%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL139-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:41:58 PM UTC 2026
% Result : Unsatisfiable 0.31s 0.59s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 89
% Number of leaves : 97
% Syntax : Number of clauses : 347 ( 177 unt; 0 nHn; 197 RR)
% Number of literals : 600 ( 599 equ; 255 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 : 373 ( 20 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_wajsberg_lemma,negated_conjecture,
implies(x,not(truth)) != not(x) ).
cnf(refute_0_0,plain,
implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(implies(not(X_33),implies(X_33,not(truth))),implies(X_33,not(truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_33,not(truth)))),bind(Y,$fot(not(X_33)))]]) ).
cnf(refute_0_1,plain,
implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_2,plain,
implies(implies(not(X_4),not(truth)),implies(truth,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_3,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_4,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_5,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( $equal(implies(truth,X_4),X_4) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(implies(not(X_4),not(truth)),X_4) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_6:[bind(X_4,$fot(not(truth)))]]) ).
cnf(refute_0_8,plain,
implies(implies(X,not(truth)),not(truth)) = implies(implies(not(truth),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_9,plain,
implies(implies(X_10,implies(not(X_12),not(truth))),implies(implies(implies(not(X_12),not(truth)),X_12),implies(X_10,X_12))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_10)),bind(Y,$fot(implies(not(X_12),not(truth)))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_10,plain,
implies(implies(not(X_12),not(truth)),X_12) = truth,
inference(subst,[],[refute_0_6:[bind(X_4,$fot(X_12))]]) ).
cnf(refute_0_11,plain,
( implies(implies(X_10,implies(not(X_12),not(truth))),implies(implies(implies(not(X_12),not(truth)),X_12),implies(X_10,X_12))) != truth
| implies(implies(not(X_12),not(truth)),X_12) != truth
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(implies(implies(not(X_12),not(truth)),X_12),implies(X_10,X_12))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_12,plain,
( implies(implies(X_10,implies(not(X_12),not(truth))),implies(implies(implies(not(X_12),not(truth)),X_12),implies(X_10,X_12))) != truth
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_12),not(truth)),X_12),truth) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(implies(implies(not(X_12),not(truth)),X_12),implies(X_10,X_12))),truth) )],[refute_0_9,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(truth,implies(X_10,X_12)) = implies(X_10,X_12),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_10,X_12)))]]) ).
cnf(refute_0_15,plain,
implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),
introduced(tautology,[refl,[$fot(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))))]]) ).
cnf(refute_0_16,plain,
( implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) != implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12)))
| implies(truth,implies(X_10,X_12)) != implies(X_10,X_12)
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12)))) ),[1,1],$fot(implies(X_10,X_12))]]) ).
cnf(refute_0_17,plain,
( implies(truth,implies(X_10,X_12)) != implies(X_10,X_12)
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) = implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_10,X_12)),implies(X_10,X_12)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) != implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12))
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) != truth
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),truth) ),[0],$fot(implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)))]]) ).
cnf(refute_0_20,plain,
( implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))) != truth
| implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(implies(X_10,implies(not(X_12),not(truth))),implies(X_10,X_12)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_10,implies(not(X_12),not(truth))),implies(truth,implies(X_10,X_12))),truth) )],[refute_0_13,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(not(truth),implies(not(X_25),not(truth))),implies(not(truth),X_25)) = truth,
inference(subst,[],[refute_0_21:[bind(X_10,$fot(not(truth))),bind(X_12,$fot(X_25))]]) ).
cnf(refute_0_23,plain,
implies(implies(X_10,truth),implies(implies(truth,X_12),implies(X_10,X_12))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_10)),bind(Y,$fot(truth)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_24,plain,
implies(truth,X_12) = X_12,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_25,plain,
( implies(implies(X_10,truth),implies(implies(truth,X_12),implies(X_10,X_12))) != truth
| implies(truth,X_12) != X_12
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,truth),implies(implies(truth,X_12),implies(X_10,X_12))),truth) ),[0,1,0],$fot(X_12)]]) ).
cnf(refute_0_26,plain,
( implies(implies(X_10,truth),implies(implies(truth,X_12),implies(X_10,X_12))) != truth
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_12),X_12) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_10,truth),implies(implies(truth,X_12),implies(X_10,X_12))),truth) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(truth,implies(X_12,implies(X_10,X_12))) = implies(X_12,implies(X_10,X_12)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_12,implies(X_10,X_12))))]]) ).
cnf(refute_0_29,plain,
implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(X_11)),bind(Z,$fot(implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_30,plain,
implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_31,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_32,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_33,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_34,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( $equal(implies(truth,X_2),X_2) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(X_4,X_4) = implies(implies(X_4,truth),truth),
inference(subst,[],[refute_0_35:[bind(X_2,$fot(X_4))]]) ).
cnf(refute_0_37,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_38,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( $equal(implies(X_4,X_4),implies(implies(X_4,truth),truth)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(X_4,X_4)),truth) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_41,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))) != truth
| implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)))),truth) )],[refute_0_29,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(truth,X_11) = X_11,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_44,plain,
implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),bind(Y,$fot(truth)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_45,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) = truth,
inference(subst,[],[refute_0_39:[bind(X_4,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_46,plain,
implies(implies(not(truth),not(truth)),truth) = truth,
inference(subst,[],[refute_0_6:[bind(X_4,$fot(truth))]]) ).
cnf(refute_0_47,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
| implies(implies(not(truth),not(truth)),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_48,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)) != truth
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),truth),truth) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(implies(not(truth),not(truth)),truth),truth)),truth) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_51,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))]]) ).
cnf(refute_0_52,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
| implies(truth,truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_53,plain,
( implies(truth,truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
inference(subst,[],[refute_0_35:[bind(X_2,$fot(not(implies(not(truth),not(truth)))))]]) ).
cnf(refute_0_56,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))]]) ).
cnf(refute_0_57,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))
| implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) ),[1,0],$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).
cnf(refute_0_58,plain,
( implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_61,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_62,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_64,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)))),bind(Y0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)))),bind(Z0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)))]]) ).
cnf(refute_0_66,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth))) )],[refute_0_59,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_54,refute_0_66]) ).
cnf(refute_0_68,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) ),[0],$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth))]]) ).
cnf(refute_0_69,plain,
( implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))),implies(truth,truth)),truth) )],[refute_0_49,refute_0_69]) ).
cnf(refute_0_71,plain,
( implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) != truth
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_72,plain,
( implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != truth
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),truth) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),truth) )],[refute_0_44,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_75,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_76,plain,
implies(not(X_5),not(X_5)) = implies(implies(not(X_5),truth),truth),
inference(subst,[],[refute_0_35:[bind(X_2,$fot(not(X_5)))]]) ).
cnf(refute_0_77,plain,
( implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)) != truth
| implies(not(X_5),not(X_5)) != implies(implies(not(X_5),truth),truth)
| implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth ),
introduced(tautology,[equality,[$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_78,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( $equal(implies(not(X_5),not(X_5)),implies(implies(not(X_5),truth),truth)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(implies(implies(not(X_5),truth),truth),implies(X_5,X_5)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_5),not(X_5)),implies(X_5,X_5)),truth) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
inference(subst,[],[refute_0_79:[bind(X_5,$fot(truth))]]) ).
cnf(refute_0_81,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_82,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( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_74,refute_0_82]) ).
cnf(refute_0_84,plain,
( implies(X_2,X_2) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,truth),truth) = implies(X_2,X_2) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(implies(X_2,X_2))),bind(Y0,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_85,plain,
implies(implies(X_2,truth),truth) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),implies(implies(X_2,truth),truth)) )],[refute_0_35,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_85:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_87,plain,
implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).
cnf(refute_0_88,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).
cnf(refute_0_89,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_90,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( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(truth,implies(not(truth),truth)),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_93,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( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_86,refute_0_93]) ).
cnf(refute_0_95,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).
cnf(refute_0_96,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_83,refute_0_96]) ).
cnf(refute_0_98,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),truth),truth) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(truth),truth),truth))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_99,plain,
( implies(not(truth),not(truth)) != truth
| implies(implies(not(truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_86,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(implies(not(truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_97,refute_0_99]) ).
cnf(refute_0_101,plain,
not(implies(not(truth),not(truth))) = not(implies(not(truth),not(truth))),
introduced(tautology,[refl,[$fot(not(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_102,plain,
( implies(not(truth),not(truth)) != truth
| not(implies(not(truth),not(truth))) != not(implies(not(truth),not(truth)))
| not(implies(not(truth),not(truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_103,plain,
( implies(not(truth),not(truth)) != truth
| not(implies(not(truth),not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(implies(not(truth),not(truth)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
not(implies(not(truth),not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_97,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(not(implies(not(truth),not(truth))),truth) = implies(not(implies(not(truth),not(truth))),truth),
introduced(tautology,[refl,[$fot(implies(not(implies(not(truth),not(truth))),truth))]]) ).
cnf(refute_0_106,plain,
( implies(not(implies(not(truth),not(truth))),truth) != implies(not(implies(not(truth),not(truth))),truth)
| not(implies(not(truth),not(truth))) != not(truth)
| implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_107,plain,
( not(implies(not(truth),not(truth))) != not(truth)
| implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(implies(not(truth),not(truth))),truth)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(not(implies(not(truth),not(truth))),truth) = implies(not(truth),truth),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(truth))),not(truth)) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(implies(not(truth),not(truth))),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))]]) ).
cnf(refute_0_110,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(implies(not(truth),not(truth))),truth),truth)
| implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).
cnf(refute_0_111,plain,
( implies(not(implies(not(truth),not(truth))),truth) != implies(not(truth),truth)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(implies(not(truth),not(truth))),truth),truth)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(not(implies(not(truth),not(truth))),truth),implies(not(truth),truth)) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(not(truth),truth),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(implies(not(truth),not(truth))),truth),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_114,plain,
( implies(implies(not(truth),truth),truth) != truth
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(implies(not(implies(not(truth),not(truth))),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),truth) )],[refute_0_100,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))]]) ).
cnf(refute_0_117,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) != implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)
| implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = implies(truth,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_118,plain,
( implies(implies(not(implies(not(truth),not(truth))),truth),truth) != truth
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = implies(truth,X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = implies(truth,X_12),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(truth),not(truth))),truth),truth),truth) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) != implies(truth,X_12)
| implies(truth,X_12) != X_12
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = X_12 ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),bind(Y0,$fot(implies(truth,X_12))),bind(Z0,$fot(X_12))]]) ).
cnf(refute_0_121,plain,
( implies(truth,X_12) != X_12
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = X_12 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12),implies(truth,X_12)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) = X_12,
inference(resolve,[$cnf( $equal(implies(truth,X_12),X_12) )],[refute_0_24,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),
introduced(tautology,[refl,[$fot(implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)))]]) ).
cnf(refute_0_124,plain,
( implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))
| implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) != X_12
| implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_125,plain,
( implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12) != X_12
| implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12) ),
inference(resolve,[$cnf( $equal(implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12),X_12) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)))]]) ).
cnf(refute_0_128,plain,
( implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))
| implies(truth,X_12) != X_12
| implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) ),[1,0],$fot(X_12)]]) ).
cnf(refute_0_129,plain,
( implies(truth,X_12) != X_12
| implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),
inference(resolve,[$cnf( $equal(implies(truth,X_12),X_12) )],[refute_0_24,refute_0_129]) ).
cnf(refute_0_131,plain,
( implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,X_12)
| implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))
| implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)))),bind(Y0,$fot(implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)))),bind(Z0,$fot(implies(X_12,X_12)))]]) ).
cnf(refute_0_132,plain,
( implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,X_12)
| implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) = implies(X_12,X_12),
inference(resolve,[$cnf( $equal(implies(X_12,implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(X_12,X_12)) )],[refute_0_126,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))))]]) ).
cnf(refute_0_135,plain,
( implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,X_12)
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = implies(X_12,X_12) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))))),bind(Y0,$fot(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)))),bind(Z0,$fot(implies(X_12,X_12)))]]) ).
cnf(refute_0_136,plain,
( implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)) != implies(X_12,X_12)
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = implies(X_12,X_12) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) = implies(X_12,X_12),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12)),implies(X_12,X_12)) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != implies(X_12,X_12)
| implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != truth
| implies(X_12,X_12) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),truth) ),[0],$fot(implies(X_12,X_12))]]) ).
cnf(refute_0_139,plain,
( implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))) != truth
| implies(X_12,X_12) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),implies(X_12,X_12)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(X_12,X_12) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_12),implies(implies(implies(not(implies(not(truth),not(truth))),truth),truth),X_12))),truth) )],[refute_0_73,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(not(X_4),not(X_4)) = truth,
inference(subst,[],[refute_0_140:[bind(X_12,$fot(not(X_4)))]]) ).
cnf(refute_0_142,plain,
implies(implies(not(X_4),not(X_4)),X_11) = implies(implies(not(X_4),not(X_4)),X_11),
introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_11))]]) ).
cnf(refute_0_143,plain,
( implies(implies(not(X_4),not(X_4)),X_11) != implies(implies(not(X_4),not(X_4)),X_11)
| implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_11) = implies(truth,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(not(X_4),not(X_4)),X_11)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_144,plain,
( implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_11) = implies(truth,X_11) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(not(X_4),not(X_4)),X_11)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
implies(implies(not(X_4),not(X_4)),X_11) = implies(truth,X_11),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
( implies(implies(not(X_4),not(X_4)),X_11) != implies(truth,X_11)
| implies(truth,X_11) != X_11
| implies(implies(not(X_4),not(X_4)),X_11) = X_11 ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_11))),bind(Y0,$fot(implies(truth,X_11))),bind(Z0,$fot(X_11))]]) ).
cnf(refute_0_147,plain,
( implies(truth,X_11) != X_11
| implies(implies(not(X_4),not(X_4)),X_11) = X_11 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_11),implies(truth,X_11)) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
implies(implies(not(X_4),not(X_4)),X_11) = X_11,
inference(resolve,[$cnf( $equal(implies(truth,X_11),X_11) )],[refute_0_43,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_150,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))
| implies(implies(not(X_4),not(X_4)),X_11) != X_11
| implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))) ),[1,0],$fot(X_11)]]) ).
cnf(refute_0_151,plain,
( implies(implies(not(X_4),not(X_4)),X_11) != X_11
| implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_11),X_11) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))
| implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_154,plain,
( implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),X_11),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_42,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(X_9,truth),truth))),bind(Y,$fot(implies(not(X_9),not(X_9))))]]) ).
cnf(refute_0_157,plain,
implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)) = truth,
inference(subst,[],[refute_0_39:[bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_158,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))
| implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)) != truth
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_159,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),truth) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(truth,implies(implies(X_9,truth),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(implies(not(X_9),not(X_9)),implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth))) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(truth,implies(implies(X_9,truth),truth)) = implies(implies(X_9,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_162,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(truth,implies(implies(X_9,truth),truth))
| implies(truth,implies(implies(X_9,truth),truth)) != implies(implies(X_9,truth),truth)
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) ),[0],$fot(implies(truth,implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_163,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(truth,implies(implies(X_9,truth),truth))
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_9,truth),truth)),implies(implies(X_9,truth),truth)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = implies(implies(X_9,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(truth,implies(implies(X_9,truth),truth))) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_4),not(X_4)))),bind(Y,$fot(implies(implies(X_4,truth),truth))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_166,plain,
( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != truth
| implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)) != truth
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_167,plain,
( implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != truth
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),truth) )],[refute_0_39,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_4),not(X_4)),implies(implies(X_4,truth),truth)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),truth) )],[refute_0_165,refute_0_167]) ).
cnf(refute_0_169,plain,
implies(implies(not(X_4),not(X_4)),X_12) = implies(implies(not(X_4),not(X_4)),X_12),
introduced(tautology,[refl,[$fot(implies(implies(not(X_4),not(X_4)),X_12))]]) ).
cnf(refute_0_170,plain,
( implies(implies(not(X_4),not(X_4)),X_12) != implies(implies(not(X_4),not(X_4)),X_12)
| implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_12) = implies(truth,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_12),implies(implies(not(X_4),not(X_4)),X_12)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_171,plain,
( implies(not(X_4),not(X_4)) != truth
| implies(implies(not(X_4),not(X_4)),X_12) = implies(truth,X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_12),implies(implies(not(X_4),not(X_4)),X_12)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(implies(not(X_4),not(X_4)),X_12) = implies(truth,X_12),
inference(resolve,[$cnf( $equal(implies(not(X_4),not(X_4)),truth) )],[refute_0_141,refute_0_171]) ).
cnf(refute_0_173,plain,
( implies(implies(not(X_4),not(X_4)),X_12) != implies(truth,X_12)
| implies(truth,X_12) != X_12
| implies(implies(not(X_4),not(X_4)),X_12) = X_12 ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(X_4),not(X_4)),X_12))),bind(Y0,$fot(implies(truth,X_12))),bind(Z0,$fot(X_12))]]) ).
cnf(refute_0_174,plain,
( implies(truth,X_12) != X_12
| implies(implies(not(X_4),not(X_4)),X_12) = X_12 ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_12),implies(truth,X_12)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(not(X_4),not(X_4)),X_12) = X_12,
inference(resolve,[$cnf( $equal(implies(truth,X_12),X_12) )],[refute_0_24,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) = implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)))]]) ).
cnf(refute_0_177,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) != implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))
| implies(implies(not(X_4),not(X_4)),X_12) != X_12
| implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) ),[1,1],$fot(X_12)]]) ).
cnf(refute_0_178,plain,
( implies(implies(not(X_4),not(X_4)),X_12) != X_12
| implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12),
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(X_4)),X_12),X_12) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))))]]) ).
cnf(refute_0_181,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) != implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))))),bind(Y0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)))),bind(Z0,$fot(implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)))]]) ).
cnf(refute_0_182,plain,
( implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)) != implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) = implies(implies(implies(implies(X_4,truth),truth),X_12),X_12),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12)),implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)
| implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != truth
| implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),truth) ),[0],$fot(implies(implies(implies(implies(X_4,truth),truth),X_12),X_12))]]) ).
cnf(refute_0_185,plain,
( implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))) != truth
| implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),implies(implies(implies(implies(X_4,truth),truth),X_12),X_12)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(implies(implies(implies(X_4,truth),truth),X_12),X_12) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X_4,truth),truth),X_12),implies(implies(not(X_4),not(X_4)),X_12))),truth) )],[refute_0_168,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) = truth,
inference(subst,[],[refute_0_186:[bind(X_12,$fot(implies(not(X_9),not(X_9)))),bind(X_4,$fot(X_9))]]) ).
cnf(refute_0_188,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(X_9,truth),truth)
| implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != truth
| truth = implies(implies(X_9,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_189,plain,
( implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))) != implies(implies(X_9,truth),truth)
| truth = implies(implies(X_9,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),truth) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
truth = implies(implies(X_9,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_9,truth),truth),implies(not(X_9),not(X_9))),implies(not(X_9),not(X_9))),implies(implies(X_9,truth),truth)) )],[refute_0_164,refute_0_189]) ).
cnf(refute_0_191,plain,
( truth != implies(implies(X_9,truth),truth)
| implies(implies(X_9,truth),truth) = truth ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X_9,truth),truth)))]]) ).
cnf(refute_0_192,plain,
implies(implies(X_9,truth),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(X_9,truth),truth)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(X_11,truth),truth) = truth,
inference(subst,[],[refute_0_192:[bind(X_9,$fot(X_11))]]) ).
cnf(refute_0_194,plain,
implies(implies(X_4,truth),truth) = truth,
inference(subst,[],[refute_0_192:[bind(X_9,$fot(X_4))]]) ).
cnf(refute_0_195,plain,
implies(X_11,implies(implies(X_4,truth),truth)) = implies(X_11,implies(implies(X_4,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_11,implies(implies(X_4,truth),truth)))]]) ).
cnf(refute_0_196,plain,
( implies(X_11,implies(implies(X_4,truth),truth)) != implies(X_11,implies(implies(X_4,truth),truth))
| implies(implies(X_4,truth),truth) != truth
| implies(X_11,implies(implies(X_4,truth),truth)) = implies(X_11,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_11,implies(implies(X_4,truth),truth)),implies(X_11,implies(implies(X_4,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_197,plain,
( implies(implies(X_4,truth),truth) != truth
| implies(X_11,implies(implies(X_4,truth),truth)) = implies(X_11,truth) ),
inference(resolve,[$cnf( $equal(implies(X_11,implies(implies(X_4,truth),truth)),implies(X_11,implies(implies(X_4,truth),truth))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(X_11,implies(implies(X_4,truth),truth)) = implies(X_11,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_4,truth),truth),truth) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_11,implies(implies(X_4,truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))]]) ).
cnf(refute_0_200,plain,
( implies(X_11,implies(implies(X_4,truth),truth)) != implies(X_11,truth)
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_11,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) ),[1,0],$fot(implies(X_11,truth))]]) ).
cnf(refute_0_201,plain,
( implies(X_11,implies(implies(X_4,truth),truth)) != implies(X_11,truth)
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_11,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth),implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = implies(implies(X_11,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_11,implies(implies(X_4,truth),truth)),implies(X_11,truth)) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) != implies(implies(X_11,truth),truth)
| implies(implies(X_11,truth),truth) != truth
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))),bind(Y0,$fot(implies(implies(X_11,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_204,plain,
( implies(implies(X_11,truth),truth) != truth
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth),implies(implies(X_11,truth),truth)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_11,truth),truth),truth) )],[refute_0_193,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),
introduced(tautology,[refl,[$fot(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)))]]) ).
cnf(refute_0_207,plain,
( implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))
| implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) != truth
| implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_208,plain,
( implies(implies(X_11,implies(implies(X_4,truth),truth)),truth) != truth
| implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,truth) ),
inference(resolve,[$cnf( $equal(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) = implies(X_11,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_11,implies(implies(X_4,truth),truth)),truth),truth) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != implies(X_11,truth)
| implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_11,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),truth) ),[0],$fot(implies(X_11,truth))]]) ).
cnf(refute_0_211,plain,
( implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)) != truth
| implies(X_11,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),implies(X_11,truth)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
implies(X_11,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_11,implies(implies(X_11,implies(implies(X_4,truth),truth)),truth)),truth) )],[refute_0_155,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(X_10,truth) = truth,
inference(subst,[],[refute_0_212:[bind(X_11,$fot(X_10))]]) ).
cnf(refute_0_214,plain,
implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),
introduced(tautology,[refl,[$fot(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))))]]) ).
cnf(refute_0_215,plain,
( implies(X_10,truth) != truth
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) != implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12)))
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(truth,implies(X_12,implies(X_10,X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_216,plain,
( implies(X_10,truth) != truth
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(truth,implies(X_12,implies(X_10,X_12))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12)))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(truth,implies(X_12,implies(X_10,X_12))),
inference(resolve,[$cnf( $equal(implies(X_10,truth),truth) )],[refute_0_213,refute_0_216]) ).
cnf(refute_0_218,plain,
( implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) != implies(truth,implies(X_12,implies(X_10,X_12)))
| implies(truth,implies(X_12,implies(X_10,X_12))) != implies(X_12,implies(X_10,X_12))
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(X_12,implies(X_10,X_12)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))))),bind(Y0,$fot(implies(truth,implies(X_12,implies(X_10,X_12))))),bind(Z0,$fot(implies(X_12,implies(X_10,X_12))))]]) ).
cnf(refute_0_219,plain,
( implies(truth,implies(X_12,implies(X_10,X_12))) != implies(X_12,implies(X_10,X_12))
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(X_12,implies(X_10,X_12)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),implies(truth,implies(X_12,implies(X_10,X_12)))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) = implies(X_12,implies(X_10,X_12)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_12,implies(X_10,X_12))),implies(X_12,implies(X_10,X_12))) )],[refute_0_28,refute_0_219]) ).
cnf(refute_0_221,plain,
( implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) != implies(X_12,implies(X_10,X_12))
| implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) != truth
| implies(X_12,implies(X_10,X_12)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),truth) ),[0],$fot(implies(X_12,implies(X_10,X_12)))]]) ).
cnf(refute_0_222,plain,
( implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))) != truth
| implies(X_12,implies(X_10,X_12)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),implies(X_12,implies(X_10,X_12))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(X_12,implies(X_10,X_12)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_10,truth),implies(X_12,implies(X_10,X_12))),truth) )],[refute_0_27,refute_0_222]) ).
cnf(refute_0_224,plain,
implies(not(truth),implies(not(X_25),not(truth))) = truth,
inference(subst,[],[refute_0_223:[bind(X_10,$fot(not(X_25))),bind(X_12,$fot(not(truth)))]]) ).
cnf(refute_0_225,plain,
( implies(implies(not(truth),implies(not(X_25),not(truth))),implies(not(truth),X_25)) != truth
| implies(not(truth),implies(not(X_25),not(truth))) != truth
| implies(truth,implies(not(truth),X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(X_25),not(truth))),implies(not(truth),X_25)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_226,plain,
( implies(implies(not(truth),implies(not(X_25),not(truth))),implies(not(truth),X_25)) != truth
| implies(truth,implies(not(truth),X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(X_25),not(truth))),truth) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(truth,implies(not(truth),X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(X_25),not(truth))),implies(not(truth),X_25)),truth) )],[refute_0_22,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(truth,implies(not(truth),X_25)) = implies(not(truth),X_25),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X_25)))]]) ).
cnf(refute_0_229,plain,
( implies(truth,implies(not(truth),X_25)) != implies(not(truth),X_25)
| implies(truth,implies(not(truth),X_25)) != truth
| implies(not(truth),X_25) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(truth),X_25)),truth) ),[0],$fot(implies(not(truth),X_25))]]) ).
cnf(refute_0_230,plain,
( implies(truth,implies(not(truth),X_25)) != truth
| implies(not(truth),X_25) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_25)),implies(not(truth),X_25)) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
implies(not(truth),X_25) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_25)),truth) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
implies(not(truth),X) = truth,
inference(subst,[],[refute_0_231:[bind(X_25,$fot(X))]]) ).
cnf(refute_0_233,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(not(truth),X) != truth
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_234,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(not(truth),X),truth) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
implies(implies(X,not(truth)),not(truth)) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) )],[refute_0_8,refute_0_234]) ).
cnf(refute_0_236,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(truth,X) != X
| implies(implies(X,not(truth)),not(truth)) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,not(truth)),not(truth)),X) ),[0],$fot(implies(truth,X))]]) ).
cnf(refute_0_237,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(implies(X,not(truth)),not(truth)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(implies(X,not(truth)),not(truth)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = not(not(truth)),
inference(subst,[],[refute_0_238:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_240,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != not(not(truth))
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_241,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_7,refute_0_241]) ).
cnf(refute_0_243,plain,
( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_244,plain,
( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) )],[refute_0_1,refute_0_244]) ).
cnf(refute_0_246,plain,
implies(truth,not(Y)) = not(Y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_247,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(implies(truth,not(Y)),implies(Y,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(Y)),implies(Y,not(truth))))]]) ).
cnf(refute_0_248,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(implies(truth,not(Y)),implies(Y,not(truth)))
| implies(truth,not(Y)) != not(Y)
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_249,plain,
( implies(truth,not(Y)) != not(Y)
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(Y)),not(Y)) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(not(Y),implies(Y,not(truth)))
| implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) ),[0],$fot(implies(not(Y),implies(Y,not(truth))))]]) ).
cnf(refute_0_252,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(not(Y),implies(Y,not(truth)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
implies(not(Y),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) )],[refute_0_245,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(not(X_33),implies(X_33,not(truth))) = truth,
inference(subst,[],[refute_0_253:[bind(Y,$fot(X_33))]]) ).
cnf(refute_0_255,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(implies(not(X_33),implies(X_33,not(truth))),implies(X_33,not(truth)))
| implies(not(X_33),implies(X_33,not(truth))) != truth
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,implies(X_33,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(implies(not(X_33),implies(X_33,not(truth))),implies(X_33,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_256,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(implies(not(X_33),implies(X_33,not(truth))),implies(X_33,not(truth)))
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,implies(X_33,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(X_33),implies(X_33,not(truth))),truth) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,implies(X_33,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(implies(not(X_33),implies(X_33,not(truth))),implies(X_33,not(truth)))) )],[refute_0_0,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(truth,not(X_33)) = not(X_33),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_33)))]]) ).
cnf(refute_0_259,plain,
implies(implies(not(not(X_32)),not(truth)),not(X_32)) = truth,
inference(subst,[],[refute_0_6:[bind(X_4,$fot(not(X_32)))]]) ).
cnf(refute_0_260,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(Y,not(not(Y))),not(not(Y))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_261,plain,
implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_262,plain,
implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth,
inference(subst,[],[refute_0_21:[bind(X_10,$fot(implies(not(not(truth)),not(not(X_25))))),bind(X_12,$fot(X_25))]]) ).
cnf(refute_0_263,plain,
implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_264,plain,
( implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_265,plain,
( implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),truth) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = implies(implies(not(not(truth)),not(not(X_25))),X_25),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25)))]]) ).
cnf(refute_0_268,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != implies(implies(not(not(truth)),not(not(X_25))),X_25)
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25))]]) ).
cnf(refute_0_269,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),implies(implies(not(not(truth)),not(not(X_25))),X_25)) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
implies(truth,not(not(X_25))) = not(not(X_25)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_25))))]]) ).
cnf(refute_0_272,plain,
implies(not(not(truth)),not(not(X_25))) = implies(not(not(truth)),not(not(X_25))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_25))))]]) ).
cnf(refute_0_273,plain,
( implies(not(not(truth)),not(not(X_25))) != implies(not(not(truth)),not(not(X_25)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(not(not(truth)),not(not(X_25)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_274,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(not(not(truth)),not(not(X_25)))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_242,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(not(not(truth)),not(not(X_25))) != implies(truth,not(not(X_25)))
| implies(truth,not(not(X_25))) != not(not(X_25))
| implies(not(not(truth)),not(not(X_25))) = not(not(X_25)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(not(not(truth)),not(not(X_25))))),bind(Y0,$fot(implies(truth,not(not(X_25))))),bind(Z0,$fot(not(not(X_25))))]]) ).
cnf(refute_0_277,plain,
( implies(truth,not(not(X_25))) != not(not(X_25))
| implies(not(not(truth)),not(not(X_25))) = not(not(X_25)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(truth,not(not(X_25)))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(not(not(truth)),not(not(X_25))) = not(not(X_25)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_25))),not(not(X_25))) )],[refute_0_271,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(implies(not(not(truth)),not(not(X_25))),X_25),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25))]]) ).
cnf(refute_0_280,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != implies(implies(not(not(truth)),not(not(X_25))),X_25)
| implies(not(not(truth)),not(not(X_25))) != not(not(X_25))
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(implies(not(not(truth)),not(not(X_25))),X_25)) ),[1,0],$fot(not(not(X_25)))]]) ).
cnf(refute_0_281,plain,
( implies(not(not(truth)),not(not(X_25))) != not(not(X_25))
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(implies(not(not(truth)),not(not(X_25))),X_25)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),not(not(X_25))) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != implies(not(not(X_25)),X_25)
| implies(implies(not(not(truth)),not(not(X_25))),X_25) != truth
| implies(not(not(X_25)),X_25) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),truth) ),[0],$fot(implies(not(not(X_25)),X_25))]]) ).
cnf(refute_0_284,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != truth
| implies(not(not(X_25)),X_25) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(not(not(X_25)),X_25)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
implies(not(not(X_25)),X_25) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),truth) )],[refute_0_270,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(not(not(not(Y))),not(Y)) = truth,
inference(subst,[],[refute_0_285:[bind(X_25,$fot(not(Y)))]]) ).
cnf(refute_0_287,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(not(not(not(Y))),not(Y)) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_288,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(Y)),truth) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(truth,implies(Y,not(not(Y)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) )],[refute_0_261,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(truth,implies(Y,not(not(Y)))) = implies(Y,not(not(Y))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(not(Y)))))]]) ).
cnf(refute_0_291,plain,
( implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
| implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) ),[0],$fot(implies(Y,not(not(Y))))]]) ).
cnf(refute_0_292,plain,
( implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(Y,not(not(Y))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( implies(Y,not(not(Y))) != truth
| implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_295,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(Y,not(not(Y))),not(not(Y)))
| implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(Y,not(not(Y))),truth) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(Y,not(not(Y))),not(not(Y)))) )],[refute_0_260,refute_0_295]) ).
cnf(refute_0_297,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_298,plain,
implies(not(not(Y)),Y) = truth,
inference(subst,[],[refute_0_285:[bind(X_25,$fot(Y))]]) ).
cnf(refute_0_299,plain,
implies(implies(not(not(Y)),Y),Y) = implies(implies(not(not(Y)),Y),Y),
introduced(tautology,[refl,[$fot(implies(implies(not(not(Y)),Y),Y))]]) ).
cnf(refute_0_300,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(implies(not(not(Y)),Y),Y)
| implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_301,plain,
( implies(not(not(Y)),Y) != truth
| implies(implies(not(not(Y)),Y),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
implies(implies(not(not(Y)),Y),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(not(not(Y)),Y),Y))),bind(Y0,$fot(implies(truth,Y))),bind(Z0,$fot(Y))]]) ).
cnf(refute_0_304,plain,
( implies(truth,Y) != Y
| implies(implies(not(not(Y)),Y),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,Y)) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
implies(implies(not(not(Y)),Y),Y) = Y,
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_297,refute_0_304]) ).
cnf(refute_0_306,plain,
( implies(implies(not(not(Y)),Y),Y) != Y
| implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) ),[0],$fot(Y)]]) ).
cnf(refute_0_307,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = implies(truth,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),Y) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(truth,not(not(Y))) = not(not(Y)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_309,plain,
( Y != implies(truth,not(not(Y)))
| implies(truth,not(not(Y))) != not(not(Y))
| Y = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Y,not(not(Y))) ),[0],$fot(implies(truth,not(not(Y))))]]) ).
cnf(refute_0_310,plain,
( Y != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(Y))),not(not(Y))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
( implies(implies(not(not(Y)),Y),Y) != implies(truth,not(not(Y)))
| Y = not(not(Y)) ),
inference(resolve,[$cnf( $equal(Y,implies(truth,not(not(Y)))) )],[refute_0_307,refute_0_310]) ).
cnf(refute_0_312,plain,
Y = not(not(Y)),
inference(resolve,[$cnf( $equal(implies(implies(not(not(Y)),Y),Y),implies(truth,not(not(Y)))) )],[refute_0_296,refute_0_311]) ).
cnf(refute_0_313,plain,
X_32 = not(not(X_32)),
inference(subst,[],[refute_0_312:[bind(Y,$fot(X_32))]]) ).
cnf(refute_0_314,plain,
( X_32 != not(not(X_32))
| not(not(X_32)) = X_32 ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(X_32)),bind(Y0,$fot(not(not(X_32))))]]) ).
cnf(refute_0_315,plain,
not(not(X_32)) = X_32,
inference(resolve,[$cnf( $equal(X_32,not(not(X_32))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
( implies(implies(not(not(X_32)),not(truth)),not(X_32)) != truth
| not(not(X_32)) != X_32
| implies(implies(X_32,not(truth)),not(X_32)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(X_32)),not(truth)),not(X_32)),truth) ),[0,0,0],$fot(X_32)]]) ).
cnf(refute_0_317,plain,
( implies(implies(not(not(X_32)),not(truth)),not(X_32)) != truth
| implies(implies(X_32,not(truth)),not(X_32)) = truth ),
inference(resolve,[$cnf( $equal(not(not(X_32)),X_32) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
implies(implies(X_32,not(truth)),not(X_32)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_32)),not(truth)),not(X_32)),truth) )],[refute_0_259,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(implies(X_33,not(truth)),not(X_33)) = truth,
inference(subst,[],[refute_0_318:[bind(X_32,$fot(X_33))]]) ).
cnf(refute_0_320,plain,
implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)))]]) ).
cnf(refute_0_321,plain,
( implies(implies(X_33,not(truth)),not(X_33)) != truth
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33))
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,not(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_322,plain,
( implies(implies(X_33,not(truth)),not(X_33)) != truth
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,not(X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = implies(truth,not(X_33)),
inference(resolve,[$cnf( $equal(implies(implies(X_33,not(truth)),not(X_33)),truth) )],[refute_0_319,refute_0_322]) ).
cnf(refute_0_324,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(truth,not(X_33))
| implies(truth,not(X_33)) != not(X_33)
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = not(X_33) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)))),bind(Y0,$fot(implies(truth,not(X_33)))),bind(Z0,$fot(not(X_33)))]]) ).
cnf(refute_0_325,plain,
( implies(truth,not(X_33)) != not(X_33)
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = not(X_33) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(truth,not(X_33))) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) = not(X_33),
inference(resolve,[$cnf( $equal(implies(truth,not(X_33)),not(X_33)) )],[refute_0_258,refute_0_325]) ).
cnf(refute_0_327,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(truth,implies(X_33,not(truth)))
| implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != not(X_33)
| not(X_33) = implies(truth,implies(X_33,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(truth,implies(X_33,not(truth)))) ),[0],$fot(not(X_33))]]) ).
cnf(refute_0_328,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(truth,implies(X_33,not(truth)))
| not(X_33) = implies(truth,implies(X_33,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),not(X_33)) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(truth,implies(X_33,not(truth))) = implies(X_33,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_33,not(truth))))]]) ).
cnf(refute_0_330,plain,
( implies(truth,implies(X_33,not(truth))) != implies(X_33,not(truth))
| not(X_33) != implies(truth,implies(X_33,not(truth)))
| not(X_33) = implies(X_33,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(X_33),implies(truth,implies(X_33,not(truth)))) ),[1],$fot(implies(X_33,not(truth)))]]) ).
cnf(refute_0_331,plain,
( not(X_33) != implies(truth,implies(X_33,not(truth)))
| not(X_33) = implies(X_33,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_33,not(truth))),implies(X_33,not(truth))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
( implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)) != implies(truth,implies(X_33,not(truth)))
| not(X_33) = implies(X_33,not(truth)) ),
inference(resolve,[$cnf( $equal(not(X_33),implies(truth,implies(X_33,not(truth)))) )],[refute_0_328,refute_0_331]) ).
cnf(refute_0_333,plain,
not(X_33) = implies(X_33,not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_33,not(truth)),not(X_33)),not(X_33)),implies(truth,implies(X_33,not(truth)))) )],[refute_0_257,refute_0_332]) ).
cnf(refute_0_334,plain,
( not(X_33) != implies(X_33,not(truth))
| implies(X_33,not(truth)) = not(X_33) ),
inference(subst,[],[refute_0_62:[bind(X0,$fot(not(X_33))),bind(Y0,$fot(implies(X_33,not(truth))))]]) ).
cnf(refute_0_335,plain,
implies(X_33,not(truth)) = not(X_33),
inference(resolve,[$cnf( $equal(not(X_33),implies(X_33,not(truth))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
implies(x,not(truth)) = not(x),
inference(subst,[],[refute_0_335:[bind(X_33,$fot(x))]]) ).
cnf(refute_0_337,plain,
( implies(x,not(truth)) != not(x)
| not(x) != not(x)
| implies(x,not(truth)) = not(x) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(x,not(truth)),not(x)) ),[0],$fot(not(x))]]) ).
cnf(refute_0_338,plain,
( not(x) != not(x)
| implies(x,not(truth)) = not(x) ),
inference(resolve,[$cnf( $equal(implies(x,not(truth)),not(x)) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
not(x) != not(x),
inference(resolve,[$cnf( $equal(implies(x,not(truth)),not(x)) )],[refute_0_338,prove_wajsberg_lemma]) ).
cnf(refute_0_340,plain,
not(x) = not(x),
introduced(tautology,[refl,[$fot(not(x))]]) ).
cnf(refute_0_341,plain,
$false,
inference(resolve,[$cnf( $equal(not(x),not(x)) )],[refute_0_340,refute_0_339]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL139-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 6 00:44:55 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.31/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.59
% 0.31/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.38/0.68
%------------------------------------------------------------------------------