TSTP Solution File: LCL114-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL114-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:49:41 EDT 2022
% Result : Unsatisfiable 1.07s 1.28s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 78
% Number of leaves : 88
% Syntax : Number of clauses : 323 ( 164 unt; 0 nHn; 199 RR)
% Number of literals : 559 ( 558 equ; 238 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 384 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_mv_36,negated_conjecture,
implies(implies(x,y),implies(not(y),not(x))) != truth ).
cnf(refute_0_0,plain,
implies(truth,implies(implies(truth,X_17),X_17)) = implies(implies(truth,X_17),X_17),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_17),X_17)))]]) ).
cnf(refute_0_1,plain,
implies(implies(truth,X_8),implies(implies(X_8,X_9),implies(truth,X_9))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_2,plain,
implies(truth,X_9) = X_9,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_3,plain,
( implies(implies(truth,X_8),implies(implies(X_8,X_9),implies(truth,X_9))) != truth
| implies(truth,X_9) != X_9
| implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),implies(truth,X_9))),truth) ),[0,1,1],$fot(X_9)]]) ).
cnf(refute_0_4,plain,
( implies(implies(truth,X_8),implies(implies(X_8,X_9),implies(truth,X_9))) != truth
| implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_9),X_9) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),implies(truth,X_9))),truth) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(truth,X_8) = X_8,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_7,plain,
implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)))]]) ).
cnf(refute_0_8,plain,
( implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) != implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9))
| implies(truth,X_8) != X_8
| implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = implies(X_8,implies(implies(X_8,X_9),X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9))) ),[1,0],$fot(X_8)]]) ).
cnf(refute_0_9,plain,
( implies(truth,X_8) != X_8
| implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = implies(X_8,implies(implies(X_8,X_9),X_9)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) = implies(X_8,implies(implies(X_8,X_9),X_9)),
inference(resolve,[$cnf( $equal(implies(truth,X_8),X_8) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) != implies(X_8,implies(implies(X_8,X_9),X_9))
| implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) != truth
| implies(X_8,implies(implies(X_8,X_9),X_9)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),truth) ),[0],$fot(implies(X_8,implies(implies(X_8,X_9),X_9)))]]) ).
cnf(refute_0_12,plain,
( implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)) != truth
| implies(X_8,implies(implies(X_8,X_9),X_9)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),implies(X_8,implies(implies(X_8,X_9),X_9))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(X_8,implies(implies(X_8,X_9),X_9)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_8),implies(implies(X_8,X_9),X_9)),truth) )],[refute_0_5,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(truth,implies(implies(truth,X_17),X_17)) = truth,
inference(subst,[],[refute_0_13:[bind(X_8,$fot(truth)),bind(X_9,$fot(X_17))]]) ).
cnf(refute_0_15,plain,
( implies(truth,implies(implies(truth,X_17),X_17)) != implies(implies(truth,X_17),X_17)
| implies(truth,implies(implies(truth,X_17),X_17)) != truth
| truth = implies(implies(truth,X_17),X_17) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_17),X_17)),implies(implies(truth,X_17),X_17)) ),[0],$fot(truth)]]) ).
cnf(refute_0_16,plain,
( implies(truth,implies(implies(truth,X_17),X_17)) != implies(implies(truth,X_17),X_17)
| truth = implies(implies(truth,X_17),X_17) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_17),X_17)),truth) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
truth = implies(implies(truth,X_17),X_17),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_17),X_17)),implies(implies(truth,X_17),X_17)) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_19,plain,
implies(implies(truth,X_17),X_17) = implies(implies(truth,X_17),X_17),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_17),X_17))]]) ).
cnf(refute_0_20,plain,
( implies(implies(truth,X_17),X_17) != implies(implies(truth,X_17),X_17)
| implies(truth,X_17) != X_17
| implies(implies(truth,X_17),X_17) = implies(X_17,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),X_17),implies(implies(truth,X_17),X_17)) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_21,plain,
( implies(truth,X_17) != X_17
| implies(implies(truth,X_17),X_17) = implies(X_17,X_17) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),X_17),implies(implies(truth,X_17),X_17)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(implies(truth,X_17),X_17) = implies(X_17,X_17),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( implies(implies(truth,X_17),X_17) != implies(X_17,X_17)
| truth != implies(implies(truth,X_17),X_17)
| truth = implies(X_17,X_17) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(truth,X_17),X_17)) ),[1],$fot(implies(X_17,X_17))]]) ).
cnf(refute_0_24,plain,
( truth != implies(implies(truth,X_17),X_17)
| truth = implies(X_17,X_17) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),X_17),implies(X_17,X_17)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
truth = implies(X_17,X_17),
inference(resolve,[$cnf( $equal(truth,implies(implies(truth,X_17),X_17)) )],[refute_0_17,refute_0_24]) ).
cnf(refute_0_26,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_27,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_28,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( truth != implies(X_17,X_17)
| implies(X_17,X_17) = truth ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_17,X_17)))]]) ).
cnf(refute_0_30,plain,
implies(X_17,X_17) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_17,X_17)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
implies(implies(x,y),implies(x,y)) = truth,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(implies(x,y)))]]) ).
cnf(refute_0_32,plain,
implies(implies(X,not(truth)),not(truth)) = implies(implies(not(truth),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_33,plain,
implies(implies(not(X),not(not(truth))),implies(not(truth),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_34,plain,
implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_35,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_36,plain,
implies(implies(X,implies(X_12,X)),implies(X_12,X)) = implies(implies(implies(X_12,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_12,X)))]]) ).
cnf(refute_0_37,plain,
implies(implies(X_12,X),X) = implies(implies(X,X_12),X_12),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_12)),bind(Y,$fot(X))]]) ).
cnf(refute_0_38,plain,
( implies(implies(X,implies(X_12,X)),implies(X_12,X)) != implies(implies(implies(X_12,X),X),X)
| implies(implies(X_12,X),X) != implies(implies(X,X_12),X_12)
| implies(implies(X,implies(X_12,X)),implies(X_12,X)) = implies(implies(implies(X,X_12),X_12),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_12,X)),implies(X_12,X)),implies(implies(implies(X_12,X),X),X)) ),[1,0],$fot(implies(implies(X,X_12),X_12))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X,implies(X_12,X)),implies(X_12,X)) != implies(implies(implies(X_12,X),X),X)
| implies(implies(X,implies(X_12,X)),implies(X_12,X)) = implies(implies(implies(X,X_12),X_12),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,X),X),implies(implies(X,X_12),X_12)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(X,implies(X_12,X)),implies(X_12,X)) = implies(implies(implies(X,X_12),X_12),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_12,X)),implies(X_12,X)),implies(implies(implies(X_12,X),X),X)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( implies(implies(X,implies(X_12,X)),implies(X_12,X)) != implies(implies(implies(X,X_12),X_12),X)
| implies(implies(X,implies(X_12,X)),implies(X_12,X)) != implies(implies(implies(X_12,X),X),X)
| implies(implies(implies(X_12,X),X),X) = implies(implies(implies(X,X_12),X_12),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_12,X)),implies(X_12,X)),implies(implies(implies(X,X_12),X_12),X)) ),[0],$fot(implies(implies(implies(X_12,X),X),X))]]) ).
cnf(refute_0_42,plain,
( implies(implies(X,implies(X_12,X)),implies(X_12,X)) != implies(implies(implies(X,X_12),X_12),X)
| implies(implies(implies(X_12,X),X),X) = implies(implies(implies(X,X_12),X_12),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_12,X)),implies(X_12,X)),implies(implies(implies(X_12,X),X),X)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(implies(X_12,X),X),X) = implies(implies(implies(X,X_12),X_12),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_12,X)),implies(X_12,X)),implies(implies(implies(X,X_12),X_12),X)) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(implies(X_25,Y),Y),Y) = implies(implies(Y,implies(X_25,Y)),implies(X_25,Y)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_25,Y)))]]) ).
cnf(refute_0_45,plain,
implies(implies(X_7,truth),implies(implies(truth,X_9),implies(X_7,X_9))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_7)),bind(Y,$fot(truth)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_46,plain,
( implies(implies(X_7,truth),implies(implies(truth,X_9),implies(X_7,X_9))) != truth
| implies(truth,X_9) != X_9
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,truth),implies(implies(truth,X_9),implies(X_7,X_9))),truth) ),[0,1,0],$fot(X_9)]]) ).
cnf(refute_0_47,plain,
( implies(implies(X_7,truth),implies(implies(truth,X_9),implies(X_7,X_9))) != truth
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_9),X_9) )],[refute_0_2,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,truth),implies(implies(truth,X_9),implies(X_7,X_9))),truth) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
implies(truth,implies(X_9,implies(X_7,X_9))) = implies(X_9,implies(X_7,X_9)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_9,implies(X_7,X_9))))]]) ).
cnf(refute_0_50,plain,
implies(X_16,implies(implies(X_16,truth),truth)) = truth,
inference(subst,[],[refute_0_13:[bind(X_8,$fot(X_16)),bind(X_9,$fot(truth))]]) ).
cnf(refute_0_51,plain,
implies(implies(truth,X_13),X_13) = implies(implies(X_13,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_52,plain,
implies(truth,X_13) = X_13,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_53,plain,
( implies(implies(truth,X_13),X_13) != implies(implies(X_13,truth),truth)
| implies(truth,X_13) != X_13
| implies(X_13,X_13) = implies(implies(X_13,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),X_13),implies(implies(X_13,truth),truth)) ),[0,0],$fot(X_13)]]) ).
cnf(refute_0_54,plain,
( implies(implies(truth,X_13),X_13) != implies(implies(X_13,truth),truth)
| implies(X_13,X_13) = implies(implies(X_13,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(X_13,X_13) = implies(implies(X_13,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),X_13),implies(implies(X_13,truth),truth)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(X_16,X_16) = implies(implies(X_16,truth),truth),
inference(subst,[],[refute_0_55:[bind(X_13,$fot(X_16))]]) ).
cnf(refute_0_57,plain,
( implies(X_16,X_16) != implies(implies(X_16,truth),truth)
| implies(implies(X_16,truth),truth) = implies(X_16,X_16) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(implies(X_16,X_16))),bind(Y0,$fot(implies(implies(X_16,truth),truth)))]]) ).
cnf(refute_0_58,plain,
implies(implies(X_16,truth),truth) = implies(X_16,X_16),
inference(resolve,[$cnf( $equal(implies(X_16,X_16),implies(implies(X_16,truth),truth)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( implies(X_16,implies(implies(X_16,truth),truth)) != truth
| implies(implies(X_16,truth),truth) != implies(X_16,X_16)
| implies(X_16,implies(X_16,X_16)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(implies(X_16,truth),truth)),truth) ),[0,1],$fot(implies(X_16,X_16))]]) ).
cnf(refute_0_60,plain,
( implies(X_16,implies(implies(X_16,truth),truth)) != truth
| implies(X_16,implies(X_16,X_16)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,truth),truth),implies(X_16,X_16)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
implies(X_16,implies(X_16,X_16)) = truth,
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_16,truth),truth)),truth) )],[refute_0_50,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(X_16,X_16) = truth,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(X_16))]]) ).
cnf(refute_0_63,plain,
implies(X_16,implies(X_16,X_16)) = implies(X_16,implies(X_16,X_16)),
introduced(tautology,[refl,[$fot(implies(X_16,implies(X_16,X_16)))]]) ).
cnf(refute_0_64,plain,
( implies(X_16,X_16) != truth
| implies(X_16,implies(X_16,X_16)) != implies(X_16,implies(X_16,X_16))
| implies(X_16,implies(X_16,X_16)) = implies(X_16,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(X_16,X_16)),implies(X_16,implies(X_16,X_16))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_65,plain,
( implies(X_16,X_16) != truth
| implies(X_16,implies(X_16,X_16)) = implies(X_16,truth) ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(X_16,X_16)),implies(X_16,implies(X_16,X_16))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
implies(X_16,implies(X_16,X_16)) = implies(X_16,truth),
inference(resolve,[$cnf( $equal(implies(X_16,X_16),truth) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
( implies(X_16,implies(X_16,X_16)) != implies(X_16,truth)
| implies(X_16,implies(X_16,X_16)) != truth
| implies(X_16,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(X_16,X_16)),truth) ),[0],$fot(implies(X_16,truth))]]) ).
cnf(refute_0_68,plain,
( implies(X_16,implies(X_16,X_16)) != truth
| implies(X_16,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(X_16,X_16)),implies(X_16,truth)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(X_16,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_16,implies(X_16,X_16)),truth) )],[refute_0_61,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(X_7,truth) = truth,
inference(subst,[],[refute_0_69:[bind(X_16,$fot(X_7))]]) ).
cnf(refute_0_71,plain,
implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),
introduced(tautology,[refl,[$fot(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))))]]) ).
cnf(refute_0_72,plain,
( implies(X_7,truth) != truth
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) != implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9)))
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(truth,implies(X_9,implies(X_7,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_73,plain,
( implies(X_7,truth) != truth
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(truth,implies(X_9,implies(X_7,X_9))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9)))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(truth,implies(X_9,implies(X_7,X_9))),
inference(resolve,[$cnf( $equal(implies(X_7,truth),truth) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_76,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_28,refute_0_75]) ).
cnf(refute_0_77,plain,
( implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) != implies(truth,implies(X_9,implies(X_7,X_9)))
| implies(truth,implies(X_9,implies(X_7,X_9))) != implies(X_9,implies(X_7,X_9))
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(X_9,implies(X_7,X_9)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))))),bind(Y0,$fot(implies(truth,implies(X_9,implies(X_7,X_9))))),bind(Z0,$fot(implies(X_9,implies(X_7,X_9))))]]) ).
cnf(refute_0_78,plain,
( implies(truth,implies(X_9,implies(X_7,X_9))) != implies(X_9,implies(X_7,X_9))
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(X_9,implies(X_7,X_9)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),implies(truth,implies(X_9,implies(X_7,X_9)))) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) = implies(X_9,implies(X_7,X_9)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_9,implies(X_7,X_9))),implies(X_9,implies(X_7,X_9))) )],[refute_0_49,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) != implies(X_9,implies(X_7,X_9))
| implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) != truth
| implies(X_9,implies(X_7,X_9)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),truth) ),[0],$fot(implies(X_9,implies(X_7,X_9)))]]) ).
cnf(refute_0_81,plain,
( implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))) != truth
| implies(X_9,implies(X_7,X_9)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),implies(X_9,implies(X_7,X_9))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(X_9,implies(X_7,X_9)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,truth),implies(X_9,implies(X_7,X_9))),truth) )],[refute_0_48,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(Y,implies(X_25,Y)) = truth,
inference(subst,[],[refute_0_82:[bind(X_7,$fot(X_25)),bind(X_9,$fot(Y))]]) ).
cnf(refute_0_84,plain,
( implies(Y,implies(X_25,Y)) != truth
| implies(implies(implies(X_25,Y),Y),Y) != implies(implies(Y,implies(X_25,Y)),implies(X_25,Y))
| implies(implies(implies(X_25,Y),Y),Y) = implies(truth,implies(X_25,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_25,Y),Y),Y),implies(implies(Y,implies(X_25,Y)),implies(X_25,Y))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_85,plain,
( implies(implies(implies(X_25,Y),Y),Y) != implies(implies(Y,implies(X_25,Y)),implies(X_25,Y))
| implies(implies(implies(X_25,Y),Y),Y) = implies(truth,implies(X_25,Y)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(X_25,Y)),truth) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(implies(implies(X_25,Y),Y),Y) = implies(truth,implies(X_25,Y)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_25,Y),Y),Y),implies(implies(Y,implies(X_25,Y)),implies(X_25,Y))) )],[refute_0_44,refute_0_85]) ).
cnf(refute_0_87,plain,
implies(truth,implies(X_25,Y)) = implies(X_25,Y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_25,Y)))]]) ).
cnf(refute_0_88,plain,
( implies(implies(implies(X_25,Y),Y),Y) != implies(truth,implies(X_25,Y))
| implies(truth,implies(X_25,Y)) != implies(X_25,Y)
| implies(implies(implies(X_25,Y),Y),Y) = implies(X_25,Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_25,Y),Y),Y),implies(X_25,Y)) ),[0],$fot(implies(truth,implies(X_25,Y)))]]) ).
cnf(refute_0_89,plain,
( implies(implies(implies(X_25,Y),Y),Y) != implies(truth,implies(X_25,Y))
| implies(implies(implies(X_25,Y),Y),Y) = implies(X_25,Y) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_25,Y)),implies(X_25,Y)) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(implies(implies(X_25,Y),Y),Y) = implies(X_25,Y),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_25,Y),Y),Y),implies(truth,implies(X_25,Y))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(implies(implies(X_12,X),X),X) = implies(X_12,X),
inference(subst,[],[refute_0_90:[bind(Y,$fot(X)),bind(X_25,$fot(X_12))]]) ).
cnf(refute_0_92,plain,
( implies(implies(implies(X_12,X),X),X) != implies(X_12,X)
| implies(implies(implies(X_12,X),X),X) != implies(implies(implies(X,X_12),X_12),X)
| implies(X_12,X) = implies(implies(implies(X,X_12),X_12),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_12,X),X),X),implies(implies(implies(X,X_12),X_12),X)) ),[0],$fot(implies(X_12,X))]]) ).
cnf(refute_0_93,plain,
( implies(implies(implies(X_12,X),X),X) != implies(implies(implies(X,X_12),X_12),X)
| implies(X_12,X) = implies(implies(implies(X,X_12),X_12),X) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_12,X),X),X),implies(X_12,X)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(X_12,X) = implies(implies(implies(X,X_12),X_12),X),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_12,X),X),X),implies(implies(implies(X,X_12),X_12),X)) )],[refute_0_43,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(not(not(truth)),not(truth)) = implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth)),
inference(subst,[],[refute_0_94:[bind(X,$fot(not(truth))),bind(X_12,$fot(not(not(truth))))]]) ).
cnf(refute_0_96,plain,
implies(not(truth),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))),
inference(subst,[],[refute_0_94:[bind(X,$fot(not(not(truth)))),bind(X_12,$fot(not(truth)))]]) ).
cnf(refute_0_97,plain,
implies(implies(not(X_1),not(truth)),implies(truth,X_1)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_98,plain,
implies(truth,X_1) = X_1,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_99,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(truth,X_1) != X_1
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) ),[0,1],$fot(X_1)]]) ).
cnf(refute_0_100,plain,
( implies(implies(not(X_1),not(truth)),implies(truth,X_1)) != truth
| implies(implies(not(X_1),not(truth)),X_1) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_1),X_1) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(implies(not(X_1),not(truth)),X_1) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_1),not(truth)),implies(truth,X_1)),truth) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_101:[bind(X_1,$fot(not(truth)))]]) ).
cnf(refute_0_103,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_104,plain,
( implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) )],[refute_0_96,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_107,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(truth),not(not(truth))),not(not(truth))) ),[0],$fot(implies(truth,not(not(truth))))]]) ).
cnf(refute_0_108,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))) ),[1,0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_111,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(implies(not(truth),not(not(truth))),not(not(truth))),not(truth))) )],[refute_0_95,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(truth,not(truth)) = not(truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_114,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(not(not(truth))))]]) ).
cnf(refute_0_115,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(implies(not(not(truth)),not(not(truth))),not(truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(truth))),not(truth)))]]) ).
cnf(refute_0_116,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_117,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = implies(truth,not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != implies(truth,not(truth))
| implies(truth,not(truth)) != not(truth)
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(not(not(truth)),not(not(truth))),not(truth)))),bind(Y0,$fot(implies(truth,not(truth)))),bind(Z0,$fot(not(truth)))]]) ).
cnf(refute_0_120,plain,
( implies(truth,not(truth)) != not(truth)
| implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),implies(truth,not(truth))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(implies(not(not(truth)),not(not(truth))),not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(truth,not(truth)),not(truth)) )],[refute_0_113,refute_0_120]) ).
cnf(refute_0_122,plain,
( implies(implies(not(not(truth)),not(not(truth))),not(truth)) != not(truth)
| implies(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) ),[1],$fot(not(truth))]]) ).
cnf(refute_0_123,plain,
( implies(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(not(truth))),not(truth))
| implies(not(not(truth)),not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),not(truth)),not(truth)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(not(truth))),not(truth))) )],[refute_0_112,refute_0_123]) ).
cnf(refute_0_125,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) != truth
| implies(not(not(truth)),not(truth)) != not(truth)
| implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),truth) ),[0,1],$fot(not(truth))]]) ).
cnf(refute_0_126,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) != truth
| implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),not(truth)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_35,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth)))),
inference(subst,[],[refute_0_94:[bind(X,$fot(not(not(not(truth))))),bind(X_12,$fot(not(not(truth))))]]) ).
cnf(refute_0_129,plain,
implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_130,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_131,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_109,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_129,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != truth
| implies(not(not(truth)),not(not(not(truth)))) != implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_134,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),truth) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),not(not(not(truth))))) )],[refute_0_128,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_137,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(truth,not(not(not(truth)))) != not(not(not(truth)))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) ),[0],$fot(implies(truth,not(not(not(truth)))))]]) ).
cnf(refute_0_138,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(truth,not(not(not(truth))))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)))]]) ).
cnf(refute_0_141,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) != implies(implies(not(not(truth)),not(not(not(truth)))),not(truth))
| implies(not(not(truth)),not(not(not(truth)))) != not(not(not(truth)))
| implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),implies(implies(not(not(truth)),not(not(not(truth)))),not(truth))) ),[1,0],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_142,plain,
( implies(not(not(truth)),not(not(not(truth)))) != not(not(not(truth)))
| implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),implies(implies(not(not(truth)),not(not(not(truth)))),not(truth))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) = implies(not(not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) != implies(not(not(not(truth))),not(truth))
| implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) != truth
| implies(not(not(not(truth))),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),truth) ),[0],$fot(implies(not(not(not(truth))),not(truth)))]]) ).
cnf(refute_0_145,plain,
( implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)) != truth
| implies(not(not(not(truth))),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),implies(not(not(not(truth))),not(truth))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(not(not(not(truth))),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(not(truth)))),not(truth)),truth) )],[refute_0_127,refute_0_145]) ).
cnf(refute_0_147,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(not(not(not(truth))),not(truth)) != truth
| implies(truth,implies(truth,not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_148,plain,
( implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))) != truth
| implies(truth,implies(truth,not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(truth)),truth) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(truth,implies(truth,not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),implies(truth,not(not(truth)))),truth) )],[refute_0_34,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(truth,implies(truth,not(not(truth)))) = implies(truth,not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(truth,not(not(truth)))))]]) ).
cnf(refute_0_151,plain,
( implies(truth,implies(truth,not(not(truth)))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) = not(not(truth)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(truth,implies(truth,not(not(truth)))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_152,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),implies(truth,not(not(truth)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(truth,implies(truth,not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_106,refute_0_152]) ).
cnf(refute_0_154,plain,
( implies(truth,implies(truth,not(not(truth)))) != not(not(truth))
| implies(truth,implies(truth,not(not(truth)))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_155,plain,
( implies(truth,implies(truth,not(not(truth)))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),not(not(truth))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(truth,not(not(truth)))),truth) )],[refute_0_149,refute_0_155]) ).
cnf(refute_0_157,plain,
( implies(implies(not(X),not(not(truth))),implies(not(truth),X)) != truth
| not(not(truth)) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(not(truth))),implies(not(truth),X)),truth) ),[0,0,1],$fot(truth)]]) ).
cnf(refute_0_158,plain,
( implies(implies(not(X),not(not(truth))),implies(not(truth),X)) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(not(truth))),implies(not(truth),X)),truth) )],[refute_0_33,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(truth,implies(not(truth),X)) = implies(not(truth),X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_161,plain,
implies(not(X),truth) = truth,
inference(subst,[],[refute_0_69:[bind(X_16,$fot(not(X)))]]) ).
cnf(refute_0_162,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(implies(not(X),truth),implies(not(truth),X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),implies(not(truth),X)))]]) ).
cnf(refute_0_163,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(implies(not(X),truth),implies(not(truth),X))
| implies(not(X),truth) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(implies(not(X),truth),implies(not(truth),X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_164,plain,
( implies(not(X),truth) != truth
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(implies(not(X),truth),implies(not(truth),X))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(truth,implies(not(truth),X)),
inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(truth,implies(not(truth),X))
| implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(not(X),truth),implies(not(truth),X)))),bind(Y0,$fot(implies(truth,implies(not(truth),X)))),bind(Z0,$fot(implies(not(truth),X)))]]) ).
cnf(refute_0_167,plain,
( implies(truth,implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(truth,implies(not(truth),X))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(not(X),truth),implies(not(truth),X)) = implies(not(truth),X),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != implies(not(truth),X)
| implies(implies(not(X),truth),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),truth) ),[0],$fot(implies(not(truth),X))]]) ).
cnf(refute_0_170,plain,
( implies(implies(not(X),truth),implies(not(truth),X)) != truth
| implies(not(truth),X) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),implies(not(truth),X)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(not(truth),X) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),implies(not(truth),X)),truth) )],[refute_0_159,refute_0_170]) ).
cnf(refute_0_172,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(implies(not(truth),X),X)
| implies(not(truth),X) != truth
| implies(implies(X,not(truth)),not(truth)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_173,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( $equal(implies(not(truth),X),truth) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(implies(X,not(truth)),not(truth)) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(implies(not(truth),X),X)) )],[refute_0_32,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(not(truth),not(X_24)),not(X_24)))),bind(Y,$fot(implies(X_24,not(truth))))]]) ).
cnf(refute_0_176,plain,
implies(implies(implies(not(X_8),not(truth)),X_8),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_8),not(truth)))),bind(Y,$fot(X_8)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_177,plain,
implies(implies(not(X_8),not(truth)),X_8) = truth,
inference(subst,[],[refute_0_101:[bind(X_1,$fot(X_8))]]) ).
cnf(refute_0_178,plain,
( implies(implies(implies(not(X_8),not(truth)),X_8),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) != truth
| implies(implies(not(X_8),not(truth)),X_8) != truth
| implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_8),not(truth)),X_8),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_179,plain,
( implies(implies(implies(not(X_8),not(truth)),X_8),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) != truth
| implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_8),not(truth)),X_8),truth) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_8),not(truth)),X_8),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))),truth) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) = implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))))]]) ).
cnf(refute_0_182,plain,
( implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) != implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))
| implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) != truth
| implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))),truth) ),[0],$fot(implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9)))]]) ).
cnf(refute_0_183,plain,
( implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) != truth
| implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))),implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_8,X_9),implies(implies(not(X_8),not(truth)),X_9))),truth) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_184:[bind(X_8,$fot(X_22)),bind(X_9,$fot(not(truth)))]]) ).
cnf(refute_0_186,plain,
implies(implies(not(truth),not(X_22)),not(X_22)) = implies(implies(not(X_22),not(truth)),not(truth)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_22)))]]) ).
cnf(refute_0_187,plain,
( implies(implies(not(truth),not(X_22)),not(X_22)) != implies(implies(not(X_22),not(truth)),not(truth))
| implies(implies(not(X_22),not(truth)),not(truth)) = implies(implies(not(truth),not(X_22)),not(X_22)) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(implies(implies(not(truth),not(X_22)),not(X_22)))),bind(Y0,$fot(implies(implies(not(X_22),not(truth)),not(truth))))]]) ).
cnf(refute_0_188,plain,
implies(implies(not(X_22),not(truth)),not(truth)) = implies(implies(not(truth),not(X_22)),not(X_22)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_22)),not(X_22)),implies(implies(not(X_22),not(truth)),not(truth))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
( implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) != truth
| implies(implies(not(X_22),not(truth)),not(truth)) != implies(implies(not(truth),not(X_22)),not(X_22))
| implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))),truth) ),[0,1],$fot(implies(implies(not(truth),not(X_22)),not(X_22)))]]) ).
cnf(refute_0_190,plain,
( implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))) != truth
| implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(implies(X_22,not(truth)),implies(implies(not(truth),not(X_22)),not(X_22))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_22,not(truth)),implies(implies(not(X_22),not(truth)),not(truth))),truth) )],[refute_0_185,refute_0_190]) ).
cnf(refute_0_192,plain,
implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))) = truth,
inference(subst,[],[refute_0_191:[bind(X_22,$fot(X_24))]]) ).
cnf(refute_0_193,plain,
( implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))) != truth
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24)))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_194,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24)))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),truth) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24)))) )],[refute_0_175,refute_0_194]) ).
cnf(refute_0_196,plain,
implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))) = implies(implies(not(truth),not(X_24)),not(X_24)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(truth),not(X_24)),not(X_24))))]]) ).
cnf(refute_0_197,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(truth,implies(implies(not(truth),not(X_24)),not(X_24)))
| implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(implies(not(truth),not(X_24)),not(X_24)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(not(truth),not(X_24)),not(X_24))) ),[0],$fot(implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))))]]) ).
cnf(refute_0_198,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(truth,implies(implies(not(truth),not(X_24)),not(X_24)))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(implies(not(truth),not(X_24)),not(X_24)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(truth),not(X_24)),not(X_24))),implies(implies(not(truth),not(X_24)),not(X_24))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(implies(not(truth),not(X_24)),not(X_24)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(truth,implies(implies(not(truth),not(X_24)),not(X_24)))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(truth,implies(X_24,not(truth))) = implies(X_24,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_24,not(truth))))]]) ).
cnf(refute_0_201,plain,
implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_202,plain,
( implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_203,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( $equal(not(not(truth)),truth) )],[refute_0_156,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(Y)),implies(Y,not(truth))),truth) )],[refute_0_201,refute_0_203]) ).
cnf(refute_0_205,plain,
implies(truth,not(Y)) = not(Y),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(Y)))]]) ).
cnf(refute_0_206,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(implies(truth,not(Y)),implies(Y,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(Y)),implies(Y,not(truth))))]]) ).
cnf(refute_0_207,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(implies(truth,not(Y)),implies(Y,not(truth)))
| implies(truth,not(Y)) != not(Y)
| implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))) ),
introduced(tautology,[equality,[$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_208,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( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(implies(truth,not(Y)),implies(Y,not(truth)))) )],[refute_0_206,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(implies(truth,not(Y)),implies(Y,not(truth))) = implies(not(Y),implies(Y,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(Y)),not(Y)) )],[refute_0_205,refute_0_208]) ).
cnf(refute_0_210,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != implies(not(Y),implies(Y,not(truth)))
| implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) ),[0],$fot(implies(not(Y),implies(Y,not(truth))))]]) ).
cnf(refute_0_211,plain,
( implies(implies(truth,not(Y)),implies(Y,not(truth))) != truth
| implies(not(Y),implies(Y,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),implies(not(Y),implies(Y,not(truth)))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
implies(not(Y),implies(Y,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(Y)),implies(Y,not(truth))),truth) )],[refute_0_204,refute_0_211]) ).
cnf(refute_0_213,plain,
implies(not(X_24),implies(X_24,not(truth))) = truth,
inference(subst,[],[refute_0_212:[bind(Y,$fot(X_24))]]) ).
cnf(refute_0_214,plain,
implies(truth,not(X_24)) = not(X_24),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_24)))]]) ).
cnf(refute_0_215,plain,
implies(not(truth),not(X_24)) = truth,
inference(subst,[],[refute_0_171:[bind(X,$fot(not(X_24)))]]) ).
cnf(refute_0_216,plain,
implies(implies(not(truth),not(X_24)),not(X_24)) = implies(implies(not(truth),not(X_24)),not(X_24)),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(X_24)),not(X_24)))]]) ).
cnf(refute_0_217,plain,
( implies(implies(not(truth),not(X_24)),not(X_24)) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(not(truth),not(X_24)) != truth
| implies(implies(not(truth),not(X_24)),not(X_24)) = implies(truth,not(X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(X_24)),not(X_24)),implies(implies(not(truth),not(X_24)),not(X_24))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_218,plain,
( implies(not(truth),not(X_24)) != truth
| implies(implies(not(truth),not(X_24)),not(X_24)) = implies(truth,not(X_24)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_24)),not(X_24)),implies(implies(not(truth),not(X_24)),not(X_24))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(not(truth),not(X_24)),not(X_24)) = implies(truth,not(X_24)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(X_24)),truth) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( implies(implies(not(truth),not(X_24)),not(X_24)) != implies(truth,not(X_24))
| implies(truth,not(X_24)) != not(X_24)
| implies(implies(not(truth),not(X_24)),not(X_24)) = not(X_24) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(not(truth),not(X_24)),not(X_24)))),bind(Y0,$fot(implies(truth,not(X_24)))),bind(Z0,$fot(not(X_24)))]]) ).
cnf(refute_0_221,plain,
( implies(truth,not(X_24)) != not(X_24)
| implies(implies(not(truth),not(X_24)),not(X_24)) = not(X_24) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_24)),not(X_24)),implies(truth,not(X_24))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(implies(not(truth),not(X_24)),not(X_24)) = not(X_24),
inference(resolve,[$cnf( $equal(implies(truth,not(X_24)),not(X_24)) )],[refute_0_214,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))))]]) ).
cnf(refute_0_224,plain,
( implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) != implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth)))
| implies(implies(not(truth),not(X_24)),not(X_24)) != not(X_24)
| implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = implies(not(X_24),implies(X_24,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth)))) ),[1,0],$fot(not(X_24))]]) ).
cnf(refute_0_225,plain,
( implies(implies(not(truth),not(X_24)),not(X_24)) != not(X_24)
| implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = implies(not(X_24),implies(X_24,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth)))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = implies(not(X_24),implies(X_24,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_24)),not(X_24)),not(X_24)) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
( implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) != implies(not(X_24),implies(X_24,not(truth)))
| implies(not(X_24),implies(X_24,not(truth))) != truth
| implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = truth ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))))),bind(Y0,$fot(implies(not(X_24),implies(X_24,not(truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_228,plain,
( implies(not(X_24),implies(X_24,not(truth))) != truth
| implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(not(X_24),implies(X_24,not(truth)))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_24),implies(X_24,not(truth))),truth) )],[refute_0_213,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))))]]) ).
cnf(refute_0_231,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth)))
| implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) != truth
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(X_24,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_232,plain,
( implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))) != truth
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(X_24,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(truth,implies(X_24,not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),truth) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(truth,implies(X_24,not(truth)))
| implies(truth,implies(X_24,not(truth))) != implies(X_24,not(truth))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(X_24,not(truth)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))))),bind(Y0,$fot(implies(truth,implies(X_24,not(truth))))),bind(Z0,$fot(implies(X_24,not(truth))))]]) ).
cnf(refute_0_235,plain,
( implies(truth,implies(X_24,not(truth))) != implies(X_24,not(truth))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(X_24,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(truth,implies(X_24,not(truth)))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) = implies(X_24,not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_24,not(truth))),implies(X_24,not(truth))) )],[refute_0_200,refute_0_235]) ).
cnf(refute_0_237,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(X_24,not(truth))
| implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(X_24,not(truth)) = implies(implies(not(truth),not(X_24)),not(X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(not(truth),not(X_24)),not(X_24))) ),[0],$fot(implies(X_24,not(truth)))]]) ).
cnf(refute_0_238,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(X_24,not(truth)) = implies(implies(not(truth),not(X_24)),not(X_24)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(X_24,not(truth))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
( implies(X_24,not(truth)) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(implies(not(truth),not(X_24)),not(X_24)) != not(X_24)
| implies(X_24,not(truth)) = not(X_24) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_24,not(truth)),not(X_24)) ),[0],$fot(implies(implies(not(truth),not(X_24)),not(X_24)))]]) ).
cnf(refute_0_240,plain,
( implies(X_24,not(truth)) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(X_24,not(truth)) = not(X_24) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(X_24)),not(X_24)),not(X_24)) )],[refute_0_222,refute_0_239]) ).
cnf(refute_0_241,plain,
( implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))) != implies(implies(not(truth),not(X_24)),not(X_24))
| implies(X_24,not(truth)) = not(X_24) ),
inference(resolve,[$cnf( $equal(implies(X_24,not(truth)),implies(implies(not(truth),not(X_24)),not(X_24))) )],[refute_0_238,refute_0_240]) ).
cnf(refute_0_242,plain,
implies(X_24,not(truth)) = not(X_24),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(truth),not(X_24)),not(X_24)),implies(X_24,not(truth))),implies(X_24,not(truth))),implies(implies(not(truth),not(X_24)),not(X_24))) )],[refute_0_199,refute_0_241]) ).
cnf(refute_0_243,plain,
implies(X,not(truth)) = not(X),
inference(subst,[],[refute_0_242:[bind(X_24,$fot(X))]]) ).
cnf(refute_0_244,plain,
not(implies(X,not(truth))) = not(implies(X,not(truth))),
introduced(tautology,[refl,[$fot(not(implies(X,not(truth))))]]) ).
cnf(refute_0_245,plain,
( implies(X,not(truth)) != not(X)
| not(implies(X,not(truth))) != not(implies(X,not(truth)))
| not(implies(X,not(truth))) = not(not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_246,plain,
( implies(X,not(truth)) != not(X)
| not(implies(X,not(truth))) = not(not(X)) ),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(implies(X,not(truth)))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
not(implies(X,not(truth))) = not(not(X)),
inference(resolve,[$cnf( $equal(implies(X,not(truth)),not(X)) )],[refute_0_243,refute_0_246]) ).
cnf(refute_0_248,plain,
implies(implies(X,not(truth)),not(truth)) = not(implies(X,not(truth))),
inference(subst,[],[refute_0_242:[bind(X_24,$fot(implies(X,not(truth))))]]) ).
cnf(refute_0_249,plain,
( implies(implies(X,not(truth)),not(truth)) != not(implies(X,not(truth)))
| not(implies(X,not(truth))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(X,not(truth)),not(truth)))),bind(Y0,$fot(not(implies(X,not(truth))))),bind(Z0,$fot(not(not(X))))]]) ).
cnf(refute_0_250,plain,
( not(implies(X,not(truth))) != not(not(X))
| implies(implies(X,not(truth)),not(truth)) = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(implies(X,not(truth)))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(implies(X,not(truth)),not(truth)) = not(not(X)),
inference(resolve,[$cnf( $equal(not(implies(X,not(truth))),not(not(X))) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| implies(implies(X,not(truth)),not(truth)) != not(not(X))
| not(not(X)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) ),[0],$fot(not(not(X)))]]) ).
cnf(refute_0_253,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| not(not(X)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),not(not(X))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
( implies(truth,X) != X
| not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(not(not(X)),implies(truth,X)) ),[1],$fot(X)]]) ).
cnf(refute_0_255,plain,
( not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_254]) ).
cnf(refute_0_256,plain,
( implies(implies(X,not(truth)),not(truth)) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(not(not(X)),implies(truth,X)) )],[refute_0_253,refute_0_255]) ).
cnf(refute_0_257,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),not(truth)),implies(truth,X)) )],[refute_0_174,refute_0_256]) ).
cnf(refute_0_258,plain,
not(not(y)) = y,
inference(subst,[],[refute_0_257:[bind(X,$fot(y))]]) ).
cnf(refute_0_259,plain,
implies(x,not(not(y))) = implies(x,not(not(y))),
introduced(tautology,[refl,[$fot(implies(x,not(not(y))))]]) ).
cnf(refute_0_260,plain,
( implies(x,not(not(y))) != implies(x,not(not(y)))
| not(not(y)) != y
| implies(x,not(not(y))) = implies(x,y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(x,not(not(y))),implies(x,not(not(y)))) ),[1,1],$fot(y)]]) ).
cnf(refute_0_261,plain,
( not(not(y)) != y
| implies(x,not(not(y))) = implies(x,y) ),
inference(resolve,[$cnf( $equal(implies(x,not(not(y))),implies(x,not(not(y)))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(x,not(not(y))) = implies(x,y),
inference(resolve,[$cnf( $equal(not(not(y)),y) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(implies(x,y),implies(x,not(not(y)))) = implies(implies(x,y),implies(x,not(not(y)))),
introduced(tautology,[refl,[$fot(implies(implies(x,y),implies(x,not(not(y)))))]]) ).
cnf(refute_0_264,plain,
( implies(implies(x,y),implies(x,not(not(y)))) != implies(implies(x,y),implies(x,not(not(y))))
| implies(x,not(not(y))) != implies(x,y)
| implies(implies(x,y),implies(x,not(not(y)))) = implies(implies(x,y),implies(x,y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(x,y),implies(x,not(not(y)))),implies(implies(x,y),implies(x,not(not(y))))) ),[1,1],$fot(implies(x,y))]]) ).
cnf(refute_0_265,plain,
( implies(x,not(not(y))) != implies(x,y)
| implies(implies(x,y),implies(x,not(not(y)))) = implies(implies(x,y),implies(x,y)) ),
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(x,not(not(y)))),implies(implies(x,y),implies(x,not(not(y))))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
implies(implies(x,y),implies(x,not(not(y)))) = implies(implies(x,y),implies(x,y)),
inference(resolve,[$cnf( $equal(implies(x,not(not(y))),implies(x,y)) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
( implies(implies(x,y),implies(x,not(not(y)))) != implies(implies(x,y),implies(x,y))
| implies(implies(x,y),implies(x,y)) != truth
| implies(implies(x,y),implies(x,not(not(y)))) = truth ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(x,y),implies(x,not(not(y)))))),bind(Y0,$fot(implies(implies(x,y),implies(x,y)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_268,plain,
( implies(implies(x,y),implies(x,y)) != truth
| implies(implies(x,y),implies(x,not(not(y)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(x,not(not(y)))),implies(implies(x,y),implies(x,y))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(implies(x,y),implies(x,not(not(y)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(x,y)),truth) )],[refute_0_31,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117)))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_119,implies(X_118,not(X_117))))),bind(Y,$fot(implies(X_119,implies(X_117,not(X_118)))))]]) ).
cnf(refute_0_271,plain,
implies(implies(X_7,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_7,implies(Y,X)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_7)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).
cnf(refute_0_272,plain,
( implies(implies(X_7,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_7,implies(Y,X)))) != truth
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_7,implies(Y,X)))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_273,plain,
( implies(implies(X_7,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_7,implies(Y,X)))) != truth
| implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_272]) ).
cnf(refute_0_274,plain,
implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(X_7,implies(Y,X)))),truth) )],[refute_0_271,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(truth,implies(X_7,implies(Y,X))) = implies(X_7,implies(Y,X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_7,implies(Y,X))))]]) ).
cnf(refute_0_276,plain,
implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),
introduced(tautology,[refl,[$fot(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))))]]) ).
cnf(refute_0_277,plain,
( implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) != implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X))))
| implies(truth,implies(X_7,implies(Y,X))) != implies(X_7,implies(Y,X))
| implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X))))) ),[1,1],$fot(implies(X_7,implies(Y,X)))]]) ).
cnf(refute_0_278,plain,
( implies(truth,implies(X_7,implies(Y,X))) != implies(X_7,implies(Y,X))
| implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X))))) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) = implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_7,implies(Y,X))),implies(X_7,implies(Y,X))) )],[refute_0_275,refute_0_278]) ).
cnf(refute_0_280,plain,
( implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) != implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X)))
| implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) != truth
| implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),truth) ),[0],$fot(implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))))]]) ).
cnf(refute_0_281,plain,
( implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))) != truth
| implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X)))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(implies(X_7,implies(not(X),not(Y))),implies(X_7,implies(Y,X))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_7,implies(not(X),not(Y))),implies(truth,implies(X_7,implies(Y,X)))),truth) )],[refute_0_274,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(implies(X_46,implies(not(not(X)),not(X_45))),implies(X_46,implies(X_45,not(X)))) = truth,
inference(subst,[],[refute_0_282:[bind(X,$fot(not(X))),bind(Y,$fot(X_45)),bind(X_7,$fot(X_46))]]) ).
cnf(refute_0_284,plain,
( implies(implies(X_46,implies(not(not(X)),not(X_45))),implies(X_46,implies(X_45,not(X)))) != truth
| not(not(X)) != X
| implies(implies(X_46,implies(X,not(X_45))),implies(X_46,implies(X_45,not(X)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_46,implies(not(not(X)),not(X_45))),implies(X_46,implies(X_45,not(X)))),truth) ),[0,0,1,0],$fot(X)]]) ).
cnf(refute_0_285,plain,
( implies(implies(X_46,implies(not(not(X)),not(X_45))),implies(X_46,implies(X_45,not(X)))) != truth
| implies(implies(X_46,implies(X,not(X_45))),implies(X_46,implies(X_45,not(X)))) = truth ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_257,refute_0_284]) ).
cnf(refute_0_286,plain,
implies(implies(X_46,implies(X,not(X_45))),implies(X_46,implies(X_45,not(X)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_46,implies(not(not(X)),not(X_45))),implies(X_46,implies(X_45,not(X)))),truth) )],[refute_0_283,refute_0_285]) ).
cnf(refute_0_287,plain,
implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))) = truth,
inference(subst,[],[refute_0_286:[bind(X,$fot(X_117)),bind(X_45,$fot(X_118)),bind(X_46,$fot(X_119))]]) ).
cnf(refute_0_288,plain,
( implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))) != truth
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117))))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_118,not(X_117)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_289,plain,
( implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117))))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_118,not(X_117)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),truth) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_118,not(X_117)))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(implies(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117))))) )],[refute_0_270,refute_0_289]) ).
cnf(refute_0_291,plain,
implies(truth,implies(X_119,implies(X_117,not(X_118)))) = implies(X_119,implies(X_117,not(X_118))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_119,implies(X_117,not(X_118)))))]]) ).
cnf(refute_0_292,plain,
implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))) = truth,
inference(subst,[],[refute_0_286:[bind(X,$fot(X_118)),bind(X_45,$fot(X_117)),bind(X_46,$fot(X_119))]]) ).
cnf(refute_0_293,plain,
implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))))]]) ).
cnf(refute_0_294,plain,
( implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))) != truth
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118))))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_117,not(X_118)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_295,plain,
( implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))) != truth
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_117,not(X_118)))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118))))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(truth,implies(X_119,implies(X_117,not(X_118)))),
inference(resolve,[$cnf( $equal(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),truth) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
( implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(truth,implies(X_119,implies(X_117,not(X_118))))
| implies(truth,implies(X_119,implies(X_117,not(X_118)))) != implies(X_119,implies(X_117,not(X_118)))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(X_119,implies(X_117,not(X_118))) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))))),bind(Y0,$fot(implies(truth,implies(X_119,implies(X_117,not(X_118)))))),bind(Z0,$fot(implies(X_119,implies(X_117,not(X_118)))))]]) ).
cnf(refute_0_298,plain,
( implies(truth,implies(X_119,implies(X_117,not(X_118)))) != implies(X_119,implies(X_117,not(X_118)))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(X_119,implies(X_117,not(X_118))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(truth,implies(X_119,implies(X_117,not(X_118))))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) = implies(X_119,implies(X_117,not(X_118))),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) )],[refute_0_291,refute_0_298]) ).
cnf(refute_0_300,plain,
( implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(X_119,implies(X_117,not(X_118)))
| implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(truth,implies(X_119,implies(X_118,not(X_117))))
| implies(X_119,implies(X_117,not(X_118))) = implies(truth,implies(X_119,implies(X_118,not(X_117)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(truth,implies(X_119,implies(X_118,not(X_117))))) ),[0],$fot(implies(X_119,implies(X_117,not(X_118))))]]) ).
cnf(refute_0_301,plain,
( implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(truth,implies(X_119,implies(X_118,not(X_117))))
| implies(X_119,implies(X_117,not(X_118))) = implies(truth,implies(X_119,implies(X_118,not(X_117)))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
implies(truth,implies(X_119,implies(X_118,not(X_117)))) = implies(X_119,implies(X_118,not(X_117))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_119,implies(X_118,not(X_117)))))]]) ).
cnf(refute_0_303,plain,
( implies(X_119,implies(X_117,not(X_118))) != implies(truth,implies(X_119,implies(X_118,not(X_117))))
| implies(truth,implies(X_119,implies(X_118,not(X_117)))) != implies(X_119,implies(X_118,not(X_117)))
| implies(X_119,implies(X_117,not(X_118))) = implies(X_119,implies(X_118,not(X_117))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))) ),[0],$fot(implies(truth,implies(X_119,implies(X_118,not(X_117)))))]]) ).
cnf(refute_0_304,plain,
( implies(X_119,implies(X_117,not(X_118))) != implies(truth,implies(X_119,implies(X_118,not(X_117))))
| implies(X_119,implies(X_117,not(X_118))) = implies(X_119,implies(X_118,not(X_117))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_119,implies(X_118,not(X_117)))),implies(X_119,implies(X_118,not(X_117)))) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
( implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))) != implies(truth,implies(X_119,implies(X_118,not(X_117))))
| implies(X_119,implies(X_117,not(X_118))) = implies(X_119,implies(X_118,not(X_117))) ),
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_117,not(X_118))),implies(truth,implies(X_119,implies(X_118,not(X_117))))) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(X_119,implies(X_117,not(X_118))) = implies(X_119,implies(X_118,not(X_117))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_119,implies(X_118,not(X_117))),implies(X_119,implies(X_117,not(X_118)))),implies(X_119,implies(X_117,not(X_118)))),implies(truth,implies(X_119,implies(X_118,not(X_117))))) )],[refute_0_290,refute_0_305]) ).
cnf(refute_0_307,plain,
( implies(X_119,implies(X_117,not(X_118))) != implies(X_119,implies(X_118,not(X_117)))
| implies(X_119,implies(X_118,not(X_117))) = implies(X_119,implies(X_117,not(X_118))) ),
inference(subst,[],[refute_0_28:[bind(X0,$fot(implies(X_119,implies(X_117,not(X_118))))),bind(Y0,$fot(implies(X_119,implies(X_118,not(X_117)))))]]) ).
cnf(refute_0_308,plain,
implies(X_119,implies(X_118,not(X_117))) = implies(X_119,implies(X_117,not(X_118))),
inference(resolve,[$cnf( $equal(implies(X_119,implies(X_117,not(X_118))),implies(X_119,implies(X_118,not(X_117)))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(implies(x,y),implies(not(y),not(x))) = implies(implies(x,y),implies(x,not(not(y)))),
inference(subst,[],[refute_0_308:[bind(X_117,$fot(x)),bind(X_118,$fot(not(y))),bind(X_119,$fot(implies(x,y)))]]) ).
cnf(refute_0_310,plain,
( implies(implies(x,y),implies(not(y),not(x))) != implies(implies(x,y),implies(x,not(not(y))))
| implies(implies(x,y),implies(x,not(not(y)))) != truth
| implies(implies(x,y),implies(not(y),not(x))) = truth ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(implies(implies(x,y),implies(not(y),not(x))))),bind(Y0,$fot(implies(implies(x,y),implies(x,not(not(y)))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_311,plain,
( implies(implies(x,y),implies(x,not(not(y)))) != truth
| implies(implies(x,y),implies(not(y),not(x))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(not(y),not(x))),implies(implies(x,y),implies(x,not(not(y))))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
implies(implies(x,y),implies(not(y),not(x))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(x,not(not(y)))),truth) )],[refute_0_269,refute_0_311]) ).
cnf(refute_0_313,plain,
( implies(implies(x,y),implies(not(y),not(x))) != truth
| truth != truth
| implies(implies(x,y),implies(not(y),not(x))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(x,y),implies(not(y),not(x))),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_314,plain,
( truth != truth
| implies(implies(x,y),implies(not(y),not(x))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(not(y),not(x))),truth) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(implies(x,y),implies(not(y),not(x))),truth) )],[refute_0_314,prove_mv_36]) ).
cnf(refute_0_316,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_317,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_316,refute_0_315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL114-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 17:44:47 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.07/1.28
% 1.07/1.28 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.14/1.31
%------------------------------------------------------------------------------