(implies(not(X_47),X_48),X_48)
| implies(not(X_47),X_48) != implies(not(X_48),X_47)
| implies(X_47,not(implies(X_48,not(X_47)))) = implies(implies(not(X_48),X_47),X_48) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47,not(implies(X_48,not(X_47)))),implies(implies(not(X_47),X_48),X_48)) ),[1,0],$fot(implies(not(X_48),X_47))]]) ).
cnf(refute_0_549,plain,
( implies(X_47,not(implies(X_48,not(X_47)))) != implies(implies(not(X_47),X_48),X_48)
| implies(X_47,not(implies(X_48,not(X_47)))) = implies(implies(not(X_48),X_47),X_48) ),
inference(resolve,[$cnf( $equal(implies(not(X_47),X_48),implies(not(X_48),X_47)) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
implies(X_47,not(implies(X_48,not(X_47)))) = implies(implies(not(X_48),X_47),X_48),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(X_48,not(X_47)))),implies(implies(not(X_47),X_48),X_48)) )],[refute_0_544,refute_0_549]) ).
cnf(refute_0_551,plain,
implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) = implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),
inference(subst,[],[refute_0_550:[bind(X_47,$fot(not(implies(not(X_50),Y)))),bind(X_48,$fot(X_50))]]) ).
cnf(refute_0_552,plain,
( implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(not(X_50),Y)
| implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) != implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50)
| implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) = implies(not(X_50),Y) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))))),bind(Y0,$fot(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50))),bind(Z0,$fot(implies(not(X_50),Y)))]]) ).
cnf(refute_0_553,plain,
( implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50) != implies(not(X_50),Y)
| implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) = implies(not(X_50),Y) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))),implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50)) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) = implies(not(X_50),Y),
inference(resolve,[$cnf( $equal(implies(implies(not(X_50),not(implies(not(X_50),Y))),X_50),implies(not(X_50),Y)) )],[refute_0_543,refute_0_553]) ).
cnf(refute_0_555,plain,
( implies(implies(Y,not(implies(Y,not(X_50)))),X_50) != implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))
| implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))) != implies(not(X_50),Y)
| implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(X_50),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(Y,not(implies(Y,not(X_50)))),X_50),implies(not(X_50),Y)) ),[0],$fot(implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))))]]) ).
cnf(refute_0_556,plain,
( implies(implies(Y,not(implies(Y,not(X_50)))),X_50) != implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))
| implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(X_50),Y) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y)))))),implies(not(X_50),Y)) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
implies(implies(Y,not(implies(Y,not(X_50)))),X_50) = implies(not(X_50),Y),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(X_50)))),X_50),implies(not(implies(not(X_50),Y)),not(implies(X_50,not(not(implies(not(X_50),Y))))))) )],[refute_0_534,refute_0_556]) ).
cnf(refute_0_558,plain,
implies(implies(X,not(implies(X,not(X_63)))),X_63) = implies(not(X_63),X),
inference(subst,[],[refute_0_557:[bind(Y,$fot(X)),bind(X_50,$fot(X_63))]]) ).
cnf(refute_0_559,plain,
implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) = implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63),
introduced(tautology,[refl,[$fot(implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63))]]) ).
cnf(refute_0_560,plain,
( implies(implies(X,not(implies(X,not(X_63)))),X_63) != implies(not(X_63),X)
| implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) != implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)
| implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) = implies(implies(not(X_63),X),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63),implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)) ),[1,0],$fot(implies(not(X_63),X))]]) ).
cnf(refute_0_561,plain,
( implies(implies(X,not(implies(X,not(X_63)))),X_63) != implies(not(X_63),X)
| implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) = implies(implies(not(X_63),X),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63),implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)) )],[refute_0_559,refute_0_560]) ).
cnf(refute_0_562,plain,
implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) = implies(implies(not(X_63),X),X_63),
inference(resolve,[$cnf( $equal(implies(implies(X,not(implies(X,not(X_63)))),X_63),implies(not(X_63),X)) )],[refute_0_558,refute_0_561]) ).
cnf(refute_0_563,plain,
( implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63) != implies(implies(not(X_63),X),X_63)
| implies(implies(not(X),X_63),X_63) != implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)
| implies(implies(not(X),X_63),X_63) = implies(implies(not(X_63),X),X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_63),X_63),implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)) ),[1],$fot(implies(implies(not(X_63),X),X_63))]]) ).
cnf(refute_0_564,plain,
( implies(implies(not(X),X_63),X_63) != implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)
| implies(implies(not(X),X_63),X_63) = implies(implies(not(X_63),X),X_63) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63),implies(implies(not(X_63),X),X_63)) )],[refute_0_562,refute_0_563]) ).
cnf(refute_0_565,plain,
implies(implies(not(X),X_63),X_63) = implies(implies(not(X_63),X),X_63),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_63),X_63),implies(implies(implies(X,not(implies(X,not(X_63)))),X_63),X_63)) )],[refute_0_527,refute_0_564]) ).
cnf(refute_0_566,plain,
implies(implies(not(X_64),Z),Z) = implies(implies(not(Z),X_64),Z),
inference(subst,[],[refute_0_565:[bind(X,$fot(X_64)),bind(X_63,$fot(Z))]]) ).
cnf(refute_0_567,plain,
( implies(implies(not(X_64),Z),Z) != implies(implies(not(Z),X_64),Z)
| implies(implies(not(Z),X_64),Z) = implies(implies(not(X_64),Z),Z) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_64),Z),Z))),bind(Y0,$fot(implies(implies(not(Z),X_64),Z)))]]) ).
cnf(refute_0_568,plain,
implies(implies(not(Z),X_64),Z) = implies(implies(not(X_64),Z),Z),
inference(resolve,[$cnf( $equal(implies(implies(not(X_64),Z),Z),implies(implies(not(Z),X_64),Z)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
( implies(implies(not(Z),X_64),Z) != implies(implies(not(X_64),Z),Z)
| implies(implies(not(Z),X_64),implies(Y,Z)) != implies(Y,implies(implies(not(Z),X_64),Z))
| implies(implies(not(Z),X_64),implies(Y,Z)) = implies(Y,implies(implies(not(X_64),Z),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Z),X_64),implies(Y,Z)),implies(Y,implies(implies(not(Z),X_64),Z))) ),[1,1],$fot(implies(implies(not(X_64),Z),Z))]]) ).
cnf(refute_0_570,plain,
( implies(implies(not(Z),X_64),implies(Y,Z)) != implies(Y,implies(implies(not(Z),X_64),Z))
| implies(implies(not(Z),X_64),implies(Y,Z)) = implies(Y,implies(implies(not(X_64),Z),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Z),X_64),Z),implies(implies(not(X_64),Z),Z)) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
implies(implies(not(Z),X_64),implies(Y,Z)) = implies(Y,implies(implies(not(X_64),Z),Z)),
inference(resolve,[$cnf( $equal(implies(implies(not(Z),X_64),implies(Y,Z)),implies(Y,implies(implies(not(Z),X_64),Z))) )],[refute_0_520,refute_0_570]) ).
cnf(refute_0_572,plain,
implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) = implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)),
inference(subst,[],[refute_0_571:[bind(Y,$fot(not(X_85))),bind(Z,$fot(X_83)),bind(X_64,$fot(implies(X_35,X_85)))]]) ).
cnf(refute_0_573,plain,
( implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) != implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83))
| implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) != implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))
| implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)))),bind(Y0,$fot(implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)))),bind(Z0,$fot(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))))]]) ).
cnf(refute_0_574,plain,
( implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)) != implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))
| implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) = implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),
inference(resolve,[$cnf( $equal(implies(not(X_85),implies(implies(not(implies(X_35,X_85)),X_83),X_83)),implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))) )],[refute_0_519,refute_0_574]) ).
cnf(refute_0_576,plain,
implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35))]]) ).
cnf(refute_0_577,plain,
( implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) != implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) != implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))
| implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)) ),[1,0],$fot(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)))]]) ).
cnf(refute_0_578,plain,
( implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)) != implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))
| implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83))) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
( implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) != implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35)
| implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35) != implies(implies(not(X_83),X_85),X_35)
| implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_83),X_85),X_35) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35))),bind(Y0,$fot(implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35))),bind(Z0,$fot(implies(implies(not(X_83),X_85),X_35)))]]) ).
cnf(refute_0_581,plain,
( implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35) != implies(implies(not(X_83),X_85),X_35)
| implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_83),X_85),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35)) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) = implies(implies(not(X_83),X_85),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),implies(implies(X_35,implies(not(X_83),X_85)),X_83)),X_35),implies(implies(not(X_83),X_85),X_35)) )],[refute_0_510,refute_0_581]) ).
cnf(refute_0_583,plain,
( implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35) != implies(implies(not(X_83),X_85),X_35)
| implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),X_85),X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)) ),[1],$fot(implies(implies(not(X_83),X_85),X_35))]]) ).
cnf(refute_0_584,plain,
( implies(implies(not(X_85),X_83),X_35) != implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)
| implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),X_85),X_35) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35),implies(implies(not(X_83),X_85),X_35)) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
implies(implies(not(X_85),X_83),X_35) = implies(implies(not(X_83),X_85),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(implies(not(X_83),implies(X_35,X_85)),implies(not(X_85),X_83)),X_35)) )],[refute_0_503,refute_0_584]) ).
cnf(refute_0_586,plain,
( implies(implies(not(X_85),X_83),X_35) != implies(implies(not(X_83),X_85),X_35)
| implies(implies(not(X_83),X_85),X_35) = implies(implies(not(X_85),X_83),X_35) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_85),X_83),X_35))),bind(Y0,$fot(implies(implies(not(X_83),X_85),X_35)))]]) ).
cnf(refute_0_587,plain,
implies(implies(not(X_83),X_85),X_35) = implies(implies(not(X_85),X_83),X_35),
inference(resolve,[$cnf( $equal(implies(implies(not(X_85),X_83),X_35),implies(implies(not(X_83),X_85),X_35)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),
inference(subst,[],[refute_0_587:[bind(X_35,$fot(not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))),bind(X_83,$fot(implies(X_119,not(X_42)))),bind(X_85,$fot(X_119))]]) ).
cnf(refute_0_589,plain,
( implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != not(implies(X_42,not(X_119)))
| implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))),bind(Y0,$fot(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))))),bind(Z0,$fot(not(implies(X_42,not(X_119)))))]]) ).
cnf(refute_0_590,plain,
( implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != not(implies(X_42,not(X_119)))
| implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) = not(implies(X_42,not(X_119))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_119),implies(X_119,not(X_42))),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),not(implies(X_42,not(X_119)))) )],[refute_0_463,refute_0_590]) ).
cnf(refute_0_592,plain,
( implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))) != not(implies(X_42,not(X_119)))
| not(implies(X_119,not(X_42))) != implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| not(implies(X_119,not(X_42))) = not(implies(X_42,not(X_119))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_119,not(X_42))),implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) ),[1],$fot(not(implies(X_42,not(X_119))))]]) ).
cnf(refute_0_593,plain,
( not(implies(X_119,not(X_42))) != implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))
| not(implies(X_119,not(X_42))) = not(implies(X_42,not(X_119))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42))))),not(implies(X_42,not(X_119)))) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
not(implies(X_119,not(X_42))) = not(implies(X_42,not(X_119))),
inference(resolve,[$cnf( $equal(not(implies(X_119,not(X_42))),implies(implies(not(implies(X_119,not(X_42))),X_119),not(implies(X_119,not(implies(implies(not(X_42),X_119),X_42)))))) )],[refute_0_364,refute_0_593]) ).
cnf(refute_0_595,plain,
not(implies(X_170,not(X_171))) = not(implies(X_171,not(X_170))),
inference(subst,[],[refute_0_594:[bind(X_119,$fot(X_170)),bind(X_42,$fot(X_171))]]) ).
cnf(refute_0_596,plain,
( implies(implies(X_170,not(X_171)),not(X_8)) != implies(X_8,not(implies(X_170,not(X_171))))
| not(implies(X_170,not(X_171))) != not(implies(X_171,not(X_170)))
| implies(implies(X_170,not(X_171)),not(X_8)) = implies(X_8,not(implies(X_171,not(X_170)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_170,not(X_171)),not(X_8)),implies(X_8,not(implies(X_170,not(X_171))))) ),[1,1],$fot(not(implies(X_171,not(X_170))))]]) ).
cnf(refute_0_597,plain,
( implies(implies(X_170,not(X_171)),not(X_8)) != implies(X_8,not(implies(X_170,not(X_171))))
| implies(implies(X_170,not(X_171)),not(X_8)) = implies(X_8,not(implies(X_171,not(X_170)))) ),
inference(resolve,[$cnf( $equal(not(implies(X_170,not(X_171))),not(implies(X_171,not(X_170)))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
implies(implies(X_170,not(X_171)),not(X_8)) = implies(X_8,not(implies(X_171,not(X_170)))),
inference(resolve,[$cnf( $equal(implies(implies(X_170,not(X_171)),not(X_8)),implies(X_8,not(implies(X_170,not(X_171))))) )],[refute_0_359,refute_0_597]) ).
cnf(refute_0_599,plain,
( implies(implies(X_170,not(X_171)),not(X_8)) != implies(X_8,not(implies(X_171,not(X_170))))
| implies(X_8,not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),not(X_8)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_170,not(X_171)),not(X_8)))),bind(Y0,$fot(implies(X_8,not(implies(X_171,not(X_170))))))]]) ).
cnf(refute_0_600,plain,
implies(X_8,not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),not(X_8)),
inference(resolve,[$cnf( $equal(implies(implies(X_170,not(X_171)),not(X_8)),implies(X_8,not(implies(X_171,not(X_170))))) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) = implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340))),
inference(subst,[],[refute_0_600:[bind(X_170,$fot(X_340)),bind(X_171,$fot(X_340)),bind(X_8,$fot(implies(not(X_340),X_340)))]]) ).
cnf(refute_0_602,plain,
( implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) != implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340)))
| implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) != truth
| implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))),truth) ),[0],$fot(implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340))))]]) ).
cnf(refute_0_603,plain,
( implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))) != truth
| implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))),implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340)))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
implies(implies(X_340,not(X_340)),not(implies(not(X_340),X_340))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_340),X_340),not(implies(X_340,not(X_340)))),truth) )],[refute_0_358,refute_0_603]) ).
cnf(refute_0_605,plain,
implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))) = truth,
inference(subst,[],[refute_0_604:[bind(X_340,$fot(not(X_116)))]]) ).
cnf(refute_0_606,plain,
( implies(implies(not(X_116),not(not(X_116))),implies(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),X_116)) != truth
| implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))) != truth
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),X_116)),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_607,plain,
( implies(implies(not(X_116),not(not(X_116))),implies(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),X_116)) != truth
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),truth) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(implies(implies(not(X_116),not(not(X_116))),not(implies(not(not(X_116)),not(X_116)))),X_116)),truth) )],[refute_0_331,refute_0_607]) ).
cnf(refute_0_609,plain,
implies(not(X_116),not(not(X_116))) = implies(not(X_116),X_116),
inference(subst,[],[lemma_10:[bind(X,$fot(X_116)),bind(Y,$fot(not(X_116)))]]) ).
cnf(refute_0_610,plain,
implies(implies(not(X_116),not(not(X_116))),X_116) = implies(implies(not(X_116),not(not(X_116))),X_116),
introduced(tautology,[refl,[$fot(implies(implies(not(X_116),not(not(X_116))),X_116))]]) ).
cnf(refute_0_611,plain,
( implies(implies(not(X_116),not(not(X_116))),X_116) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(not(X_116),not(not(X_116))) != implies(not(X_116),X_116)
| implies(implies(not(X_116),not(not(X_116))),X_116) = implies(implies(not(X_116),X_116),X_116) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),X_116),implies(implies(not(X_116),not(not(X_116))),X_116)) ),[1,0],$fot(implies(not(X_116),X_116))]]) ).
cnf(refute_0_612,plain,
( implies(not(X_116),not(not(X_116))) != implies(not(X_116),X_116)
| implies(implies(not(X_116),not(not(X_116))),X_116) = implies(implies(not(X_116),X_116),X_116) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),X_116),implies(implies(not(X_116),not(not(X_116))),X_116)) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
implies(implies(not(X_116),not(not(X_116))),X_116) = implies(implies(not(X_116),X_116),X_116),
inference(resolve,[$cnf( $equal(implies(not(X_116),not(not(X_116))),implies(not(X_116),X_116)) )],[refute_0_609,refute_0_612]) ).
cnf(refute_0_614,plain,
implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(X_116),not(not(X_116))),X_116)))]]) ).
cnf(refute_0_615,plain,
implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) = implies(Y,implies(implies(implies(Z,X_66),X_66),Z)),
inference(subst,[],[lemma_7:[bind(X,$fot(implies(implies(Z,X_66),X_66)))]]) ).
cnf(refute_0_616,plain,
implies(X_66,Z) = implies(implies(implies(Z,X_66),X_66),Z),
inference(subst,[],[refute_0_491:[bind(Y,$fot(X_66)),bind(X_35,$fot(Z))]]) ).
cnf(refute_0_617,plain,
( implies(X_66,Z) != implies(implies(implies(Z,X_66),X_66),Z)
| implies(implies(implies(Z,X_66),X_66),Z) = implies(X_66,Z) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_66,Z))),bind(Y0,$fot(implies(implies(implies(Z,X_66),X_66),Z)))]]) ).
cnf(refute_0_618,plain,
implies(implies(implies(Z,X_66),X_66),Z) = implies(X_66,Z),
inference(resolve,[$cnf( $equal(implies(X_66,Z),implies(implies(implies(Z,X_66),X_66),Z)) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
( implies(implies(implies(Z,X_66),X_66),Z) != implies(X_66,Z)
| implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) != implies(Y,implies(implies(implies(Z,X_66),X_66),Z))
| implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) = implies(Y,implies(X_66,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Z,X_66),X_66),implies(Y,Z)),implies(Y,implies(implies(implies(Z,X_66),X_66),Z))) ),[1,1],$fot(implies(X_66,Z))]]) ).
cnf(refute_0_620,plain,
( implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) != implies(Y,implies(implies(implies(Z,X_66),X_66),Z))
| implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) = implies(Y,implies(X_66,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,X_66),X_66),Z),implies(X_66,Z)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
implies(implies(implies(Z,X_66),X_66),implies(Y,Z)) = implies(Y,implies(X_66,Z)),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,X_66),X_66),implies(Y,Z)),implies(Y,implies(implies(implies(Z,X_66),X_66),Z))) )],[refute_0_615,refute_0_620]) ).
cnf(refute_0_622,plain,
implies(implies(implies(Z,implies(not(X_290),X_292)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)),
inference(subst,[],[refute_0_621:[bind(X_66,$fot(implies(not(X_290),X_292)))]]) ).
cnf(refute_0_623,plain,
implies(not(implies(X_72,X_73)),X_71) = implies(X_72,implies(not(X_71),X_73)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_71)),bind(X_30,$fot(X_72)),bind(X_31,$fot(X_73))]]) ).
cnf(refute_0_624,plain,
implies(not(X_73),X_71) = implies(not(X_71),X_73),
inference(subst,[],[refute_0_26:[bind(X,$fot(X_71)),bind(X_7,$fot(X_73))]]) ).
cnf(refute_0_625,plain,
( implies(not(X_73),X_71) != implies(not(X_71),X_73)
| implies(not(X_71),X_73) = implies(not(X_73),X_71) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_73),X_71))),bind(Y0,$fot(implies(not(X_71),X_73)))]]) ).
cnf(refute_0_626,plain,
implies(not(X_71),X_73) = implies(not(X_73),X_71),
inference(resolve,[$cnf( $equal(implies(not(X_73),X_71),implies(not(X_71),X_73)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
( implies(not(X_71),X_73) != implies(not(X_73),X_71)
| implies(not(implies(X_72,X_73)),X_71) != implies(X_72,implies(not(X_71),X_73))
| implies(not(implies(X_72,X_73)),X_71) = implies(X_72,implies(not(X_73),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_72,X_73)),X_71),implies(X_72,implies(not(X_71),X_73))) ),[1,1],$fot(implies(not(X_73),X_71))]]) ).
cnf(refute_0_628,plain,
( implies(not(implies(X_72,X_73)),X_71) != implies(X_72,implies(not(X_71),X_73))
| implies(not(implies(X_72,X_73)),X_71) = implies(X_72,implies(not(X_73),X_71)) ),
inference(resolve,[$cnf( $equal(implies(not(X_71),X_73),implies(not(X_73),X_71)) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
implies(not(implies(X_72,X_73)),X_71) = implies(X_72,implies(not(X_73),X_71)),
inference(resolve,[$cnf( $equal(implies(not(implies(X_72,X_73)),X_71),implies(X_72,implies(not(X_71),X_73))) )],[refute_0_623,refute_0_628]) ).
cnf(refute_0_630,plain,
( implies(not(implies(X_72,X_73)),X_71) != implies(X_72,implies(not(X_71),X_73))
| implies(not(implies(X_72,X_73)),X_71) != implies(X_72,implies(not(X_73),X_71))
| implies(X_72,implies(not(X_71),X_73)) = implies(X_72,implies(not(X_73),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_72,X_73)),X_71),implies(X_72,implies(not(X_73),X_71))) ),[0],$fot(implies(X_72,implies(not(X_71),X_73)))]]) ).
cnf(refute_0_631,plain,
( implies(not(implies(X_72,X_73)),X_71) != implies(X_72,implies(not(X_73),X_71))
| implies(X_72,implies(not(X_71),X_73)) = implies(X_72,implies(not(X_73),X_71)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_72,X_73)),X_71),implies(X_72,implies(not(X_71),X_73))) )],[refute_0_623,refute_0_630]) ).
cnf(refute_0_632,plain,
implies(X_72,implies(not(X_71),X_73)) = implies(X_72,implies(not(X_73),X_71)),
inference(resolve,[$cnf( $equal(implies(not(implies(X_72,X_73)),X_71),implies(X_72,implies(not(X_73),X_71))) )],[refute_0_629,refute_0_631]) ).
cnf(refute_0_633,plain,
implies(Z,implies(not(X_290),X_292)) = implies(Z,implies(not(X_292),X_290)),
inference(subst,[],[refute_0_632:[bind(X_71,$fot(X_290)),bind(X_72,$fot(Z)),bind(X_73,$fot(X_292))]]) ).
cnf(refute_0_634,plain,
( implies(Z,implies(not(X_290),X_292)) != implies(Z,implies(not(X_292),X_290))
| implies(implies(implies(Z,implies(not(X_290),X_292)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_290),X_292),Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_290),X_292)),implies(not(X_290),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_290),X_292),Z))) ),[0,0,0],$fot(implies(Z,implies(not(X_292),X_290)))]]) ).
cnf(refute_0_635,plain,
( implies(implies(implies(Z,implies(not(X_290),X_292)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_290),X_292),Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)) ),
inference(resolve,[$cnf( $equal(implies(Z,implies(not(X_290),X_292)),implies(Z,implies(not(X_292),X_290))) )],[refute_0_633,refute_0_634]) ).
cnf(refute_0_636,plain,
implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_290),X_292)),implies(not(X_290),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_290),X_292),Z))) )],[refute_0_622,refute_0_635]) ).
cnf(refute_0_637,plain,
implies(implies(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),
inference(subst,[],[refute_0_621:[bind(Y,$fot(X_233)),bind(Z,$fot(X_234)),bind(X_66,$fot(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))))]]) ).
cnf(refute_0_638,plain,
implies(not(X),implies(implies(not(X),X_16),X_16)) = truth,
inference(subst,[],[refute_0_186:[bind(X,$fot(X_16)),bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_639,plain,
implies(not(X_16),X) = implies(not(X),X_16),
inference(subst,[],[refute_0_26:[bind(X_7,$fot(X_16))]]) ).
cnf(refute_0_640,plain,
( implies(not(X_16),X) != implies(not(X),X_16)
| implies(not(X),X_16) = implies(not(X_16),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_16),X))),bind(Y0,$fot(implies(not(X),X_16)))]]) ).
cnf(refute_0_641,plain,
implies(not(X),X_16) = implies(not(X_16),X),
inference(resolve,[$cnf( $equal(implies(not(X_16),X),implies(not(X),X_16)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( implies(not(X),X_16) != implies(not(X_16),X)
| implies(not(X),implies(implies(not(X),X_16),X_16)) != truth
| implies(not(X),implies(implies(not(X_16),X),X_16)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X),implies(implies(not(X),X_16),X_16)),truth) ),[0,1,0],$fot(implies(not(X_16),X))]]) ).
cnf(refute_0_643,plain,
( implies(not(X),implies(implies(not(X),X_16),X_16)) != truth
| implies(not(X),implies(implies(not(X_16),X),X_16)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),X_16),implies(not(X_16),X)) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
implies(not(X),implies(implies(not(X_16),X),X_16)) = truth,
inference(resolve,[$cnf( $equal(implies(not(X),implies(implies(not(X),X_16),X_16)),truth) )],[refute_0_638,refute_0_643]) ).
cnf(refute_0_645,plain,
implies(not(implies(X_29,X_31)),implies(implies(not(X_16),implies(X_29,X_31)),X_16)) = truth,
inference(subst,[],[refute_0_644:[bind(X,$fot(implies(X_29,X_31)))]]) ).
cnf(refute_0_646,plain,
implies(X_29,implies(not(X_16),X_31)) = implies(not(X_16),implies(X_29,X_31)),
inference(subst,[],[lemma_7:[bind(X,$fot(X_29)),bind(Y,$fot(not(X_16))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_647,plain,
( implies(X_29,implies(not(X_16),X_31)) != implies(not(X_16),implies(X_29,X_31))
| implies(not(X_16),implies(X_29,X_31)) = implies(X_29,implies(not(X_16),X_31)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_29,implies(not(X_16),X_31)))),bind(Y0,$fot(implies(not(X_16),implies(X_29,X_31))))]]) ).
cnf(refute_0_648,plain,
implies(not(X_16),implies(X_29,X_31)) = implies(X_29,implies(not(X_16),X_31)),
inference(resolve,[$cnf( $equal(implies(X_29,implies(not(X_16),X_31)),implies(not(X_16),implies(X_29,X_31))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
( implies(not(X_16),implies(X_29,X_31)) != implies(X_29,implies(not(X_16),X_31))
| implies(not(implies(X_29,X_31)),implies(implies(not(X_16),implies(X_29,X_31)),X_16)) != truth
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(not(X_16),implies(X_29,X_31)),X_16)),truth) ),[0,1,0],$fot(implies(X_29,implies(not(X_16),X_31)))]]) ).
cnf(refute_0_650,plain,
( implies(not(implies(X_29,X_31)),implies(implies(not(X_16),implies(X_29,X_31)),X_16)) != truth
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_16),implies(X_29,X_31)),implies(X_29,implies(not(X_16),X_31))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = truth,
inference(resolve,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(not(X_16),implies(X_29,X_31)),X_16)),truth) )],[refute_0_645,refute_0_650]) ).
cnf(refute_0_652,plain,
implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)) = implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),
inference(subst,[],[refute_0_4:[bind(X,$fot(not(X_31))),bind(Y,$fot(implies(X_29,implies(not(X_16),X_31)))),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_653,plain,
implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) = implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_31)),bind(X_30,$fot(implies(X_29,implies(not(X_16),X_31)))),bind(X_31,$fot(X_16))]]) ).
cnf(refute_0_654,plain,
( implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)) != implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))
| implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) != implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16))
| implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) = implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))),bind(Y0,$fot(implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)))),bind(Z0,$fot(implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))))]]) ).
cnf(refute_0_655,plain,
( implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)) != implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))
| implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) = implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31),implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) = implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),
inference(resolve,[$cnf( $equal(implies(implies(X_29,implies(not(X_16),X_31)),implies(not(X_31),X_16)),implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) )],[refute_0_652,refute_0_655]) ).
cnf(refute_0_657,plain,
implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) = implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)),
introduced(tautology,[refl,[$fot(implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)))]]) ).
cnf(refute_0_658,plain,
( implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) != implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))
| implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) != implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))
| implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)),implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))) ),[1,1],$fot(implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))]]) ).
cnf(refute_0_659,plain,
( implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31) != implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))
| implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) ),
inference(resolve,[$cnf( $equal(implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)),implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31),implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) )],[refute_0_656,refute_0_659]) ).
cnf(refute_0_661,plain,
implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)),
inference(subst,[],[refute_0_31:[bind(X,$fot(implies(implies(X_29,implies(not(X_16),X_31)),X_16))),bind(X_30,$fot(X_29))]]) ).
cnf(refute_0_662,plain,
( implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) != implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) != implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))),bind(Y0,$fot(implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)))),bind(Z0,$fot(implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))))]]) ).
cnf(refute_0_663,plain,
( implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)) != implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) = implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))),
inference(resolve,[$cnf( $equal(implies(X_29,implies(not(implies(implies(X_29,implies(not(X_16),X_31)),X_16)),X_31)),implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))) )],[refute_0_660,refute_0_663]) ).
cnf(refute_0_665,plain,
( implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) != implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))
| implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) != truth
| implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),truth) ),[0],$fot(implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))))]]) ).
cnf(refute_0_666,plain,
( implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)) != truth
| implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16)))) )],[refute_0_664,refute_0_665]) ).
cnf(refute_0_667,plain,
implies(X_29,implies(not(X_31),implies(implies(X_29,implies(not(X_16),X_31)),X_16))) = truth,
inference(resolve,[$cnf( $equal(implies(not(implies(X_29,X_31)),implies(implies(X_29,implies(not(X_16),X_31)),X_16)),truth) )],[refute_0_651,refute_0_666]) ).
cnf(refute_0_668,plain,
implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) = truth,
inference(subst,[],[refute_0_667:[bind(X_29,$fot(X_234))]]) ).
cnf(refute_0_669,plain,
( implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) != truth
| implies(implies(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_670,plain,
( implies(implies(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) ),
inference(resolve,[$cnf( $equal(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),truth) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_234,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) )],[refute_0_637,refute_0_670]) ).
cnf(refute_0_672,plain,
implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) = implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))))]]) ).
cnf(refute_0_673,plain,
implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)))]]) ).
cnf(refute_0_674,plain,
( implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234))
| implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) != implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))
| implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234))) ),[1,0],$fot(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)))]]) ).
cnf(refute_0_675,plain,
( implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) != implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))
| implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) = implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))) )],[refute_0_672,refute_0_675]) ).
cnf(refute_0_677,plain,
( implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) ),[0],$fot(implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)))]]) ).
cnf(refute_0_678,plain,
( implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234))) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234) = implies(implies(not(X_16),X_31),X_234),
inference(subst,[],[refute_0_509:[bind(X_35,$fot(X_234)),bind(X_83,$fot(X_31)),bind(X_85,$fot(X_16))]]) ).
cnf(refute_0_680,plain,
implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) = implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),
introduced(tautology,[refl,[$fot(implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)))]]) ).
cnf(refute_0_681,plain,
( implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234) != implies(implies(not(X_16),X_31),X_234)
| implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) ),[1,1],$fot(implies(implies(not(X_16),X_31),X_234))]]) ).
cnf(refute_0_682,plain,
( implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234) != implies(implies(not(X_16),X_31),X_234)
| implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)) ),
inference(resolve,[$cnf( $equal(implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234),implies(implies(not(X_16),X_31),X_234)) )],[refute_0_679,refute_0_682]) ).
cnf(refute_0_684,plain,
( implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)) != implies(X_233,implies(implies(not(X_16),X_31),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) ),[1],$fot(implies(X_233,implies(implies(not(X_16),X_31),X_234)))]]) ).
cnf(refute_0_685,plain,
( implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)) ),
inference(resolve,[$cnf( $equal(implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234)),implies(X_233,implies(implies(not(X_16),X_31),X_234))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
( implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)) != implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))
| implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) )],[refute_0_678,refute_0_685]) ).
cnf(refute_0_687,plain,
implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),implies(X_233,X_234)) = implies(X_233,implies(implies(not(X_16),X_31),X_234)),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16))),implies(X_233,X_234)),implies(X_233,implies(implies(not(X_31),implies(implies(X_234,implies(not(X_16),X_31)),X_16)),X_234))) )],[refute_0_671,refute_0_686]) ).
cnf(refute_0_688,plain,
implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)),
inference(subst,[],[refute_0_687:[bind(X_16,$fot(X_292)),bind(X_233,$fot(Y)),bind(X_234,$fot(Z)),bind(X_31,$fot(X_290))]]) ).
cnf(refute_0_689,plain,
implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)),
inference(subst,[],[lemma_7:[bind(Y,$fot(implies(implies(not(implies(X,Z)),X_43),implies(X,Z))))]]) ).
cnf(refute_0_690,plain,
implies(not(implies(X,Z)),X_43) = implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)),
inference(subst,[],[refute_0_238:[bind(X_35,$fot(implies(X,Z))),bind(X_7,$fot(X_43))]]) ).
cnf(refute_0_691,plain,
( implies(not(implies(X,Z)),X_43) != implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))
| implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)) = implies(not(implies(X,Z)),X_43) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(implies(X,Z)),X_43))),bind(Y0,$fot(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))))]]) ).
cnf(refute_0_692,plain,
implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)) = implies(not(implies(X,Z)),X_43),
inference(resolve,[$cnf( $equal(implies(not(implies(X,Z)),X_43),implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))
| implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)) != implies(not(implies(X,Z)),X_43)
| implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(not(implies(X,Z)),X_43) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(not(implies(X,Z)),X_43)) ),[0],$fot(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)))]]) ).
cnf(refute_0_694,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))
| implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(not(implies(X,Z)),X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z)),implies(not(implies(X,Z)),X_43)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(not(implies(X,Z)),X_43),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,Z))) )],[refute_0_689,refute_0_694]) ).
cnf(refute_0_696,plain,
implies(not(implies(X,Z)),X_43) = implies(X,implies(not(X_43),Z)),
inference(subst,[],[refute_0_31:[bind(X,$fot(X_43)),bind(X_30,$fot(X)),bind(X_31,$fot(Z))]]) ).
cnf(refute_0_697,plain,
implies(implies(not(implies(X,Z)),X_43),Z) = implies(implies(not(implies(X,Z)),X_43),Z),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(X,Z)),X_43),Z))]]) ).
cnf(refute_0_698,plain,
( implies(implies(not(implies(X,Z)),X_43),Z) != implies(implies(not(implies(X,Z)),X_43),Z)
| implies(not(implies(X,Z)),X_43) != implies(X,implies(not(X_43),Z))
| implies(implies(not(implies(X,Z)),X_43),Z) = implies(implies(X,implies(not(X_43),Z)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(X,Z)),X_43),Z),implies(implies(not(implies(X,Z)),X_43),Z)) ),[1,0],$fot(implies(X,implies(not(X_43),Z)))]]) ).
cnf(refute_0_699,plain,
( implies(not(implies(X,Z)),X_43) != implies(X,implies(not(X_43),Z))
| implies(implies(not(implies(X,Z)),X_43),Z) = implies(implies(X,implies(not(X_43),Z)),Z) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X,Z)),X_43),Z),implies(implies(not(implies(X,Z)),X_43),Z)) )],[refute_0_697,refute_0_698]) ).
cnf(refute_0_700,plain,
implies(implies(not(implies(X,Z)),X_43),Z) = implies(implies(X,implies(not(X_43),Z)),Z),
inference(resolve,[$cnf( $equal(implies(not(implies(X,Z)),X_43),implies(X,implies(not(X_43),Z))) )],[refute_0_696,refute_0_699]) ).
cnf(refute_0_701,plain,
implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) = implies(X,implies(implies(not(implies(X,Z)),X_43),Z)),
introduced(tautology,[refl,[$fot(implies(X,implies(implies(not(implies(X,Z)),X_43),Z)))]]) ).
cnf(refute_0_702,plain,
( implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) != implies(X,implies(implies(not(implies(X,Z)),X_43),Z))
| implies(implies(not(implies(X,Z)),X_43),Z) != implies(implies(X,implies(not(X_43),Z)),Z)
| implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(implies(not(implies(X,Z)),X_43),Z)),implies(X,implies(implies(not(implies(X,Z)),X_43),Z))) ),[1,1],$fot(implies(implies(X,implies(not(X_43),Z)),Z))]]) ).
cnf(refute_0_703,plain,
( implies(implies(not(implies(X,Z)),X_43),Z) != implies(implies(X,implies(not(X_43),Z)),Z)
| implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(not(implies(X,Z)),X_43),Z)),implies(X,implies(implies(not(implies(X,Z)),X_43),Z))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X,Z)),X_43),Z),implies(implies(X,implies(not(X_43),Z)),Z)) )],[refute_0_700,refute_0_703]) ).
cnf(refute_0_705,plain,
implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) = implies(X,implies(implies(not(implies(X,Z)),X_43),Z)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(implies(not(implies(X,Z)),X_43)))]]) ).
cnf(refute_0_706,plain,
( implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) != implies(X,implies(implies(X,implies(not(X_43),Z)),Z))
| implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) != implies(X,implies(implies(not(implies(X,Z)),X_43),Z))
| implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)))),bind(Y0,$fot(implies(X,implies(implies(not(implies(X,Z)),X_43),Z)))),bind(Z0,$fot(implies(X,implies(implies(X,implies(not(X_43),Z)),Z))))]]) ).
cnf(refute_0_707,plain,
( implies(X,implies(implies(not(implies(X,Z)),X_43),Z)) != implies(X,implies(implies(X,implies(not(X_43),Z)),Z))
| implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,implies(implies(not(implies(X,Z)),X_43),Z))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) = implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(not(implies(X,Z)),X_43),Z)),implies(X,implies(implies(X,implies(not(X_43),Z)),Z))) )],[refute_0_704,refute_0_707]) ).
cnf(refute_0_709,plain,
implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) = implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z))]]) ).
cnf(refute_0_710,plain,
( implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) != implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)
| implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) != implies(X,implies(implies(X,implies(not(X_43),Z)),Z))
| implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z),implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) ),[1,0],$fot(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)))]]) ).
cnf(refute_0_711,plain,
( implies(implies(not(implies(X,Z)),X_43),implies(X,Z)) != implies(X,implies(implies(X,implies(not(X_43),Z)),Z))
| implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z),implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) )],[refute_0_709,refute_0_710]) ).
cnf(refute_0_712,plain,
implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),implies(X,implies(implies(X,implies(not(X_43),Z)),Z))) )],[refute_0_708,refute_0_711]) ).
cnf(refute_0_713,plain,
implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),
introduced(tautology,[refl,[$fot(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)))]]) ).
cnf(refute_0_714,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z))
| implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) != implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)
| implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z))) ),[1,1],$fot(implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z))]]) ).
cnf(refute_0_715,plain,
( implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z) != implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)
| implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z),implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) )],[refute_0_712,refute_0_715]) ).
cnf(refute_0_717,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z))
| implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(not(implies(X,Z)),X_43)
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(not(implies(X,Z)),X_43) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(not(implies(X,Z)),X_43)) ),[0],$fot(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)))]]) ).
cnf(refute_0_718,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(not(implies(X,Z)),X_43)
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(not(implies(X,Z)),X_43) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
( implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) != implies(not(implies(X,Z)),X_43)
| implies(not(implies(X,Z)),X_43) != implies(X,implies(not(X_43),Z))
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(X,implies(not(X_43),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),implies(X,implies(not(X_43),Z))) ),[0],$fot(implies(not(implies(X,Z)),X_43))]]) ).
cnf(refute_0_720,plain,
( implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) != implies(not(implies(X,Z)),X_43)
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(X,implies(not(X_43),Z)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X,Z)),X_43),implies(X,implies(not(X_43),Z))) )],[refute_0_696,refute_0_719]) ).
cnf(refute_0_721,plain,
( implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)) != implies(not(implies(X,Z)),X_43)
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(X,implies(not(X_43),Z)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),implies(not(implies(X,Z)),X_43)) )],[refute_0_718,refute_0_720]) ).
cnf(refute_0_722,plain,
implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(X,implies(not(X_43),Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(not(implies(X,Z)),X_43),implies(X,Z)),Z)),implies(not(implies(X,Z)),X_43)) )],[refute_0_695,refute_0_721]) ).
cnf(refute_0_723,plain,
implies(X_62,implies(X,Z)) = implies(implies(implies(X_62,implies(X,Z)),implies(X,Z)),implies(X,Z)),
inference(subst,[],[refute_0_478:[bind(Y,$fot(X_62)),bind(X_35,$fot(implies(X,Z)))]]) ).
cnf(refute_0_724,plain,
implies(X,implies(X_62,Z)) = implies(X_62,implies(X,Z)),
inference(subst,[],[lemma_7:[bind(Y,$fot(X_62))]]) ).
cnf(refute_0_725,plain,
( implies(X,implies(X_62,Z)) != implies(X_62,implies(X,Z))
| implies(X_62,implies(X,Z)) = implies(X,implies(X_62,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(X_62,Z)))),bind(Y0,$fot(implies(X_62,implies(X,Z))))]]) ).
cnf(refute_0_726,plain,
implies(X_62,implies(X,Z)) = implies(X,implies(X_62,Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(X_62,Z)),implies(X_62,implies(X,Z))) )],[refute_0_724,refute_0_725]) ).
cnf(refute_0_727,plain,
( implies(X_62,implies(X,Z)) != implies(X,implies(X_62,Z))
| implies(X_62,implies(X,Z)) != implies(implies(implies(X_62,implies(X,Z)),implies(X,Z)),implies(X,Z))
| implies(X_62,implies(X,Z)) = implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_62,implies(X,Z)),implies(implies(implies(X_62,implies(X,Z)),implies(X,Z)),implies(X,Z))) ),[1,0,0],$fot(implies(X,implies(X_62,Z)))]]) ).
cnf(refute_0_728,plain,
( implies(X_62,implies(X,Z)) != implies(implies(implies(X_62,implies(X,Z)),implies(X,Z)),implies(X,Z))
| implies(X_62,implies(X,Z)) = implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) ),
inference(resolve,[$cnf( $equal(implies(X_62,implies(X,Z)),implies(X,implies(X_62,Z))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
implies(X_62,implies(X,Z)) = implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(X_62,implies(X,Z)),implies(implies(implies(X_62,implies(X,Z)),implies(X,Z)),implies(X,Z))) )],[refute_0_723,refute_0_728]) ).
cnf(refute_0_730,plain,
implies(implies(X,implies(X_62,Z)),implies(X,Z)) = implies(X,implies(implies(X,implies(X_62,Z)),Z)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(implies(X,implies(X_62,Z))))]]) ).
cnf(refute_0_731,plain,
implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) = implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z),
introduced(tautology,[refl,[$fot(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))]]) ).
cnf(refute_0_732,plain,
( implies(implies(X,implies(X_62,Z)),implies(X,Z)) != implies(X,implies(implies(X,implies(X_62,Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) != implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z),implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) ),[1,0],$fot(implies(X,implies(implies(X,implies(X_62,Z)),Z)))]]) ).
cnf(refute_0_733,plain,
( implies(implies(X,implies(X_62,Z)),implies(X,Z)) != implies(X,implies(implies(X,implies(X_62,Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z),implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) = implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,implies(implies(X,implies(X_62,Z)),Z))) )],[refute_0_730,refute_0_733]) ).
cnf(refute_0_735,plain,
implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) = implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)),
introduced(tautology,[refl,[$fot(implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)))]]) ).
cnf(refute_0_736,plain,
( implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) != implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) != implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)
| implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)),implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))) ),[1,1],$fot(implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))]]) ).
cnf(refute_0_737,plain,
( implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z) != implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)
| implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)),implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z),implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) )],[refute_0_734,refute_0_737]) ).
cnf(refute_0_739,plain,
implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) = implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)),
inference(subst,[],[refute_0_4:[bind(Y,$fot(implies(implies(X,implies(X_62,Z)),implies(X,Z))))]]) ).
cnf(refute_0_740,plain,
( implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) != implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) != implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)))),bind(Y0,$fot(implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)))),bind(Z0,$fot(implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))))]]) ).
cnf(refute_0_741,plain,
( implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)) != implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)),implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z))) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),Z)),implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))) )],[refute_0_738,refute_0_741]) ).
cnf(refute_0_743,plain,
( implies(X_62,implies(X,Z)) != implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z))
| implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)) != implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))
| implies(X_62,implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_62,implies(X,Z)),implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))) ),[0],$fot(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)))]]) ).
cnf(refute_0_744,plain,
( implies(X_62,implies(X,Z)) != implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z))
| implies(X_62,implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z)),implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))) )],[refute_0_742,refute_0_743]) ).
cnf(refute_0_745,plain,
implies(X_62,implies(X,Z)) = implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)),
inference(resolve,[$cnf( $equal(implies(X_62,implies(X,Z)),implies(implies(implies(X,implies(X_62,Z)),implies(X,Z)),implies(X,Z))) )],[refute_0_729,refute_0_744]) ).
cnf(refute_0_746,plain,
( implies(X_62,implies(X,Z)) != implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))
| implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) = implies(X_62,implies(X,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_62,implies(X,Z)))),bind(Y0,$fot(implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))))]]) ).
cnf(refute_0_747,plain,
implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z)) = implies(X_62,implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(X_62,implies(X,Z)),implies(X,implies(implies(X,implies(implies(X,implies(X_62,Z)),Z)),Z))) )],[refute_0_745,refute_0_746]) ).
cnf(refute_0_748,plain,
implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) = implies(not(X_43),implies(X,Z)),
inference(subst,[],[refute_0_747:[bind(X_62,$fot(not(X_43)))]]) ).
cnf(refute_0_749,plain,
( implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) != implies(X,implies(not(X_43),Z))
| implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) != implies(not(X_43),implies(X,Z))
| implies(not(X_43),implies(X,Z)) = implies(X,implies(not(X_43),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),implies(X,implies(not(X_43),Z))) ),[0],$fot(implies(not(X_43),implies(X,Z)))]]) ).
cnf(refute_0_750,plain,
( implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)) != implies(X,implies(not(X_43),Z))
| implies(not(X_43),implies(X,Z)) = implies(X,implies(not(X_43),Z)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),implies(not(X_43),implies(X,Z))) )],[refute_0_748,refute_0_749]) ).
cnf(refute_0_751,plain,
implies(not(X_43),implies(X,Z)) = implies(X,implies(not(X_43),Z)),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,implies(implies(X,implies(not(X_43),Z)),Z)),Z)),implies(X,implies(not(X_43),Z))) )],[refute_0_722,refute_0_750]) ).
cnf(refute_0_752,plain,
( implies(not(X_43),implies(X,Z)) != implies(X,implies(not(X_43),Z))
| implies(X,implies(not(X_43),Z)) = implies(not(X_43),implies(X,Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_43),implies(X,Z)))),bind(Y0,$fot(implies(X,implies(not(X_43),Z))))]]) ).
cnf(refute_0_753,plain,
implies(X,implies(not(X_43),Z)) = implies(not(X_43),implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(not(X_43),implies(X,Z)),implies(X,implies(not(X_43),Z))) )],[refute_0_751,refute_0_752]) ).
cnf(refute_0_754,plain,
implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)) = implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),
inference(subst,[],[refute_0_753:[bind(X,$fot(implies(Z,implies(not(X_292),X_290)))),bind(Z,$fot(X_292)),bind(X_43,$fot(X_290))]]) ).
cnf(refute_0_755,plain,
implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),
introduced(tautology,[refl,[$fot(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)))]]) ).
cnf(refute_0_756,plain,
( implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)) != implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z))) ),[1,0],$fot(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)))]]) ).
cnf(refute_0_757,plain,
( implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)) != implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z))) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)),
inference(resolve,[$cnf( $equal(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292))) )],[refute_0_754,refute_0_757]) ).
cnf(refute_0_759,plain,
( implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z))
| implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_292),X_290),Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)))),bind(Y0,$fot(implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)))),bind(Z0,$fot(implies(Y,implies(implies(not(X_292),X_290),Z))))]]) ).
cnf(refute_0_760,plain,
( implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_292),X_290),Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_290),implies(implies(Z,implies(not(X_292),X_290)),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_292),X_290),Z))) )],[refute_0_688,refute_0_760]) ).
cnf(refute_0_762,plain,
( implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_290),X_292),Z))
| implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_292),X_290),Z))
| implies(Y,implies(implies(not(X_292),X_290),Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_290),X_292),Z))) ),[0],$fot(implies(Y,implies(implies(not(X_292),X_290),Z)))]]) ).
cnf(refute_0_763,plain,
( implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)) != implies(Y,implies(implies(not(X_290),X_292),Z))
| implies(Y,implies(implies(not(X_292),X_290),Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_292),X_290),Z))) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
implies(Y,implies(implies(not(X_292),X_290),Z)) = implies(Y,implies(implies(not(X_290),X_292),Z)),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,implies(not(X_292),X_290)),implies(not(X_290),X_292)),implies(Y,Z)),implies(Y,implies(implies(not(X_290),X_292),Z))) )],[refute_0_636,refute_0_763]) ).
cnf(refute_0_765,plain,
( implies(Y,implies(implies(not(X_292),X_290),Z)) != implies(Y,implies(implies(not(X_290),X_292),Z))
| implies(Y,implies(implies(not(X_290),X_292),Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(Y,implies(implies(not(X_292),X_290),Z)))),bind(Y0,$fot(implies(Y,implies(implies(not(X_290),X_292),Z))))]]) ).
cnf(refute_0_766,plain,
implies(Y,implies(implies(not(X_290),X_292),Z)) = implies(Y,implies(implies(not(X_292),X_290),Z)),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(not(X_292),X_290),Z)),implies(Y,implies(implies(not(X_290),X_292),Z))) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) = implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)),
inference(subst,[],[refute_0_766:[bind(Y,$fot(truth)),bind(Z,$fot(X_116)),bind(X_290,$fot(not(not(X_116)))),bind(X_292,$fot(X_116))]]) ).
cnf(refute_0_768,plain,
( implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) != implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116))
| implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)))),bind(Y0,$fot(implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)))),bind(Z0,$fot(implies(implies(not(X_116),not(not(X_116))),X_116)))]]) ).
cnf(refute_0_769,plain,
( implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)),implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116))) )],[refute_0_767,refute_0_768]) ).
cnf(refute_0_770,plain,
implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X_116),not(not(X_116))),X_116)),implies(implies(not(X_116),not(not(X_116))),X_116)) )],[refute_0_614,refute_0_769]) ).
cnf(refute_0_771,plain,
implies(implies(not(X),X_55),implies(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),implies(X_53,X))) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)),
inference(subst,[],[refute_0_151:[bind(X,$fot(implies(not(X),X_55))),bind(Z,$fot(implies(X_53,X))),bind(X_35,$fot(not(X_55)))]]) ).
cnf(refute_0_772,plain,
implies(implies(X_30,X_31),implies(Y,implies(X_30,X_31))) = truth,
inference(subst,[],[lemma_4:[bind(X,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_773,plain,
implies(Y,implies(X_30,X_31)) = implies(X_30,implies(Y,X_31)),
inference(subst,[],[lemma_7:[bind(X,$fot(Y)),bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_774,plain,
( implies(Y,implies(X_30,X_31)) != implies(X_30,implies(Y,X_31))
| implies(implies(X_30,X_31),implies(Y,implies(X_30,X_31))) != truth
| implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_30,X_31),implies(Y,implies(X_30,X_31))),truth) ),[0,1],$fot(implies(X_30,implies(Y,X_31)))]]) ).
cnf(refute_0_775,plain,
( implies(implies(X_30,X_31),implies(Y,implies(X_30,X_31))) != truth
| implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) = truth ),
inference(resolve,[$cnf( $equal(implies(Y,implies(X_30,X_31)),implies(X_30,implies(Y,X_31))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_30,X_31),implies(Y,implies(X_30,X_31))),truth) )],[refute_0_772,refute_0_775]) ).
cnf(refute_0_777,plain,
implies(X,implies(Y,implies(X_30,X_31))) = implies(Y,implies(X,implies(X_30,X_31))),
inference(subst,[],[lemma_7:[bind(Z,$fot(implies(X_30,X_31)))]]) ).
cnf(refute_0_778,plain,
implies(X,implies(X_30,X_31)) = implies(X_30,implies(X,X_31)),
inference(subst,[],[lemma_7:[bind(Y,$fot(X_30)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_779,plain,
( implies(X,implies(Y,implies(X_30,X_31))) != implies(Y,implies(X,implies(X_30,X_31)))
| implies(X,implies(X_30,X_31)) != implies(X_30,implies(X,X_31))
| implies(X,implies(Y,implies(X_30,X_31))) = implies(Y,implies(X_30,implies(X,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X,implies(Y,implies(X_30,X_31))),implies(Y,implies(X,implies(X_30,X_31)))) ),[1,1],$fot(implies(X_30,implies(X,X_31)))]]) ).
cnf(refute_0_780,plain,
( implies(X,implies(Y,implies(X_30,X_31))) != implies(Y,implies(X,implies(X_30,X_31)))
| implies(X,implies(Y,implies(X_30,X_31))) = implies(Y,implies(X_30,implies(X,X_31))) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_30,X_31)),implies(X_30,implies(X,X_31))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
implies(X,implies(Y,implies(X_30,X_31))) = implies(Y,implies(X_30,implies(X,X_31))),
inference(resolve,[$cnf( $equal(implies(X,implies(Y,implies(X_30,X_31))),implies(Y,implies(X,implies(X_30,X_31)))) )],[refute_0_777,refute_0_780]) ).
cnf(refute_0_782,plain,
implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) = implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31))),
inference(subst,[],[refute_0_781:[bind(X,$fot(implies(X_30,X_31))),bind(Y,$fot(X_30)),bind(X_30,$fot(Y))]]) ).
cnf(refute_0_783,plain,
( implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) != implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31)))
| implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) != truth
| implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))),truth) ),[0],$fot(implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31))))]]) ).
cnf(refute_0_784,plain,
( implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))) != truth
| implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))),implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31)))) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
implies(X_30,implies(Y,implies(implies(X_30,X_31),X_31))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_30,X_31),implies(X_30,implies(Y,X_31))),truth) )],[refute_0_776,refute_0_784]) ).
cnf(refute_0_786,plain,
implies(implies(not(X),X_55),implies(X_53,implies(implies(implies(not(X),X_55),X_55),X_55))) = truth,
inference(subst,[],[refute_0_785:[bind(Y,$fot(X_53)),bind(X_30,$fot(implies(not(X),X_55))),bind(X_31,$fot(X_55))]]) ).
cnf(refute_0_787,plain,
implies(X,not(implies(X,not(X_55)))) = implies(implies(not(X),X_55),X_55),
inference(subst,[],[refute_0_50:[bind(X_35,$fot(X_55))]]) ).
cnf(refute_0_788,plain,
( implies(X,not(implies(X,not(X_55)))) != implies(implies(not(X),X_55),X_55)
| implies(implies(not(X),X_55),X_55) = implies(X,not(implies(X,not(X_55)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,not(implies(X,not(X_55)))))),bind(Y0,$fot(implies(implies(not(X),X_55),X_55)))]]) ).
cnf(refute_0_789,plain,
implies(implies(not(X),X_55),X_55) = implies(X,not(implies(X,not(X_55)))),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,not(X_55)))),implies(implies(not(X),X_55),X_55)) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
( implies(implies(not(X),X_55),X_55) != implies(X,not(implies(X,not(X_55))))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(implies(not(X),X_55),X_55),X_55))) != truth
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(implies(not(X),X_55),X_55),X_55))),truth) ),[0,1,1,0],$fot(implies(X,not(implies(X,not(X_55)))))]]) ).
cnf(refute_0_791,plain,
( implies(implies(not(X),X_55),implies(X_53,implies(implies(implies(not(X),X_55),X_55),X_55))) != truth
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),X_55),implies(X,not(implies(X,not(X_55))))) )],[refute_0_789,refute_0_790]) ).
cnf(refute_0_792,plain,
implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(implies(not(X),X_55),X_55),X_55))),truth) )],[refute_0_786,refute_0_791]) ).
cnf(refute_0_793,plain,
( implies(X,implies(Y,implies(X_30,X_31))) != implies(Y,implies(X_30,implies(X,X_31)))
| implies(Y,implies(X_30,implies(X,X_31))) = implies(X,implies(Y,implies(X_30,X_31))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X,implies(Y,implies(X_30,X_31))))),bind(Y0,$fot(implies(Y,implies(X_30,implies(X,X_31)))))]]) ).
cnf(refute_0_794,plain,
implies(Y,implies(X_30,implies(X,X_31))) = implies(X,implies(Y,implies(X_30,X_31))),
inference(resolve,[$cnf( $equal(implies(X,implies(Y,implies(X_30,X_31))),implies(Y,implies(X_30,implies(X,X_31)))) )],[refute_0_781,refute_0_793]) ).
cnf(refute_0_795,plain,
implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))) = implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),
inference(subst,[],[refute_0_794:[bind(X,$fot(not(X_55))),bind(Y,$fot(implies(not(X),X_55))),bind(X_30,$fot(X_53)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_796,plain,
implies(implies(X,not(implies(X,not(X_55)))),X_55) = implies(not(X_55),X),
inference(subst,[],[refute_0_557:[bind(Y,$fot(X)),bind(X_50,$fot(X_55))]]) ).
cnf(refute_0_797,plain,
implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) = implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)),
introduced(tautology,[refl,[$fot(implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)))]]) ).
cnf(refute_0_798,plain,
( implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) != implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))
| implies(implies(X,not(implies(X,not(X_55)))),X_55) != implies(not(X_55),X)
| implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) = implies(X_53,implies(not(X_55),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) ),[1,1],$fot(implies(not(X_55),X))]]) ).
cnf(refute_0_799,plain,
( implies(implies(X,not(implies(X,not(X_55)))),X_55) != implies(not(X_55),X)
| implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) = implies(X_53,implies(not(X_55),X)) ),
inference(resolve,[$cnf( $equal(implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) = implies(X_53,implies(not(X_55),X)),
inference(resolve,[$cnf( $equal(implies(implies(X,not(implies(X,not(X_55)))),X_55),implies(not(X_55),X)) )],[refute_0_796,refute_0_799]) ).
cnf(refute_0_801,plain,
implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),
introduced(tautology,[refl,[$fot(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))))]]) ).
cnf(refute_0_802,plain,
( implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) != implies(X_53,implies(not(X_55),X))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) != implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)))) ),[1,1],$fot(implies(X_53,implies(not(X_55),X)))]]) ).
cnf(refute_0_803,plain,
( implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)) != implies(X_53,implies(not(X_55),X))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)))) )],[refute_0_801,refute_0_802]) ).
cnf(refute_0_804,plain,
implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))),
inference(resolve,[$cnf( $equal(implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55)),implies(X_53,implies(not(X_55),X))) )],[refute_0_800,refute_0_803]) ).
cnf(refute_0_805,plain,
( implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) != implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X)))
| implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))) != implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))))),bind(Y0,$fot(implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))))),bind(Z0,$fot(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))))]]) ).
cnf(refute_0_806,plain,
( implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))) != implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X)))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) = implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(not(X_55),X))),implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))) )],[refute_0_795,refute_0_806]) ).
cnf(refute_0_808,plain,
( implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) != implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))
| implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) != truth
| implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),truth) ),[0],$fot(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))))]]) ).
cnf(refute_0_809,plain,
( implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))) != truth
| implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X)))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(X_53,implies(implies(X,not(implies(X,not(X_55)))),X_55))),truth) )],[refute_0_792,refute_0_809]) ).
cnf(refute_0_811,plain,
( implies(implies(not(X),X_55),implies(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),implies(X_53,X))) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))) != truth
| implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_55),implies(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),implies(X_53,X))),implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_812,plain,
( implies(implies(not(X),X_55),implies(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),implies(X_53,X))) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) ),
inference(resolve,[$cnf( $equal(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),truth) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(implies(not(X_55),implies(implies(not(X),X_55),implies(X_53,X))),implies(X_53,X))),implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))) )],[refute_0_771,refute_0_812]) ).
cnf(refute_0_814,plain,
implies(truth,implies(X_53,implies(implies(not(X_55),X),X))) = implies(X_53,implies(implies(not(X_55),X),X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_53,implies(implies(not(X_55),X),X))))]]) ).
cnf(refute_0_815,plain,
implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) = implies(X_224,implies(X_225,implies(implies(not(X_226),X),X_226))),
inference(subst,[],[refute_0_781:[bind(X,$fot(implies(not(X_226),X))),bind(Y,$fot(X_224)),bind(X_30,$fot(X_225)),bind(X_31,$fot(X_226))]]) ).
cnf(refute_0_816,plain,
implies(implies(not(X),X_226),X_226) = implies(implies(not(X_226),X),X_226),
inference(subst,[],[refute_0_565:[bind(X_63,$fot(X_226))]]) ).
cnf(refute_0_817,plain,
( implies(implies(not(X),X_226),X_226) != implies(implies(not(X_226),X),X_226)
| implies(implies(not(X_226),X),X_226) = implies(implies(not(X),X_226),X_226) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X),X_226),X_226))),bind(Y0,$fot(implies(implies(not(X_226),X),X_226)))]]) ).
cnf(refute_0_818,plain,
implies(implies(not(X_226),X),X_226) = implies(implies(not(X),X_226),X_226),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_226),X_226),implies(implies(not(X_226),X),X_226)) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
( implies(implies(not(X_226),X),X_226) != implies(implies(not(X),X_226),X_226)
| implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) != implies(X_224,implies(X_225,implies(implies(not(X_226),X),X_226)))
| implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) = implies(X_224,implies(X_225,implies(implies(not(X),X_226),X_226))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))),implies(X_224,implies(X_225,implies(implies(not(X_226),X),X_226)))) ),[1,1,1],$fot(implies(implies(not(X),X_226),X_226))]]) ).
cnf(refute_0_820,plain,
( implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) != implies(X_224,implies(X_225,implies(implies(not(X_226),X),X_226)))
| implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) = implies(X_224,implies(X_225,implies(implies(not(X),X_226),X_226))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_226),X),X_226),implies(implies(not(X),X_226),X_226)) )],[refute_0_818,refute_0_819]) ).
cnf(refute_0_821,plain,
implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))) = implies(X_224,implies(X_225,implies(implies(not(X),X_226),X_226))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_226),X),implies(X_224,implies(X_225,X_226))),implies(X_224,implies(X_225,implies(implies(not(X_226),X),X_226)))) )],[refute_0_815,refute_0_820]) ).
cnf(refute_0_822,plain,
implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(truth,implies(X_53,implies(implies(not(X_55),X),X))),
inference(subst,[],[refute_0_821:[bind(X,$fot(X_55)),bind(X_224,$fot(truth)),bind(X_225,$fot(X_53)),bind(X_226,$fot(X))]]) ).
cnf(refute_0_823,plain,
( implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) != implies(truth,implies(X_53,implies(implies(not(X_55),X),X)))
| implies(truth,implies(X_53,implies(implies(not(X_55),X),X))) != implies(X_53,implies(implies(not(X_55),X),X))
| implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(X_53,implies(implies(not(X_55),X),X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X),X_55),implies(truth,implies(X_53,X))))),bind(Y0,$fot(implies(truth,implies(X_53,implies(implies(not(X_55),X),X))))),bind(Z0,$fot(implies(X_53,implies(implies(not(X_55),X),X))))]]) ).
cnf(refute_0_824,plain,
( implies(truth,implies(X_53,implies(implies(not(X_55),X),X))) != implies(X_53,implies(implies(not(X_55),X),X))
| implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(X_53,implies(implies(not(X_55),X),X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(truth,implies(X_53,X))),implies(truth,implies(X_53,implies(implies(not(X_55),X),X)))) )],[refute_0_822,refute_0_823]) ).
cnf(refute_0_825,plain,
implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) = implies(X_53,implies(implies(not(X_55),X),X)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_53,implies(implies(not(X_55),X),X))),implies(X_53,implies(implies(not(X_55),X),X))) )],[refute_0_814,refute_0_824]) ).
cnf(refute_0_826,plain,
( implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) != implies(X_53,implies(implies(not(X_55),X),X))
| implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_55),implies(truth,implies(X_53,X))),implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))) ),[0],$fot(implies(X_53,implies(implies(not(X_55),X),X)))]]) ).
cnf(refute_0_827,plain,
( implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(truth,implies(X_53,X))),implies(X_53,implies(implies(not(X_55),X),X))) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201))))))),
inference(subst,[],[refute_0_305:[bind(Y,$fot(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),bind(X_40,$fot(not(X_203)))]]) ).
cnf(refute_0_829,plain,
implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201))) = truth,
inference(subst,[],[refute_0_810:[bind(X,$fot(X_201)),bind(X_53,$fot(X_202)),bind(X_55,$fot(X_203))]]) ).
cnf(refute_0_830,plain,
( implies(implies(not(X_201),X_203),implies(X_202,X_201)) != implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))
| implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201))) != truth
| implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_201),X_203),implies(X_202,X_201)),implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))) ),[1,1,0,1,0],$fot(truth)]]) ).
cnf(refute_0_831,plain,
( implies(implies(not(X_201),X_203),implies(X_202,X_201)) != implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))
| implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201))),truth) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_201),X_203),implies(X_202,X_201)),implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(implies(not(X_203),implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))) )],[refute_0_828,refute_0_831]) ).
cnf(refute_0_833,plain,
not(not(X_203)) = X_203,
inference(subst,[],[lemma_9:[bind(X,$fot(X_203))]]) ).
cnf(refute_0_834,plain,
implies(truth,not(not(X_203))) = not(not(X_203)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_203))))]]) ).
cnf(refute_0_835,plain,
( implies(truth,not(not(X_203))) != not(not(X_203))
| not(not(X_203)) != X_203
| implies(truth,not(not(X_203))) = X_203 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(truth,not(not(X_203))))),bind(Y0,$fot(not(not(X_203)))),bind(Z0,$fot(X_203))]]) ).
cnf(refute_0_836,plain,
( not(not(X_203)) != X_203
| implies(truth,not(not(X_203))) = X_203 ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_203))),not(not(X_203))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
implies(truth,not(not(X_203))) = X_203,
inference(resolve,[$cnf( $equal(not(not(X_203)),X_203) )],[refute_0_833,refute_0_836]) ).
cnf(refute_0_838,plain,
implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))]]) ).
cnf(refute_0_839,plain,
( implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) != implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(truth,not(not(X_203))) != X_203
| implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) ),[1,0],$fot(X_203)]]) ).
cnf(refute_0_840,plain,
( implies(truth,not(not(X_203))) != X_203
| implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_838,refute_0_839]) ).
cnf(refute_0_841,plain,
implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_203))),X_203) )],[refute_0_837,refute_0_840]) ).
cnf(refute_0_842,plain,
implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))) = implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
inference(subst,[],[refute_0_600:[bind(X_170,$fot(truth)),bind(X_171,$fot(not(X_203))),bind(X_8,$fot(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))]]) ).
cnf(refute_0_843,plain,
implies(not(X),not(implies(X_170,not(X_171)))) = implies(implies(X_170,not(X_171)),X),
inference(subst,[],[lemma_10:[bind(Y,$fot(implies(X_170,not(X_171))))]]) ).
cnf(refute_0_844,plain,
( implies(not(X),not(implies(X_170,not(X_171)))) != implies(implies(X_170,not(X_171)),X)
| not(implies(X_170,not(X_171))) != not(implies(X_171,not(X_170)))
| implies(not(X),not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X),not(implies(X_170,not(X_171)))),implies(implies(X_170,not(X_171)),X)) ),[0,1],$fot(not(implies(X_171,not(X_170))))]]) ).
cnf(refute_0_845,plain,
( implies(not(X),not(implies(X_170,not(X_171)))) != implies(implies(X_170,not(X_171)),X)
| implies(not(X),not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),X) ),
inference(resolve,[$cnf( $equal(not(implies(X_170,not(X_171))),not(implies(X_171,not(X_170)))) )],[refute_0_595,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(not(X),not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),X),
inference(resolve,[$cnf( $equal(implies(not(X),not(implies(X_170,not(X_171)))),implies(implies(X_170,not(X_171)),X)) )],[refute_0_843,refute_0_845]) ).
cnf(refute_0_847,plain,
implies(not(X),not(implies(X_171,not(X_170)))) = implies(implies(X_171,not(X_170)),X),
inference(subst,[],[lemma_10:[bind(Y,$fot(implies(X_171,not(X_170))))]]) ).
cnf(refute_0_848,plain,
( implies(not(X),not(implies(X_171,not(X_170)))) != implies(implies(X_170,not(X_171)),X)
| implies(not(X),not(implies(X_171,not(X_170)))) != implies(implies(X_171,not(X_170)),X)
| implies(implies(X_171,not(X_170)),X) = implies(implies(X_170,not(X_171)),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X),not(implies(X_171,not(X_170)))),implies(implies(X_170,not(X_171)),X)) ),[0],$fot(implies(implies(X_171,not(X_170)),X))]]) ).
cnf(refute_0_849,plain,
( implies(not(X),not(implies(X_171,not(X_170)))) != implies(implies(X_170,not(X_171)),X)
| implies(implies(X_171,not(X_170)),X) = implies(implies(X_170,not(X_171)),X) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(implies(X_171,not(X_170)))),implies(implies(X_171,not(X_170)),X)) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
implies(implies(X_171,not(X_170)),X) = implies(implies(X_170,not(X_171)),X),
inference(resolve,[$cnf( $equal(implies(not(X),not(implies(X_171,not(X_170)))),implies(implies(X_170,not(X_171)),X)) )],[refute_0_846,refute_0_849]) ).
cnf(refute_0_851,plain,
( implies(implies(X_171,not(X_170)),X) != implies(implies(X_170,not(X_171)),X)
| implies(implies(X_170,not(X_171)),X) = implies(implies(X_171,not(X_170)),X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(X_171,not(X_170)),X))),bind(Y0,$fot(implies(implies(X_170,not(X_171)),X)))]]) ).
cnf(refute_0_852,plain,
implies(implies(X_170,not(X_171)),X) = implies(implies(X_171,not(X_170)),X),
inference(resolve,[$cnf( $equal(implies(implies(X_171,not(X_170)),X),implies(implies(X_170,not(X_171)),X)) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))),
inference(subst,[],[refute_0_852:[bind(X,$fot(not(implies(not(X_203),not(truth))))),bind(X_170,$fot(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),bind(X_171,$fot(X_203))]]) ).
cnf(refute_0_854,plain,
( implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))) != implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) != implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth))))
| implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))))),bind(Y0,$fot(implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))))),bind(Z0,$fot(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))))]]) ).
cnf(refute_0_855,plain,
( implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))) != implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))),implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth))))) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
inference(resolve,[$cnf( $equal(implies(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),not(implies(not(X_203),not(truth)))),implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_842,refute_0_855]) ).
cnf(refute_0_857,plain,
( implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) != implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) != implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))))),bind(Y0,$fot(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))),bind(Z0,$fot(implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))))]]) ).
cnf(refute_0_858,plain,
( implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) != implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))),implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_856,refute_0_857]) ).
cnf(refute_0_859,plain,
implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(X_203))),not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_841,refute_0_858]) ).
cnf(refute_0_860,plain,
( implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))) != implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(implies(not(X_201),X_203),implies(X_202,X_201)) != implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth))))
| implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_201),X_203),implies(X_202,X_201)),implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth))))) ),[1],$fot(implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))))]]) ).
cnf(refute_0_861,plain,
( implies(implies(not(X_201),X_203),implies(X_202,X_201)) != implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth))))
| implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth)))),implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
implies(implies(not(X_201),X_203),implies(X_202,X_201)) = implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_201),X_203),implies(X_202,X_201)),implies(implies(implies(implies(not(X_201),X_203),implies(X_202,X_201)),not(X_203)),not(implies(not(X_203),not(truth))))) )],[refute_0_832,refute_0_861]) ).
cnf(refute_0_863,plain,
( implies(implies(not(X_201),X_203),implies(X_202,X_201)) != implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))
| implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(implies(not(X_201),X_203),implies(X_202,X_201)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_201),X_203),implies(X_202,X_201)))),bind(Y0,$fot(implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))))]]) ).
cnf(refute_0_864,plain,
implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201)))))) = implies(implies(not(X_201),X_203),implies(X_202,X_201)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_201),X_203),implies(X_202,X_201)),implies(X_203,not(implies(X_203,not(implies(implies(not(X_201),X_203),implies(X_202,X_201))))))) )],[refute_0_862,refute_0_863]) ).
cnf(refute_0_865,plain,
implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))) = implies(implies(not(X),X_55),implies(X_53,X)),
inference(subst,[],[refute_0_864:[bind(X_201,$fot(X)),bind(X_202,$fot(X_53)),bind(X_203,$fot(X_55))]]) ).
cnf(refute_0_866,plain,
implies(X_50,not(implies(X_170,not(X_171)))) = implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))),
inference(subst,[],[refute_0_415:[bind(X,$fot(implies(X_170,not(X_171))))]]) ).
cnf(refute_0_867,plain,
( implies(X_50,not(implies(X_170,not(X_171)))) != implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))
| not(implies(X_170,not(X_171))) != not(implies(X_171,not(X_170)))
| implies(X_50,not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_50,not(implies(X_170,not(X_171)))),implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))) ),[0,1],$fot(not(implies(X_171,not(X_170))))]]) ).
cnf(refute_0_868,plain,
( implies(X_50,not(implies(X_170,not(X_171)))) != implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))
| implies(X_50,not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))) ),
inference(resolve,[$cnf( $equal(not(implies(X_170,not(X_171))),not(implies(X_171,not(X_170)))) )],[refute_0_595,refute_0_867]) ).
cnf(refute_0_869,plain,
implies(X_50,not(implies(X_171,not(X_170)))) = implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))),
inference(resolve,[$cnf( $equal(implies(X_50,not(implies(X_170,not(X_171)))),implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))) )],[refute_0_866,refute_0_868]) ).
cnf(refute_0_870,plain,
implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))) = implies(X_50,not(implies(X_170,not(X_171)))),
inference(subst,[],[refute_0_417:[bind(X,$fot(implies(X_170,not(X_171))))]]) ).
cnf(refute_0_871,plain,
( implies(X_50,not(implies(X_171,not(X_170)))) != implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))
| implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))) != implies(X_50,not(implies(X_170,not(X_171))))
| implies(X_50,not(implies(X_171,not(X_170)))) = implies(X_50,not(implies(X_170,not(X_171)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_50,not(implies(X_171,not(X_170)))),implies(X_50,not(implies(X_170,not(X_171))))) ),[0],$fot(implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))))]]) ).
cnf(refute_0_872,plain,
( implies(X_50,not(implies(X_171,not(X_170)))) != implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))
| implies(X_50,not(implies(X_171,not(X_170)))) = implies(X_50,not(implies(X_170,not(X_171)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50))),implies(X_50,not(implies(X_170,not(X_171))))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
implies(X_50,not(implies(X_171,not(X_170)))) = implies(X_50,not(implies(X_170,not(X_171)))),
inference(resolve,[$cnf( $equal(implies(X_50,not(implies(X_171,not(X_170)))),implies(implies(X_170,not(X_171)),not(implies(implies(not(X_50),implies(X_170,not(X_171))),X_50)))) )],[refute_0_869,refute_0_872]) ).
cnf(refute_0_874,plain,
( implies(X_50,not(implies(X_171,not(X_170)))) != implies(X_50,not(implies(X_170,not(X_171))))
| implies(X_50,not(implies(X_170,not(X_171)))) = implies(X_50,not(implies(X_171,not(X_170)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_50,not(implies(X_171,not(X_170)))))),bind(Y0,$fot(implies(X_50,not(implies(X_170,not(X_171))))))]]) ).
cnf(refute_0_875,plain,
implies(X_50,not(implies(X_170,not(X_171)))) = implies(X_50,not(implies(X_171,not(X_170)))),
inference(resolve,[$cnf( $equal(implies(X_50,not(implies(X_171,not(X_170)))),implies(X_50,not(implies(X_170,not(X_171))))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) = implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))),
inference(subst,[],[refute_0_875:[bind(X_170,$fot(implies(implies(not(X),X_55),implies(X_53,X)))),bind(X_171,$fot(X_55)),bind(X_50,$fot(X_55))]]) ).
cnf(refute_0_877,plain,
( implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) != implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X))))))
| implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))))),bind(Y0,$fot(implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))))),bind(Z0,$fot(implies(implies(not(X),X_55),implies(X_53,X))))]]) ).
cnf(refute_0_878,plain,
( implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(resolve,[$cnf( $equal(implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))),implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X))))))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) = implies(implies(not(X),X_55),implies(X_53,X)),
inference(resolve,[$cnf( $equal(implies(X_55,not(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))))),implies(implies(not(X),X_55),implies(X_53,X))) )],[refute_0_865,refute_0_878]) ).
cnf(refute_0_880,plain,
implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) = implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))),
inference(subst,[],[refute_0_598:[bind(X_170,$fot(X_55)),bind(X_171,$fot(implies(implies(not(X),X_55),implies(X_53,X)))),bind(X_8,$fot(X_55))]]) ).
cnf(refute_0_881,plain,
( implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) != implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55))))
| implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)))),bind(Y0,$fot(implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))))),bind(Z0,$fot(implies(implies(not(X),X_55),implies(X_53,X))))]]) ).
cnf(refute_0_882,plain,
( implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)),implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55))))) )],[refute_0_880,refute_0_881]) ).
cnf(refute_0_883,plain,
implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)),
inference(resolve,[$cnf( $equal(implies(X_55,not(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)))),implies(implies(not(X),X_55),implies(X_53,X))) )],[refute_0_879,refute_0_882]) ).
cnf(refute_0_884,plain,
implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) = implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)),
inference(subst,[],[refute_0_852:[bind(X,$fot(not(X_55))),bind(X_170,$fot(implies(implies(not(X),X_55),implies(X_53,X)))),bind(X_171,$fot(X_55))]]) ).
cnf(refute_0_885,plain,
( implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) != implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55))
| implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)))),bind(Y0,$fot(implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)))),bind(Z0,$fot(implies(implies(not(X),X_55),implies(X_53,X))))]]) ).
cnf(refute_0_886,plain,
( implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)),implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55))) )],[refute_0_884,refute_0_885]) ).
cnf(refute_0_887,plain,
implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) = implies(implies(not(X),X_55),implies(X_53,X)),
inference(resolve,[$cnf( $equal(implies(implies(X_55,not(implies(implies(not(X),X_55),implies(X_53,X)))),not(X_55)),implies(implies(not(X),X_55),implies(X_53,X))) )],[refute_0_883,refute_0_886]) ).
cnf(refute_0_888,plain,
( implies(X_53,implies(implies(not(X_55),X),X)) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_53,implies(implies(not(X_55),X),X)),implies(implies(not(X),X_55),implies(X_53,X))) ),[0],$fot(implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)))]]) ).
cnf(refute_0_889,plain,
( implies(X_53,implies(implies(not(X_55),X),X)) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55)),implies(implies(not(X),X_55),implies(X_53,X))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
( implies(implies(not(X),X_55),implies(truth,implies(X_53,X))) != implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))
| implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(not(X),X_55),implies(X_53,X)) ),
inference(resolve,[$cnf( $equal(implies(X_53,implies(implies(not(X_55),X),X)),implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))) )],[refute_0_827,refute_0_889]) ).
cnf(refute_0_891,plain,
implies(X_53,implies(implies(not(X_55),X),X)) = implies(implies(not(X),X_55),implies(X_53,X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_55),implies(truth,implies(X_53,X))),implies(implies(implies(implies(not(X),X_55),implies(X_53,X)),not(X_55)),not(X_55))) )],[refute_0_813,refute_0_890]) ).
cnf(refute_0_892,plain,
( implies(X_53,implies(implies(not(X_55),X),X)) != implies(implies(not(X),X_55),implies(X_53,X))
| implies(implies(not(X),X_55),implies(X_53,X)) = implies(X_53,implies(implies(not(X_55),X),X)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_53,implies(implies(not(X_55),X),X)))),bind(Y0,$fot(implies(implies(not(X),X_55),implies(X_53,X))))]]) ).
cnf(refute_0_893,plain,
implies(implies(not(X),X_55),implies(X_53,X)) = implies(X_53,implies(implies(not(X_55),X),X)),
inference(resolve,[$cnf( $equal(implies(X_53,implies(implies(not(X_55),X),X)),implies(implies(not(X),X_55),implies(X_53,X))) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)),
inference(subst,[],[refute_0_893:[bind(X,$fot(X_116)),bind(X_53,$fot(truth)),bind(X_55,$fot(not(not(X_116))))]]) ).
cnf(refute_0_895,plain,
( implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) != implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116))
| implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)))),bind(Y0,$fot(implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)))),bind(Z0,$fot(implies(implies(not(X_116),not(not(X_116))),X_116)))]]) ).
cnf(refute_0_896,plain,
( implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)),implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116))) )],[refute_0_894,refute_0_895]) ).
cnf(refute_0_897,plain,
implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),not(not(X_116))),X_116),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(not(X_116))),X_116),X_116)),implies(implies(not(X_116),not(not(X_116))),X_116)) )],[refute_0_770,refute_0_896]) ).
cnf(refute_0_898,plain,
( implies(implies(not(X_116),not(not(X_116))),X_116) != implies(implies(not(X_116),X_116),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) != implies(implies(not(X_116),not(not(X_116))),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),X_116),X_116) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)))),bind(Y0,$fot(implies(implies(not(X_116),not(not(X_116))),X_116))),bind(Z0,$fot(implies(implies(not(X_116),X_116),X_116)))]]) ).
cnf(refute_0_899,plain,
( implies(implies(not(X_116),not(not(X_116))),X_116) != implies(implies(not(X_116),X_116),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),X_116),X_116) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)),implies(implies(not(X_116),not(not(X_116))),X_116)) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) = implies(implies(not(X_116),X_116),X_116),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),X_116),implies(implies(not(X_116),X_116),X_116)) )],[refute_0_613,refute_0_899]) ).
cnf(refute_0_901,plain,
( implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) != implies(implies(not(X_116),X_116),X_116)
| implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) != truth
| implies(implies(not(X_116),X_116),X_116) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)),truth) ),[0],$fot(implies(implies(not(X_116),X_116),X_116))]]) ).
cnf(refute_0_902,plain,
( implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)) != truth
| implies(implies(not(X_116),X_116),X_116) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)),implies(implies(not(X_116),X_116),X_116)) )],[refute_0_900,refute_0_901]) ).
cnf(refute_0_903,plain,
implies(implies(not(X_116),X_116),X_116) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_116),not(not(X_116))),implies(truth,X_116)),truth) )],[refute_0_608,refute_0_902]) ).
cnf(refute_0_904,plain,
implies(implies(not(X_40),X_40),X_40) = truth,
inference(subst,[],[refute_0_903:[bind(X_116,$fot(X_40))]]) ).
cnf(refute_0_905,plain,
( implies(implies(not(X_40),X_40),X_40) != truth
| implies(not(X_40),X_40) != implies(implies(implies(not(X_40),X_40),X_40),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))
| implies(not(X_40),X_40) = implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_40),X_40),implies(implies(implies(not(X_40),X_40),X_40),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_906,plain,
( implies(not(X_40),X_40) != implies(implies(implies(not(X_40),X_40),X_40),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))
| implies(not(X_40),X_40) = implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_40),X_40),X_40),truth) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
implies(not(X_40),X_40) = implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))),
inference(resolve,[$cnf( $equal(implies(not(X_40),X_40),implies(implies(implies(not(X_40),X_40),X_40),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))) )],[refute_0_306,refute_0_906]) ).
cnf(refute_0_908,plain,
not(not(X_40)) = X_40,
inference(subst,[],[lemma_9:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_909,plain,
implies(X_40,not(truth)) = not(X_40),
inference(subst,[],[lemma_8:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_910,plain,
implies(X_40,X_40) = truth,
inference(subst,[],[lemma_1:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_911,plain,
implies(implies(X_35,Z),implies(Y,Z)) = implies(Y,implies(implies(X_35,Z),Z)),
inference(subst,[],[lemma_7:[bind(X,$fot(implies(X_35,Z)))]]) ).
cnf(refute_0_912,plain,
implies(implies(X_35,Z),Z) = implies(implies(Z,X_35),X_35),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_35)),bind(Y,$fot(Z))]]) ).
cnf(refute_0_913,plain,
( implies(implies(X_35,Z),Z) != implies(implies(Z,X_35),X_35)
| implies(implies(X_35,Z),implies(Y,Z)) != implies(Y,implies(implies(X_35,Z),Z))
| implies(implies(X_35,Z),implies(Y,Z)) = implies(Y,implies(implies(Z,X_35),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,Z),implies(Y,Z)),implies(Y,implies(implies(X_35,Z),Z))) ),[1,1],$fot(implies(implies(Z,X_35),X_35))]]) ).
cnf(refute_0_914,plain,
( implies(implies(X_35,Z),implies(Y,Z)) != implies(Y,implies(implies(X_35,Z),Z))
| implies(implies(X_35,Z),implies(Y,Z)) = implies(Y,implies(implies(Z,X_35),X_35)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,Z),Z),implies(implies(Z,X_35),X_35)) )],[refute_0_912,refute_0_913]) ).
cnf(refute_0_915,plain,
implies(implies(X_35,Z),implies(Y,Z)) = implies(Y,implies(implies(Z,X_35),X_35)),
inference(resolve,[$cnf( $equal(implies(implies(X_35,Z),implies(Y,Z)),implies(Y,implies(implies(X_35,Z),Z))) )],[refute_0_911,refute_0_914]) ).
cnf(refute_0_916,plain,
implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)),
inference(subst,[],[refute_0_915:[bind(Z,$fot(implies(not(X_35),X_35)))]]) ).
cnf(refute_0_917,plain,
implies(implies(not(X_35),X_35),X_35) = truth,
inference(subst,[],[refute_0_903:[bind(X_116,$fot(X_35))]]) ).
cnf(refute_0_918,plain,
( implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))
| implies(implies(not(X_35),X_35),X_35) != truth
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(truth,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))) ),[1,1,0],$fot(truth)]]) ).
cnf(refute_0_919,plain,
( implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(truth,X_35)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_35),X_35),X_35),truth) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(truth,X_35)),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))) )],[refute_0_916,refute_0_919]) ).
cnf(refute_0_921,plain,
implies(implies(implies(not(X_35),X_35),X_35),X_35) = implies(not(X_35),X_35),
inference(subst,[],[refute_0_480:[bind(Y,$fot(not(X_35)))]]) ).
cnf(refute_0_922,plain,
implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) = implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)),
introduced(tautology,[refl,[$fot(implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)))]]) ).
cnf(refute_0_923,plain,
( implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) != implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))
| implies(implies(implies(not(X_35),X_35),X_35),X_35) != implies(not(X_35),X_35)
| implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) = implies(Y,implies(not(X_35),X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)),implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))) ),[1,1],$fot(implies(not(X_35),X_35))]]) ).
cnf(refute_0_924,plain,
( implies(implies(implies(not(X_35),X_35),X_35),X_35) != implies(not(X_35),X_35)
| implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) = implies(Y,implies(not(X_35),X_35)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)),implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))) )],[refute_0_922,refute_0_923]) ).
cnf(refute_0_925,plain,
implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) = implies(Y,implies(not(X_35),X_35)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_35),X_35),X_35),X_35),implies(not(X_35),X_35)) )],[refute_0_921,refute_0_924]) ).
cnf(refute_0_926,plain,
( implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) != implies(Y,implies(not(X_35),X_35))
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(not(X_35),X_35)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))))),bind(Y0,$fot(implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)))),bind(Z0,$fot(implies(Y,implies(not(X_35),X_35))))]]) ).
cnf(refute_0_927,plain,
( implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)) != implies(Y,implies(not(X_35),X_35))
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(not(X_35),X_35)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35))) )],[refute_0_916,refute_0_926]) ).
cnf(refute_0_928,plain,
implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) = implies(Y,implies(not(X_35),X_35)),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(implies(not(X_35),X_35),X_35),X_35)),implies(Y,implies(not(X_35),X_35))) )],[refute_0_925,refute_0_927]) ).
cnf(refute_0_929,plain,
( implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(not(X_35),X_35))
| implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(truth,X_35))
| implies(Y,implies(not(X_35),X_35)) = implies(Y,implies(truth,X_35)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(truth,X_35))) ),[0],$fot(implies(Y,implies(not(X_35),X_35)))]]) ).
cnf(refute_0_930,plain,
( implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(truth,X_35))
| implies(Y,implies(not(X_35),X_35)) = implies(Y,implies(truth,X_35)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(not(X_35),X_35))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
implies(truth,X_35) = X_35,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_35))]]) ).
cnf(refute_0_932,plain,
implies(Y,implies(truth,X_35)) = implies(Y,implies(truth,X_35)),
introduced(tautology,[refl,[$fot(implies(Y,implies(truth,X_35)))]]) ).
cnf(refute_0_933,plain,
( implies(Y,implies(truth,X_35)) != implies(Y,implies(truth,X_35))
| implies(truth,X_35) != X_35
| implies(Y,implies(truth,X_35)) = implies(Y,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(truth,X_35)),implies(Y,implies(truth,X_35))) ),[1,1],$fot(X_35)]]) ).
cnf(refute_0_934,plain,
( implies(truth,X_35) != X_35
| implies(Y,implies(truth,X_35)) = implies(Y,X_35) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(truth,X_35)),implies(Y,implies(truth,X_35))) )],[refute_0_932,refute_0_933]) ).
cnf(refute_0_935,plain,
implies(Y,implies(truth,X_35)) = implies(Y,X_35),
inference(resolve,[$cnf( $equal(implies(truth,X_35),X_35) )],[refute_0_931,refute_0_934]) ).
cnf(refute_0_936,plain,
( implies(Y,implies(not(X_35),X_35)) != implies(Y,implies(truth,X_35))
| implies(Y,implies(truth,X_35)) != implies(Y,X_35)
| implies(Y,implies(not(X_35),X_35)) = implies(Y,X_35) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(Y,implies(not(X_35),X_35)),implies(Y,X_35)) ),[0],$fot(implies(Y,implies(truth,X_35)))]]) ).
cnf(refute_0_937,plain,
( implies(Y,implies(not(X_35),X_35)) != implies(Y,implies(truth,X_35))
| implies(Y,implies(not(X_35),X_35)) = implies(Y,X_35) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(truth,X_35)),implies(Y,X_35)) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
( implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))) != implies(Y,implies(truth,X_35))
| implies(Y,implies(not(X_35),X_35)) = implies(Y,X_35) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(not(X_35),X_35)),implies(Y,implies(truth,X_35))) )],[refute_0_930,refute_0_937]) ).
cnf(refute_0_939,plain,
implies(Y,implies(not(X_35),X_35)) = implies(Y,X_35),
inference(resolve,[$cnf( $equal(implies(implies(X_35,implies(not(X_35),X_35)),implies(Y,implies(not(X_35),X_35))),implies(Y,implies(truth,X_35))) )],[refute_0_920,refute_0_938]) ).
cnf(refute_0_940,plain,
implies(X_40,implies(not(X_40),X_40)) = implies(X_40,X_40),
inference(subst,[],[refute_0_939:[bind(Y,$fot(X_40)),bind(X_35,$fot(X_40))]]) ).
cnf(refute_0_941,plain,
( implies(X_40,X_40) != truth
| implies(X_40,implies(not(X_40),X_40)) != implies(X_40,X_40)
| implies(X_40,implies(not(X_40),X_40)) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_40,implies(not(X_40),X_40)))),bind(Y0,$fot(implies(X_40,X_40))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_942,plain,
( implies(X_40,X_40) != truth
| implies(X_40,implies(not(X_40),X_40)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_40,implies(not(X_40),X_40)),implies(X_40,X_40)) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
implies(X_40,implies(not(X_40),X_40)) = truth,
inference(resolve,[$cnf( $equal(implies(X_40,X_40),truth) )],[refute_0_910,refute_0_942]) ).
cnf(refute_0_944,plain,
not(implies(X_40,implies(not(X_40),X_40))) = not(implies(X_40,implies(not(X_40),X_40))),
introduced(tautology,[refl,[$fot(not(implies(X_40,implies(not(X_40),X_40))))]]) ).
cnf(refute_0_945,plain,
( implies(X_40,implies(not(X_40),X_40)) != truth
| not(implies(X_40,implies(not(X_40),X_40))) != not(implies(X_40,implies(not(X_40),X_40)))
| not(implies(X_40,implies(not(X_40),X_40))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_40,implies(not(X_40),X_40))),not(implies(X_40,implies(not(X_40),X_40)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_946,plain,
( implies(X_40,implies(not(X_40),X_40)) != truth
| not(implies(X_40,implies(not(X_40),X_40))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_40,implies(not(X_40),X_40))),not(implies(X_40,implies(not(X_40),X_40)))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
not(implies(X_40,implies(not(X_40),X_40))) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_40,implies(not(X_40),X_40)),truth) )],[refute_0_943,refute_0_946]) ).
cnf(refute_0_948,plain,
implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))),
introduced(tautology,[refl,[$fot(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))]]) ).
cnf(refute_0_949,plain,
( implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) != implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))
| not(implies(X_40,implies(not(X_40),X_40))) != not(truth)
| implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = implies(X_40,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))),implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_950,plain,
( not(implies(X_40,implies(not(X_40),X_40))) != not(truth)
| implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = implies(X_40,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))),implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) )],[refute_0_948,refute_0_949]) ).
cnf(refute_0_951,plain,
implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = implies(X_40,not(truth)),
inference(resolve,[$cnf( $equal(not(implies(X_40,implies(not(X_40),X_40))),not(truth)) )],[refute_0_947,refute_0_950]) ).
cnf(refute_0_952,plain,
( implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) != implies(X_40,not(truth))
| implies(X_40,not(truth)) != not(X_40)
| implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = not(X_40) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))),bind(Y0,$fot(implies(X_40,not(truth)))),bind(Z0,$fot(not(X_40)))]]) ).
cnf(refute_0_953,plain,
( implies(X_40,not(truth)) != not(X_40)
| implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = not(X_40) ),
inference(resolve,[$cnf( $equal(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))),implies(X_40,not(truth))) )],[refute_0_951,refute_0_952]) ).
cnf(refute_0_954,plain,
implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) = not(X_40),
inference(resolve,[$cnf( $equal(implies(X_40,not(truth)),not(X_40)) )],[refute_0_909,refute_0_953]) ).
cnf(refute_0_955,plain,
not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),
introduced(tautology,[refl,[$fot(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))]]) ).
cnf(refute_0_956,plain,
( implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) != not(X_40)
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) != not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = not(not(X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) ),[1,0],$fot(not(X_40))]]) ).
cnf(refute_0_957,plain,
( implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))) != not(X_40)
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = not(not(X_40)) ),
inference(resolve,[$cnf( $equal(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = not(not(X_40)),
inference(resolve,[$cnf( $equal(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))),not(X_40)) )],[refute_0_954,refute_0_957]) ).
cnf(refute_0_959,plain,
( not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) != not(not(X_40))
| not(not(X_40)) != X_40
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = X_40 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))),bind(Y0,$fot(not(not(X_40)))),bind(Z0,$fot(X_40))]]) ).
cnf(refute_0_960,plain,
( not(not(X_40)) != X_40
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = X_40 ),
inference(resolve,[$cnf( $equal(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),not(not(X_40))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) = X_40,
inference(resolve,[$cnf( $equal(not(not(X_40)),X_40) )],[refute_0_908,refute_0_960]) ).
cnf(refute_0_962,plain,
implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) = not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))))]]) ).
cnf(refute_0_963,plain,
( implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) != not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))
| not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) != X_40
| implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) = X_40 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))))),bind(Y0,$fot(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))),bind(Z0,$fot(X_40))]]) ).
cnf(refute_0_964,plain,
( not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))) != X_40
| implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) = X_40 ),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))),not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) )],[refute_0_962,refute_0_963]) ).
cnf(refute_0_965,plain,
implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) = X_40,
inference(resolve,[$cnf( $equal(not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))),X_40) )],[refute_0_961,refute_0_964]) ).
cnf(refute_0_966,plain,
( implies(not(X_40),X_40) != implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))
| implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))) != X_40
| implies(not(X_40),X_40) = X_40 ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_40),X_40),X_40) ),[0],$fot(implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))))]]) ).
cnf(refute_0_967,plain,
( implies(not(X_40),X_40) != implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))
| implies(not(X_40),X_40) = X_40 ),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40)))))),X_40) )],[refute_0_965,refute_0_966]) ).
cnf(refute_0_968,plain,
implies(not(X_40),X_40) = X_40,
inference(resolve,[$cnf( $equal(implies(not(X_40),X_40),implies(truth,not(implies(X_40,not(implies(X_40,implies(not(X_40),X_40))))))) )],[refute_0_907,refute_0_967]) ).
cnf(refute_0_969,plain,
implies(not(not(Y)),not(Y)) = not(Y),
inference(subst,[],[refute_0_968:[bind(X_40,$fot(not(Y)))]]) ).
cnf(refute_0_970,plain,
( implies(not(not(Y)),implies(Y,X)) != implies(not(X),implies(not(not(Y)),not(Y)))
| implies(not(not(Y)),not(Y)) != not(Y)
| implies(not(not(Y)),implies(Y,X)) = implies(not(X),not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(not(X),implies(not(not(Y)),not(Y)))) ),[1,1],$fot(not(Y))]]) ).
cnf(refute_0_971,plain,
( implies(not(not(Y)),implies(Y,X)) != implies(not(X),implies(not(not(Y)),not(Y)))
| implies(not(not(Y)),implies(Y,X)) = implies(not(X),not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),not(Y)),not(Y)) )],[refute_0_969,refute_0_970]) ).
cnf(refute_0_972,plain,
implies(not(not(Y)),implies(Y,X)) = implies(not(X),not(Y)),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(not(X),implies(not(not(Y)),not(Y)))) )],[refute_0_280,refute_0_971]) ).
cnf(refute_0_973,plain,
not(not(Y)) = Y,
inference(subst,[],[lemma_9:[bind(X,$fot(Y))]]) ).
cnf(refute_0_974,plain,
implies(not(not(Y)),X) = implies(not(not(Y)),X),
introduced(tautology,[refl,[$fot(implies(not(not(Y)),X))]]) ).
cnf(refute_0_975,plain,
( implies(not(not(Y)),X) != implies(not(not(Y)),X)
| not(not(Y)) != Y
| implies(not(not(Y)),X) = implies(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(Y)),X),implies(not(not(Y)),X)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_976,plain,
( not(not(Y)) != Y
| implies(not(not(Y)),X) = implies(Y,X) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),X),implies(not(not(Y)),X)) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
implies(not(not(Y)),X) = implies(Y,X),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
implies(Y,implies(not(not(Y)),X)) = implies(Y,implies(not(not(Y)),X)),
introduced(tautology,[refl,[$fot(implies(Y,implies(not(not(Y)),X)))]]) ).
cnf(refute_0_979,plain,
( implies(Y,implies(not(not(Y)),X)) != implies(Y,implies(not(not(Y)),X))
| implies(not(not(Y)),X) != implies(Y,X)
| implies(Y,implies(not(not(Y)),X)) = implies(Y,implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(not(not(Y)),X)),implies(Y,implies(not(not(Y)),X))) ),[1,1],$fot(implies(Y,X))]]) ).
cnf(refute_0_980,plain,
( implies(not(not(Y)),X) != implies(Y,X)
| implies(Y,implies(not(not(Y)),X)) = implies(Y,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(not(not(Y)),X)),implies(Y,implies(not(not(Y)),X))) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
implies(Y,implies(not(not(Y)),X)) = implies(Y,implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),X),implies(Y,X)) )],[refute_0_977,refute_0_980]) ).
cnf(refute_0_982,plain,
implies(not(not(Y)),implies(Y,X)) = implies(Y,implies(not(not(Y)),X)),
inference(subst,[],[refute_0_751:[bind(X,$fot(Y)),bind(Z,$fot(X)),bind(X_43,$fot(not(Y)))]]) ).
cnf(refute_0_983,plain,
( implies(Y,implies(not(not(Y)),X)) != implies(Y,implies(Y,X))
| implies(not(not(Y)),implies(Y,X)) != implies(Y,implies(not(not(Y)),X))
| implies(not(not(Y)),implies(Y,X)) = implies(Y,implies(Y,X)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(not(Y)),implies(Y,X)))),bind(Y0,$fot(implies(Y,implies(not(not(Y)),X)))),bind(Z0,$fot(implies(Y,implies(Y,X))))]]) ).
cnf(refute_0_984,plain,
( implies(Y,implies(not(not(Y)),X)) != implies(Y,implies(Y,X))
| implies(not(not(Y)),implies(Y,X)) = implies(Y,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(Y,implies(not(not(Y)),X))) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
implies(not(not(Y)),implies(Y,X)) = implies(Y,implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(Y,implies(not(not(Y)),X)),implies(Y,implies(Y,X))) )],[refute_0_981,refute_0_984]) ).
cnf(refute_0_986,plain,
( implies(not(not(Y)),implies(Y,X)) != implies(Y,implies(Y,X))
| implies(not(not(Y)),implies(Y,X)) != implies(not(X),not(Y))
| implies(Y,implies(Y,X)) = implies(not(X),not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(not(X),not(Y))) ),[0],$fot(implies(Y,implies(Y,X)))]]) ).
cnf(refute_0_987,plain,
( implies(not(not(Y)),implies(Y,X)) != implies(not(X),not(Y))
| implies(Y,implies(Y,X)) = implies(not(X),not(Y)) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(Y,implies(Y,X))) )],[refute_0_985,refute_0_986]) ).
cnf(refute_0_988,plain,
( implies(Y,implies(Y,X)) != implies(not(X),not(Y))
| implies(not(X),not(Y)) != implies(Y,X)
| implies(Y,implies(Y,X)) = implies(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(Y,implies(Y,X)),implies(Y,X)) ),[0],$fot(implies(not(X),not(Y)))]]) ).
cnf(refute_0_989,plain,
( implies(Y,implies(Y,X)) != implies(not(X),not(Y))
| implies(Y,implies(Y,X)) = implies(Y,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),implies(Y,X)) )],[lemma_10,refute_0_988]) ).
cnf(refute_0_990,plain,
( implies(not(not(Y)),implies(Y,X)) != implies(not(X),not(Y))
| implies(Y,implies(Y,X)) = implies(Y,X) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(Y,X)),implies(not(X),not(Y))) )],[refute_0_987,refute_0_989]) ).
cnf(refute_0_991,plain,
implies(Y,implies(Y,X)) = implies(Y,X),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),implies(Y,X)),implies(not(X),not(Y))) )],[refute_0_972,refute_0_990]) ).
cnf(refute_0_992,plain,
implies(X_40,implies(X_40,X_348)) = implies(X_40,X_348),
inference(subst,[],[refute_0_991:[bind(X,$fot(X_348)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_993,plain,
( implies(X_40,implies(X_40,X_348)) != implies(X_40,X_348)
| implies(implies(X_40,X_348),X_40) != implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,implies(X_40,X_348))))))
| implies(implies(X_40,X_348),X_40) = implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_40,X_348),X_40),implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,implies(X_40,X_348))))))) ),[1,1,0,1,0],$fot(implies(X_40,X_348))]]) ).
cnf(refute_0_994,plain,
( implies(implies(X_40,X_348),X_40) != implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,implies(X_40,X_348))))))
| implies(implies(X_40,X_348),X_40) = implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) ),
inference(resolve,[$cnf( $equal(implies(X_40,implies(X_40,X_348)),implies(X_40,X_348)) )],[refute_0_992,refute_0_993]) ).
cnf(refute_0_995,plain,
implies(implies(X_40,X_348),X_40) = implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))),
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_348),X_40),implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,implies(X_40,X_348))))))) )],[refute_0_279,refute_0_994]) ).
cnf(refute_0_996,plain,
implies(truth,X_40) = X_40,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_997,plain,
implies(not(X_348),truth) = truth,
inference(subst,[],[lemma_3:[bind(X,$fot(not(X_348)))]]) ).
cnf(refute_0_998,plain,
implies(not(X_348),implies(X_40,X_40)) = implies(not(X_348),implies(X_40,X_40)),
introduced(tautology,[refl,[$fot(implies(not(X_348),implies(X_40,X_40)))]]) ).
cnf(refute_0_999,plain,
( implies(X_40,X_40) != truth
| implies(not(X_348),implies(X_40,X_40)) != implies(not(X_348),implies(X_40,X_40))
| implies(not(X_348),implies(X_40,X_40)) = implies(not(X_348),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_348),implies(X_40,X_40)),implies(not(X_348),implies(X_40,X_40))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_1000,plain,
( implies(X_40,X_40) != truth
| implies(not(X_348),implies(X_40,X_40)) = implies(not(X_348),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X_348),implies(X_40,X_40)),implies(not(X_348),implies(X_40,X_40))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
implies(not(X_348),implies(X_40,X_40)) = implies(not(X_348),truth),
inference(resolve,[$cnf( $equal(implies(X_40,X_40),truth) )],[refute_0_910,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( implies(not(X_348),implies(X_40,X_40)) != implies(not(X_348),truth)
| implies(not(X_348),truth) != truth
| implies(not(X_348),implies(X_40,X_40)) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(not(X_348),implies(X_40,X_40)))),bind(Y0,$fot(implies(not(X_348),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_1003,plain,
( implies(not(X_348),truth) != truth
| implies(not(X_348),implies(X_40,X_40)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_348),implies(X_40,X_40)),implies(not(X_348),truth)) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
implies(not(X_348),implies(X_40,X_40)) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_348),truth),truth) )],[refute_0_997,refute_0_1003]) ).
cnf(refute_0_1005,plain,
implies(implies(not(X_348),implies(X_40,X_40)),X_40) = implies(implies(not(X_348),implies(X_40,X_40)),X_40),
introduced(tautology,[refl,[$fot(implies(implies(not(X_348),implies(X_40,X_40)),X_40))]]) ).
cnf(refute_0_1006,plain,
( implies(implies(not(X_348),implies(X_40,X_40)),X_40) != implies(implies(not(X_348),implies(X_40,X_40)),X_40)
| implies(not(X_348),implies(X_40,X_40)) != truth
| implies(implies(not(X_348),implies(X_40,X_40)),X_40) = implies(truth,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_348),implies(X_40,X_40)),X_40),implies(implies(not(X_348),implies(X_40,X_40)),X_40)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_1007,plain,
( implies(not(X_348),implies(X_40,X_40)) != truth
| implies(implies(not(X_348),implies(X_40,X_40)),X_40) = implies(truth,X_40) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_348),implies(X_40,X_40)),X_40),implies(implies(not(X_348),implies(X_40,X_40)),X_40)) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
implies(implies(not(X_348),implies(X_40,X_40)),X_40) = implies(truth,X_40),
inference(resolve,[$cnf( $equal(implies(not(X_348),implies(X_40,X_40)),truth) )],[refute_0_1004,refute_0_1007]) ).
cnf(refute_0_1009,plain,
( implies(implies(not(X_348),implies(X_40,X_40)),X_40) != implies(truth,X_40)
| implies(truth,X_40) != X_40
| implies(implies(not(X_348),implies(X_40,X_40)),X_40) = X_40 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(not(X_348),implies(X_40,X_40)),X_40))),bind(Y0,$fot(implies(truth,X_40))),bind(Z0,$fot(X_40))]]) ).
cnf(refute_0_1010,plain,
( implies(truth,X_40) != X_40
| implies(implies(not(X_348),implies(X_40,X_40)),X_40) = X_40 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_348),implies(X_40,X_40)),X_40),implies(truth,X_40)) )],[refute_0_1008,refute_0_1009]) ).
cnf(refute_0_1011,plain,
implies(implies(not(X_348),implies(X_40,X_40)),X_40) = X_40,
inference(resolve,[$cnf( $equal(implies(truth,X_40),X_40) )],[refute_0_996,refute_0_1010]) ).
cnf(refute_0_1012,plain,
implies(implies(not(X_36),implies(X_338,X_337)),X_36) = implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))),
inference(subst,[],[refute_0_377:[bind(X,$fot(implies(X_338,X_337)))]]) ).
cnf(refute_0_1013,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176))),
inference(subst,[],[refute_0_93:[bind(X,$fot(X_175)),bind(Y,$fot(X_176)),bind(X_29,$fot(implies(Y,not(implies(Y,not(not(X_176)))))))]]) ).
cnf(refute_0_1014,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)) = implies(not(not(X_176)),Y),
inference(subst,[],[refute_0_557:[bind(X_50,$fot(not(X_176)))]]) ).
cnf(refute_0_1015,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)) != implies(not(not(X_176)),Y)
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(X_175),implies(not(not(X_176)),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(not(X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)))) ),[1,1],$fot(implies(not(not(X_176)),Y))]]) ).
cnf(refute_0_1016,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(X_175),implies(not(not(X_176)),Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)),implies(not(not(X_176)),Y)) )],[refute_0_1014,refute_0_1015]) ).
cnf(refute_0_1017,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(X_175),implies(not(not(X_176)),Y)),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(not(X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),not(X_176)))) )],[refute_0_1013,refute_0_1016]) ).
cnf(refute_0_1018,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(not(X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176))),
inference(subst,[],[refute_0_93:[bind(X,$fot(X_175)),bind(Y,$fot(X_176)),bind(X_29,$fot(implies(X_47,not(implies(not(X_176),not(X_47))))))]]) ).
cnf(refute_0_1019,plain,
implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(implies(implies(not(X_47),X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(not(X_47),X)))]]) ).
cnf(refute_0_1020,plain,
implies(X_47,not(implies(X,not(X_47)))) = implies(implies(not(X_47),X),X),
inference(subst,[],[refute_0_387:[bind(X,$fot(X_47)),bind(X_35,$fot(X))]]) ).
cnf(refute_0_1021,plain,
( implies(X_47,not(implies(X,not(X_47)))) != implies(implies(not(X_47),X),X)
| implies(implies(not(X_47),X),X) = implies(X_47,not(implies(X,not(X_47)))) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_47,not(implies(X,not(X_47)))))),bind(Y0,$fot(implies(implies(not(X_47),X),X)))]]) ).
cnf(refute_0_1022,plain,
implies(implies(not(X_47),X),X) = implies(X_47,not(implies(X,not(X_47)))),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(X,not(X_47)))),implies(implies(not(X_47),X),X)) )],[refute_0_1020,refute_0_1021]) ).
cnf(refute_0_1023,plain,
( implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(implies(implies(not(X_47),X),X),X)
| implies(implies(not(X_47),X),X) != implies(X_47,not(implies(X,not(X_47))))
| implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(implies(X_47,not(implies(X,not(X_47)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(implies(implies(not(X_47),X),X),X)) ),[1,0],$fot(implies(X_47,not(implies(X,not(X_47)))))]]) ).
cnf(refute_0_1024,plain,
( implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(implies(implies(not(X_47),X),X),X)
| implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(implies(X_47,not(implies(X,not(X_47)))),X) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_47),X),X),implies(X_47,not(implies(X,not(X_47))))) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(implies(X_47,not(implies(X,not(X_47)))),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(implies(implies(not(X_47),X),X),X)) )],[refute_0_1019,refute_0_1024]) ).
cnf(refute_0_1026,plain,
implies(implies(implies(not(X_47),X),X),X) = implies(not(X_47),X),
inference(subst,[],[refute_0_480:[bind(Y,$fot(not(X_47))),bind(X_35,$fot(X))]]) ).
cnf(refute_0_1027,plain,
( implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(implies(implies(not(X_47),X),X),X)
| implies(implies(implies(not(X_47),X),X),X) != implies(not(X_47),X)
| implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(not(X_47),X) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)))),bind(Y0,$fot(implies(implies(implies(not(X_47),X),X),X))),bind(Z0,$fot(implies(not(X_47),X)))]]) ).
cnf(refute_0_1028,plain,
( implies(implies(implies(not(X_47),X),X),X) != implies(not(X_47),X)
| implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(not(X_47),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(implies(implies(not(X_47),X),X),X)) )],[refute_0_1019,refute_0_1027]) ).
cnf(refute_0_1029,plain,
implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) = implies(not(X_47),X),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_47),X),X),X),implies(not(X_47),X)) )],[refute_0_1026,refute_0_1028]) ).
cnf(refute_0_1030,plain,
( implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(implies(X_47,not(implies(X,not(X_47)))),X)
| implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(not(X_47),X)
| implies(not(X_47),X) = implies(implies(X_47,not(implies(X,not(X_47)))),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(implies(X_47,not(implies(X,not(X_47)))),X)) ),[0],$fot(implies(not(X_47),X))]]) ).
cnf(refute_0_1031,plain,
( implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)) != implies(implies(X_47,not(implies(X,not(X_47)))),X)
| implies(not(X_47),X) = implies(implies(X_47,not(implies(X,not(X_47)))),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(not(X_47),X)) )],[refute_0_1029,refute_0_1030]) ).
cnf(refute_0_1032,plain,
implies(not(X_47),X) = implies(implies(X_47,not(implies(X,not(X_47)))),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(X_47),X)),implies(not(X_47),X)),implies(implies(X_47,not(implies(X,not(X_47)))),X)) )],[refute_0_1025,refute_0_1031]) ).
cnf(refute_0_1033,plain,
implies(not(X_47),not(X_176)) = implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)),
inference(subst,[],[refute_0_1032:[bind(X,$fot(not(X_176)))]]) ).
cnf(refute_0_1034,plain,
( implies(not(X_47),not(X_176)) != implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)) = implies(not(X_47),not(X_176)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(not(X_47),not(X_176)))),bind(Y0,$fot(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176))))]]) ).
cnf(refute_0_1035,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)) = implies(not(X_47),not(X_176)),
inference(resolve,[$cnf( $equal(implies(not(X_47),not(X_176)),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176))) )],[refute_0_1033,refute_0_1034]) ).
cnf(refute_0_1036,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(not(X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)) != implies(not(X_47),not(X_176))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(not(X_175),implies(not(X_47),not(X_176))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(not(X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)))) ),[1,1],$fot(implies(not(X_47),not(X_176)))]]) ).
cnf(refute_0_1037,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(not(X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(not(X_175),implies(not(X_47),not(X_176))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)),implies(not(X_47),not(X_176))) )],[refute_0_1035,refute_0_1036]) ).
cnf(refute_0_1038,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(not(X_175),implies(not(X_47),not(X_176))),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(not(X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),not(X_176)))) )],[refute_0_1018,refute_0_1037]) ).
cnf(refute_0_1039,plain,
implies(not(X_176),not(X_47)) = implies(X_47,X_176),
inference(subst,[],[lemma_10:[bind(X,$fot(X_176)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_1040,plain,
not(implies(not(X_176),not(X_47))) = not(implies(not(X_176),not(X_47))),
introduced(tautology,[refl,[$fot(not(implies(not(X_176),not(X_47))))]]) ).
cnf(refute_0_1041,plain,
( implies(not(X_176),not(X_47)) != implies(X_47,X_176)
| not(implies(not(X_176),not(X_47))) != not(implies(not(X_176),not(X_47)))
| not(implies(not(X_176),not(X_47))) = not(implies(X_47,X_176)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(X_176),not(X_47))),not(implies(not(X_176),not(X_47)))) ),[1,0],$fot(implies(X_47,X_176))]]) ).
cnf(refute_0_1042,plain,
( implies(not(X_176),not(X_47)) != implies(X_47,X_176)
| not(implies(not(X_176),not(X_47))) = not(implies(X_47,X_176)) ),
inference(resolve,[$cnf( $equal(not(implies(not(X_176),not(X_47))),not(implies(not(X_176),not(X_47)))) )],[refute_0_1040,refute_0_1041]) ).
cnf(refute_0_1043,plain,
not(implies(not(X_176),not(X_47))) = not(implies(X_47,X_176)),
inference(resolve,[$cnf( $equal(implies(not(X_176),not(X_47)),implies(X_47,X_176)) )],[refute_0_1039,refute_0_1042]) ).
cnf(refute_0_1044,plain,
implies(X_47,not(implies(not(X_176),not(X_47)))) = implies(X_47,not(implies(not(X_176),not(X_47)))),
introduced(tautology,[refl,[$fot(implies(X_47,not(implies(not(X_176),not(X_47)))))]]) ).
cnf(refute_0_1045,plain,
( implies(X_47,not(implies(not(X_176),not(X_47)))) != implies(X_47,not(implies(not(X_176),not(X_47))))
| not(implies(not(X_176),not(X_47))) != not(implies(X_47,X_176))
| implies(X_47,not(implies(not(X_176),not(X_47)))) = implies(X_47,not(implies(X_47,X_176))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_47,not(implies(not(X_176),not(X_47))))) ),[1,1],$fot(not(implies(X_47,X_176)))]]) ).
cnf(refute_0_1046,plain,
( not(implies(not(X_176),not(X_47))) != not(implies(X_47,X_176))
| implies(X_47,not(implies(not(X_176),not(X_47)))) = implies(X_47,not(implies(X_47,X_176))) ),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_47,not(implies(not(X_176),not(X_47))))) )],[refute_0_1044,refute_0_1045]) ).
cnf(refute_0_1047,plain,
implies(X_47,not(implies(not(X_176),not(X_47)))) = implies(X_47,not(implies(X_47,X_176))),
inference(resolve,[$cnf( $equal(not(implies(not(X_176),not(X_47))),not(implies(X_47,X_176))) )],[refute_0_1043,refute_0_1046]) ).
cnf(refute_0_1048,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) = implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175),
introduced(tautology,[refl,[$fot(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))]]) ).
cnf(refute_0_1049,plain,
( implies(X_47,not(implies(not(X_176),not(X_47)))) != implies(X_47,not(implies(X_47,X_176)))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) != implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) = implies(implies(X_47,not(implies(X_47,X_176))),X_175) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) ),[1,0],$fot(implies(X_47,not(implies(X_47,X_176))))]]) ).
cnf(refute_0_1050,plain,
( implies(X_47,not(implies(not(X_176),not(X_47)))) != implies(X_47,not(implies(X_47,X_176)))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) = implies(implies(X_47,not(implies(X_47,X_176))),X_175) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175),implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) )],[refute_0_1048,refute_0_1049]) ).
cnf(refute_0_1051,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) = implies(implies(X_47,not(implies(X_47,X_176))),X_175),
inference(resolve,[$cnf( $equal(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_47,not(implies(X_47,X_176)))) )],[refute_0_1047,refute_0_1050]) ).
cnf(refute_0_1052,plain,
implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) = implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)),
introduced(tautology,[refl,[$fot(implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)))]]) ).
cnf(refute_0_1053,plain,
( implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) != implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) != implies(implies(X_47,not(implies(X_47,X_176))),X_175)
| implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)),implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))) ),[1,1],$fot(implies(implies(X_47,not(implies(X_47,X_176))),X_175))]]) ).
cnf(refute_0_1054,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175) != implies(implies(X_47,not(implies(X_47,X_176))),X_175)
| implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) ),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)),implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))) )],[refute_0_1052,refute_0_1053]) ).
cnf(refute_0_1055,plain,
implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175),implies(implies(X_47,not(implies(X_47,X_176))),X_175)) )],[refute_0_1051,refute_0_1054]) ).
cnf(refute_0_1056,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_176)),bind(Y,$fot(implies(X_47,not(implies(not(X_176),not(X_47)))))),bind(Z,$fot(X_175))]]) ).
cnf(refute_0_1057,plain,
( implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) != implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)))),bind(Y0,$fot(implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)))),bind(Z0,$fot(implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))))]]) ).
cnf(refute_0_1058,plain,
( implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)) != implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) = implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(X_47,not(implies(not(X_176),not(X_47)))),X_175)),implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))) )],[refute_0_1055,refute_0_1058]) ).
cnf(refute_0_1060,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))
| implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(not(X_175),implies(not(X_47),not(X_176)))
| implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_175),implies(not(X_47),not(X_176))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(not(X_175),implies(not(X_47),not(X_176)))) ),[0],$fot(implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)))]]) ).
cnf(refute_0_1061,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(not(X_175),implies(not(X_47),not(X_176)))
| implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_175),implies(not(X_47),not(X_176))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175))) )],[refute_0_1059,refute_0_1060]) ).
cnf(refute_0_1062,plain,
implies(not(X_175),implies(not(X_47),not(X_176))) = implies(not(X_47),implies(X_176,X_175)),
inference(subst,[],[refute_0_102:[bind(X,$fot(X_175)),bind(Y,$fot(X_176)),bind(X_29,$fot(not(X_47)))]]) ).
cnf(refute_0_1063,plain,
( implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) != implies(not(X_175),implies(not(X_47),not(X_176)))
| implies(not(X_175),implies(not(X_47),not(X_176))) != implies(not(X_47),implies(X_176,X_175))
| implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_47),implies(X_176,X_175)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)),implies(not(X_47),implies(X_176,X_175))) ),[0],$fot(implies(not(X_175),implies(not(X_47),not(X_176))))]]) ).
cnf(refute_0_1064,plain,
( implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) != implies(not(X_175),implies(not(X_47),not(X_176)))
| implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_47),implies(X_176,X_175)) ),
inference(resolve,[$cnf( $equal(implies(not(X_175),implies(not(X_47),not(X_176))),implies(not(X_47),implies(X_176,X_175))) )],[refute_0_1062,refute_0_1063]) ).
cnf(refute_0_1065,plain,
( implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)) != implies(not(X_175),implies(not(X_47),not(X_176)))
| implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_47),implies(X_176,X_175)) ),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)),implies(not(X_175),implies(not(X_47),not(X_176)))) )],[refute_0_1061,refute_0_1064]) ).
cnf(refute_0_1066,plain,
implies(X_176,implies(implies(X_47,not(implies(X_47,X_176))),X_175)) = implies(not(X_47),implies(X_176,X_175)),
inference(resolve,[$cnf( $equal(implies(implies(X_47,not(implies(not(X_176),not(X_47)))),implies(X_176,X_175)),implies(not(X_175),implies(not(X_47),not(X_176)))) )],[refute_0_1038,refute_0_1065]) ).
cnf(refute_0_1067,plain,
implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)) = implies(not(Y),implies(X_176,X_175)),
inference(subst,[],[refute_0_1066:[bind(X_47,$fot(Y))]]) ).
cnf(refute_0_1068,plain,
not(not(X_176)) = X_176,
inference(subst,[],[lemma_9:[bind(X,$fot(X_176))]]) ).
cnf(refute_0_1069,plain,
implies(Y,not(not(X_176))) = implies(Y,not(not(X_176))),
introduced(tautology,[refl,[$fot(implies(Y,not(not(X_176))))]]) ).
cnf(refute_0_1070,plain,
( implies(Y,not(not(X_176))) != implies(Y,not(not(X_176)))
| not(not(X_176)) != X_176
| implies(Y,not(not(X_176))) = implies(Y,X_176) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,not(not(X_176))),implies(Y,not(not(X_176)))) ),[1,1],$fot(X_176)]]) ).
cnf(refute_0_1071,plain,
( not(not(X_176)) != X_176
| implies(Y,not(not(X_176))) = implies(Y,X_176) ),
inference(resolve,[$cnf( $equal(implies(Y,not(not(X_176))),implies(Y,not(not(X_176)))) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
implies(Y,not(not(X_176))) = implies(Y,X_176),
inference(resolve,[$cnf( $equal(not(not(X_176)),X_176) )],[refute_0_1068,refute_0_1071]) ).
cnf(refute_0_1073,plain,
not(implies(Y,not(not(X_176)))) = not(implies(Y,not(not(X_176)))),
introduced(tautology,[refl,[$fot(not(implies(Y,not(not(X_176)))))]]) ).
cnf(refute_0_1074,plain,
( implies(Y,not(not(X_176))) != implies(Y,X_176)
| not(implies(Y,not(not(X_176)))) != not(implies(Y,not(not(X_176))))
| not(implies(Y,not(not(X_176)))) = not(implies(Y,X_176)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,not(not(X_176)))),not(implies(Y,not(not(X_176))))) ),[1,0],$fot(implies(Y,X_176))]]) ).
cnf(refute_0_1075,plain,
( implies(Y,not(not(X_176))) != implies(Y,X_176)
| not(implies(Y,not(not(X_176)))) = not(implies(Y,X_176)) ),
inference(resolve,[$cnf( $equal(not(implies(Y,not(not(X_176)))),not(implies(Y,not(not(X_176))))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
not(implies(Y,not(not(X_176)))) = not(implies(Y,X_176)),
inference(resolve,[$cnf( $equal(implies(Y,not(not(X_176))),implies(Y,X_176)) )],[refute_0_1072,refute_0_1075]) ).
cnf(refute_0_1077,plain,
implies(Y,not(implies(Y,not(not(X_176))))) = implies(Y,not(implies(Y,not(not(X_176))))),
introduced(tautology,[refl,[$fot(implies(Y,not(implies(Y,not(not(X_176))))))]]) ).
cnf(refute_0_1078,plain,
( implies(Y,not(implies(Y,not(not(X_176))))) != implies(Y,not(implies(Y,not(not(X_176)))))
| not(implies(Y,not(not(X_176)))) != not(implies(Y,X_176))
| implies(Y,not(implies(Y,not(not(X_176))))) = implies(Y,not(implies(Y,X_176))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,not(implies(Y,not(not(X_176))))),implies(Y,not(implies(Y,not(not(X_176)))))) ),[1,1],$fot(not(implies(Y,X_176)))]]) ).
cnf(refute_0_1079,plain,
( not(implies(Y,not(not(X_176)))) != not(implies(Y,X_176))
| implies(Y,not(implies(Y,not(not(X_176))))) = implies(Y,not(implies(Y,X_176))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(not(X_176))))),implies(Y,not(implies(Y,not(not(X_176)))))) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
implies(Y,not(implies(Y,not(not(X_176))))) = implies(Y,not(implies(Y,X_176))),
inference(resolve,[$cnf( $equal(not(implies(Y,not(not(X_176)))),not(implies(Y,X_176))) )],[refute_0_1076,refute_0_1079]) ).
cnf(refute_0_1081,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) = implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175),
introduced(tautology,[refl,[$fot(implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))]]) ).
cnf(refute_0_1082,plain,
( implies(Y,not(implies(Y,not(not(X_176))))) != implies(Y,not(implies(Y,X_176)))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) != implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)
| implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) = implies(implies(Y,not(implies(Y,X_176))),X_175) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) ),[1,0],$fot(implies(Y,not(implies(Y,X_176))))]]) ).
cnf(refute_0_1083,plain,
( implies(Y,not(implies(Y,not(not(X_176))))) != implies(Y,not(implies(Y,X_176)))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) = implies(implies(Y,not(implies(Y,X_176))),X_175) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175),implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) = implies(implies(Y,not(implies(Y,X_176))),X_175),
inference(resolve,[$cnf( $equal(implies(Y,not(implies(Y,not(not(X_176))))),implies(Y,not(implies(Y,X_176)))) )],[refute_0_1080,refute_0_1083]) ).
cnf(refute_0_1085,plain,
implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),
introduced(tautology,[refl,[$fot(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)))]]) ).
cnf(refute_0_1086,plain,
( implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) != implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) != implies(implies(Y,not(implies(Y,X_176))),X_175)
| implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))) ),[1,1],$fot(implies(implies(Y,not(implies(Y,X_176))),X_175))]]) ).
cnf(refute_0_1087,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175) != implies(implies(Y,not(implies(Y,X_176))),X_175)
| implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)) ),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175),implies(implies(Y,not(implies(Y,X_176))),X_175)) )],[refute_0_1084,refute_0_1087]) ).
cnf(refute_0_1089,plain,
( implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)) != implies(not(Y),implies(X_176,X_175))
| implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) != implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175))
| implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(not(Y),implies(X_176,X_175)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)))),bind(Y0,$fot(implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)))),bind(Z0,$fot(implies(not(Y),implies(X_176,X_175))))]]) ).
cnf(refute_0_1090,plain,
( implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)) != implies(not(Y),implies(X_176,X_175))
| implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(not(Y),implies(X_176,X_175)) ),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175))) )],[refute_0_1088,refute_0_1089]) ).
cnf(refute_0_1091,plain,
implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) = implies(not(Y),implies(X_176,X_175)),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(Y,not(implies(Y,X_176))),X_175)),implies(not(Y),implies(X_176,X_175))) )],[refute_0_1067,refute_0_1090]) ).
cnf(refute_0_1092,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_176)),bind(Y,$fot(implies(Y,not(implies(Y,not(not(X_176))))))),bind(Z,$fot(X_175))]]) ).
cnf(refute_0_1093,plain,
( implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) != implies(not(Y),implies(X_176,X_175))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(Y),implies(X_176,X_175)) ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)))),bind(Y0,$fot(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)))),bind(Z0,$fot(implies(not(Y),implies(X_176,X_175))))]]) ).
cnf(refute_0_1094,plain,
( implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)) != implies(not(Y),implies(X_176,X_175))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(Y),implies(X_176,X_175)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175))) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) = implies(not(Y),implies(X_176,X_175)),
inference(resolve,[$cnf( $equal(implies(X_176,implies(implies(Y,not(implies(Y,not(not(X_176))))),X_175)),implies(not(Y),implies(X_176,X_175))) )],[refute_0_1091,refute_0_1094]) ).
cnf(refute_0_1096,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(Y),implies(X_176,X_175))
| implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(not(not(X_176)),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(not(X_175),implies(not(not(X_176)),Y))) ),[0],$fot(implies(not(Y),implies(X_176,X_175)))]]) ).
cnf(refute_0_1097,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(not(not(X_176)),Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(not(Y),implies(X_176,X_175))) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
implies(not(not(X_176)),Y) = implies(not(not(X_176)),Y),
introduced(tautology,[refl,[$fot(implies(not(not(X_176)),Y))]]) ).
cnf(refute_0_1099,plain,
( implies(not(not(X_176)),Y) != implies(not(not(X_176)),Y)
| not(not(X_176)) != X_176
| implies(not(not(X_176)),Y) = implies(X_176,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_176)),Y),implies(not(not(X_176)),Y)) ),[1,0],$fot(X_176)]]) ).
cnf(refute_0_1100,plain,
( not(not(X_176)) != X_176
| implies(not(not(X_176)),Y) = implies(X_176,Y) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_176)),Y),implies(not(not(X_176)),Y)) )],[refute_0_1098,refute_0_1099]) ).
cnf(refute_0_1101,plain,
implies(not(not(X_176)),Y) = implies(X_176,Y),
inference(resolve,[$cnf( $equal(not(not(X_176)),X_176) )],[refute_0_1068,refute_0_1100]) ).
cnf(refute_0_1102,plain,
implies(not(X_175),implies(not(not(X_176)),Y)) = implies(not(X_175),implies(not(not(X_176)),Y)),
introduced(tautology,[refl,[$fot(implies(not(X_175),implies(not(not(X_176)),Y)))]]) ).
cnf(refute_0_1103,plain,
( implies(not(X_175),implies(not(not(X_176)),Y)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(not(X_176)),Y) != implies(X_176,Y)
| implies(not(X_175),implies(not(not(X_176)),Y)) = implies(not(X_175),implies(X_176,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_175),implies(not(not(X_176)),Y)),implies(not(X_175),implies(not(not(X_176)),Y))) ),[1,1],$fot(implies(X_176,Y))]]) ).
cnf(refute_0_1104,plain,
( implies(not(not(X_176)),Y) != implies(X_176,Y)
| implies(not(X_175),implies(not(not(X_176)),Y)) = implies(not(X_175),implies(X_176,Y)) ),
inference(resolve,[$cnf( $equal(implies(not(X_175),implies(not(not(X_176)),Y)),implies(not(X_175),implies(not(not(X_176)),Y))) )],[refute_0_1102,refute_0_1103]) ).
cnf(refute_0_1105,plain,
implies(not(X_175),implies(not(not(X_176)),Y)) = implies(not(X_175),implies(X_176,Y)),
inference(resolve,[$cnf( $equal(implies(not(not(X_176)),Y),implies(X_176,Y)) )],[refute_0_1101,refute_0_1104]) ).
cnf(refute_0_1106,plain,
( implies(not(Y),implies(X_176,X_175)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(X_175),implies(not(not(X_176)),Y)) != implies(not(X_175),implies(X_176,Y))
| implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(X_176,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(Y),implies(X_176,X_175)),implies(not(X_175),implies(X_176,Y))) ),[0],$fot(implies(not(X_175),implies(not(not(X_176)),Y)))]]) ).
cnf(refute_0_1107,plain,
( implies(not(Y),implies(X_176,X_175)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(X_176,Y)) ),
inference(resolve,[$cnf( $equal(implies(not(X_175),implies(not(not(X_176)),Y)),implies(not(X_175),implies(X_176,Y))) )],[refute_0_1105,refute_0_1106]) ).
cnf(refute_0_1108,plain,
( implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)) != implies(not(X_175),implies(not(not(X_176)),Y))
| implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(X_176,Y)) ),
inference(resolve,[$cnf( $equal(implies(not(Y),implies(X_176,X_175)),implies(not(X_175),implies(not(not(X_176)),Y))) )],[refute_0_1097,refute_0_1107]) ).
cnf(refute_0_1109,plain,
implies(not(Y),implies(X_176,X_175)) = implies(not(X_175),implies(X_176,Y)),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(implies(Y,not(not(X_176))))),implies(X_176,X_175)),implies(not(X_175),implies(not(not(X_176)),Y))) )],[refute_0_1017,refute_0_1108]) ).
cnf(refute_0_1110,plain,
implies(not(X_36),implies(X_338,X_337)) = implies(not(X_337),implies(X_338,X_36)),
inference(subst,[],[refute_0_1109:[bind(Y,$fot(X_36)),bind(X_175,$fot(X_337)),bind(X_176,$fot(X_338))]]) ).
cnf(refute_0_1111,plain,
( implies(implies(not(X_36),implies(X_338,X_337)),X_36) != implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))
| implies(not(X_36),implies(X_338,X_337)) != implies(not(X_337),implies(X_338,X_36))
| implies(implies(not(X_337),implies(X_338,X_36)),X_36) = implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_36),implies(X_338,X_337)),X_36),implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))) ),[0,0],$fot(implies(not(X_337),implies(X_338,X_36)))]]) ).
cnf(refute_0_1112,plain,
( implies(implies(not(X_36),implies(X_338,X_337)),X_36) != implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))
| implies(implies(not(X_337),implies(X_338,X_36)),X_36) = implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))) ),
inference(resolve,[$cnf( $equal(implies(not(X_36),implies(X_338,X_337)),implies(not(X_337),implies(X_338,X_36))) )],[refute_0_1110,refute_0_1111]) ).
cnf(refute_0_1113,plain,
implies(implies(not(X_337),implies(X_338,X_36)),X_36) = implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_36),implies(X_338,X_337)),X_36),implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))) )],[refute_0_1012,refute_0_1112]) ).
cnf(refute_0_1114,plain,
( implies(implies(not(X_337),implies(X_338,X_36)),X_36) != implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))
| implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))) = implies(implies(not(X_337),implies(X_338,X_36)),X_36) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(implies(not(X_337),implies(X_338,X_36)),X_36))),bind(Y0,$fot(implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))))]]) ).
cnf(refute_0_1115,plain,
implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337))))) = implies(implies(not(X_337),implies(X_338,X_36)),X_36),
inference(resolve,[$cnf( $equal(implies(implies(not(X_337),implies(X_338,X_36)),X_36),implies(implies(X_338,X_337),not(implies(X_36,not(implies(X_338,X_337)))))) )],[refute_0_1113,refute_0_1114]) ).
cnf(refute_0_1116,plain,
implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) = implies(implies(not(X_348),implies(X_40,X_40)),X_40),
inference(subst,[],[refute_0_1115:[bind(X_337,$fot(X_348)),bind(X_338,$fot(X_40)),bind(X_36,$fot(X_40))]]) ).
cnf(refute_0_1117,plain,
( implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) != implies(implies(not(X_348),implies(X_40,X_40)),X_40)
| implies(implies(not(X_348),implies(X_40,X_40)),X_40) != X_40
| implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) = X_40 ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))))),bind(Y0,$fot(implies(implies(not(X_348),implies(X_40,X_40)),X_40))),bind(Z0,$fot(X_40))]]) ).
cnf(refute_0_1118,plain,
( implies(implies(not(X_348),implies(X_40,X_40)),X_40) != X_40
| implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) = X_40 ),
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))),implies(implies(not(X_348),implies(X_40,X_40)),X_40)) )],[refute_0_1116,refute_0_1117]) ).
cnf(refute_0_1119,plain,
implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) = X_40,
inference(resolve,[$cnf( $equal(implies(implies(not(X_348),implies(X_40,X_40)),X_40),X_40) )],[refute_0_1011,refute_0_1118]) ).
cnf(refute_0_1120,plain,
( implies(implies(X_40,X_348),X_40) != implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348)))))
| implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))) != X_40
| implies(implies(X_40,X_348),X_40) = X_40 ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_40,X_348),X_40),X_40) ),[0],$fot(implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))))]]) ).
cnf(refute_0_1121,plain,
( implies(implies(X_40,X_348),X_40) != implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348)))))
| implies(implies(X_40,X_348),X_40) = X_40 ),
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348))))),X_40) )],[refute_0_1119,refute_0_1120]) ).
cnf(refute_0_1122,plain,
implies(implies(X_40,X_348),X_40) = X_40,
inference(resolve,[$cnf( $equal(implies(implies(X_40,X_348),X_40),implies(implies(X_40,X_348),not(implies(X_40,not(implies(X_40,X_348)))))) )],[refute_0_995,refute_0_1121]) ).
cnf(refute_0_1123,plain,
implies(implies(b,a),b) = b,
inference(subst,[],[refute_0_1122:[bind(X_348,$fot(a)),bind(X_40,$fot(b))]]) ).
cnf(refute_0_1124,plain,
implies(a,implies(implies(b,a),b)) = implies(a,implies(implies(b,a),b)),
introduced(tautology,[refl,[$fot(implies(a,implies(implies(b,a),b)))]]) ).
cnf(refute_0_1125,plain,
( implies(a,implies(implies(b,a),b)) != implies(a,implies(implies(b,a),b))
| implies(implies(b,a),b) != b
| implies(a,implies(implies(b,a),b)) = implies(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(implies(a,implies(implies(b,a),b)),implies(a,implies(implies(b,a),b))) ),[1,1],$fot(b)]]) ).
cnf(refute_0_1126,plain,
( implies(implies(b,a),b) != b
| implies(a,implies(implies(b,a),b)) = implies(a,b) ),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(b,a),b)),implies(a,implies(implies(b,a),b))) )],[refute_0_1124,refute_0_1125]) ).
cnf(refute_0_1127,plain,
implies(a,implies(implies(b,a),b)) = implies(a,b),
inference(resolve,[$cnf( $equal(implies(implies(b,a),b),b) )],[refute_0_1123,refute_0_1126]) ).
cnf(refute_0_1128,plain,
implies(implies(a,implies(implies(b,a),b)),b) = implies(implies(a,implies(implies(b,a),b)),b),
introduced(tautology,[refl,[$fot(implies(implies(a,implies(implies(b,a),b)),b))]]) ).
cnf(refute_0_1129,plain,
( implies(a,implies(implies(b,a),b)) != implies(a,b)
| implies(implies(a,implies(implies(b,a),b)),b) != implies(implies(a,implies(implies(b,a),b)),b)
| implies(implies(a,implies(implies(b,a),b)),b) = implies(implies(a,b),b) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(a,implies(implies(b,a),b)),b),implies(implies(a,implies(implies(b,a),b)),b)) ),[1,0],$fot(implies(a,b))]]) ).
cnf(refute_0_1130,plain,
( implies(a,implies(implies(b,a),b)) != implies(a,b)
| implies(implies(a,implies(implies(b,a),b)),b) = implies(implies(a,b),b) ),
inference(resolve,[$cnf( $equal(implies(implies(a,implies(implies(b,a),b)),b),implies(implies(a,implies(implies(b,a),b)),b)) )],[refute_0_1128,refute_0_1129]) ).
cnf(refute_0_1131,plain,
implies(implies(a,implies(implies(b,a),b)),b) = implies(implies(a,b),b),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(b,a),b)),implies(a,b)) )],[refute_0_1127,refute_0_1130]) ).
cnf(refute_0_1132,plain,
implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = implies(a,implies(implies(a,implies(implies(b,a),b)),b)),
introduced(tautology,[refl,[$fot(implies(a,implies(implies(a,implies(implies(b,a),b)),b)))]]) ).
cnf(refute_0_1133,plain,
( implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != implies(a,implies(implies(a,implies(implies(b,a),b)),b))
| implies(implies(a,implies(implies(b,a),b)),b) != implies(implies(a,b),b)
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = implies(a,implies(implies(a,b),b)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),implies(a,implies(implies(a,implies(implies(b,a),b)),b))) ),[1,1],$fot(implies(implies(a,b),b))]]) ).
cnf(refute_0_1134,plain,
( implies(implies(a,implies(implies(b,a),b)),b) != implies(implies(a,b),b)
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = implies(a,implies(implies(a,b),b)) ),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),implies(a,implies(implies(a,implies(implies(b,a),b)),b))) )],[refute_0_1132,refute_0_1133]) ).
cnf(refute_0_1135,plain,
implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = implies(a,implies(implies(a,b),b)),
inference(resolve,[$cnf( $equal(implies(implies(a,implies(implies(b,a),b)),b),implies(implies(a,b),b)) )],[refute_0_1131,refute_0_1134]) ).
cnf(refute_0_1136,plain,
( implies(a,implies(implies(a,b),b)) != truth
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != implies(a,implies(implies(a,b),b))
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth ),
inference(subst,[],[refute_0_16:[bind(X0,$fot(implies(a,implies(implies(a,implies(implies(b,a),b)),b)))),bind(Y0,$fot(implies(a,implies(implies(a,b),b)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_1137,plain,
( implies(a,implies(implies(a,b),b)) != truth
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth ),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),implies(a,implies(implies(a,b),b))) )],[refute_0_1135,refute_0_1136]) ).
cnf(refute_0_1138,plain,
implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth,
inference(resolve,[$cnf( $equal(implies(a,implies(implies(a,b),b)),truth) )],[refute_0_187,refute_0_1137]) ).
cnf(refute_0_1139,plain,
( implies(a,implies(implies(a,implies(implies(b,a),b)),b)) != truth
| truth != truth
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_1140,plain,
( truth != truth
| implies(a,implies(implies(a,implies(implies(b,a),b)),b)) = truth ),
inference(resolve,[$cnf( $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),truth) )],[refute_0_1138,refute_0_1139]) ).
cnf(refute_0_1141,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(a,implies(implies(a,implies(implies(b,a),b)),b)),truth) )],[refute_0_1140,refute_0_171]) ).
cnf(refute_0_1142,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_1143,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_1142,refute_0_1141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL109-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 21:58:39 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 66.00/66.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 66.00/66.17
% 66.00/66.17 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 66.10/66.32
%------------------------------------------------------------------------------