TSTP Solution File: LCL140-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL140-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 12:49:53 EDT 2022
% Result : Unsatisfiable 9.84s 9.99s
% Output : CNFRefutation 9.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 100
% Number of leaves : 187
% Syntax : Number of clauses : 698 ( 357 unt; 0 nHn; 391 RR)
% Number of literals : 1200 (1199 equ; 504 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 933 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_wajsberg_lemma,negated_conjecture,
not(not(x)) != x ).
cnf(refute_0_0,plain,
implies(implies(not(truth),Y),Y) = implies(implies(Y,not(truth)),not(truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_1,plain,
implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(implies(not(X_125),implies(X_125,not(truth))),implies(X_125,not(truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_125,not(truth)))),bind(Y,$fot(not(X_125)))]]) ).
cnf(refute_0_2,plain,
implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(Z,X_21),X_21),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(Z,X_21),X_21)))]]) ).
cnf(refute_0_3,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X_1,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_1,X)))]]) ).
cnf(refute_0_4,plain,
implies(implies(X_1,X),X) = implies(implies(X,X_1),X_1),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_1)),bind(Y,$fot(X))]]) ).
cnf(refute_0_5,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X_1,X),X) != implies(implies(X,X_1),X_1)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) ),[1,0],$fot(implies(implies(X,X_1),X_1))]]) ).
cnf(refute_0_6,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1,X),X),implies(implies(X,X_1),X_1)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) ),[0],$fot(implies(implies(implies(X_1,X),X),X))]]) ).
cnf(refute_0_9,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_3,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
implies(implies(implies(X_21,Z),Z),Z) = implies(implies(implies(Z,X_21),X_21),Z),
inference(subst,[],[refute_0_10:[bind(X,$fot(Z)),bind(X_1,$fot(X_21))]]) ).
cnf(refute_0_12,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_13,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_14,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(implies(implies(X_21,Z),Z),Z) != implies(implies(implies(Z,X_21),X_21),Z)
| implies(implies(implies(Z,X_21),X_21),Z) = implies(implies(implies(X_21,Z),Z),Z) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(implies(X_21,Z),Z),Z))),bind(Y0,$fot(implies(implies(implies(Z,X_21),X_21),Z)))]]) ).
cnf(refute_0_16,plain,
implies(implies(implies(Z,X_21),X_21),Z) = implies(implies(implies(X_21,Z),Z),Z),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,Z),Z),Z),implies(implies(implies(Z,X_21),X_21),Z)) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
( implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(Z,X_21),X_21),Z),implies(X,Z))) != truth
| implies(implies(implies(Z,X_21),X_21),Z) != implies(implies(implies(X_21,Z),Z),Z)
| implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(X_21,Z),Z),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(Z,X_21),X_21),Z),implies(X,Z))),truth) ),[0,1,0],$fot(implies(implies(implies(X_21,Z),Z),Z))]]) ).
cnf(refute_0_18,plain,
( implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(Z,X_21),X_21),Z),implies(X,Z))) != truth
| implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(X_21,Z),Z),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Z,X_21),X_21),Z),implies(implies(implies(X_21,Z),Z),Z)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(X_21,Z),Z),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(Z,X_21),X_21)),implies(implies(implies(implies(Z,X_21),X_21),Z),implies(X,Z))),truth) )],[refute_0_2,refute_0_18]) ).
cnf(refute_0_20,plain,
implies(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = truth,
inference(subst,[],[refute_0_19:[bind(X,$fot(implies(not(X_93),not(implies(implies(X_93,Y),Y))))),bind(Z,$fot(implies(Y,X_93))),bind(X_21,$fot(X_93))]]) ).
cnf(refute_0_21,plain,
implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(implies(Y,X_4)))]]) ).
cnf(refute_0_22,plain,
implies(implies(X_4,Y),Y) = implies(implies(Y,X_4),X_4),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_23,plain,
( implies(implies(X_4,Y),Y) != implies(implies(Y,X_4),X_4)
| implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_4,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_4),X_4)))]]) ).
cnf(refute_0_24,plain,
implies(implies(Y,X_4),X_4) = implies(implies(X_4,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_4,Y),Y),implies(implies(Y,X_4),X_4)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(implies(Y,X_4),X_4) != implies(implies(X_4,Y),Y)
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) ),[0,1],$fot(implies(implies(X_4,Y),Y))]]) ).
cnf(refute_0_26,plain,
( implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)) != truth
| implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_4),X_4),implies(implies(X_4,Y),Y)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(X_4,Y),Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(implies(Y,X_4))),implies(implies(Y,X_4),X_4)),truth) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth,
inference(subst,[],[refute_0_27:[bind(Y,$fot(implies(Y,X_19))),bind(X_4,$fot(X_19))]]) ).
cnf(refute_0_29,plain,
implies(implies(X_19,Y),Y) = implies(implies(Y,X_19),X_19),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_19))]]) ).
cnf(refute_0_30,plain,
( implies(implies(X_19,Y),Y) != implies(implies(Y,X_19),X_19)
| implies(implies(Y,X_19),X_19) = implies(implies(X_19,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_19,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_19),X_19)))]]) ).
cnf(refute_0_31,plain,
implies(implies(Y,X_19),X_19) = implies(implies(X_19,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_19,Y),Y),implies(implies(Y,X_19),X_19)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( implies(implies(Y,X_19),X_19) != implies(implies(X_19,Y),Y)
| implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) ),[0,0,1,0],$fot(implies(implies(X_19,Y),Y))]]) ).
cnf(refute_0_33,plain,
( implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_19),X_19),implies(implies(X_19,Y),Y)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(Y,X_19),X_19))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) = implies(implies(X,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X,Y),Y))),bind(Y0,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_36,plain,
implies(implies(Y,X),X) = implies(implies(X,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) = implies(implies(implies(Y,X_19),X_19),X_19),
inference(subst,[],[refute_0_36:[bind(X,$fot(implies(Y,X_19))),bind(Y,$fot(X_19))]]) ).
cnf(refute_0_38,plain,
implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),
introduced(tautology,[refl,[$fot(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) != implies(implies(implies(Y,X_19),X_19),X_19)
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))) ),[1,1],$fot(implies(implies(implies(Y,X_19),X_19),X_19))]]) ).
cnf(refute_0_40,plain,
( implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)) != implies(implies(implies(Y,X_19),X_19),X_19)
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) = implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)),
inference(resolve,[$cnf( $equal(implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19)),implies(implies(implies(Y,X_19),X_19),X_19)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19))
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) ),[0],$fot(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)))]]) ).
cnf(refute_0_43,plain,
( implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))) != truth
| implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(implies(Y,X_19),X_19),X_19)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_19),not(implies(implies(X_19,Y),Y))),implies(implies(X_19,implies(Y,X_19)),implies(Y,X_19))),truth) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)) = truth,
inference(subst,[],[refute_0_44:[bind(X_19,$fot(X_93))]]) ).
cnf(refute_0_46,plain,
( implies(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != truth
| implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)) != truth
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_47,plain,
( implies(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != truth
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),truth) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(implies(implies(Y,X_93),X_93),X_93)),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),truth) )],[refute_0_20,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))]]) ).
cnf(refute_0_50,plain,
implies(implies(X,implies(implies(X,X_23),X_23)),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(X,X_23),X_23)))]]) ).
cnf(refute_0_51,plain,
implies(implies(truth,X_14),implies(implies(X_14,X_15),implies(truth,X_15))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_52,plain,
implies(truth,X_15) = X_15,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_53,plain,
( implies(implies(truth,X_14),implies(implies(X_14,X_15),implies(truth,X_15))) != truth
| implies(truth,X_15) != X_15
| implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),implies(truth,X_15))),truth) ),[0,1,1],$fot(X_15)]]) ).
cnf(refute_0_54,plain,
( implies(implies(truth,X_14),implies(implies(X_14,X_15),implies(truth,X_15))) != truth
| implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_15),X_15) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),implies(truth,X_15))),truth) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(truth,X_14) = X_14,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_57,plain,
implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)))]]) ).
cnf(refute_0_58,plain,
( implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) != implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15))
| implies(truth,X_14) != X_14
| implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = implies(X_14,implies(implies(X_14,X_15),X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15))) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_59,plain,
( implies(truth,X_14) != X_14
| implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = implies(X_14,implies(implies(X_14,X_15),X_15)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) = implies(X_14,implies(implies(X_14,X_15),X_15)),
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) != implies(X_14,implies(implies(X_14,X_15),X_15))
| implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) != truth
| implies(X_14,implies(implies(X_14,X_15),X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),truth) ),[0],$fot(implies(X_14,implies(implies(X_14,X_15),X_15)))]]) ).
cnf(refute_0_62,plain,
( implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)) != truth
| implies(X_14,implies(implies(X_14,X_15),X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),implies(X_14,implies(implies(X_14,X_15),X_15))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(X_14,implies(implies(X_14,X_15),X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_14),implies(implies(X_14,X_15),X_15)),truth) )],[refute_0_55,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(X,implies(implies(X,X_23),X_23)) = truth,
inference(subst,[],[refute_0_63:[bind(X_14,$fot(X)),bind(X_15,$fot(X_23))]]) ).
cnf(refute_0_65,plain,
( implies(X,implies(implies(X,X_23),X_23)) != truth
| implies(implies(X,implies(implies(X,X_23),X_23)),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X,X_23),X_23)),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_66,plain,
( implies(implies(X,implies(implies(X,X_23),X_23)),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,X_23),X_23)),truth) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X,X_23),X_23)),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))),truth) )],[refute_0_50,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) = implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))))]]) ).
cnf(refute_0_69,plain,
( implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) != implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))
| implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z)))]]) ).
cnf(refute_0_70,plain,
( implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))),implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_23),X_23),Z),implies(X,Z))),truth) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)) = truth,
inference(subst,[],[refute_0_71:[bind(X,$fot(Y)),bind(Z,$fot(X_93)),bind(X_23,$fot(X_93))]]) ).
cnf(refute_0_73,plain,
implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) = implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)),
inference(subst,[],[refute_0_10:[bind(X,$fot(implies(Y,X_93))),bind(X_1,$fot(X_93))]]) ).
cnf(refute_0_74,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_75,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_14,refute_0_74]) ).
cnf(refute_0_76,plain,
( implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) != implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93))
| implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)) != truth
| implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)))),bind(Y0,$fot(implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_77,plain,
( implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)) != truth
| implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_93),X_93),X_93),implies(Y,X_93)),truth) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))]]) ).
cnf(refute_0_80,plain,
( implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) != truth
| implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))
| implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_81,plain,
( implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)) != truth
| implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),truth) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
( implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))
| implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))
| implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))),bind(Y0,$fot(implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))),bind(Z0,$fot(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))]]) ).
cnf(refute_0_84,plain,
( implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))
| implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) )],[refute_0_49,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))))]]) ).
cnf(refute_0_87,plain,
( implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))))),bind(Y0,$fot(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))),bind(Z0,$fot(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))))]]) ).
cnf(refute_0_88,plain,
( implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) != implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) = implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
( implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))
| implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != truth
| implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),truth) ),[0],$fot(implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))]]) ).
cnf(refute_0_91,plain,
( implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))) != truth
| implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_93,implies(Y,X_93)),implies(Y,X_93)),implies(Y,X_93)),implies(implies(not(X_93),not(implies(implies(X_93,Y),Y))),implies(Y,X_93)))),truth) )],[refute_0_48,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(not(not(truth)),not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = truth,
inference(subst,[],[refute_0_92:[bind(X_93,$fot(not(truth)))]]) ).
cnf(refute_0_94,plain,
implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(X,not(not(truth))))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(not(not(truth)),not(truth)),not(not(truth))))),bind(Z,$fot(not(not(truth))))]]) ).
cnf(refute_0_95,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(X_21,Y),Y),Y),Y)) = truth,
inference(subst,[],[refute_0_27:[bind(X_4,$fot(implies(implies(X_21,Y),Y)))]]) ).
cnf(refute_0_96,plain,
implies(implies(implies(X_21,Y),Y),Y) = implies(implies(implies(Y,X_21),X_21),Y),
inference(subst,[],[refute_0_10:[bind(X,$fot(Y)),bind(X_1,$fot(X_21))]]) ).
cnf(refute_0_97,plain,
( implies(implies(implies(X_21,Y),Y),Y) != implies(implies(implies(Y,X_21),X_21),Y)
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(X_21,Y),Y),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(X_21,Y),Y),Y),Y)),truth) ),[0,1,0],$fot(implies(implies(implies(Y,X_21),X_21),Y))]]) ).
cnf(refute_0_98,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(X_21,Y),Y),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,Y),Y),Y),implies(implies(implies(Y,X_21),X_21),Y)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(X_21,Y),Y),Y),Y)),truth) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(implies(X_15,truth),truth),X_15),implies(X_13,X_15))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_13)),bind(Y,$fot(implies(implies(X_15,truth),truth))),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_101,plain,
implies(implies(X,X),X) = implies(implies(X,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(X))]]) ).
cnf(refute_0_102,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_103,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_104,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(truth,X_2) != X_2
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) ),[0,0],$fot(X_2)]]) ).
cnf(refute_0_105,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(subst,[],[refute_0_106:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_108,plain,
( implies(X,X) != implies(implies(X,truth),truth)
| implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) ),[1,0],$fot(implies(implies(X,truth),truth))]]) ).
cnf(refute_0_109,plain,
( implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
inference(resolve,[$cnf( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X),
inference(resolve,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) )],[refute_0_101,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(implies(X_15,X_15),X_15) = implies(implies(implies(X_15,truth),truth),X_15),
inference(subst,[],[refute_0_110:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_112,plain,
( implies(implies(X_15,X_15),X_15) != implies(implies(implies(X_15,truth),truth),X_15)
| implies(implies(implies(X_15,truth),truth),X_15) = implies(implies(X_15,X_15),X_15) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_15,X_15),X_15))),bind(Y0,$fot(implies(implies(implies(X_15,truth),truth),X_15)))]]) ).
cnf(refute_0_113,plain,
implies(implies(implies(X_15,truth),truth),X_15) = implies(implies(X_15,X_15),X_15),
inference(resolve,[$cnf( $equal(implies(implies(X_15,X_15),X_15),implies(implies(implies(X_15,truth),truth),X_15)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(implies(X_15,truth),truth),X_15),implies(X_13,X_15))) != truth
| implies(implies(implies(X_15,truth),truth),X_15) != implies(implies(X_15,X_15),X_15)
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(implies(X_15,truth),truth),X_15),implies(X_13,X_15))),truth) ),[0,1,0],$fot(implies(implies(X_15,X_15),X_15))]]) ).
cnf(refute_0_115,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(implies(X_15,truth),truth),X_15),implies(X_13,X_15))) != truth
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_15,truth),truth),X_15),implies(implies(X_15,X_15),X_15)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(implies(X_15,truth),truth),X_15),implies(X_13,X_15))),truth) )],[refute_0_100,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(truth,implies(X_15,implies(X_13,X_15))) = implies(X_15,implies(X_13,X_15)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_15,implies(X_13,X_15))))]]) ).
cnf(refute_0_118,plain,
implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(not(truth)),not(not(truth))))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_119,plain,
implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_5)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_120,plain,
implies(not(X_5),not(X_5)) = implies(implies(not(X_5),truth),truth),
inference(subst,[],[refute_0_106:[bind(X_2,$fot(not(X_5)))]]) ).
cnf(refute_0_121,plain,
( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
| implies(not(X_5),not(X_5)) != implies(implies(not(X_5),truth),truth)
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) ),[0,0],$fot(implies(implies(not(X_5),truth),truth))]]) ).
cnf(refute_0_122,plain,
( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_5),not(X_5)),implies(implies(not(X_5),truth),truth)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) = truth,
inference(subst,[],[refute_0_123:[bind(X_5,$fot(not(truth)))]]) ).
cnf(refute_0_125,plain,
implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_126,plain,
implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
inference(subst,[],[refute_0_123:[bind(X_5,$fot(truth))]]) ).
cnf(refute_0_127,plain,
( implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) != truth
| implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_128,plain,
( implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
( implies(X_2,X_2) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,truth),truth) = implies(X_2,X_2) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X_2,X_2))),bind(Y0,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_131,plain,
implies(implies(X_2,truth),truth) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),implies(implies(X_2,truth),truth)) )],[refute_0_106,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_131:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_133,plain,
implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).
cnf(refute_0_134,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).
cnf(refute_0_135,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(truth,implies(not(truth),truth)),truth)
| implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).
cnf(refute_0_136,plain,
( implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(truth,implies(not(truth),truth)),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_139,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).
cnf(refute_0_142,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_129,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) != truth
| implies(not(truth),not(truth)) != truth
| implies(implies(implies(not(not(truth)),truth),truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_145,plain,
( implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) != truth
| implies(implies(implies(not(not(truth)),truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(implies(implies(not(not(truth)),truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))),truth) )],[refute_0_124,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) = implies(implies(implies(X_3,truth),truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_3,truth)))]]) ).
cnf(refute_0_148,plain,
implies(X_3,X_3) = implies(implies(X_3,truth),truth),
inference(subst,[],[refute_0_106:[bind(X_2,$fot(X_3))]]) ).
cnf(refute_0_149,plain,
( implies(X_3,X_3) != implies(implies(X_3,truth),truth)
| implies(implies(X_3,truth),truth) = implies(X_3,X_3) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X_3,X_3))),bind(Y0,$fot(implies(implies(X_3,truth),truth)))]]) ).
cnf(refute_0_150,plain,
implies(implies(X_3,truth),truth) = implies(X_3,X_3),
inference(resolve,[$cnf( $equal(implies(X_3,X_3),implies(implies(X_3,truth),truth)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( implies(implies(X_3,truth),truth) != implies(X_3,X_3)
| implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) = implies(implies(X_3,X_3),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) ),[1,0],$fot(implies(X_3,X_3))]]) ).
cnf(refute_0_152,plain,
( implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) = implies(implies(X_3,X_3),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_3,truth),truth),implies(X_3,X_3)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) = implies(implies(X_3,X_3),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
( implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) != implies(implies(X_3,X_3),truth)
| implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(implies(X_3,truth),truth),truth) = implies(implies(X_3,X_3),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)),implies(implies(X_3,X_3),truth)) ),[0],$fot(implies(implies(implies(X_3,truth),truth),truth))]]) ).
cnf(refute_0_155,plain,
( implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)) != implies(implies(X_3,X_3),truth)
| implies(implies(implies(X_3,truth),truth),truth) = implies(implies(X_3,X_3),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) )],[refute_0_147,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(implies(implies(X_3,truth),truth),truth) = implies(implies(X_3,X_3),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_3,truth)),implies(X_3,truth)),implies(implies(X_3,X_3),truth)) )],[refute_0_153,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(implies(not(not(truth)),truth),truth),truth) = implies(implies(not(not(truth)),not(not(truth))),truth),
inference(subst,[],[refute_0_156:[bind(X_3,$fot(not(not(truth))))]]) ).
cnf(refute_0_158,plain,
( implies(implies(implies(not(not(truth)),truth),truth),truth) != implies(implies(not(not(truth)),not(not(truth))),truth)
| implies(implies(implies(not(not(truth)),truth),truth),truth) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(truth))),truth))]]) ).
cnf(refute_0_159,plain,
( implies(implies(implies(not(not(truth)),truth),truth),truth) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),implies(implies(not(not(truth)),not(not(truth))),truth)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(implies(not(not(truth)),not(not(truth))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),truth) )],[refute_0_146,refute_0_159]) ).
cnf(refute_0_161,plain,
( implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_162,plain,
( implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),truth),truth) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) )],[refute_0_118,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(truth,Z) = Z,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_165,plain,
implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),
introduced(tautology,[refl,[$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_166,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) ),[1,0],$fot(Z)]]) ).
cnf(refute_0_167,plain,
( implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))))]]) ).
cnf(refute_0_170,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))))),bind(Y0,$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)))),bind(Z0,$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))))]]) ).
cnf(refute_0_171,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) ),[0],$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_174,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) )],[refute_0_163,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_177,plain,
implies(implies(X_13,not(not(X_13))),implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_13)),bind(Y,$fot(not(not(X_13)))),bind(Z,$fot(not(X_13)))]]) ).
cnf(refute_0_178,plain,
implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(X_13))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_179,plain,
( implies(implies(X_13,not(not(X_13))),implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13)))) != truth
| implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13))) != truth
| implies(implies(X_13,not(not(X_13))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,not(not(X_13))),implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_180,plain,
( implies(implies(X_13,not(not(X_13))),implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13)))) != truth
| implies(implies(X_13,not(not(X_13))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13))),truth) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(implies(X_13,not(not(X_13))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,not(not(X_13))),implies(implies(not(not(X_13)),not(X_13)),implies(X_13,not(X_13)))),truth) )],[refute_0_177,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(implies(truth,not(not(truth))),truth) = truth,
inference(subst,[],[refute_0_181:[bind(X_13,$fot(truth))]]) ).
cnf(refute_0_183,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_184,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(not(truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) ),[0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_185,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(not(not(truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(not(not(truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(not(not(truth)),truth) != truth
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_188,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),truth),truth) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) )],[refute_0_176,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(implies(not(not(truth)),truth),truth) = implies(not(not(truth)),not(not(truth))),
inference(subst,[],[refute_0_131:[bind(X_2,$fot(not(not(truth))))]]) ).
cnf(refute_0_191,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(truth,not(not(truth))),not(not(truth))))),bind(Y0,$fot(implies(implies(not(not(truth)),truth),truth))),bind(Z0,$fot(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_192,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) )],[refute_0_176,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),truth),truth),implies(not(not(truth)),not(not(truth)))) )],[refute_0_190,refute_0_192]) ).
cnf(refute_0_194,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(truth,truth)) ),[0],$fot(implies(not(not(truth)),not(not(truth))))]]) ).
cnf(refute_0_195,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_197,plain,
( implies(not(not(truth)),not(not(truth))) != implies(truth,truth)
| implies(truth,truth) != truth
| implies(not(not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(truth)),not(not(truth))),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_198,plain,
( implies(not(not(truth)),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),implies(truth,truth)) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(truth,truth)) )],[refute_0_189,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = implies(implies(not(not(truth)),not(not(truth))),Z),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(truth))),Z))]]) ).
cnf(refute_0_202,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != implies(implies(not(not(truth)),not(not(truth))),Z)
| implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(implies(not(not(truth)),not(not(truth))),Z)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_203,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(implies(not(not(truth)),not(not(truth))),Z)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_200,refute_0_203]) ).
cnf(refute_0_205,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != implies(truth,Z)
| implies(truth,Z) != Z
| implies(implies(not(not(truth)),not(not(truth))),Z) = Z ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(not(truth)),not(not(truth))),Z))),bind(Y0,$fot(implies(truth,Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_206,plain,
( implies(truth,Z) != Z
| implies(implies(not(not(truth)),not(not(truth))),Z) = Z ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(truth,Z)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = Z,
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_164,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
introduced(tautology,[refl,[$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_209,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(implies(not(not(truth)),not(not(truth))),Z) != Z
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_210,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != Z
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z) ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),Z) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,Z)
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != truth
| implies(Z,Z) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),truth) ),[0],$fot(implies(Z,Z))]]) ).
cnf(refute_0_213,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != truth
| implies(Z,Z) = truth ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,Z)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(Z,Z) = truth,
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),truth) )],[refute_0_175,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(X_15,X_15) = truth,
inference(subst,[],[refute_0_214:[bind(Z,$fot(X_15))]]) ).
cnf(refute_0_216,plain,
implies(implies(X_15,X_15),X_15) = implies(implies(X_15,X_15),X_15),
introduced(tautology,[refl,[$fot(implies(implies(X_15,X_15),X_15))]]) ).
cnf(refute_0_217,plain,
( implies(X_15,X_15) != truth
| implies(implies(X_15,X_15),X_15) != implies(implies(X_15,X_15),X_15)
| implies(implies(X_15,X_15),X_15) = implies(truth,X_15) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_15,X_15),X_15),implies(implies(X_15,X_15),X_15)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_218,plain,
( implies(X_15,X_15) != truth
| implies(implies(X_15,X_15),X_15) = implies(truth,X_15) ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,X_15),X_15),implies(implies(X_15,X_15),X_15)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(X_15,X_15),X_15) = implies(truth,X_15),
inference(resolve,[$cnf( $equal(implies(X_15,X_15),truth) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( implies(implies(X_15,X_15),X_15) != implies(truth,X_15)
| implies(truth,X_15) != X_15
| implies(implies(X_15,X_15),X_15) = X_15 ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(X_15,X_15),X_15))),bind(Y0,$fot(implies(truth,X_15))),bind(Z0,$fot(X_15))]]) ).
cnf(refute_0_221,plain,
( implies(truth,X_15) != X_15
| implies(implies(X_15,X_15),X_15) = X_15 ),
inference(resolve,[$cnf( $equal(implies(implies(X_15,X_15),X_15),implies(truth,X_15)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(implies(X_15,X_15),X_15) = X_15,
inference(resolve,[$cnf( $equal(implies(truth,X_15),X_15) )],[refute_0_52,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) = implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))]]) ).
cnf(refute_0_224,plain,
( implies(implies(X_15,X_15),X_15) != X_15
| implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) != implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))
| implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) = implies(X_15,implies(X_13,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_225,plain,
( implies(implies(X_15,X_15),X_15) != X_15
| implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) = implies(X_15,implies(X_13,X_15)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) = implies(X_15,implies(X_13,X_15)),
inference(resolve,[$cnf( $equal(implies(implies(X_15,X_15),X_15),X_15) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),
introduced(tautology,[refl,[$fot(implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))))]]) ).
cnf(refute_0_228,plain,
( implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) != implies(X_15,implies(X_13,X_15))
| implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))
| implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))) ),[1,1],$fot(implies(X_15,implies(X_13,X_15)))]]) ).
cnf(refute_0_229,plain,
( implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)) != implies(X_15,implies(X_13,X_15))
| implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)),implies(X_15,implies(X_13,X_15))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(X_5),truth),truth))),bind(Y,$fot(X_14)),bind(Z,$fot(implies(X_5,X_5)))]]) ).
cnf(refute_0_232,plain,
( implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)))) != truth
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) != truth
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_233,plain,
( implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)))) != truth
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)),truth) )],[refute_0_123,refute_0_232]) ).
cnf(refute_0_234,plain,
implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)))),truth) )],[refute_0_231,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_236,plain,
implies(X_4,X_4) = implies(implies(X_4,truth),truth),
inference(subst,[],[refute_0_106:[bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_237,plain,
( implies(X_4,X_4) != implies(implies(X_4,truth),truth)
| implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) ),[0,1],$fot(implies(implies(X_4,truth),truth))]]) ).
cnf(refute_0_238,plain,
( implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_4,X_4),implies(implies(X_4,truth),truth)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) )],[refute_0_235,refute_0_238]) ).
cnf(refute_0_240,plain,
implies(truth,implies(implies(X_4,truth),truth)) = implies(implies(X_4,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_241,plain,
implies(not(X_4),not(X_4)) = truth,
inference(subst,[],[refute_0_214:[bind(Z,$fot(not(X_4)))]]) ).
cnf(refute_0_242,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_243,plain,
( implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth))
| implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(truth,implies(implies(X_4,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_244,plain,
( implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(truth,implies(implies(X_4,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(truth,implies(implies(X_4,truth),truth)),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_241,refute_0_244]) ).
cnf(refute_0_246,plain,
( implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != implies(truth,implies(implies(X_4,truth),truth))
| implies(truth,implies(implies(X_4,truth),truth)) != implies(implies(X_4,truth),truth)
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(implies(X_4,truth),truth) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),bind(Y0,$fot(implies(truth,implies(implies(X_4,truth),truth)))),bind(Z0,$fot(implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_247,plain,
( implies(truth,implies(implies(X_4,truth),truth)) != implies(implies(X_4,truth),truth)
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(implies(X_4,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(truth,implies(implies(X_4,truth),truth))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = implies(implies(X_4,truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_4,truth),truth)),implies(implies(X_4,truth),truth)) )],[refute_0_240,refute_0_247]) ).
cnf(refute_0_249,plain,
( implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != implies(implies(X_4,truth),truth)
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(implies(X_4,truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) ),[0],$fot(implies(implies(X_4,truth),truth))]]) ).
cnf(refute_0_250,plain,
( implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(implies(X_4,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(X_4,truth),truth)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(implies(X_4,truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_239,refute_0_250]) ).
cnf(refute_0_252,plain,
implies(implies(X_14,truth),truth) = truth,
inference(subst,[],[refute_0_251:[bind(X_4,$fot(X_14))]]) ).
cnf(refute_0_253,plain,
implies(X_5,X_5) = truth,
inference(subst,[],[refute_0_214:[bind(Z,$fot(X_5))]]) ).
cnf(refute_0_254,plain,
implies(X_14,implies(X_5,X_5)) = implies(X_14,implies(X_5,X_5)),
introduced(tautology,[refl,[$fot(implies(X_14,implies(X_5,X_5)))]]) ).
cnf(refute_0_255,plain,
( implies(X_14,implies(X_5,X_5)) != implies(X_14,implies(X_5,X_5))
| implies(X_5,X_5) != truth
| implies(X_14,implies(X_5,X_5)) = implies(X_14,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_14,implies(X_5,X_5)),implies(X_14,implies(X_5,X_5))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_256,plain,
( implies(X_5,X_5) != truth
| implies(X_14,implies(X_5,X_5)) = implies(X_14,truth) ),
inference(resolve,[$cnf( $equal(implies(X_14,implies(X_5,X_5)),implies(X_14,implies(X_5,X_5))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(X_14,implies(X_5,X_5)) = implies(X_14,truth),
inference(resolve,[$cnf( $equal(implies(X_5,X_5),truth) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(implies(X_14,implies(X_5,X_5)),truth) = implies(implies(X_14,implies(X_5,X_5)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_14,implies(X_5,X_5)),truth))]]) ).
cnf(refute_0_259,plain,
( implies(X_14,implies(X_5,X_5)) != implies(X_14,truth)
| implies(implies(X_14,implies(X_5,X_5)),truth) != implies(implies(X_14,implies(X_5,X_5)),truth)
| implies(implies(X_14,implies(X_5,X_5)),truth) = implies(implies(X_14,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,implies(X_5,X_5)),truth),implies(implies(X_14,implies(X_5,X_5)),truth)) ),[1,0],$fot(implies(X_14,truth))]]) ).
cnf(refute_0_260,plain,
( implies(X_14,implies(X_5,X_5)) != implies(X_14,truth)
| implies(implies(X_14,implies(X_5,X_5)),truth) = implies(implies(X_14,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(X_5,X_5)),truth),implies(implies(X_14,implies(X_5,X_5)),truth)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
implies(implies(X_14,implies(X_5,X_5)),truth) = implies(implies(X_14,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_14,implies(X_5,X_5)),implies(X_14,truth)) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
( implies(implies(X_14,implies(X_5,X_5)),truth) != implies(implies(X_14,truth),truth)
| implies(implies(X_14,truth),truth) != truth
| implies(implies(X_14,implies(X_5,X_5)),truth) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(X_14,implies(X_5,X_5)),truth))),bind(Y0,$fot(implies(implies(X_14,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_263,plain,
( implies(implies(X_14,truth),truth) != truth
| implies(implies(X_14,implies(X_5,X_5)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(X_5,X_5)),truth),implies(implies(X_14,truth),truth)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(implies(X_14,implies(X_5,X_5)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_14,truth),truth),truth) )],[refute_0_252,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)),
introduced(tautology,[refl,[$fot(implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)))]]) ).
cnf(refute_0_266,plain,
( implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth))
| implies(implies(X_14,implies(X_5,X_5)),truth) != truth
| implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)),implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_267,plain,
( implies(implies(X_14,implies(X_5,X_5)),truth) != truth
| implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth) ),
inference(resolve,[$cnf( $equal(implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)),implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_14,implies(X_5,X_5)),truth),truth) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(implies(not(X_5),truth),truth) = truth,
inference(subst,[],[refute_0_251:[bind(X_4,$fot(not(X_5)))]]) ).
cnf(refute_0_270,plain,
implies(implies(implies(not(X_5),truth),truth),X_14) = implies(implies(implies(not(X_5),truth),truth),X_14),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_5),truth),truth),X_14))]]) ).
cnf(refute_0_271,plain,
( implies(implies(implies(not(X_5),truth),truth),X_14) != implies(implies(implies(not(X_5),truth),truth),X_14)
| implies(implies(not(X_5),truth),truth) != truth
| implies(implies(implies(not(X_5),truth),truth),X_14) = implies(truth,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(implies(not(X_5),truth),truth),X_14)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_272,plain,
( implies(implies(not(X_5),truth),truth) != truth
| implies(implies(implies(not(X_5),truth),truth),X_14) = implies(truth,X_14) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(implies(not(X_5),truth),truth),X_14)) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(implies(implies(not(X_5),truth),truth),X_14) = implies(truth,X_14),
inference(resolve,[$cnf( $equal(implies(implies(not(X_5),truth),truth),truth) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
( implies(implies(implies(not(X_5),truth),truth),X_14) != implies(truth,X_14)
| implies(truth,X_14) != X_14
| implies(implies(implies(not(X_5),truth),truth),X_14) = X_14 ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(not(X_5),truth),truth),X_14))),bind(Y0,$fot(implies(truth,X_14))),bind(Z0,$fot(X_14))]]) ).
cnf(refute_0_275,plain,
( implies(truth,X_14) != X_14
| implies(implies(implies(not(X_5),truth),truth),X_14) = X_14 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_5),truth),truth),X_14),implies(truth,X_14)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(implies(implies(not(X_5),truth),truth),X_14) = X_14,
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_56,refute_0_275]) ).
cnf(refute_0_277,plain,
implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)))]]) ).
cnf(refute_0_278,plain,
( implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth))
| implies(implies(implies(not(X_5),truth),truth),X_14) != X_14
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth))) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_279,plain,
( implies(implies(implies(not(X_5),truth),truth),X_14) != X_14
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_5),truth),truth),X_14),X_14) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
( implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(X_14,truth)
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth))
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)))),bind(Y0,$fot(implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)))),bind(Z0,$fot(implies(X_14,truth)))]]) ).
cnf(refute_0_282,plain,
( implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(X_14,truth)
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) = implies(X_14,truth),
inference(resolve,[$cnf( $equal(implies(X_14,implies(implies(X_14,implies(X_5,X_5)),truth)),implies(X_14,truth)) )],[refute_0_268,refute_0_282]) ).
cnf(refute_0_284,plain,
( implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) != implies(X_14,truth)
| implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) != truth
| implies(X_14,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),truth) ),[0],$fot(implies(X_14,truth))]]) ).
cnf(refute_0_285,plain,
( implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)) != truth
| implies(X_14,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),implies(X_14,truth)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(X_14,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_5),truth),truth),X_14),implies(implies(X_14,implies(X_5,X_5)),truth)),truth) )],[refute_0_234,refute_0_285]) ).
cnf(refute_0_287,plain,
implies(X_13,truth) = truth,
inference(subst,[],[refute_0_286:[bind(X_14,$fot(X_13))]]) ).
cnf(refute_0_288,plain,
implies(implies(X_15,truth),truth) = truth,
inference(subst,[],[refute_0_286:[bind(X_14,$fot(implies(X_15,truth)))]]) ).
cnf(refute_0_289,plain,
implies(X_13,implies(implies(X_15,truth),truth)) = implies(X_13,implies(implies(X_15,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(implies(X_15,truth),truth)))]]) ).
cnf(refute_0_290,plain,
( implies(X_13,implies(implies(X_15,truth),truth)) != implies(X_13,implies(implies(X_15,truth),truth))
| implies(implies(X_15,truth),truth) != truth
| implies(X_13,implies(implies(X_15,truth),truth)) = implies(X_13,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(implies(X_15,truth),truth)),implies(X_13,implies(implies(X_15,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_291,plain,
( implies(implies(X_15,truth),truth) != truth
| implies(X_13,implies(implies(X_15,truth),truth)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_15,truth),truth)),implies(X_13,implies(implies(X_15,truth),truth))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
implies(X_13,implies(implies(X_15,truth),truth)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_15,truth),truth),truth) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
( implies(X_13,implies(implies(X_15,truth),truth)) != implies(X_13,truth)
| implies(X_13,truth) != truth
| implies(X_13,implies(implies(X_15,truth),truth)) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(X_13,implies(implies(X_15,truth),truth)))),bind(Y0,$fot(implies(X_13,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_294,plain,
( implies(X_13,truth) != truth
| implies(X_13,implies(implies(X_15,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_15,truth),truth)),implies(X_13,truth)) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(X_13,implies(implies(X_15,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(X_13,truth),truth) )],[refute_0_287,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),
introduced(tautology,[refl,[$fot(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))))]]) ).
cnf(refute_0_297,plain,
( implies(X_13,implies(implies(X_15,truth),truth)) != truth
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_298,plain,
( implies(X_13,implies(implies(X_15,truth),truth)) != truth
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_15,truth),truth)),truth) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))
| implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(truth,implies(X_15,implies(X_13,X_15)))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))))),bind(Y0,$fot(implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))))),bind(Z0,$fot(implies(truth,implies(X_15,implies(X_13,X_15)))))]]) ).
cnf(refute_0_301,plain,
( implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(truth,implies(X_15,implies(X_13,X_15)))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(truth,implies(X_15,implies(X_13,X_15))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(truth,implies(X_15,implies(X_13,X_15)))) )],[refute_0_230,refute_0_301]) ).
cnf(refute_0_303,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(truth,implies(X_15,implies(X_13,X_15)))
| implies(truth,implies(X_15,implies(X_13,X_15))) != implies(X_15,implies(X_13,X_15))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(X_15,implies(X_13,X_15)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))))),bind(Y0,$fot(implies(truth,implies(X_15,implies(X_13,X_15))))),bind(Z0,$fot(implies(X_15,implies(X_13,X_15))))]]) ).
cnf(refute_0_304,plain,
( implies(truth,implies(X_15,implies(X_13,X_15))) != implies(X_15,implies(X_13,X_15))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(X_15,implies(X_13,X_15)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(truth,implies(X_15,implies(X_13,X_15)))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) = implies(X_15,implies(X_13,X_15)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_15,implies(X_13,X_15))),implies(X_15,implies(X_13,X_15))) )],[refute_0_117,refute_0_304]) ).
cnf(refute_0_306,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != implies(X_15,implies(X_13,X_15))
| implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != truth
| implies(X_15,implies(X_13,X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),truth) ),[0],$fot(implies(X_15,implies(X_13,X_15)))]]) ).
cnf(refute_0_307,plain,
( implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))) != truth
| implies(X_15,implies(X_13,X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),implies(X_15,implies(X_13,X_15))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(X_15,implies(X_13,X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(implies(X_15,truth),truth)),implies(implies(implies(X_15,X_15),X_15),implies(X_13,X_15))),truth) )],[refute_0_116,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(Y,implies(implies(X_21,Y),Y)) = truth,
inference(subst,[],[refute_0_308:[bind(X_13,$fot(implies(X_21,Y))),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_310,plain,
not(implies(Y,implies(implies(X_21,Y),Y))) = not(implies(Y,implies(implies(X_21,Y),Y))),
introduced(tautology,[refl,[$fot(not(implies(Y,implies(implies(X_21,Y),Y))))]]) ).
cnf(refute_0_311,plain,
( implies(Y,implies(implies(X_21,Y),Y)) != truth
| not(implies(Y,implies(implies(X_21,Y),Y))) != not(implies(Y,implies(implies(X_21,Y),Y)))
| not(implies(Y,implies(implies(X_21,Y),Y))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,implies(implies(X_21,Y),Y))),not(implies(Y,implies(implies(X_21,Y),Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_312,plain,
( implies(Y,implies(implies(X_21,Y),Y)) != truth
| not(implies(Y,implies(implies(X_21,Y),Y))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(Y,implies(implies(X_21,Y),Y))),not(implies(Y,implies(implies(X_21,Y),Y)))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
not(implies(Y,implies(implies(X_21,Y),Y))) = not(truth),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(X_21,Y),Y)),truth) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) = implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),
introduced(tautology,[refl,[$fot(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))))]]) ).
cnf(refute_0_315,plain,
( implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) != implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y))))
| not(implies(Y,implies(implies(X_21,Y),Y))) != not(truth)
| implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) = implies(not(implies(implies(X_21,Y),Y)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_316,plain,
( not(implies(Y,implies(implies(X_21,Y),Y))) != not(truth)
| implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) = implies(not(implies(implies(X_21,Y),Y)),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y))))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) = implies(not(implies(implies(X_21,Y),Y)),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(Y,implies(implies(X_21,Y),Y))),not(truth)) )],[refute_0_313,refute_0_316]) ).
cnf(refute_0_318,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)))]]) ).
cnf(refute_0_319,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))
| implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) != implies(not(implies(implies(X_21,Y),Y)),not(truth))
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))) ),[1,0],$fot(implies(not(implies(implies(X_21,Y),Y)),not(truth)))]]) ).
cnf(refute_0_320,plain,
( implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))) != implies(not(implies(implies(X_21,Y),Y)),not(truth))
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),
inference(resolve,[$cnf( $equal(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(not(implies(implies(X_21,Y),Y)),not(truth))) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))
| implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),truth) ),[0],$fot(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)))]]) ).
cnf(refute_0_323,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(implies(Y,implies(implies(X_21,Y),Y)))),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),truth) )],[refute_0_99,refute_0_323]) ).
cnf(refute_0_325,plain,
implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(implies(Y,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(Y,X_23),X_23)))]]) ).
cnf(refute_0_326,plain,
implies(Y,implies(implies(Y,X_23),X_23)) = truth,
inference(subst,[],[refute_0_63:[bind(X_14,$fot(Y)),bind(X_15,$fot(X_23))]]) ).
cnf(refute_0_327,plain,
( implies(Y,implies(implies(Y,X_23),X_23)) != truth
| implies(implies(implies(implies(Y,X_23),X_23),Y),Y) != implies(implies(Y,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23))
| implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(truth,implies(implies(Y,X_23),X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_23),X_23),Y),Y),implies(implies(Y,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_328,plain,
( implies(implies(implies(implies(Y,X_23),X_23),Y),Y) != implies(implies(Y,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23))
| implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(truth,implies(implies(Y,X_23),X_23)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(implies(Y,X_23),X_23)),truth) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(truth,implies(implies(Y,X_23),X_23)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_23),X_23),Y),Y),implies(implies(Y,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23))) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
implies(truth,implies(implies(Y,X_23),X_23)) = implies(implies(Y,X_23),X_23),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(Y,X_23),X_23)))]]) ).
cnf(refute_0_331,plain,
( implies(implies(implies(implies(Y,X_23),X_23),Y),Y) != implies(truth,implies(implies(Y,X_23),X_23))
| implies(truth,implies(implies(Y,X_23),X_23)) != implies(implies(Y,X_23),X_23)
| implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(implies(Y,X_23),X_23) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(Y,X_23),X_23),Y),Y),implies(implies(Y,X_23),X_23)) ),[0],$fot(implies(truth,implies(implies(Y,X_23),X_23)))]]) ).
cnf(refute_0_332,plain,
( implies(implies(implies(implies(Y,X_23),X_23),Y),Y) != implies(truth,implies(implies(Y,X_23),X_23))
| implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(implies(Y,X_23),X_23) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(Y,X_23),X_23)),implies(implies(Y,X_23),X_23)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
implies(implies(implies(implies(Y,X_23),X_23),Y),Y) = implies(implies(Y,X_23),X_23),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_23),X_23),Y),Y),implies(truth,implies(implies(Y,X_23),X_23))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(implies(implies(implies(Y,X_21),X_21),Y),Y) = implies(implies(Y,X_21),X_21),
inference(subst,[],[refute_0_333:[bind(X_23,$fot(X_21))]]) ).
cnf(refute_0_335,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)))]]) ).
cnf(refute_0_336,plain,
( implies(implies(implies(implies(Y,X_21),X_21),Y),Y) != implies(implies(Y,X_21),X_21)
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))) ),[1,1],$fot(implies(implies(Y,X_21),X_21))]]) ).
cnf(refute_0_337,plain,
( implies(implies(implies(implies(Y,X_21),X_21),Y),Y) != implies(implies(Y,X_21),X_21)
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) = implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_21),X_21),Y),Y),implies(implies(Y,X_21),X_21)) )],[refute_0_334,refute_0_337]) ).
cnf(refute_0_339,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21))
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),truth) ),[0],$fot(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)))]]) ).
cnf(refute_0_340,plain,
( implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)) != truth
| implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(Y,X_21),X_21)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(X_21,Y),Y)),not(truth)),implies(implies(implies(implies(Y,X_21),X_21),Y),Y)),truth) )],[refute_0_324,refute_0_340]) ).
cnf(refute_0_342,plain,
implies(implies(not(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = truth,
inference(subst,[],[refute_0_341:[bind(Y,$fot(implies(not(not(truth)),not(truth)))),bind(X_21,$fot(not(not(truth))))]]) ).
cnf(refute_0_343,plain,
implies(implies(X_13,implies(not(X_15),not(truth))),implies(implies(implies(not(X_15),not(truth)),X_15),implies(X_13,X_15))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_13)),bind(Y,$fot(implies(not(X_15),not(truth)))),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_344,plain,
implies(implies(not(X_4),not(truth)),implies(truth,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_345,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_346,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(truth,X_4) != X_4
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_347,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
implies(implies(not(X_4),not(truth)),X_4) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
implies(implies(not(X_15),not(truth)),X_15) = truth,
inference(subst,[],[refute_0_348:[bind(X_4,$fot(X_15))]]) ).
cnf(refute_0_350,plain,
( implies(implies(X_13,implies(not(X_15),not(truth))),implies(implies(implies(not(X_15),not(truth)),X_15),implies(X_13,X_15))) != truth
| implies(implies(not(X_15),not(truth)),X_15) != truth
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(implies(implies(not(X_15),not(truth)),X_15),implies(X_13,X_15))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_351,plain,
( implies(implies(X_13,implies(not(X_15),not(truth))),implies(implies(implies(not(X_15),not(truth)),X_15),implies(X_13,X_15))) != truth
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_15),not(truth)),X_15),truth) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(implies(implies(not(X_15),not(truth)),X_15),implies(X_13,X_15))),truth) )],[refute_0_343,refute_0_351]) ).
cnf(refute_0_353,plain,
implies(truth,implies(X_13,X_15)) = implies(X_13,X_15),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_13,X_15)))]]) ).
cnf(refute_0_354,plain,
implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),
introduced(tautology,[refl,[$fot(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))))]]) ).
cnf(refute_0_355,plain,
( implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) != implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15)))
| implies(truth,implies(X_13,X_15)) != implies(X_13,X_15)
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15)))) ),[1,1],$fot(implies(X_13,X_15))]]) ).
cnf(refute_0_356,plain,
( implies(truth,implies(X_13,X_15)) != implies(X_13,X_15)
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15)))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) = implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_13,X_15)),implies(X_13,X_15)) )],[refute_0_353,refute_0_356]) ).
cnf(refute_0_358,plain,
( implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) != implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15))
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) != truth
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),truth) ),[0],$fot(implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)))]]) ).
cnf(refute_0_359,plain,
( implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))) != truth
| implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(implies(X_13,implies(not(X_15),not(truth))),implies(X_13,X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X_15),not(truth))),implies(truth,implies(X_13,X_15))),truth) )],[refute_0_352,refute_0_359]) ).
cnf(refute_0_361,plain,
implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_360:[bind(X_13,$fot(not(not(truth)))),bind(X_15,$fot(not(truth)))]]) ).
cnf(refute_0_362,plain,
( implies(implies(not(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) != truth
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),truth) ),[0,0,0,0],$fot(truth)]]) ).
cnf(refute_0_363,plain,
( implies(implies(not(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),truth) )],[refute_0_342,refute_0_363]) ).
cnf(refute_0_365,plain,
implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_366,plain,
implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_367,plain,
( implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))
| implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_368,plain,
( implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_143,refute_0_368]) ).
cnf(refute_0_370,plain,
( implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))
| implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))))),bind(Y0,$fot(implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))))),bind(Z0,$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_371,plain,
( implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) )],[refute_0_365,refute_0_371]) ).
cnf(refute_0_373,plain,
( implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))
| implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),truth) ),[0],$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_374,plain,
( implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))),truth) )],[refute_0_364,refute_0_374]) ).
cnf(refute_0_376,plain,
( implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(X,not(not(truth))))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(X,not(not(truth))))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_377,plain,
( implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) )],[refute_0_375,refute_0_376]) ).
cnf(refute_0_378,plain,
implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(X,not(not(truth))))),truth) )],[refute_0_94,refute_0_377]) ).
cnf(refute_0_379,plain,
implies(truth,implies(X,not(not(truth)))) = implies(X,not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X,not(not(truth)))))]]) ).
cnf(refute_0_380,plain,
implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))))]]) ).
cnf(refute_0_381,plain,
( implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) != implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth)))))
| implies(truth,implies(X,not(not(truth)))) != implies(X,not(not(truth)))
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth)))))) ),[1,1],$fot(implies(X,not(not(truth))))]]) ).
cnf(refute_0_382,plain,
( implies(truth,implies(X,not(not(truth)))) != implies(X,not(not(truth)))
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth)))))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X,not(not(truth)))),implies(X,not(not(truth)))) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
( implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) != implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth))))
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),truth) ),[0],$fot(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))))]]) ).
cnf(refute_0_385,plain,
( implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth))))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(X,not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(truth,implies(X,not(not(truth))))),truth) )],[refute_0_378,refute_0_385]) ).
cnf(refute_0_387,plain,
implies(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth,
inference(subst,[],[refute_0_386:[bind(X,$fot(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth)))))]]) ).
cnf(refute_0_388,plain,
implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) = truth,
inference(subst,[],[refute_0_360:[bind(X_13,$fot(implies(not(not(truth)),not(truth)))),bind(X_15,$fot(not(not(truth))))]]) ).
cnf(refute_0_389,plain,
( implies(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))) != truth
| implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_390,plain,
( implies(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
| implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),truth) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),implies(implies(not(not(truth)),not(truth)),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) )],[refute_0_387,refute_0_390]) ).
cnf(refute_0_392,plain,
implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) = implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))))]]) ).
cnf(refute_0_393,plain,
( implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) ),[0],$fot(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))))]]) ).
cnf(refute_0_394,plain,
( implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))),truth) )],[refute_0_391,refute_0_394]) ).
cnf(refute_0_396,plain,
implies(implies(implies(not(X_14),not(truth)),X_14),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_14),not(truth)))),bind(Y,$fot(X_14)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_397,plain,
implies(implies(not(X_14),not(truth)),X_14) = truth,
inference(subst,[],[refute_0_348:[bind(X_4,$fot(X_14))]]) ).
cnf(refute_0_398,plain,
( implies(implies(implies(not(X_14),not(truth)),X_14),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) != truth
| implies(implies(not(X_14),not(truth)),X_14) != truth
| implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_14),not(truth)),X_14),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_399,plain,
( implies(implies(implies(not(X_14),not(truth)),X_14),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) != truth
| implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_14),not(truth)),X_14),truth) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_14),not(truth)),X_14),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))),truth) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) = implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))))]]) ).
cnf(refute_0_402,plain,
( implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) != implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))
| implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) != truth
| implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))),truth) ),[0],$fot(implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15)))]]) ).
cnf(refute_0_403,plain,
( implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) != truth
| implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))),implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_14,X_15),implies(implies(not(X_14),not(truth)),X_15))),truth) )],[refute_0_400,refute_0_403]) ).
cnf(refute_0_405,plain,
implies(implies(X_43,implies(implies(X_43,X_15),X_15)),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) = truth,
inference(subst,[],[refute_0_404:[bind(X_14,$fot(X_43)),bind(X_15,$fot(implies(implies(X_43,X_15),X_15)))]]) ).
cnf(refute_0_406,plain,
implies(X_43,implies(implies(X_43,X_15),X_15)) = truth,
inference(subst,[],[refute_0_63:[bind(X_14,$fot(X_43))]]) ).
cnf(refute_0_407,plain,
( implies(X_43,implies(implies(X_43,X_15),X_15)) != truth
| implies(implies(X_43,implies(implies(X_43,X_15),X_15)),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) != truth
| implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,implies(implies(X_43,X_15),X_15)),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_408,plain,
( implies(implies(X_43,implies(implies(X_43,X_15),X_15)),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) != truth
| implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) = truth ),
inference(resolve,[$cnf( $equal(implies(X_43,implies(implies(X_43,X_15),X_15)),truth) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_43,implies(implies(X_43,X_15),X_15)),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))),truth) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) = implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))))]]) ).
cnf(refute_0_411,plain,
( implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) != implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))
| implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) != truth
| implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))),truth) ),[0],$fot(implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15)))]]) ).
cnf(refute_0_412,plain,
( implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) != truth
| implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))),implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X_43),not(truth)),implies(implies(X_43,X_15),X_15))),truth) )],[refute_0_409,refute_0_412]) ).
cnf(refute_0_414,plain,
implies(implies(not(X_60),not(truth)),implies(implies(X_60,X_59),X_59)) = truth,
inference(subst,[],[refute_0_413:[bind(X_15,$fot(X_59)),bind(X_43,$fot(X_60))]]) ).
cnf(refute_0_415,plain,
implies(implies(X_59,X_60),X_60) = implies(implies(X_60,X_59),X_59),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_59)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_416,plain,
( implies(implies(X_59,X_60),X_60) != implies(implies(X_60,X_59),X_59)
| implies(implies(X_60,X_59),X_59) = implies(implies(X_59,X_60),X_60) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_59,X_60),X_60))),bind(Y0,$fot(implies(implies(X_60,X_59),X_59)))]]) ).
cnf(refute_0_417,plain,
implies(implies(X_60,X_59),X_59) = implies(implies(X_59,X_60),X_60),
inference(resolve,[$cnf( $equal(implies(implies(X_59,X_60),X_60),implies(implies(X_60,X_59),X_59)) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
( implies(implies(X_60,X_59),X_59) != implies(implies(X_59,X_60),X_60)
| implies(implies(not(X_60),not(truth)),implies(implies(X_60,X_59),X_59)) != truth
| implies(implies(not(X_60),not(truth)),implies(implies(X_59,X_60),X_60)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_60),not(truth)),implies(implies(X_60,X_59),X_59)),truth) ),[0,1],$fot(implies(implies(X_59,X_60),X_60))]]) ).
cnf(refute_0_419,plain,
( implies(implies(not(X_60),not(truth)),implies(implies(X_60,X_59),X_59)) != truth
| implies(implies(not(X_60),not(truth)),implies(implies(X_59,X_60),X_60)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_60,X_59),X_59),implies(implies(X_59,X_60),X_60)) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
implies(implies(not(X_60),not(truth)),implies(implies(X_59,X_60),X_60)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_60),not(truth)),implies(implies(X_60,X_59),X_59)),truth) )],[refute_0_414,refute_0_419]) ).
cnf(refute_0_421,plain,
implies(implies(not(X_114),not(truth)),implies(implies(implies(Y,X_114),X_114),X_114)) = truth,
inference(subst,[],[refute_0_420:[bind(X_59,$fot(implies(Y,X_114))),bind(X_60,$fot(X_114))]]) ).
cnf(refute_0_422,plain,
implies(implies(X_114,Y),Y) = implies(implies(Y,X_114),X_114),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_114))]]) ).
cnf(refute_0_423,plain,
( implies(implies(X_114,Y),Y) != implies(implies(Y,X_114),X_114)
| implies(implies(Y,X_114),X_114) = implies(implies(X_114,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_114,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_114),X_114)))]]) ).
cnf(refute_0_424,plain,
implies(implies(Y,X_114),X_114) = implies(implies(X_114,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_114,Y),Y),implies(implies(Y,X_114),X_114)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
( implies(implies(Y,X_114),X_114) != implies(implies(X_114,Y),Y)
| implies(implies(not(X_114),not(truth)),implies(implies(implies(Y,X_114),X_114),X_114)) != truth
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(Y,X_114),X_114),X_114)),truth) ),[0,1,0],$fot(implies(implies(X_114,Y),Y))]]) ).
cnf(refute_0_426,plain,
( implies(implies(not(X_114),not(truth)),implies(implies(implies(Y,X_114),X_114),X_114)) != truth
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_114),X_114),implies(implies(X_114,Y),Y)) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(Y,X_114),X_114),X_114)),truth) )],[refute_0_421,refute_0_426]) ).
cnf(refute_0_428,plain,
implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(implies(X_119,X_118),X_118),X_119))),bind(Y,$fot(implies(X_118,X_119)))]]) ).
cnf(refute_0_429,plain,
implies(implies(Y,X_23),implies(implies(implies(Y,X_23),X_23),X_23)) = truth,
inference(subst,[],[refute_0_63:[bind(X_14,$fot(implies(Y,X_23))),bind(X_15,$fot(X_23))]]) ).
cnf(refute_0_430,plain,
implies(implies(X_23,Y),Y) = implies(implies(Y,X_23),X_23),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_431,plain,
( implies(implies(X_23,Y),Y) != implies(implies(Y,X_23),X_23)
| implies(implies(Y,X_23),X_23) = implies(implies(X_23,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_23,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_23),X_23)))]]) ).
cnf(refute_0_432,plain,
implies(implies(Y,X_23),X_23) = implies(implies(X_23,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_23,Y),Y),implies(implies(Y,X_23),X_23)) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
( implies(implies(Y,X_23),X_23) != implies(implies(X_23,Y),Y)
| implies(implies(Y,X_23),implies(implies(implies(Y,X_23),X_23),X_23)) != truth
| implies(implies(Y,X_23),implies(implies(implies(X_23,Y),Y),X_23)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,X_23),implies(implies(implies(Y,X_23),X_23),X_23)),truth) ),[0,1,0],$fot(implies(implies(X_23,Y),Y))]]) ).
cnf(refute_0_434,plain,
( implies(implies(Y,X_23),implies(implies(implies(Y,X_23),X_23),X_23)) != truth
| implies(implies(Y,X_23),implies(implies(implies(X_23,Y),Y),X_23)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_23),X_23),implies(implies(X_23,Y),Y)) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
implies(implies(Y,X_23),implies(implies(implies(X_23,Y),Y),X_23)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(Y,X_23),implies(implies(implies(Y,X_23),X_23),X_23)),truth) )],[refute_0_429,refute_0_434]) ).
cnf(refute_0_436,plain,
implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)) = truth,
inference(subst,[],[refute_0_435:[bind(Y,$fot(X_118)),bind(X_23,$fot(X_119))]]) ).
cnf(refute_0_437,plain,
( implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)) != truth
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_438,plain,
( implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),truth) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(implies(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119))) )],[refute_0_428,refute_0_438]) ).
cnf(refute_0_440,plain,
implies(truth,implies(X_118,X_119)) = implies(X_118,X_119),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_118,X_119)))]]) ).
cnf(refute_0_441,plain,
implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),
inference(subst,[],[refute_0_10:[bind(X,$fot(implies(X_21,X_1)))]]) ).
cnf(refute_0_442,plain,
implies(implies(implies(X_21,X_1),X_1),X_1) = implies(implies(implies(X_1,X_21),X_21),X_1),
inference(subst,[],[refute_0_10:[bind(X,$fot(X_1)),bind(X_1,$fot(X_21))]]) ).
cnf(refute_0_443,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(X_21,X_1),X_1),X_1) != implies(implies(implies(X_1,X_21),X_21),X_1)
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) ),[1,0],$fot(implies(implies(implies(X_1,X_21),X_21),X_1))]]) ).
cnf(refute_0_444,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,X_1),X_1),X_1),implies(implies(implies(X_1,X_21),X_21),X_1)) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) )],[refute_0_441,refute_0_444]) ).
cnf(refute_0_446,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) ),[0],$fot(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)))]]) ).
cnf(refute_0_447,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) )],[refute_0_441,refute_0_446]) ).
cnf(refute_0_448,plain,
implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_445,refute_0_447]) ).
cnf(refute_0_449,plain,
implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = truth,
inference(subst,[],[refute_0_71:[bind(X,$fot(X_21)),bind(Z,$fot(X_1)),bind(X_23,$fot(X_1))]]) ).
cnf(refute_0_450,plain,
( implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != truth
| truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) ),[0],$fot(truth)]]) ).
cnf(refute_0_451,plain,
( implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),truth) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( truth != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) = truth ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))))]]) ).
cnf(refute_0_454,plain,
implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)) = truth,
inference(subst,[],[refute_0_454:[bind(X_1,$fot(X_119)),bind(X_21,$fot(X_118))]]) ).
cnf(refute_0_456,plain,
implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)))]]) ).
cnf(refute_0_457,plain,
( implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)) != truth
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119))
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(X_118,X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_458,plain,
( implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)) != truth
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(X_118,X_119)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119))) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(truth,implies(X_118,X_119)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),truth) )],[refute_0_455,refute_0_458]) ).
cnf(refute_0_460,plain,
( implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(truth,implies(X_118,X_119))
| implies(truth,implies(X_118,X_119)) != implies(X_118,X_119)
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(X_118,X_119) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)))),bind(Y0,$fot(implies(truth,implies(X_118,X_119)))),bind(Z0,$fot(implies(X_118,X_119)))]]) ).
cnf(refute_0_461,plain,
( implies(truth,implies(X_118,X_119)) != implies(X_118,X_119)
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(X_118,X_119) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(truth,implies(X_118,X_119))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) = implies(X_118,X_119),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_118,X_119)),implies(X_118,X_119)) )],[refute_0_440,refute_0_461]) ).
cnf(refute_0_463,plain,
( implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(X_118,X_119)
| implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(X_118,X_119) = implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))) ),[0],$fot(implies(X_118,X_119))]]) ).
cnf(refute_0_464,plain,
( implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(X_118,X_119) = implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(X_118,X_119)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) = implies(implies(implies(X_119,X_118),X_118),X_119),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(X_119,X_118),X_118),X_119)))]]) ).
cnf(refute_0_466,plain,
( implies(X_118,X_119) != implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)) != implies(implies(implies(X_119,X_118),X_118),X_119)
| implies(X_118,X_119) = implies(implies(implies(X_119,X_118),X_118),X_119) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)) ),[0],$fot(implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)))]]) ).
cnf(refute_0_467,plain,
( implies(X_118,X_119) != implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(X_118,X_119) = implies(implies(implies(X_119,X_118),X_118),X_119) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119)),implies(implies(implies(X_119,X_118),X_118),X_119)) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
( implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)) != implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))
| implies(X_118,X_119) = implies(implies(implies(X_119,X_118),X_118),X_119) ),
inference(resolve,[$cnf( $equal(implies(X_118,X_119),implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))) )],[refute_0_464,refute_0_467]) ).
cnf(refute_0_469,plain,
implies(X_118,X_119) = implies(implies(implies(X_119,X_118),X_118),X_119),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_119,X_118),X_118),X_119),implies(X_118,X_119)),implies(X_118,X_119)),implies(truth,implies(implies(implies(X_119,X_118),X_118),X_119))) )],[refute_0_439,refute_0_468]) ).
cnf(refute_0_470,plain,
( implies(X_118,X_119) != implies(implies(implies(X_119,X_118),X_118),X_119)
| implies(implies(implies(X_119,X_118),X_118),X_119) = implies(X_118,X_119) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(X_118,X_119))),bind(Y0,$fot(implies(implies(implies(X_119,X_118),X_118),X_119)))]]) ).
cnf(refute_0_471,plain,
implies(implies(implies(X_119,X_118),X_118),X_119) = implies(X_118,X_119),
inference(resolve,[$cnf( $equal(implies(X_118,X_119),implies(implies(implies(X_119,X_118),X_118),X_119)) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
implies(implies(implies(X_114,Y),Y),X_114) = implies(Y,X_114),
inference(subst,[],[refute_0_471:[bind(X_118,$fot(Y)),bind(X_119,$fot(X_114))]]) ).
cnf(refute_0_473,plain,
implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)))]]) ).
cnf(refute_0_474,plain,
( implies(implies(implies(X_114,Y),Y),X_114) != implies(Y,X_114)
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) != implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114))
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = implies(implies(not(X_114),not(truth)),implies(Y,X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114))) ),[1,1],$fot(implies(Y,X_114))]]) ).
cnf(refute_0_475,plain,
( implies(implies(implies(X_114,Y),Y),X_114) != implies(Y,X_114)
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = implies(implies(not(X_114),not(truth)),implies(Y,X_114)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) = implies(implies(not(X_114),not(truth)),implies(Y,X_114)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_114,Y),Y),X_114),implies(Y,X_114)) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
( implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) != implies(implies(not(X_114),not(truth)),implies(Y,X_114))
| implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) != truth
| implies(implies(not(X_114),not(truth)),implies(Y,X_114)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),truth) ),[0],$fot(implies(implies(not(X_114),not(truth)),implies(Y,X_114)))]]) ).
cnf(refute_0_478,plain,
( implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)) != truth
| implies(implies(not(X_114),not(truth)),implies(Y,X_114)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),implies(implies(not(X_114),not(truth)),implies(Y,X_114))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
implies(implies(not(X_114),not(truth)),implies(Y,X_114)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_114),not(truth)),implies(implies(implies(X_114,Y),Y),X_114)),truth) )],[refute_0_427,refute_0_478]) ).
cnf(refute_0_480,plain,
implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))) = truth,
inference(subst,[],[refute_0_479:[bind(Y,$fot(not(not(not(truth))))),bind(X_114,$fot(not(truth)))]]) ).
cnf(refute_0_481,plain,
implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))))]]) ).
cnf(refute_0_482,plain,
( implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_483,plain,
( implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),truth) )],[refute_0_480,refute_0_483]) ).
cnf(refute_0_485,plain,
( implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_486,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_183,refute_0_486]) ).
cnf(refute_0_488,plain,
( implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_489,plain,
( implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) )],[refute_0_395,refute_0_489]) ).
cnf(refute_0_491,plain,
( implies(implies(not(not(truth)),not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_492,plain,
( implies(implies(not(not(truth)),not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != truth
| implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),truth) )],[refute_0_93,refute_0_492]) ).
cnf(refute_0_494,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_495,plain,
implies(implies(X_13,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_13,implies(Y,X)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_13)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).
cnf(refute_0_496,plain,
( implies(implies(X_13,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_13,implies(Y,X)))) != truth
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_13,implies(Y,X)))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_497,plain,
( implies(implies(X_13,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_13,implies(Y,X)))) != truth
| implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_496]) ).
cnf(refute_0_498,plain,
implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_13,implies(Y,X)))),truth) )],[refute_0_495,refute_0_497]) ).
cnf(refute_0_499,plain,
implies(truth,implies(X_13,implies(Y,X))) = implies(X_13,implies(Y,X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_13,implies(Y,X))))]]) ).
cnf(refute_0_500,plain,
implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),
introduced(tautology,[refl,[$fot(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))))]]) ).
cnf(refute_0_501,plain,
( implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) != implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X))))
| implies(truth,implies(X_13,implies(Y,X))) != implies(X_13,implies(Y,X))
| implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X))))) ),[1,1],$fot(implies(X_13,implies(Y,X)))]]) ).
cnf(refute_0_502,plain,
( implies(truth,implies(X_13,implies(Y,X))) != implies(X_13,implies(Y,X))
| implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X))))) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) = implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_13,implies(Y,X))),implies(X_13,implies(Y,X))) )],[refute_0_499,refute_0_502]) ).
cnf(refute_0_504,plain,
( implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) != implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X)))
| implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) != truth
| implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),truth) ),[0],$fot(implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))))]]) ).
cnf(refute_0_505,plain,
( implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))) != truth
| implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X)))) )],[refute_0_503,refute_0_504]) ).
cnf(refute_0_506,plain,
implies(implies(X_13,implies(not(X),not(Y))),implies(X_13,implies(Y,X))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(not(X),not(Y))),implies(truth,implies(X_13,implies(Y,X)))),truth) )],[refute_0_498,refute_0_505]) ).
cnf(refute_0_507,plain,
implies(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) = truth,
inference(subst,[],[refute_0_506:[bind(Y,$fot(not(truth))),bind(X_13,$fot(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth)))))]]) ).
cnf(refute_0_508,plain,
implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),implies(X,not(not(truth))))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(not(implies(not(truth),not(not(truth)))),not(truth)))),bind(Z,$fot(not(not(truth))))]]) ).
cnf(refute_0_509,plain,
implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(Y,X_18),X_18),X_18)) = truth,
inference(subst,[],[refute_0_27:[bind(Y,$fot(X_18)),bind(X_4,$fot(implies(Y,X_18)))]]) ).
cnf(refute_0_510,plain,
implies(implies(X_18,Y),Y) = implies(implies(Y,X_18),X_18),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_511,plain,
( implies(implies(X_18,Y),Y) != implies(implies(Y,X_18),X_18)
| implies(implies(Y,X_18),X_18) = implies(implies(X_18,Y),Y) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(X_18,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_18),X_18)))]]) ).
cnf(refute_0_512,plain,
implies(implies(Y,X_18),X_18) = implies(implies(X_18,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_18,Y),Y),implies(implies(Y,X_18),X_18)) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
( implies(implies(Y,X_18),X_18) != implies(implies(X_18,Y),Y)
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(Y,X_18),X_18),X_18)) != truth
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(Y,X_18),X_18),X_18)),truth) ),[0,1,0],$fot(implies(implies(X_18,Y),Y))]]) ).
cnf(refute_0_514,plain,
( implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(Y,X_18),X_18),X_18)) != truth
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_18),X_18),implies(implies(X_18,Y),Y)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(Y,X_18),X_18),X_18)),truth) )],[refute_0_509,refute_0_514]) ).
cnf(refute_0_516,plain,
implies(X_18,implies(Y,X_18)) = truth,
inference(subst,[],[refute_0_308:[bind(X_13,$fot(Y)),bind(X_15,$fot(X_18))]]) ).
cnf(refute_0_517,plain,
not(implies(X_18,implies(Y,X_18))) = not(implies(X_18,implies(Y,X_18))),
introduced(tautology,[refl,[$fot(not(implies(X_18,implies(Y,X_18))))]]) ).
cnf(refute_0_518,plain,
( implies(X_18,implies(Y,X_18)) != truth
| not(implies(X_18,implies(Y,X_18))) != not(implies(X_18,implies(Y,X_18)))
| not(implies(X_18,implies(Y,X_18))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_18,implies(Y,X_18))),not(implies(X_18,implies(Y,X_18)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_519,plain,
( implies(X_18,implies(Y,X_18)) != truth
| not(implies(X_18,implies(Y,X_18))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_18,implies(Y,X_18))),not(implies(X_18,implies(Y,X_18)))) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
not(implies(X_18,implies(Y,X_18))) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_18,implies(Y,X_18)),truth) )],[refute_0_516,refute_0_519]) ).
cnf(refute_0_521,plain,
implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) = implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),
introduced(tautology,[refl,[$fot(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))))]]) ).
cnf(refute_0_522,plain,
( implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) != implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18))))
| not(implies(X_18,implies(Y,X_18))) != not(truth)
| implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) = implies(not(implies(Y,X_18)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_523,plain,
( not(implies(X_18,implies(Y,X_18))) != not(truth)
| implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) = implies(not(implies(Y,X_18)),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18))))) )],[refute_0_521,refute_0_522]) ).
cnf(refute_0_524,plain,
implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) = implies(not(implies(Y,X_18)),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(X_18,implies(Y,X_18))),not(truth)) )],[refute_0_520,refute_0_523]) ).
cnf(refute_0_525,plain,
implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)))]]) ).
cnf(refute_0_526,plain,
( implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) != implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18))
| implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) != implies(not(implies(Y,X_18)),not(truth))
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18))) ),[1,0],$fot(implies(not(implies(Y,X_18)),not(truth)))]]) ).
cnf(refute_0_527,plain,
( implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))) != implies(not(implies(Y,X_18)),not(truth))
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) = implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)),
inference(resolve,[$cnf( $equal(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(not(implies(Y,X_18)),not(truth))) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
( implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) != implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18))
| implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) != truth
| implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),truth) ),[0],$fot(implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)))]]) ).
cnf(refute_0_530,plain,
( implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)) != truth
| implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18))) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
implies(implies(not(implies(Y,X_18)),not(truth)),implies(implies(implies(X_18,Y),Y),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(Y,X_18)),not(implies(X_18,implies(Y,X_18)))),implies(implies(implies(X_18,Y),Y),X_18)),truth) )],[refute_0_515,refute_0_530]) ).
cnf(refute_0_532,plain,
implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) = truth,
inference(subst,[],[refute_0_531:[bind(Y,$fot(not(truth))),bind(X_18,$fot(not(not(truth))))]]) ).
cnf(refute_0_533,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_348:[bind(X_4,$fot(not(truth)))]]) ).
cnf(refute_0_534,plain,
( implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) != truth
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_535,plain,
( implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) != truth
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))),truth) )],[refute_0_532,refute_0_535]) ).
cnf(refute_0_537,plain,
implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))))]]) ).
cnf(refute_0_538,plain,
( implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) != implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth))))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth))))) ),[1,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_539,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth))))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) = implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_183,refute_0_539]) ).
cnf(refute_0_541,plain,
( implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) != implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth)))
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),truth) ),[0],$fot(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))))]]) ).
cnf(refute_0_542,plain,
( implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth)))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(truth,not(not(truth)))),truth) )],[refute_0_536,refute_0_542]) ).
cnf(refute_0_544,plain,
( implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),implies(X,not(not(truth))))) != truth
| implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))) != truth
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),implies(X,not(not(truth))))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_545,plain,
( implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),truth) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(implies(implies(not(implies(not(truth),not(not(truth)))),not(truth)),not(not(truth))),implies(X,not(not(truth))))),truth) )],[refute_0_508,refute_0_545]) ).
cnf(refute_0_547,plain,
implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))))]]) ).
cnf(refute_0_548,plain,
( implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) != implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth)))))
| implies(truth,implies(X,not(not(truth)))) != implies(X,not(not(truth)))
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth)))))) ),[1,1],$fot(implies(X,not(not(truth))))]]) ).
cnf(refute_0_549,plain,
( implies(truth,implies(X,not(not(truth)))) != implies(X,not(not(truth)))
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth)))))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) = implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X,not(not(truth)))),implies(X,not(not(truth)))) )],[refute_0_379,refute_0_549]) ).
cnf(refute_0_551,plain,
( implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) != implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth))))
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),truth) ),[0],$fot(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))))]]) ).
cnf(refute_0_552,plain,
( implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))) != truth
| implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth))))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(X,not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(truth,implies(X,not(not(truth))))),truth) )],[refute_0_546,refute_0_552]) ).
cnf(refute_0_554,plain,
implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))) = truth,
inference(subst,[],[refute_0_553:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_555,plain,
( implies(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) != truth
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))) != truth
| implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_556,plain,
( implies(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) != truth
| implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),truth) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),not(not(truth)))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))),truth) )],[refute_0_507,refute_0_556]) ).
cnf(refute_0_558,plain,
implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) = implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))))]]) ).
cnf(refute_0_559,plain,
( implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) != implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))
| implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) != truth
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))),truth) ),[0],$fot(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)))]]) ).
cnf(refute_0_560,plain,
( implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) != truth
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))),truth) )],[refute_0_557,refute_0_560]) ).
cnf(refute_0_562,plain,
implies(truth,implies(not(truth),X)) = implies(not(truth),X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_563,plain,
implies(not(X),truth) = truth,
inference(subst,[],[refute_0_286:[bind(X_14,$fot(not(X)))]]) ).
cnf(refute_0_564,plain,
implies(not(truth),truth) = truth,
inference(subst,[],[refute_0_286:[bind(X_14,$fot(not(truth)))]]) ).
cnf(refute_0_565,plain,
implies(not(truth),not(not(truth))) = implies(not(truth),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(not(truth))))]]) ).
cnf(refute_0_566,plain,
( implies(not(truth),not(not(truth))) != implies(not(truth),not(not(truth)))
| not(not(truth)) != truth
| implies(not(truth),not(not(truth))) = implies(not(truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(not(truth),not(not(truth)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_567,plain,
( not(not(truth)) != truth
| implies(not(truth),not(not(truth))) = implies(not(truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(not(truth),not(not(truth)))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
implies(not(truth),not(not(truth))) = implies(not(truth),truth),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_490,refute_0_567]) ).
cnf(refute_0_569,plain,
( implies(not(truth),not(not(truth))) != implies(not(truth),truth)
| implies(not(truth),truth) != truth
| implies(not(truth),not(not(truth))) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(not(truth),not(not(truth))))),bind(Y0,$fot(implies(not(truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_570,plain,
( implies(not(truth),truth) != truth
| implies(not(truth),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(not(truth),truth)) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
implies(not(truth),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),truth),truth) )],[refute_0_564,refute_0_570]) ).
cnf(refute_0_572,plain,
not(implies(not(truth),not(not(truth)))) = not(implies(not(truth),not(not(truth)))),
introduced(tautology,[refl,[$fot(not(implies(not(truth),not(not(truth)))))]]) ).
cnf(refute_0_573,plain,
( implies(not(truth),not(not(truth))) != truth
| not(implies(not(truth),not(not(truth)))) != not(implies(not(truth),not(not(truth))))
| not(implies(not(truth),not(not(truth)))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(truth),not(not(truth)))),not(implies(not(truth),not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_574,plain,
( implies(not(truth),not(not(truth))) != truth
| not(implies(not(truth),not(not(truth)))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(not(truth)))),not(implies(not(truth),not(not(truth))))) )],[refute_0_572,refute_0_573]) ).
cnf(refute_0_575,plain,
not(implies(not(truth),not(not(truth)))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),truth) )],[refute_0_571,refute_0_574]) ).
cnf(refute_0_576,plain,
implies(not(implies(not(truth),not(not(truth)))),not(truth)) = implies(not(implies(not(truth),not(not(truth)))),not(truth)),
introduced(tautology,[refl,[$fot(implies(not(implies(not(truth),not(not(truth)))),not(truth)))]]) ).
cnf(refute_0_577,plain,
( implies(not(implies(not(truth),not(not(truth)))),not(truth)) != implies(not(implies(not(truth),not(not(truth)))),not(truth))
| not(implies(not(truth),not(not(truth)))) != not(truth)
| implies(not(implies(not(truth),not(not(truth)))),not(truth)) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(not(implies(not(truth),not(not(truth)))),not(truth))) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_578,plain,
( not(implies(not(truth),not(not(truth)))) != not(truth)
| implies(not(implies(not(truth),not(not(truth)))),not(truth)) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(not(implies(not(truth),not(not(truth)))),not(truth))) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
implies(not(implies(not(truth),not(not(truth)))),not(truth)) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(not(truth)))),not(truth)) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
( implies(not(implies(not(truth),not(not(truth)))),not(truth)) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(implies(not(truth),not(not(truth)))),not(truth)) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(not(implies(not(truth),not(not(truth)))),not(truth)))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_581,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(implies(not(truth),not(not(truth)))),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(not(truth)))),not(truth)),implies(not(truth),not(truth))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
implies(not(implies(not(truth),not(not(truth)))),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_143,refute_0_581]) ).
cnf(refute_0_583,plain,
implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),
introduced(tautology,[refl,[$fot(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))))]]) ).
cnf(refute_0_584,plain,
( implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) != implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth)))
| implies(not(implies(not(truth),not(not(truth)))),not(truth)) != truth
| implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = implies(not(X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_585,plain,
( implies(not(implies(not(truth),not(not(truth)))),not(truth)) != truth
| implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = implies(not(X),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth)))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = implies(not(X),truth),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(not(truth)))),not(truth)),truth) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
( implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) != implies(not(X),truth)
| implies(not(X),truth) != truth
| implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = truth ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))))),bind(Y0,$fot(implies(not(X),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_588,plain,
( implies(not(X),truth) != truth
| implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(X),truth)) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_563,refute_0_588]) ).
cnf(refute_0_590,plain,
implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)))]]) ).
cnf(refute_0_591,plain,
( implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) != implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))
| implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) != truth
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_592,plain,
( implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))) != truth
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(truth,implies(not(truth),X)),
inference(resolve,[$cnf( $equal(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),truth) )],[refute_0_589,refute_0_592]) ).
cnf(refute_0_594,plain,
( implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) != implies(truth,implies(not(truth),X))
| implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(not(truth),X) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)))),bind(Y0,$fot(implies(truth,implies(not(truth),X)))),bind(Z0,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_595,plain,
( implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(not(truth),X) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),implies(truth,implies(not(truth),X))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) = implies(not(truth),X),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_562,refute_0_595]) ).
cnf(refute_0_597,plain,
( implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),truth) ),[0],$fot(implies(not(truth),X))]]) ).
cnf(refute_0_598,plain,
( implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
implies(not(truth),X) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),implies(not(implies(not(truth),not(not(truth)))),not(truth))),implies(not(truth),X)),truth) )],[refute_0_561,refute_0_598]) ).
cnf(refute_0_600,plain,
implies(not(truth),Y) = truth,
inference(subst,[],[refute_0_599:[bind(X,$fot(Y))]]) ).
cnf(refute_0_601,plain,
implies(implies(not(truth),Y),Y) = implies(implies(not(truth),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),Y),Y))]]) ).
cnf(refute_0_602,plain,
( implies(implies(not(truth),Y),Y) != implies(implies(not(truth),Y),Y)
| implies(not(truth),Y) != truth
| implies(implies(not(truth),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(not(truth),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_603,plain,
( implies(not(truth),Y) != truth
| implies(implies(not(truth),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(not(truth),Y),Y)) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
implies(implies(not(truth),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(truth),Y),truth) )],[refute_0_600,refute_0_603]) ).
cnf(refute_0_605,plain,
( implies(implies(not(truth),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(truth),Y),Y) = Y ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(truth),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_606,plain,
( implies(truth,Y) != Y
| implies(implies(not(truth),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(truth,Y)) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
implies(implies(not(truth),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_494,refute_0_606]) ).
cnf(refute_0_608,plain,
not(implies(implies(not(truth),Y),Y)) = not(implies(implies(not(truth),Y),Y)),
introduced(tautology,[refl,[$fot(not(implies(implies(not(truth),Y),Y)))]]) ).
cnf(refute_0_609,plain,
( implies(implies(not(truth),Y),Y) != Y
| not(implies(implies(not(truth),Y),Y)) != not(implies(implies(not(truth),Y),Y))
| not(implies(implies(not(truth),Y),Y)) = not(Y) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(truth),Y),Y)),not(implies(implies(not(truth),Y),Y))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_610,plain,
( implies(implies(not(truth),Y),Y) != Y
| not(implies(implies(not(truth),Y),Y)) = not(Y) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(truth),Y),Y)),not(implies(implies(not(truth),Y),Y))) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
not(implies(implies(not(truth),Y),Y)) = not(Y),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),Y) )],[refute_0_607,refute_0_610]) ).
cnf(refute_0_612,plain,
implies(truth,not(implies(implies(not(truth),Y),Y))) = not(implies(implies(not(truth),Y),Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(implies(implies(not(truth),Y),Y))))]]) ).
cnf(refute_0_613,plain,
( implies(truth,not(implies(implies(not(truth),Y),Y))) != not(implies(implies(not(truth),Y),Y))
| not(implies(implies(not(truth),Y),Y)) != not(Y)
| implies(truth,not(implies(implies(not(truth),Y),Y))) = not(Y) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(truth,not(implies(implies(not(truth),Y),Y))))),bind(Y0,$fot(not(implies(implies(not(truth),Y),Y)))),bind(Z0,$fot(not(Y)))]]) ).
cnf(refute_0_614,plain,
( not(implies(implies(not(truth),Y),Y)) != not(Y)
| implies(truth,not(implies(implies(not(truth),Y),Y))) = not(Y) ),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(implies(not(truth),Y),Y))),not(implies(implies(not(truth),Y),Y))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
implies(truth,not(implies(implies(not(truth),Y),Y))) = not(Y),
inference(resolve,[$cnf( $equal(not(implies(implies(not(truth),Y),Y)),not(Y)) )],[refute_0_611,refute_0_614]) ).
cnf(refute_0_616,plain,
implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))))]]) ).
cnf(refute_0_617,plain,
( implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth)))
| implies(truth,not(implies(implies(not(truth),Y),Y))) != not(Y)
| implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_618,plain,
( implies(truth,not(implies(implies(not(truth),Y),Y))) != not(Y)
| implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth)))) )],[refute_0_616,refute_0_617]) ).
cnf(refute_0_619,plain,
implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(implies(not(truth),Y),Y))),not(Y)) )],[refute_0_615,refute_0_618]) ).
cnf(refute_0_620,plain,
( implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != implies(not(Y),implies(Y,not(truth)))
| implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),truth) ),[0],$fot(implies(not(Y),implies(Y,not(truth))))]]) ).
cnf(refute_0_621,plain,
( implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),implies(not(Y),implies(Y,not(truth)))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
implies(not(Y),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(implies(not(truth),Y),Y))),implies(Y,not(truth))),truth) )],[refute_0_493,refute_0_621]) ).
cnf(refute_0_623,plain,
implies(not(X_125),implies(X_125,not(truth))) = truth,
inference(subst,[],[refute_0_622:[bind(Y,$fot(X_125))]]) ).
cnf(refute_0_624,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(implies(not(X_125),implies(X_125,not(truth))),implies(X_125,not(truth)))
| implies(not(X_125),implies(X_125,not(truth))) != truth
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,implies(X_125,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(implies(not(X_125),implies(X_125,not(truth))),implies(X_125,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_625,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(implies(not(X_125),implies(X_125,not(truth))),implies(X_125,not(truth)))
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,implies(X_125,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(X_125),implies(X_125,not(truth))),truth) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,implies(X_125,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(implies(not(X_125),implies(X_125,not(truth))),implies(X_125,not(truth)))) )],[refute_0_1,refute_0_625]) ).
cnf(refute_0_627,plain,
implies(truth,not(X_125)) = not(X_125),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_125)))]]) ).
cnf(refute_0_628,plain,
implies(implies(X_43,not(truth)),implies(implies(not(X_43),not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_404:[bind(X_14,$fot(X_43)),bind(X_15,$fot(not(truth)))]]) ).
cnf(refute_0_629,plain,
implies(implies(not(truth),not(X_43)),not(X_43)) = implies(implies(not(X_43),not(truth)),not(truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_43)))]]) ).
cnf(refute_0_630,plain,
( implies(implies(not(truth),not(X_43)),not(X_43)) != implies(implies(not(X_43),not(truth)),not(truth))
| implies(implies(not(X_43),not(truth)),not(truth)) = implies(implies(not(truth),not(X_43)),not(X_43)) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(implies(implies(not(truth),not(X_43)),not(X_43)))),bind(Y0,$fot(implies(implies(not(X_43),not(truth)),not(truth))))]]) ).
cnf(refute_0_631,plain,
implies(implies(not(X_43),not(truth)),not(truth)) = implies(implies(not(truth),not(X_43)),not(X_43)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_43)),not(X_43)),implies(implies(not(X_43),not(truth)),not(truth))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
( implies(implies(X_43,not(truth)),implies(implies(not(X_43),not(truth)),not(truth))) != truth
| implies(implies(not(X_43),not(truth)),not(truth)) != implies(implies(not(truth),not(X_43)),not(X_43))
| implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(X_43),not(truth)),not(truth))),truth) ),[0,1],$fot(implies(implies(not(truth),not(X_43)),not(X_43)))]]) ).
cnf(refute_0_633,plain,
( implies(implies(X_43,not(truth)),implies(implies(not(X_43),not(truth)),not(truth))) != truth
| implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_43),not(truth)),not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) )],[refute_0_631,refute_0_632]) ).
cnf(refute_0_634,plain,
implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(X_43),not(truth)),not(truth))),truth) )],[refute_0_628,refute_0_633]) ).
cnf(refute_0_635,plain,
implies(truth,not(X_43)) = not(X_43),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_43)))]]) ).
cnf(refute_0_636,plain,
implies(not(truth),not(X_43)) = truth,
inference(subst,[],[refute_0_599:[bind(X,$fot(not(X_43)))]]) ).
cnf(refute_0_637,plain,
implies(implies(not(truth),not(X_43)),not(X_43)) = implies(implies(not(truth),not(X_43)),not(X_43)),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(X_43)),not(X_43)))]]) ).
cnf(refute_0_638,plain,
( implies(implies(not(truth),not(X_43)),not(X_43)) != implies(implies(not(truth),not(X_43)),not(X_43))
| implies(not(truth),not(X_43)) != truth
| implies(implies(not(truth),not(X_43)),not(X_43)) = implies(truth,not(X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(X_43)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_639,plain,
( implies(not(truth),not(X_43)) != truth
| implies(implies(not(truth),not(X_43)),not(X_43)) = implies(truth,not(X_43)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_43)),not(X_43)),implies(implies(not(truth),not(X_43)),not(X_43))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
implies(implies(not(truth),not(X_43)),not(X_43)) = implies(truth,not(X_43)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(X_43)),truth) )],[refute_0_636,refute_0_639]) ).
cnf(refute_0_641,plain,
( implies(implies(not(truth),not(X_43)),not(X_43)) != implies(truth,not(X_43))
| implies(truth,not(X_43)) != not(X_43)
| implies(implies(not(truth),not(X_43)),not(X_43)) = not(X_43) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(not(truth),not(X_43)),not(X_43)))),bind(Y0,$fot(implies(truth,not(X_43)))),bind(Z0,$fot(not(X_43)))]]) ).
cnf(refute_0_642,plain,
( implies(truth,not(X_43)) != not(X_43)
| implies(implies(not(truth),not(X_43)),not(X_43)) = not(X_43) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_43)),not(X_43)),implies(truth,not(X_43))) )],[refute_0_640,refute_0_641]) ).
cnf(refute_0_643,plain,
implies(implies(not(truth),not(X_43)),not(X_43)) = not(X_43),
inference(resolve,[$cnf( $equal(implies(truth,not(X_43)),not(X_43)) )],[refute_0_635,refute_0_642]) ).
cnf(refute_0_644,plain,
implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),
introduced(tautology,[refl,[$fot(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))))]]) ).
cnf(refute_0_645,plain,
( implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) != implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43)))
| implies(implies(not(truth),not(X_43)),not(X_43)) != not(X_43)
| implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = implies(implies(X_43,not(truth)),not(X_43)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43)))) ),[1,1],$fot(not(X_43))]]) ).
cnf(refute_0_646,plain,
( implies(implies(not(truth),not(X_43)),not(X_43)) != not(X_43)
| implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = implies(implies(X_43,not(truth)),not(X_43)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43)))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) = implies(implies(X_43,not(truth)),not(X_43)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_43)),not(X_43)),not(X_43)) )],[refute_0_643,refute_0_646]) ).
cnf(refute_0_648,plain,
( implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) != implies(implies(X_43,not(truth)),not(X_43))
| implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) != truth
| implies(implies(X_43,not(truth)),not(X_43)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),truth) ),[0],$fot(implies(implies(X_43,not(truth)),not(X_43)))]]) ).
cnf(refute_0_649,plain,
( implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))) != truth
| implies(implies(X_43,not(truth)),not(X_43)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),implies(implies(X_43,not(truth)),not(X_43))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
implies(implies(X_43,not(truth)),not(X_43)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_43,not(truth)),implies(implies(not(truth),not(X_43)),not(X_43))),truth) )],[refute_0_634,refute_0_649]) ).
cnf(refute_0_651,plain,
implies(implies(X_125,not(truth)),not(X_125)) = truth,
inference(subst,[],[refute_0_650:[bind(X_43,$fot(X_125))]]) ).
cnf(refute_0_652,plain,
implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)))]]) ).
cnf(refute_0_653,plain,
( implies(implies(X_125,not(truth)),not(X_125)) != truth
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125))
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,not(X_125)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_654,plain,
( implies(implies(X_125,not(truth)),not(X_125)) != truth
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,not(X_125)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = implies(truth,not(X_125)),
inference(resolve,[$cnf( $equal(implies(implies(X_125,not(truth)),not(X_125)),truth) )],[refute_0_651,refute_0_654]) ).
cnf(refute_0_656,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(truth,not(X_125))
| implies(truth,not(X_125)) != not(X_125)
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = not(X_125) ),
inference(subst,[],[refute_0_75:[bind(X0,$fot(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)))),bind(Y0,$fot(implies(truth,not(X_125)))),bind(Z0,$fot(not(X_125)))]]) ).
cnf(refute_0_657,plain,
( implies(truth,not(X_125)) != not(X_125)
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = not(X_125) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(truth,not(X_125))) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) = not(X_125),
inference(resolve,[$cnf( $equal(implies(truth,not(X_125)),not(X_125)) )],[refute_0_627,refute_0_657]) ).
cnf(refute_0_659,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(truth,implies(X_125,not(truth)))
| implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != not(X_125)
| not(X_125) = implies(truth,implies(X_125,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(truth,implies(X_125,not(truth)))) ),[0],$fot(not(X_125))]]) ).
cnf(refute_0_660,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(truth,implies(X_125,not(truth)))
| not(X_125) = implies(truth,implies(X_125,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),not(X_125)) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
implies(truth,implies(X_125,not(truth))) = implies(X_125,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_125,not(truth))))]]) ).
cnf(refute_0_662,plain,
( implies(truth,implies(X_125,not(truth))) != implies(X_125,not(truth))
| not(X_125) != implies(truth,implies(X_125,not(truth)))
| not(X_125) = implies(X_125,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(X_125),implies(truth,implies(X_125,not(truth)))) ),[1],$fot(implies(X_125,not(truth)))]]) ).
cnf(refute_0_663,plain,
( not(X_125) != implies(truth,implies(X_125,not(truth)))
| not(X_125) = implies(X_125,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_125,not(truth))),implies(X_125,not(truth))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
( implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)) != implies(truth,implies(X_125,not(truth)))
| not(X_125) = implies(X_125,not(truth)) ),
inference(resolve,[$cnf( $equal(not(X_125),implies(truth,implies(X_125,not(truth)))) )],[refute_0_660,refute_0_663]) ).
cnf(refute_0_665,plain,
not(X_125) = implies(X_125,not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_125,not(truth)),not(X_125)),not(X_125)),implies(truth,implies(X_125,not(truth)))) )],[refute_0_626,refute_0_664]) ).
cnf(refute_0_666,plain,
not(implies(Y,not(truth))) = implies(implies(Y,not(truth)),not(truth)),
inference(subst,[],[refute_0_665:[bind(X_125,$fot(implies(Y,not(truth))))]]) ).
cnf(refute_0_667,plain,
( not(implies(Y,not(truth))) != implies(implies(Y,not(truth)),not(truth))
| implies(implies(Y,not(truth)),not(truth)) = not(implies(Y,not(truth))) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(not(implies(Y,not(truth))))),bind(Y0,$fot(implies(implies(Y,not(truth)),not(truth))))]]) ).
cnf(refute_0_668,plain,
implies(implies(Y,not(truth)),not(truth)) = not(implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(not(implies(Y,not(truth))),implies(implies(Y,not(truth)),not(truth))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
( implies(implies(Y,not(truth)),not(truth)) != not(implies(Y,not(truth)))
| implies(implies(not(truth),Y),Y) != implies(implies(Y,not(truth)),not(truth))
| implies(implies(not(truth),Y),Y) = not(implies(Y,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(Y,not(truth)),not(truth))) ),[1],$fot(not(implies(Y,not(truth))))]]) ).
cnf(refute_0_670,plain,
( implies(implies(not(truth),Y),Y) != implies(implies(Y,not(truth)),not(truth))
| implies(implies(not(truth),Y),Y) = not(implies(Y,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,not(truth)),not(truth)),not(implies(Y,not(truth)))) )],[refute_0_668,refute_0_669]) ).
cnf(refute_0_671,plain,
implies(implies(not(truth),Y),Y) = not(implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),implies(implies(Y,not(truth)),not(truth))) )],[refute_0_0,refute_0_670]) ).
cnf(refute_0_672,plain,
( implies(implies(not(truth),Y),Y) != Y
| implies(implies(not(truth),Y),Y) != not(implies(Y,not(truth)))
| Y = not(implies(Y,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),Y),Y),not(implies(Y,not(truth)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_673,plain,
( implies(implies(not(truth),Y),Y) != not(implies(Y,not(truth)))
| Y = not(implies(Y,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),Y) )],[refute_0_607,refute_0_672]) ).
cnf(refute_0_674,plain,
( not(X_125) != implies(X_125,not(truth))
| implies(X_125,not(truth)) = not(X_125) ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(not(X_125))),bind(Y0,$fot(implies(X_125,not(truth))))]]) ).
cnf(refute_0_675,plain,
implies(X_125,not(truth)) = not(X_125),
inference(resolve,[$cnf( $equal(not(X_125),implies(X_125,not(truth))) )],[refute_0_665,refute_0_674]) ).
cnf(refute_0_676,plain,
implies(Y,not(truth)) = not(Y),
inference(subst,[],[refute_0_675:[bind(X_125,$fot(Y))]]) ).
cnf(refute_0_677,plain,
not(implies(Y,not(truth))) = not(implies(Y,not(truth))),
introduced(tautology,[refl,[$fot(not(implies(Y,not(truth))))]]) ).
cnf(refute_0_678,plain,
( implies(Y,not(truth)) != not(Y)
| not(implies(Y,not(truth))) != not(implies(Y,not(truth)))
| not(implies(Y,not(truth))) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(Y,not(truth))),not(implies(Y,not(truth)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_679,plain,
( implies(Y,not(truth)) != not(Y)
| not(implies(Y,not(truth))) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(implies(Y,not(truth))),not(implies(Y,not(truth)))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
not(implies(Y,not(truth))) = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(Y,not(truth)),not(Y)) )],[refute_0_676,refute_0_679]) ).
cnf(refute_0_681,plain,
( Y != not(implies(Y,not(truth)))
| not(implies(Y,not(truth))) != not(not(Y))
| Y = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(Y))) ),[0],$fot(not(implies(Y,not(truth))))]]) ).
cnf(refute_0_682,plain,
( Y != not(implies(Y,not(truth)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(not(implies(Y,not(truth))),not(not(Y))) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
( implies(implies(not(truth),Y),Y) != not(implies(Y,not(truth)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,not(implies(Y,not(truth)))) )],[refute_0_673,refute_0_682]) ).
cnf(refute_0_684,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),Y),Y),not(implies(Y,not(truth)))) )],[refute_0_671,refute_0_683]) ).
cnf(refute_0_685,plain,
( Y != not(not(Y))
| not(not(Y)) = Y ),
inference(subst,[],[refute_0_14:[bind(X0,$fot(Y)),bind(Y0,$fot(not(not(Y))))]]) ).
cnf(refute_0_686,plain,
not(not(Y)) = Y,
inference(resolve,[$cnf( $equal(Y,not(not(Y))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
not(not(x)) = x,
inference(subst,[],[refute_0_686:[bind(Y,$fot(x))]]) ).
cnf(refute_0_688,plain,
( not(not(x)) != x
| x != x
| not(not(x)) = x ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(not(x)),x) ),[0],$fot(x)]]) ).
cnf(refute_0_689,plain,
( x != x
| not(not(x)) = x ),
inference(resolve,[$cnf( $equal(not(not(x)),x) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
x != x,
inference(resolve,[$cnf( $equal(not(not(x)),x) )],[refute_0_689,prove_wajsberg_lemma]) ).
cnf(refute_0_691,plain,
x = x,
introduced(tautology,[refl,[$fot(x)]]) ).
cnf(refute_0_692,plain,
$false,
inference(resolve,[$cnf( $equal(x,x) )],[refute_0_691,refute_0_690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL140-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jul 3 16:52:31 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.84/9.99 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.84/9.99
% 9.84/9.99 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.93/10.08
%------------------------------------------------------------------------------