TSTP Solution File: LCL145-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL145-1 : 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 12:49:57 EDT 2022
% Result : Unsatisfiable 1.39s 1.60s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 107
% Number of leaves : 147
% Syntax : Number of clauses : 550 ( 273 unt; 0 nHn; 336 RR)
% Number of literals : 956 ( 955 equ; 408 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 580 ( 26 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(big_V_definition,axiom,
big_V(X,Y) = implies(implies(X,Y),Y) ).
cnf(big_hat_definition,axiom,
big_hat(X,Y) = not(big_V(not(X),not(Y))) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
not(big_V(x,y)) != big_hat(not(x),not(y)) ).
cnf(refute_0_0,plain,
big_hat(not(X_98),Y) = not(big_V(not(not(X_98)),not(Y))),
inference(subst,[],[big_hat_definition:[bind(X,$fot(not(X_98)))]]) ).
cnf(refute_0_1,plain,
big_V(X,not(not(X))) = implies(implies(X,not(not(X))),not(not(X))),
inference(subst,[],[big_V_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_2,plain,
big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = implies(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(X_7,X_6)),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X_6),not(X_7)))),bind(Y,$fot(implies(X_7,X_6)))]]) ).
cnf(refute_0_3,plain,
implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_4,plain,
( big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != implies(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(X_7,X_6))
| implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != truth
| big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = implies(truth,implies(X_7,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(X_7,X_6))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_5,plain,
( big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != implies(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(X_7,X_6))
| big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = implies(truth,implies(X_7,X_6)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),truth) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = implies(truth,implies(X_7,X_6)),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(implies(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(X_7,X_6))) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( big_V(X,Y) != implies(implies(X,Y),Y)
| implies(implies(X,Y),Y) = big_V(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(implies(implies(X,Y),Y)))]]) ).
cnf(refute_0_11,plain,
implies(implies(X,Y),Y) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(X,Y),Y)) )],[big_V_definition,refute_0_10]) ).
cnf(refute_0_12,plain,
( implies(implies(X,Y),Y) != big_V(X,Y)
| implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) ),[0],$fot(big_V(X,Y))]]) ).
cnf(refute_0_13,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),big_V(X,Y)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(implies(Y,X),X) = big_V(Y,X),
inference(subst,[],[refute_0_11:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_15,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) != big_V(Y,X)
| big_V(X,Y) = big_V(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,Y),big_V(Y,X)) ),[0],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_16,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),X),big_V(Y,X)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(Y,X),X)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
big_V(X,Y) = big_V(Y,X),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( big_V(X,Y) != big_V(Y,X)
| big_V(Y,X) = big_V(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(big_V(Y,X)))]]) ).
cnf(refute_0_20,plain,
big_V(Y,X) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),big_V(Y,X)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) = big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))),
inference(subst,[],[refute_0_20:[bind(X,$fot(implies(X_7,X_6))),bind(Y,$fot(implies(not(X_6),not(X_7))))]]) ).
cnf(refute_0_22,plain,
( big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != big_V(implies(X_7,X_6),implies(not(X_6),not(X_7)))
| big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != implies(truth,implies(X_7,X_6))
| big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(truth,implies(X_7,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(truth,implies(X_7,X_6))) ),[0],$fot(big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))))]]) ).
cnf(refute_0_23,plain,
( big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != implies(truth,implies(X_7,X_6))
| big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(truth,implies(X_7,X_6)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)),big_V(implies(X_7,X_6),implies(not(X_6),not(X_7)))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
implies(truth,implies(X_7,X_6)) = implies(X_7,X_6),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_7,X_6)))]]) ).
cnf(refute_0_25,plain,
( big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) != implies(truth,implies(X_7,X_6))
| implies(truth,implies(X_7,X_6)) != implies(X_7,X_6)
| big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(X_7,X_6) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))),implies(X_7,X_6)) ),[0],$fot(implies(truth,implies(X_7,X_6)))]]) ).
cnf(refute_0_26,plain,
( big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) != implies(truth,implies(X_7,X_6))
| big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(X_7,X_6) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_7,X_6)),implies(X_7,X_6)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)) != implies(truth,implies(X_7,X_6))
| big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(X_7,X_6) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))),implies(truth,implies(X_7,X_6))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
big_V(implies(X_7,X_6),implies(not(X_6),not(X_7))) = implies(X_7,X_6),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_6),not(X_7)),implies(X_7,X_6)),implies(truth,implies(X_7,X_6))) )],[refute_0_6,refute_0_27]) ).
cnf(refute_0_29,plain,
big_V(implies(X_7,not(not(X_7))),implies(not(not(not(X_7))),not(X_7))) = implies(X_7,not(not(X_7))),
inference(subst,[],[refute_0_28:[bind(X_6,$fot(not(not(X_7))))]]) ).
cnf(refute_0_30,plain,
implies(implies(X_31,implies(not(X_33),not(truth))),implies(implies(implies(not(X_33),not(truth)),X_33),implies(X_31,X_33))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_31)),bind(Y,$fot(implies(not(X_33),not(truth)))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_31,plain,
implies(implies(not(X_6),not(truth)),implies(truth,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_32,plain,
implies(truth,X_6) = X_6,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_33,plain,
( implies(implies(not(X_6),not(truth)),implies(truth,X_6)) != truth
| implies(truth,X_6) != X_6
| implies(implies(not(X_6),not(truth)),X_6) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(truth)),implies(truth,X_6)),truth) ),[0,1],$fot(X_6)]]) ).
cnf(refute_0_34,plain,
( implies(implies(not(X_6),not(truth)),implies(truth,X_6)) != truth
| implies(implies(not(X_6),not(truth)),X_6) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_6),X_6) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(not(X_6),not(truth)),X_6) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(truth)),implies(truth,X_6)),truth) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(implies(not(X_33),not(truth)),X_33) = truth,
inference(subst,[],[refute_0_35:[bind(X_6,$fot(X_33))]]) ).
cnf(refute_0_37,plain,
( implies(implies(X_31,implies(not(X_33),not(truth))),implies(implies(implies(not(X_33),not(truth)),X_33),implies(X_31,X_33))) != truth
| implies(implies(not(X_33),not(truth)),X_33) != truth
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(implies(implies(not(X_33),not(truth)),X_33),implies(X_31,X_33))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_38,plain,
( implies(implies(X_31,implies(not(X_33),not(truth))),implies(implies(implies(not(X_33),not(truth)),X_33),implies(X_31,X_33))) != truth
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_33),not(truth)),X_33),truth) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(implies(implies(not(X_33),not(truth)),X_33),implies(X_31,X_33))),truth) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(truth,implies(X_31,X_33)) = implies(X_31,X_33),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_31,X_33)))]]) ).
cnf(refute_0_41,plain,
implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),
introduced(tautology,[refl,[$fot(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))))]]) ).
cnf(refute_0_42,plain,
( implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) != implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33)))
| implies(truth,implies(X_31,X_33)) != implies(X_31,X_33)
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33)))) ),[1,1],$fot(implies(X_31,X_33))]]) ).
cnf(refute_0_43,plain,
( implies(truth,implies(X_31,X_33)) != implies(X_31,X_33)
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) = implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_31,X_33)),implies(X_31,X_33)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) != implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33))
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) != truth
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),truth) ),[0],$fot(implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)))]]) ).
cnf(refute_0_46,plain,
( implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))) != truth
| implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(implies(X_31,implies(not(X_33),not(truth))),implies(X_31,X_33)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_31,implies(not(X_33),not(truth))),implies(truth,implies(X_31,X_33))),truth) )],[refute_0_39,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),implies(implies(not(not(truth)),not(not(X_86))),X_86)) = truth,
inference(subst,[],[refute_0_47:[bind(X_31,$fot(implies(not(not(truth)),not(not(X_86))))),bind(X_33,$fot(X_86))]]) ).
cnf(refute_0_49,plain,
implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_86)))]]) ).
cnf(refute_0_50,plain,
( implies(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),implies(implies(not(not(truth)),not(not(X_86))),X_86)) != truth
| implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),implies(implies(not(not(truth)),not(not(X_86))),X_86)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_51,plain,
( implies(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),implies(implies(not(not(truth)),not(not(X_86))),X_86)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),truth) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_86))),implies(not(X_86),not(truth))),implies(implies(not(not(truth)),not(not(X_86))),X_86)),truth) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(truth,not(not(X_86))) = not(not(X_86)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_86))))]]) ).
cnf(refute_0_54,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(subst,[],[refute_0_47:[bind(X_31,$fot(not(truth))),bind(X_33,$fot(not(not(truth))))]]) ).
cnf(refute_0_55,plain,
big_V(implies(X_1,Y),Y) = implies(implies(implies(X_1,Y),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(X_1,Y)))]]) ).
cnf(refute_0_56,plain,
big_V(X_1,Y) = implies(implies(X_1,Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_57,plain,
( big_V(X_1,Y) != implies(implies(X_1,Y),Y)
| implies(implies(X_1,Y),Y) = big_V(X_1,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(X_1,Y))),bind(Y0,$fot(implies(implies(X_1,Y),Y)))]]) ).
cnf(refute_0_58,plain,
implies(implies(X_1,Y),Y) = big_V(X_1,Y),
inference(resolve,[$cnf( $equal(big_V(X_1,Y),implies(implies(X_1,Y),Y)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( big_V(implies(X_1,Y),Y) != implies(implies(implies(X_1,Y),Y),Y)
| implies(implies(X_1,Y),Y) != big_V(X_1,Y)
| big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(implies(implies(X_1,Y),Y),Y)) ),[1,0],$fot(big_V(X_1,Y))]]) ).
cnf(refute_0_60,plain,
( big_V(implies(X_1,Y),Y) != implies(implies(implies(X_1,Y),Y),Y)
| big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1,Y),Y),big_V(X_1,Y)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(implies(implies(X_1,Y),Y),Y)) )],[refute_0_55,refute_0_60]) ).
cnf(refute_0_62,plain,
big_V(implies(X_1,Y),Y) = big_V(Y,implies(X_1,Y)),
inference(subst,[],[refute_0_20:[bind(X,$fot(Y)),bind(Y,$fot(implies(X_1,Y)))]]) ).
cnf(refute_0_63,plain,
( big_V(implies(X_1,Y),Y) != big_V(Y,implies(X_1,Y))
| big_V(implies(X_1,Y),Y) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(big_V(X_1,Y),Y)) ),[0],$fot(big_V(Y,implies(X_1,Y)))]]) ).
cnf(refute_0_64,plain,
( big_V(implies(X_1,Y),Y) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),big_V(Y,implies(X_1,Y))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(big_V(X_1,Y),Y)) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(big_V(not(truth),not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_65:[bind(Y,$fot(not(not(truth)))),bind(X_1,$fot(not(truth)))]]) ).
cnf(refute_0_67,plain,
big_V(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(truth)),not(truth)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_68,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_35:[bind(X_6,$fot(not(truth)))]]) ).
cnf(refute_0_69,plain,
( big_V(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(truth)),not(truth))
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| big_V(not(not(truth)),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(truth)),not(truth)))]]) ).
cnf(refute_0_70,plain,
( big_V(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(truth)),not(truth))
| big_V(not(not(truth)),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(truth)),not(truth))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
big_V(not(not(truth)),not(truth)) = big_V(not(truth),not(not(truth))),
inference(subst,[],[refute_0_20:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_73,plain,
( big_V(not(not(truth)),not(truth)) != big_V(not(truth),not(not(truth)))
| big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(big_V(not(truth),not(not(truth))))]]) ).
cnf(refute_0_74,plain,
( big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),big_V(not(truth),not(not(truth)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
big_V(not(truth),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(big_V(not(truth),not(not(truth))),not(not(truth)))
| big_V(not(truth),not(not(truth))) != truth
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(big_V(not(truth),not(not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_77,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(big_V(not(truth),not(not(truth))),not(not(truth)))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(truth),not(not(truth))),truth) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(big_V(not(truth),not(not(truth))),not(not(truth)))) )],[refute_0_66,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_80,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),not(not(truth))) ),[0],$fot(implies(truth,not(not(truth))))]]) ).
cnf(refute_0_81,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(truth,not(not(truth)))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(truth,not(not(truth)))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
big_V(X,implies(X_48,X)) = implies(implies(X,implies(X_48,X)),implies(X_48,X)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(implies(X_48,X)))]]) ).
cnf(refute_0_84,plain,
implies(implies(X_31,truth),implies(implies(truth,X_33),implies(X_31,X_33))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_31)),bind(Y,$fot(truth)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_85,plain,
implies(truth,X_33) = X_33,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_33))]]) ).
cnf(refute_0_86,plain,
( implies(implies(X_31,truth),implies(implies(truth,X_33),implies(X_31,X_33))) != truth
| implies(truth,X_33) != X_33
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,truth),implies(implies(truth,X_33),implies(X_31,X_33))),truth) ),[0,1,0],$fot(X_33)]]) ).
cnf(refute_0_87,plain,
( implies(implies(X_31,truth),implies(implies(truth,X_33),implies(X_31,X_33))) != truth
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_33),X_33) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_31,truth),implies(implies(truth,X_33),implies(X_31,X_33))),truth) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
implies(truth,implies(X_33,implies(X_31,X_33))) = implies(X_33,implies(X_31,X_33)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_33,implies(X_31,X_33))))]]) ).
cnf(refute_0_90,plain,
implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(big_V(truth,not(X_6)))),bind(Y,$fot(X_32)),bind(Z,$fot(big_V(truth,X_6)))]]) ).
cnf(refute_0_91,plain,
implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_92,plain,
big_V(truth,X_2) = implies(implies(truth,X_2),X_2),
inference(subst,[],[big_V_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_93,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_94,plain,
( big_V(truth,X_2) != implies(implies(truth,X_2),X_2)
| implies(truth,X_2) != X_2
| big_V(truth,X_2) = implies(X_2,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_2),implies(implies(truth,X_2),X_2)) ),[1,0],$fot(X_2)]]) ).
cnf(refute_0_95,plain,
( big_V(truth,X_2) != implies(implies(truth,X_2),X_2)
| big_V(truth,X_2) = implies(X_2,X_2) ),
inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
big_V(truth,X_2) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),implies(implies(truth,X_2),X_2)) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
big_V(truth,X_6) = implies(X_6,X_6),
inference(subst,[],[refute_0_96:[bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_98,plain,
( big_V(truth,X_6) != implies(X_6,X_6)
| implies(X_6,X_6) = big_V(truth,X_6) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(truth,X_6))),bind(Y0,$fot(implies(X_6,X_6)))]]) ).
cnf(refute_0_99,plain,
implies(X_6,X_6) = big_V(truth,X_6),
inference(resolve,[$cnf( $equal(big_V(truth,X_6),implies(X_6,X_6)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( implies(X_6,X_6) != big_V(truth,X_6)
| implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) ),[0,1],$fot(big_V(truth,X_6))]]) ).
cnf(refute_0_101,plain,
( implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_6,X_6),big_V(truth,X_6)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) )],[refute_0_91,refute_0_101]) ).
cnf(refute_0_103,plain,
( big_V(truth,X_2) != implies(X_2,X_2)
| implies(X_2,X_2) = big_V(truth,X_2) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(truth,X_2))),bind(Y0,$fot(implies(X_2,X_2)))]]) ).
cnf(refute_0_104,plain,
implies(X_2,X_2) = big_V(truth,X_2),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),implies(X_2,X_2)) )],[refute_0_96,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(not(X_6),not(X_6)) = big_V(truth,not(X_6)),
inference(subst,[],[refute_0_104:[bind(X_2,$fot(not(X_6)))]]) ).
cnf(refute_0_106,plain,
implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)))]]) ).
cnf(refute_0_107,plain,
( implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) != implies(implies(not(X_6),not(X_6)),big_V(truth,X_6))
| implies(not(X_6),not(X_6)) != big_V(truth,not(X_6))
| implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = implies(big_V(truth,not(X_6)),big_V(truth,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),implies(implies(not(X_6),not(X_6)),big_V(truth,X_6))) ),[1,0],$fot(big_V(truth,not(X_6)))]]) ).
cnf(refute_0_108,plain,
( implies(not(X_6),not(X_6)) != big_V(truth,not(X_6))
| implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = implies(big_V(truth,not(X_6)),big_V(truth,X_6)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),implies(implies(not(X_6),not(X_6)),big_V(truth,X_6))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) = implies(big_V(truth,not(X_6)),big_V(truth,X_6)),
inference(resolve,[$cnf( $equal(implies(not(X_6),not(X_6)),big_V(truth,not(X_6))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) != implies(big_V(truth,not(X_6)),big_V(truth,X_6))
| implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(truth,X_6)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),truth) ),[0],$fot(implies(big_V(truth,not(X_6)),big_V(truth,X_6)))]]) ).
cnf(refute_0_111,plain,
( implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(truth,X_6)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(big_V(truth,not(X_6)),big_V(truth,X_6)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),big_V(truth,X_6)),truth) )],[refute_0_102,refute_0_111]) ).
cnf(refute_0_113,plain,
( implies(big_V(truth,not(X_6)),big_V(truth,X_6)) != truth
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6)))) != truth
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_114,plain,
( implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6)))) != truth
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(truth,X_6)),truth) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),implies(big_V(truth,not(X_6)),big_V(truth,X_6)))),truth) )],[refute_0_90,refute_0_114]) ).
cnf(refute_0_116,plain,
big_V(truth,X_6) = big_V(X_6,truth),
inference(subst,[],[refute_0_18:[bind(X,$fot(truth)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_117,plain,
( big_V(truth,X_6) != big_V(X_6,truth)
| implies(big_V(truth,not(X_6)),big_V(truth,X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(truth,X_6)),truth) ),[0,1],$fot(big_V(X_6,truth))]]) ).
cnf(refute_0_118,plain,
( implies(big_V(truth,not(X_6)),big_V(truth,X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,X_6),big_V(X_6,truth)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(truth,X_6)),truth) )],[refute_0_112,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(truth,big_V(X_6,truth)) = big_V(X_6,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X_6,truth)))]]) ).
cnf(refute_0_121,plain,
implies(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))))),bind(Y,$fot(truth)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_122,plain,
implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(truth)),bind(Y,$fot(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))))]]) ).
cnf(refute_0_123,plain,
implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))) = truth,
inference(subst,[],[refute_0_112:[bind(X_6,$fot(big_V(truth,not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_124,plain,
big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) = implies(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth),
inference(subst,[],[big_V_definition:[bind(X,$fot(big_V(truth,not(big_V(truth,not(truth)))))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_125,plain,
implies(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,big_V(truth,not(truth)))) = truth,
inference(subst,[],[refute_0_112:[bind(X_6,$fot(big_V(truth,not(truth))))]]) ).
cnf(refute_0_126,plain,
big_V(big_V(truth,not(truth)),truth) = implies(implies(big_V(truth,not(truth)),truth),truth),
inference(subst,[],[big_V_definition:[bind(X,$fot(big_V(truth,not(truth)))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_127,plain,
implies(implies(not(truth),not(truth)),truth) = truth,
inference(subst,[],[refute_0_35:[bind(X_6,$fot(truth))]]) ).
cnf(refute_0_128,plain,
big_V(truth,not(truth)) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_96:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_129,plain,
( big_V(truth,not(truth)) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) = big_V(truth,not(truth)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(truth,not(truth)))),bind(Y0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_130,plain,
implies(not(truth),not(truth)) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),implies(not(truth),not(truth))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( implies(implies(not(truth),not(truth)),truth) != truth
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(big_V(truth,not(truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),truth),truth) ),[0,0],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_132,plain,
( implies(implies(not(truth),not(truth)),truth) != truth
| implies(big_V(truth,not(truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(big_V(truth,not(truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),truth),truth) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
( big_V(big_V(truth,not(truth)),truth) != implies(implies(big_V(truth,not(truth)),truth),truth)
| implies(big_V(truth,not(truth)),truth) != truth
| big_V(big_V(truth,not(truth)),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),truth),implies(implies(big_V(truth,not(truth)),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_135,plain,
( big_V(big_V(truth,not(truth)),truth) != implies(implies(big_V(truth,not(truth)),truth),truth)
| big_V(big_V(truth,not(truth)),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(truth)),truth),truth) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
big_V(big_V(truth,not(truth)),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),truth),implies(implies(big_V(truth,not(truth)),truth),truth)) )],[refute_0_126,refute_0_135]) ).
cnf(refute_0_137,plain,
big_V(big_V(truth,not(truth)),truth) = big_V(truth,big_V(truth,not(truth))),
inference(subst,[],[refute_0_20:[bind(X,$fot(truth)),bind(Y,$fot(big_V(truth,not(truth))))]]) ).
cnf(refute_0_138,plain,
( big_V(big_V(truth,not(truth)),truth) != big_V(truth,big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(truth))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),truth),implies(truth,truth)) ),[0],$fot(big_V(truth,big_V(truth,not(truth))))]]) ).
cnf(refute_0_139,plain,
( big_V(big_V(truth,not(truth)),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(truth))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),truth),big_V(truth,big_V(truth,not(truth)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_141,plain,
( big_V(truth,big_V(truth,not(truth))) != implies(truth,truth)
| implies(truth,truth) != truth
| big_V(truth,big_V(truth,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,big_V(truth,not(truth))),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_142,plain,
( big_V(truth,big_V(truth,not(truth))) != implies(truth,truth)
| big_V(truth,big_V(truth,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
( big_V(big_V(truth,not(truth)),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,not(truth))),implies(truth,truth)) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
big_V(truth,big_V(truth,not(truth))) = truth,
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),truth),implies(truth,truth)) )],[refute_0_136,refute_0_143]) ).
cnf(refute_0_145,plain,
( big_V(truth,big_V(truth,not(truth))) != truth
| implies(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,big_V(truth,not(truth)))) != truth
| implies(big_V(truth,not(big_V(truth,not(truth)))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,big_V(truth,not(truth)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_146,plain,
( implies(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,big_V(truth,not(truth)))) != truth
| implies(big_V(truth,not(big_V(truth,not(truth)))),truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,not(truth))),truth) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(big_V(truth,not(big_V(truth,not(truth)))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,big_V(truth,not(truth)))),truth) )],[refute_0_125,refute_0_146]) ).
cnf(refute_0_148,plain,
( big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != implies(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth)
| implies(big_V(truth,not(big_V(truth,not(truth)))),truth) != truth
| big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(big_V(truth,not(truth)))),truth),implies(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_149,plain,
( big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != implies(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth)
| big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(big_V(truth,not(truth)))),truth),implies(implies(big_V(truth,not(big_V(truth,not(truth)))),truth),truth)) )],[refute_0_124,refute_0_149]) ).
cnf(refute_0_151,plain,
big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) = big_V(truth,big_V(truth,not(big_V(truth,not(truth))))),
inference(subst,[],[refute_0_20:[bind(X,$fot(truth)),bind(Y,$fot(big_V(truth,not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_152,plain,
( big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))
| big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(big_V(truth,not(truth)))),truth),implies(truth,truth)) ),[0],$fot(big_V(truth,big_V(truth,not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_153,plain,
( big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(big_V(truth,not(truth)))),truth),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
( big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) != implies(truth,truth)
| implies(truth,truth) != truth
| big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,big_V(truth,not(big_V(truth,not(truth))))),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_155,plain,
( big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) != implies(truth,truth)
| big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_140,refute_0_154]) ).
cnf(refute_0_156,plain,
( big_V(big_V(truth,not(big_V(truth,not(truth)))),truth) != implies(truth,truth)
| big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,not(big_V(truth,not(truth))))),implies(truth,truth)) )],[refute_0_153,refute_0_155]) ).
cnf(refute_0_157,plain,
big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) = truth,
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(big_V(truth,not(truth)))),truth),implies(truth,truth)) )],[refute_0_150,refute_0_156]) ).
cnf(refute_0_158,plain,
( big_V(truth,big_V(truth,not(big_V(truth,not(truth))))) != truth
| implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))) != truth
| implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_159,plain,
( implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))) != truth
| implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,not(big_V(truth,not(truth))))),truth) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,big_V(truth,not(big_V(truth,not(truth)))))),truth) )],[refute_0_123,refute_0_159]) ).
cnf(refute_0_161,plain,
( implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth)) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_162,plain,
( implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth)) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth),truth) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth)),truth) )],[refute_0_122,refute_0_162]) ).
cnf(refute_0_164,plain,
( implies(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth) != truth
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_165,plain,
( implies(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != truth
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),truth) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),truth) )],[refute_0_121,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)))]]) ).
cnf(refute_0_168,plain,
( implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(truth,X_33) != X_33
| implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) ),[1,0],$fot(X_33)]]) ).
cnf(refute_0_169,plain,
( implies(truth,X_33) != X_33
| implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),
inference(resolve,[$cnf( $equal(implies(truth,X_33),X_33) )],[refute_0_85,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))))]]) ).
cnf(refute_0_172,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_173,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_172]) ).
cnf(refute_0_174,plain,
( implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))))),bind(Y0,$fot(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)))),bind(Z0,$fot(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))))]]) ).
cnf(refute_0_175,plain,
( implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) )],[refute_0_170,refute_0_175]) ).
cnf(refute_0_177,plain,
( implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != truth
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),truth) ),[0],$fot(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)))]]) ).
cnf(refute_0_178,plain,
( implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) != truth
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),truth) )],[refute_0_166,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(X_33,X_33) = big_V(truth,X_33),
inference(subst,[],[refute_0_104:[bind(X_2,$fot(X_33))]]) ).
cnf(refute_0_181,plain,
big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = implies(big_V(truth,big_V(truth,not(truth))),big_V(truth,not(truth))),
inference(subst,[],[refute_0_65:[bind(Y,$fot(big_V(truth,not(truth)))),bind(X_1,$fot(truth))]]) ).
cnf(refute_0_182,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != implies(big_V(truth,big_V(truth,not(truth))),big_V(truth,not(truth)))
| big_V(truth,big_V(truth,not(truth))) != truth
| big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = implies(truth,big_V(truth,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),implies(big_V(truth,big_V(truth,not(truth))),big_V(truth,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_183,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != implies(big_V(truth,big_V(truth,not(truth))),big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = implies(truth,big_V(truth,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,not(truth))),truth) )],[refute_0_144,refute_0_182]) ).
cnf(refute_0_184,plain,
big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = implies(truth,big_V(truth,not(truth))),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),implies(big_V(truth,big_V(truth,not(truth))),big_V(truth,not(truth)))) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(truth,big_V(truth,not(truth))) = big_V(truth,not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(truth,not(truth))))]]) ).
cnf(refute_0_186,plain,
big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),
introduced(tautology,[refl,[$fot(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))))]]) ).
cnf(refute_0_187,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth))))
| implies(truth,big_V(truth,not(truth))) != big_V(truth,not(truth))
| big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth))))) ),[1,1],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_188,plain,
( implies(truth,big_V(truth,not(truth))) != big_V(truth,not(truth))
| big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth))))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) = big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,not(truth))),big_V(truth,not(truth))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != big_V(big_V(truth,not(truth)),big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != implies(truth,big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = implies(truth,big_V(truth,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),implies(truth,big_V(truth,not(truth)))) ),[0],$fot(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))))]]) ).
cnf(refute_0_191,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != implies(truth,big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = implies(truth,big_V(truth,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),big_V(big_V(truth,not(truth)),big_V(truth,not(truth)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
( big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) != implies(truth,big_V(truth,not(truth)))
| implies(truth,big_V(truth,not(truth))) != big_V(truth,not(truth))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = big_V(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),big_V(truth,not(truth))) ),[0],$fot(implies(truth,big_V(truth,not(truth))))]]) ).
cnf(refute_0_193,plain,
( big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) != implies(truth,big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,not(truth))),big_V(truth,not(truth))) )],[refute_0_185,refute_0_192]) ).
cnf(refute_0_194,plain,
( big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))) != implies(truth,big_V(truth,not(truth)))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),implies(truth,big_V(truth,not(truth)))) )],[refute_0_191,refute_0_193]) ).
cnf(refute_0_195,plain,
big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),implies(truth,big_V(truth,not(truth)))),implies(truth,big_V(truth,not(truth)))) )],[refute_0_184,refute_0_194]) ).
cnf(refute_0_196,plain,
big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = implies(big_V(truth,big_V(truth,X_30)),big_V(truth,X_30)),
inference(subst,[],[refute_0_65:[bind(Y,$fot(big_V(truth,X_30))),bind(X_1,$fot(truth))]]) ).
cnf(refute_0_197,plain,
big_V(X_1,Y) = big_V(Y,X_1),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_198,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| big_V(X_1,Y) != big_V(Y,X_1)
| big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) ),[1,0],$fot(big_V(Y,X_1))]]) ).
cnf(refute_0_199,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y) ),
inference(resolve,[$cnf( $equal(big_V(X_1,Y),big_V(Y,X_1)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) )],[refute_0_65,refute_0_199]) ).
cnf(refute_0_201,plain,
big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = implies(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(X_9,truth)),
inference(subst,[],[refute_0_200:[bind(Y,$fot(big_V(X_9,truth))),bind(X_1,$fot(big_V(truth,not(X_9))))]]) ).
cnf(refute_0_202,plain,
big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) = implies(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(truth,X_9)),
inference(subst,[],[big_V_definition:[bind(X,$fot(big_V(truth,not(X_9)))),bind(Y,$fot(big_V(truth,X_9)))]]) ).
cnf(refute_0_203,plain,
implies(big_V(truth,not(X_9)),big_V(truth,X_9)) = truth,
inference(subst,[],[refute_0_112:[bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_204,plain,
( big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != implies(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(truth,X_9))
| implies(big_V(truth,not(X_9)),big_V(truth,X_9)) != truth
| big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) = implies(truth,big_V(truth,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(X_9)),big_V(truth,X_9)),implies(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(truth,X_9))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_205,plain,
( big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != implies(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(truth,X_9))
| big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) = implies(truth,big_V(truth,X_9)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),truth) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) = implies(truth,big_V(truth,X_9)),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(X_9)),big_V(truth,X_9)),implies(implies(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(truth,X_9))) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) = big_V(big_V(truth,X_9),big_V(truth,not(X_9))),
inference(subst,[],[refute_0_20:[bind(X,$fot(big_V(truth,X_9))),bind(Y,$fot(big_V(truth,not(X_9))))]]) ).
cnf(refute_0_208,plain,
( big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != big_V(big_V(truth,X_9),big_V(truth,not(X_9)))
| big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != implies(truth,big_V(truth,X_9))
| big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = implies(truth,big_V(truth,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(X_9)),big_V(truth,X_9)),implies(truth,big_V(truth,X_9))) ),[0],$fot(big_V(big_V(truth,X_9),big_V(truth,not(X_9))))]]) ).
cnf(refute_0_209,plain,
( big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != implies(truth,big_V(truth,X_9))
| big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = implies(truth,big_V(truth,X_9)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(X_9)),big_V(truth,X_9)),big_V(big_V(truth,X_9),big_V(truth,not(X_9)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(truth,big_V(truth,X_9)) = big_V(truth,X_9),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(truth,X_9)))]]) ).
cnf(refute_0_211,plain,
( big_V(big_V(truth,X_9),big_V(truth,not(X_9))) != implies(truth,big_V(truth,X_9))
| implies(truth,big_V(truth,X_9)) != big_V(truth,X_9)
| big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = big_V(truth,X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(truth,X_9),big_V(truth,not(X_9))),big_V(truth,X_9)) ),[0],$fot(implies(truth,big_V(truth,X_9)))]]) ).
cnf(refute_0_212,plain,
( big_V(big_V(truth,X_9),big_V(truth,not(X_9))) != implies(truth,big_V(truth,X_9))
| big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = big_V(truth,X_9) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_9)),big_V(truth,X_9)) )],[refute_0_210,refute_0_211]) ).
cnf(refute_0_213,plain,
( big_V(big_V(truth,not(X_9)),big_V(truth,X_9)) != implies(truth,big_V(truth,X_9))
| big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = big_V(truth,X_9) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_9),big_V(truth,not(X_9))),implies(truth,big_V(truth,X_9))) )],[refute_0_209,refute_0_212]) ).
cnf(refute_0_214,plain,
big_V(big_V(truth,X_9),big_V(truth,not(X_9))) = big_V(truth,X_9),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(X_9)),big_V(truth,X_9)),implies(truth,big_V(truth,X_9))) )],[refute_0_206,refute_0_213]) ).
cnf(refute_0_215,plain,
big_V(truth,X_9) = big_V(X_9,truth),
inference(subst,[],[refute_0_18:[bind(X,$fot(truth)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_216,plain,
( big_V(big_V(truth,X_9),big_V(truth,not(X_9))) != big_V(truth,X_9)
| big_V(truth,X_9) != big_V(X_9,truth)
| big_V(big_V(X_9,truth),big_V(truth,not(X_9))) = big_V(truth,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,X_9),big_V(truth,not(X_9))),big_V(truth,X_9)) ),[0,0],$fot(big_V(X_9,truth))]]) ).
cnf(refute_0_217,plain,
( big_V(big_V(truth,X_9),big_V(truth,not(X_9))) != big_V(truth,X_9)
| big_V(big_V(X_9,truth),big_V(truth,not(X_9))) = big_V(truth,X_9) ),
inference(resolve,[$cnf( $equal(big_V(truth,X_9),big_V(X_9,truth)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
big_V(big_V(X_9,truth),big_V(truth,not(X_9))) = big_V(truth,X_9),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_9),big_V(truth,not(X_9))),big_V(truth,X_9)) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
( big_V(big_V(X_9,truth),big_V(truth,not(X_9))) != big_V(truth,X_9)
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != implies(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(X_9,truth))
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = implies(big_V(truth,X_9),big_V(X_9,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),implies(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(X_9,truth))) ),[1,0],$fot(big_V(truth,X_9))]]) ).
cnf(refute_0_220,plain,
( big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != implies(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(X_9,truth))
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = implies(big_V(truth,X_9),big_V(X_9,truth)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(truth,X_9)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = implies(big_V(truth,X_9),big_V(X_9,truth)),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),implies(big_V(big_V(X_9,truth),big_V(truth,not(X_9))),big_V(X_9,truth))) )],[refute_0_201,refute_0_220]) ).
cnf(refute_0_222,plain,
big_V(big_V(X_9,truth),truth) = big_V(truth,big_V(X_9,truth)),
inference(subst,[],[refute_0_20:[bind(X,$fot(truth)),bind(Y,$fot(big_V(X_9,truth)))]]) ).
cnf(refute_0_223,plain,
implies(big_V(truth,not(X_9)),big_V(X_9,truth)) = truth,
inference(subst,[],[refute_0_119:[bind(X_6,$fot(X_9))]]) ).
cnf(refute_0_224,plain,
big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),
introduced(tautology,[refl,[$fot(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))))]]) ).
cnf(refute_0_225,plain,
( big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth)))
| implies(big_V(truth,not(X_9)),big_V(X_9,truth)) != truth
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(big_V(X_9,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_226,plain,
( implies(big_V(truth,not(X_9)),big_V(X_9,truth)) != truth
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(big_V(X_9,truth),truth) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth)))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(big_V(X_9,truth),truth),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_9)),big_V(X_9,truth)),truth) )],[refute_0_223,refute_0_226]) ).
cnf(refute_0_228,plain,
( big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != big_V(big_V(X_9,truth),truth)
| big_V(big_V(X_9,truth),truth) != big_V(truth,big_V(X_9,truth))
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(truth,big_V(X_9,truth)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))))),bind(Y0,$fot(big_V(big_V(X_9,truth),truth))),bind(Z0,$fot(big_V(truth,big_V(X_9,truth))))]]) ).
cnf(refute_0_229,plain,
( big_V(big_V(X_9,truth),truth) != big_V(truth,big_V(X_9,truth))
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(truth,big_V(X_9,truth)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),big_V(big_V(X_9,truth),truth)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) = big_V(truth,big_V(X_9,truth)),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),truth),big_V(truth,big_V(X_9,truth))) )],[refute_0_222,refute_0_229]) ).
cnf(refute_0_231,plain,
( big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != big_V(truth,big_V(X_9,truth))
| big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != implies(big_V(truth,X_9),big_V(X_9,truth))
| big_V(truth,big_V(X_9,truth)) = implies(big_V(truth,X_9),big_V(X_9,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),implies(big_V(truth,X_9),big_V(X_9,truth))) ),[0],$fot(big_V(truth,big_V(X_9,truth)))]]) ).
cnf(refute_0_232,plain,
( big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))) != implies(big_V(truth,X_9),big_V(X_9,truth))
| big_V(truth,big_V(X_9,truth)) = implies(big_V(truth,X_9),big_V(X_9,truth)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),big_V(truth,big_V(X_9,truth))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
big_V(truth,big_V(X_9,truth)) = implies(big_V(truth,X_9),big_V(X_9,truth)),
inference(resolve,[$cnf( $equal(big_V(big_V(X_9,truth),implies(big_V(truth,not(X_9)),big_V(X_9,truth))),implies(big_V(truth,X_9),big_V(X_9,truth))) )],[refute_0_221,refute_0_232]) ).
cnf(refute_0_234,plain,
big_V(truth,big_V(X_26,truth)) = implies(big_V(truth,X_26),big_V(X_26,truth)),
inference(subst,[],[refute_0_233:[bind(X_9,$fot(X_26))]]) ).
cnf(refute_0_235,plain,
big_V(truth,X_26) = big_V(X_26,truth),
inference(subst,[],[refute_0_18:[bind(X,$fot(truth)),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_236,plain,
( big_V(truth,X_26) != big_V(X_26,truth)
| big_V(X_26,truth) = big_V(truth,X_26) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(truth,X_26))),bind(Y0,$fot(big_V(X_26,truth)))]]) ).
cnf(refute_0_237,plain,
big_V(X_26,truth) = big_V(truth,X_26),
inference(resolve,[$cnf( $equal(big_V(truth,X_26),big_V(X_26,truth)) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
( big_V(X_26,truth) != big_V(truth,X_26)
| big_V(truth,big_V(X_26,truth)) != implies(big_V(truth,X_26),big_V(X_26,truth))
| big_V(truth,big_V(truth,X_26)) = implies(big_V(truth,X_26),big_V(X_26,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,big_V(X_26,truth)),implies(big_V(truth,X_26),big_V(X_26,truth))) ),[0,1],$fot(big_V(truth,X_26))]]) ).
cnf(refute_0_239,plain,
( big_V(truth,big_V(X_26,truth)) != implies(big_V(truth,X_26),big_V(X_26,truth))
| big_V(truth,big_V(truth,X_26)) = implies(big_V(truth,X_26),big_V(X_26,truth)) ),
inference(resolve,[$cnf( $equal(big_V(X_26,truth),big_V(truth,X_26)) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
big_V(truth,big_V(truth,X_26)) = implies(big_V(truth,X_26),big_V(X_26,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(X_26,truth)),implies(big_V(truth,X_26),big_V(X_26,truth))) )],[refute_0_234,refute_0_239]) ).
cnf(refute_0_241,plain,
( big_V(truth,big_V(X_9,truth)) != implies(big_V(truth,X_9),big_V(X_9,truth))
| implies(big_V(truth,X_9),big_V(X_9,truth)) = big_V(truth,big_V(X_9,truth)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(truth,big_V(X_9,truth)))),bind(Y0,$fot(implies(big_V(truth,X_9),big_V(X_9,truth))))]]) ).
cnf(refute_0_242,plain,
implies(big_V(truth,X_9),big_V(X_9,truth)) = big_V(truth,big_V(X_9,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(X_9,truth)),implies(big_V(truth,X_9),big_V(X_9,truth))) )],[refute_0_233,refute_0_241]) ).
cnf(refute_0_243,plain,
implies(big_V(truth,X_26),big_V(X_26,truth)) = big_V(truth,big_V(X_26,truth)),
inference(subst,[],[refute_0_242:[bind(X_9,$fot(X_26))]]) ).
cnf(refute_0_244,plain,
( big_V(truth,big_V(truth,X_26)) != implies(big_V(truth,X_26),big_V(X_26,truth))
| implies(big_V(truth,X_26),big_V(X_26,truth)) != big_V(truth,big_V(X_26,truth))
| big_V(truth,big_V(truth,X_26)) = big_V(truth,big_V(X_26,truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,big_V(truth,X_26)),big_V(truth,big_V(X_26,truth))) ),[0],$fot(implies(big_V(truth,X_26),big_V(X_26,truth)))]]) ).
cnf(refute_0_245,plain,
( big_V(truth,big_V(truth,X_26)) != implies(big_V(truth,X_26),big_V(X_26,truth))
| big_V(truth,big_V(truth,X_26)) = big_V(truth,big_V(X_26,truth)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,X_26),big_V(X_26,truth)),big_V(truth,big_V(X_26,truth))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
big_V(truth,big_V(truth,X_26)) = big_V(truth,big_V(X_26,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,X_26)),implies(big_V(truth,X_26),big_V(X_26,truth))) )],[refute_0_240,refute_0_245]) ).
cnf(refute_0_247,plain,
big_V(truth,big_V(truth,X_30)) = big_V(truth,big_V(X_30,truth)),
inference(subst,[],[refute_0_246:[bind(X_26,$fot(X_30))]]) ).
cnf(refute_0_248,plain,
( big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != implies(big_V(truth,big_V(truth,X_30)),big_V(truth,X_30))
| big_V(truth,big_V(truth,X_30)) != big_V(truth,big_V(X_30,truth))
| big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),implies(big_V(truth,big_V(truth,X_30)),big_V(truth,X_30))) ),[1,0],$fot(big_V(truth,big_V(X_30,truth)))]]) ).
cnf(refute_0_249,plain,
( big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != implies(big_V(truth,big_V(truth,X_30)),big_V(truth,X_30))
| big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) ),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(truth,X_30)),big_V(truth,big_V(X_30,truth))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),implies(big_V(truth,big_V(truth,X_30)),big_V(truth,X_30))) )],[refute_0_196,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(truth,big_V(truth,X_30)) = big_V(truth,X_30),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(truth,X_30)))]]) ).
cnf(refute_0_252,plain,
big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),
introduced(tautology,[refl,[$fot(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))))]]) ).
cnf(refute_0_253,plain,
( big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30)))
| implies(truth,big_V(truth,X_30)) != big_V(truth,X_30)
| big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = big_V(big_V(truth,X_30),big_V(truth,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30)))) ),[1,1],$fot(big_V(truth,X_30))]]) ).
cnf(refute_0_254,plain,
( implies(truth,big_V(truth,X_30)) != big_V(truth,X_30)
| big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = big_V(big_V(truth,X_30),big_V(truth,X_30)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30)))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) = big_V(big_V(truth,X_30),big_V(truth,X_30)),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_30)),big_V(truth,X_30)) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
( big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != big_V(big_V(truth,X_30),big_V(truth,X_30))
| big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))
| big_V(big_V(truth,X_30),big_V(truth,X_30)) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))) ),[0],$fot(big_V(big_V(truth,X_30),big_V(truth,X_30)))]]) ).
cnf(refute_0_257,plain,
( big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))) != implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))
| big_V(big_V(truth,X_30),big_V(truth,X_30)) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),big_V(big_V(truth,X_30),big_V(truth,X_30))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
big_V(big_V(truth,X_30),big_V(truth,X_30)) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_30),implies(truth,big_V(truth,X_30))),implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))) )],[refute_0_250,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(implies(truth,X_32),implies(implies(X_32,X_33),implies(truth,X_33))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_260,plain,
( implies(implies(truth,X_32),implies(implies(X_32,X_33),implies(truth,X_33))) != truth
| implies(truth,X_33) != X_33
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),implies(truth,X_33))),truth) ),[0,1,1],$fot(X_33)]]) ).
cnf(refute_0_261,plain,
( implies(implies(truth,X_32),implies(implies(X_32,X_33),implies(truth,X_33))) != truth
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_33),X_33) )],[refute_0_85,refute_0_260]) ).
cnf(refute_0_262,plain,
implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),implies(truth,X_33))),truth) )],[refute_0_259,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(implies(X_32,X_33),X_33) = big_V(X_32,X_33),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_32)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_264,plain,
implies(X_32,implies(implies(X_32,X_33),X_33)) = implies(X_32,implies(implies(X_32,X_33),X_33)),
introduced(tautology,[refl,[$fot(implies(X_32,implies(implies(X_32,X_33),X_33)))]]) ).
cnf(refute_0_265,plain,
( implies(X_32,implies(implies(X_32,X_33),X_33)) != implies(X_32,implies(implies(X_32,X_33),X_33))
| implies(implies(X_32,X_33),X_33) != big_V(X_32,X_33)
| implies(X_32,implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_32,implies(implies(X_32,X_33),X_33)),implies(X_32,implies(implies(X_32,X_33),X_33))) ),[1,1],$fot(big_V(X_32,X_33))]]) ).
cnf(refute_0_266,plain,
( implies(implies(X_32,X_33),X_33) != big_V(X_32,X_33)
| implies(X_32,implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(implies(X_32,implies(implies(X_32,X_33),X_33)),implies(X_32,implies(implies(X_32,X_33),X_33))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
implies(X_32,implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)),
inference(resolve,[$cnf( $equal(implies(implies(X_32,X_33),X_33),big_V(X_32,X_33)) )],[refute_0_263,refute_0_266]) ).
cnf(refute_0_268,plain,
implies(truth,X_32) = X_32,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_32))]]) ).
cnf(refute_0_269,plain,
implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)))]]) ).
cnf(refute_0_270,plain,
( implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) != implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33))
| implies(truth,X_32) != X_32
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,implies(implies(X_32,X_33),X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33))) ),[1,0],$fot(X_32)]]) ).
cnf(refute_0_271,plain,
( implies(truth,X_32) != X_32
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,implies(implies(X_32,X_33),X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,implies(implies(X_32,X_33),X_33)),
inference(resolve,[$cnf( $equal(implies(truth,X_32),X_32) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
( implies(X_32,implies(implies(X_32,X_33),X_33)) != implies(X_32,big_V(X_32,X_33))
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) != implies(X_32,implies(implies(X_32,X_33),X_33))
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)))),bind(Y0,$fot(implies(X_32,implies(implies(X_32,X_33),X_33)))),bind(Z0,$fot(implies(X_32,big_V(X_32,X_33))))]]) ).
cnf(refute_0_274,plain,
( implies(X_32,implies(implies(X_32,X_33),X_33)) != implies(X_32,big_V(X_32,X_33))
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),implies(X_32,implies(implies(X_32,X_33),X_33))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) = implies(X_32,big_V(X_32,X_33)),
inference(resolve,[$cnf( $equal(implies(X_32,implies(implies(X_32,X_33),X_33)),implies(X_32,big_V(X_32,X_33))) )],[refute_0_267,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) != implies(X_32,big_V(X_32,X_33))
| implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) != truth
| implies(X_32,big_V(X_32,X_33)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),truth) ),[0],$fot(implies(X_32,big_V(X_32,X_33)))]]) ).
cnf(refute_0_277,plain,
( implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)) != truth
| implies(X_32,big_V(X_32,X_33)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),implies(X_32,big_V(X_32,X_33))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(X_32,big_V(X_32,X_33)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_32),implies(implies(X_32,X_33),X_33)),truth) )],[refute_0_262,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(truth,big_V(truth,X_30)) = truth,
inference(subst,[],[refute_0_278:[bind(X_32,$fot(truth)),bind(X_33,$fot(X_30))]]) ).
cnf(refute_0_280,plain,
big_V(truth,implies(implies(X_35,truth),truth)) = implies(big_V(truth,implies(X_35,truth)),truth),
inference(subst,[],[refute_0_200:[bind(Y,$fot(truth)),bind(X_1,$fot(implies(X_35,truth)))]]) ).
cnf(refute_0_281,plain,
implies(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(Y,X_33),X_33))),bind(Z,$fot(implies(Y,X_33)))]]) ).
cnf(refute_0_282,plain,
implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,X_33))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_283,plain,
( implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33))) != truth
| implies(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33)))) != truth
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_284,plain,
( implies(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33)))) != truth
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33))),truth) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(Y,implies(Y,X_33)),implies(implies(implies(Y,X_33),X_33),implies(Y,X_33)))),truth) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(Y,X_1),Y)
| implies(big_V(Y,X_1),Y) = big_V(Y,implies(X_1,Y)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(big_V(Y,implies(X_1,Y)))),bind(Y0,$fot(implies(big_V(Y,X_1),Y)))]]) ).
cnf(refute_0_287,plain,
implies(big_V(Y,X_1),Y) = big_V(Y,implies(X_1,Y)),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(Y,X_1),Y)) )],[refute_0_200,refute_0_286]) ).
cnf(refute_0_288,plain,
implies(big_V(Y,X_33),Y) = big_V(Y,implies(X_33,Y)),
inference(subst,[],[refute_0_287:[bind(X_1,$fot(X_33))]]) ).
cnf(refute_0_289,plain,
implies(implies(Y,X_33),X_33) = big_V(Y,X_33),
inference(subst,[],[refute_0_11:[bind(X,$fot(Y)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_290,plain,
implies(implies(implies(Y,X_33),X_33),Y) = implies(implies(implies(Y,X_33),X_33),Y),
introduced(tautology,[refl,[$fot(implies(implies(implies(Y,X_33),X_33),Y))]]) ).
cnf(refute_0_291,plain,
( implies(implies(Y,X_33),X_33) != big_V(Y,X_33)
| implies(implies(implies(Y,X_33),X_33),Y) != implies(implies(implies(Y,X_33),X_33),Y)
| implies(implies(implies(Y,X_33),X_33),Y) = implies(big_V(Y,X_33),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(implies(Y,X_33),X_33),Y)) ),[1,0],$fot(big_V(Y,X_33))]]) ).
cnf(refute_0_292,plain,
( implies(implies(Y,X_33),X_33) != big_V(Y,X_33)
| implies(implies(implies(Y,X_33),X_33),Y) = implies(big_V(Y,X_33),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_33),X_33),Y),implies(implies(implies(Y,X_33),X_33),Y)) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(implies(implies(Y,X_33),X_33),Y) = implies(big_V(Y,X_33),Y),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_33),X_33),big_V(Y,X_33)) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( implies(big_V(Y,X_33),Y) != big_V(Y,implies(X_33,Y))
| implies(implies(implies(Y,X_33),X_33),Y) != implies(big_V(Y,X_33),Y)
| implies(implies(implies(Y,X_33),X_33),Y) = big_V(Y,implies(X_33,Y)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(implies(Y,X_33),X_33),Y))),bind(Y0,$fot(implies(big_V(Y,X_33),Y))),bind(Z0,$fot(big_V(Y,implies(X_33,Y))))]]) ).
cnf(refute_0_295,plain,
( implies(big_V(Y,X_33),Y) != big_V(Y,implies(X_33,Y))
| implies(implies(implies(Y,X_33),X_33),Y) = big_V(Y,implies(X_33,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_33),X_33),Y),implies(big_V(Y,X_33),Y)) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(implies(implies(Y,X_33),X_33),Y) = big_V(Y,implies(X_33,Y)),
inference(resolve,[$cnf( $equal(implies(big_V(Y,X_33),Y),big_V(Y,implies(X_33,Y))) )],[refute_0_288,refute_0_295]) ).
cnf(refute_0_297,plain,
implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = implies(implies(implies(implies(Y,X_33),X_33),Y),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(Y,X_33),X_33),Y),truth))]]) ).
cnf(refute_0_298,plain,
( implies(implies(implies(Y,X_33),X_33),Y) != big_V(Y,implies(X_33,Y))
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) != implies(implies(implies(implies(Y,X_33),X_33),Y),truth)
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = implies(big_V(Y,implies(X_33,Y)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),truth),implies(implies(implies(implies(Y,X_33),X_33),Y),truth)) ),[1,0],$fot(big_V(Y,implies(X_33,Y)))]]) ).
cnf(refute_0_299,plain,
( implies(implies(implies(Y,X_33),X_33),Y) != big_V(Y,implies(X_33,Y))
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = implies(big_V(Y,implies(X_33,Y)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),truth),implies(implies(implies(implies(Y,X_33),X_33),Y),truth)) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
implies(implies(implies(implies(Y,X_33),X_33),Y),truth) = implies(big_V(Y,implies(X_33,Y)),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_33),X_33),Y),big_V(Y,implies(X_33,Y))) )],[refute_0_296,refute_0_299]) ).
cnf(refute_0_301,plain,
( implies(implies(implies(implies(Y,X_33),X_33),Y),truth) != implies(big_V(Y,implies(X_33,Y)),truth)
| implies(implies(implies(implies(Y,X_33),X_33),Y),truth) != truth
| implies(big_V(Y,implies(X_33,Y)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),truth),truth) ),[0],$fot(implies(big_V(Y,implies(X_33,Y)),truth))]]) ).
cnf(refute_0_302,plain,
( implies(implies(implies(implies(Y,X_33),X_33),Y),truth) != truth
| implies(big_V(Y,implies(X_33,Y)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),truth),implies(big_V(Y,implies(X_33,Y)),truth)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
implies(big_V(Y,implies(X_33,Y)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_33),X_33),Y),truth),truth) )],[refute_0_285,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(big_V(truth,implies(X_35,truth)),truth) = truth,
inference(subst,[],[refute_0_303:[bind(Y,$fot(truth)),bind(X_33,$fot(X_35))]]) ).
cnf(refute_0_305,plain,
( big_V(truth,implies(implies(X_35,truth),truth)) != implies(big_V(truth,implies(X_35,truth)),truth)
| implies(big_V(truth,implies(X_35,truth)),truth) != truth
| big_V(truth,implies(implies(X_35,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,implies(implies(X_35,truth),truth)),truth) ),[0],$fot(implies(big_V(truth,implies(X_35,truth)),truth))]]) ).
cnf(refute_0_306,plain,
( big_V(truth,implies(implies(X_35,truth),truth)) != implies(big_V(truth,implies(X_35,truth)),truth)
| big_V(truth,implies(implies(X_35,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,implies(X_35,truth)),truth),truth) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
big_V(truth,implies(implies(X_35,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),implies(big_V(truth,implies(X_35,truth)),truth)) )],[refute_0_280,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(implies(X_35,truth),truth) = big_V(X_35,truth),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_35)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_309,plain,
big_V(truth,implies(implies(X_35,truth),truth)) = big_V(truth,implies(implies(X_35,truth),truth)),
introduced(tautology,[refl,[$fot(big_V(truth,implies(implies(X_35,truth),truth)))]]) ).
cnf(refute_0_310,plain,
( big_V(truth,implies(implies(X_35,truth),truth)) != big_V(truth,implies(implies(X_35,truth),truth))
| implies(implies(X_35,truth),truth) != big_V(X_35,truth)
| big_V(truth,implies(implies(X_35,truth),truth)) = big_V(truth,big_V(X_35,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),big_V(truth,implies(implies(X_35,truth),truth))) ),[1,1],$fot(big_V(X_35,truth))]]) ).
cnf(refute_0_311,plain,
( implies(implies(X_35,truth),truth) != big_V(X_35,truth)
| big_V(truth,implies(implies(X_35,truth),truth)) = big_V(truth,big_V(X_35,truth)) ),
inference(resolve,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),big_V(truth,implies(implies(X_35,truth),truth))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
big_V(truth,implies(implies(X_35,truth),truth)) = big_V(truth,big_V(X_35,truth)),
inference(resolve,[$cnf( $equal(implies(implies(X_35,truth),truth),big_V(X_35,truth)) )],[refute_0_308,refute_0_311]) ).
cnf(refute_0_313,plain,
( big_V(truth,implies(implies(X_35,truth),truth)) != big_V(truth,big_V(X_35,truth))
| big_V(truth,implies(implies(X_35,truth),truth)) != truth
| big_V(truth,big_V(X_35,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),truth) ),[0],$fot(big_V(truth,big_V(X_35,truth)))]]) ).
cnf(refute_0_314,plain,
( big_V(truth,implies(implies(X_35,truth),truth)) != truth
| big_V(truth,big_V(X_35,truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),big_V(truth,big_V(X_35,truth))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
big_V(truth,big_V(X_35,truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,implies(implies(X_35,truth),truth)),truth) )],[refute_0_307,refute_0_314]) ).
cnf(refute_0_316,plain,
big_V(truth,big_V(X_30,truth)) = truth,
inference(subst,[],[refute_0_315:[bind(X_35,$fot(X_30))]]) ).
cnf(refute_0_317,plain,
implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)))]]) ).
cnf(refute_0_318,plain,
( big_V(truth,big_V(X_30,truth)) != truth
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) != implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = implies(truth,big_V(truth,X_30)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_319,plain,
( big_V(truth,big_V(X_30,truth)) != truth
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = implies(truth,big_V(truth,X_30)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = implies(truth,big_V(truth,X_30)),
inference(resolve,[$cnf( $equal(big_V(truth,big_V(X_30,truth)),truth) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
( implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) != implies(truth,big_V(truth,X_30))
| implies(truth,big_V(truth,X_30)) != truth
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)))),bind(Y0,$fot(implies(truth,big_V(truth,X_30)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_322,plain,
( implies(truth,big_V(truth,X_30)) != truth
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),implies(truth,big_V(truth,X_30))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_30)),truth) )],[refute_0_279,refute_0_322]) ).
cnf(refute_0_324,plain,
( big_V(big_V(truth,X_30),big_V(truth,X_30)) != implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))
| implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)) != truth
| big_V(big_V(truth,X_30),big_V(truth,X_30)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(truth,X_30),big_V(truth,X_30)),truth) ),[0],$fot(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)))]]) ).
cnf(refute_0_325,plain,
( big_V(big_V(truth,X_30),big_V(truth,X_30)) != implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))
| big_V(big_V(truth,X_30),big_V(truth,X_30)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30)),truth) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
big_V(big_V(truth,X_30),big_V(truth,X_30)) = truth,
inference(resolve,[$cnf( $equal(big_V(big_V(truth,X_30),big_V(truth,X_30)),implies(big_V(truth,big_V(X_30,truth)),big_V(truth,X_30))) )],[refute_0_258,refute_0_325]) ).
cnf(refute_0_327,plain,
big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) = truth,
inference(subst,[],[refute_0_326:[bind(X_30,$fot(not(truth)))]]) ).
cnf(refute_0_328,plain,
( big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) != big_V(truth,not(truth))
| big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) != truth
| truth = big_V(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),big_V(truth,not(truth))) ),[0],$fot(truth)]]) ).
cnf(refute_0_329,plain,
( big_V(big_V(truth,not(truth)),big_V(truth,not(truth))) != big_V(truth,not(truth))
| truth = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),truth) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
truth = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(big_V(big_V(truth,not(truth)),big_V(truth,not(truth))),big_V(truth,not(truth))) )],[refute_0_195,refute_0_329]) ).
cnf(refute_0_331,plain,
( truth != big_V(truth,not(truth))
| big_V(truth,not(truth)) = truth ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(truth)),bind(Y0,$fot(big_V(truth,not(truth))))]]) ).
cnf(refute_0_332,plain,
big_V(truth,not(truth)) = truth,
inference(resolve,[$cnf( $equal(truth,big_V(truth,not(truth))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
( big_V(truth,not(truth)) != truth
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(not(truth),not(truth)) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(truth),not(truth)))),bind(Y0,$fot(big_V(truth,not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_334,plain,
( big_V(truth,not(truth)) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_130,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_332,refute_0_334]) ).
cnf(refute_0_336,plain,
not(big_V(truth,not(truth))) = not(big_V(truth,not(truth))),
introduced(tautology,[refl,[$fot(not(big_V(truth,not(truth))))]]) ).
cnf(refute_0_337,plain,
( big_V(truth,not(truth)) != truth
| not(big_V(truth,not(truth))) != not(big_V(truth,not(truth)))
| not(big_V(truth,not(truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,not(truth))),not(big_V(truth,not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_338,plain,
( big_V(truth,not(truth)) != truth
| not(big_V(truth,not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(truth))),not(big_V(truth,not(truth)))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
not(big_V(truth,not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_332,refute_0_338]) ).
cnf(refute_0_340,plain,
big_V(truth,not(big_V(truth,not(truth)))) = big_V(truth,not(big_V(truth,not(truth)))),
introduced(tautology,[refl,[$fot(big_V(truth,not(big_V(truth,not(truth)))))]]) ).
cnf(refute_0_341,plain,
( big_V(truth,not(big_V(truth,not(truth)))) != big_V(truth,not(big_V(truth,not(truth))))
| not(big_V(truth,not(truth))) != not(truth)
| big_V(truth,not(big_V(truth,not(truth)))) = big_V(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,not(big_V(truth,not(truth))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_342,plain,
( not(big_V(truth,not(truth))) != not(truth)
| big_V(truth,not(big_V(truth,not(truth)))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,not(big_V(truth,not(truth))))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
big_V(truth,not(big_V(truth,not(truth)))) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(truth))),not(truth)) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
( big_V(truth,not(big_V(truth,not(truth)))) != big_V(truth,not(truth))
| big_V(truth,not(truth)) != truth
| big_V(truth,not(big_V(truth,not(truth)))) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(truth,not(big_V(truth,not(truth)))))),bind(Y0,$fot(big_V(truth,not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_345,plain,
( big_V(truth,not(truth)) != truth
| big_V(truth,not(big_V(truth,not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(truth)))),big_V(truth,not(truth))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
big_V(truth,not(big_V(truth,not(truth)))) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_332,refute_0_345]) ).
cnf(refute_0_347,plain,
not(big_V(truth,not(big_V(truth,not(truth))))) = not(big_V(truth,not(big_V(truth,not(truth))))),
introduced(tautology,[refl,[$fot(not(big_V(truth,not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_348,plain,
( big_V(truth,not(big_V(truth,not(truth)))) != truth
| not(big_V(truth,not(big_V(truth,not(truth))))) != not(big_V(truth,not(big_V(truth,not(truth)))))
| not(big_V(truth,not(big_V(truth,not(truth))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(truth))))),not(big_V(truth,not(big_V(truth,not(truth)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_349,plain,
( big_V(truth,not(big_V(truth,not(truth)))) != truth
| not(big_V(truth,not(big_V(truth,not(truth))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(truth))))),not(big_V(truth,not(big_V(truth,not(truth)))))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
not(big_V(truth,not(big_V(truth,not(truth))))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(truth)))),truth) )],[refute_0_346,refute_0_349]) ).
cnf(refute_0_351,plain,
big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),
introduced(tautology,[refl,[$fot(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))]]) ).
cnf(refute_0_352,plain,
( big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) != big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))
| not(big_V(truth,not(big_V(truth,not(truth))))) != not(truth)
| big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_353,plain,
( not(big_V(truth,not(big_V(truth,not(truth))))) != not(truth)
| big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(truth))))),not(truth)) )],[refute_0_350,refute_0_353]) ).
cnf(refute_0_355,plain,
( big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) != big_V(truth,not(truth))
| big_V(truth,not(truth)) != truth
| big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),bind(Y0,$fot(big_V(truth,not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_356,plain,
( big_V(truth,not(truth)) != truth
| big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),big_V(truth,not(truth))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_332,refute_0_356]) ).
cnf(refute_0_358,plain,
not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) = not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))),
introduced(tautology,[refl,[$fot(not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))))]]) ).
cnf(refute_0_359,plain,
( big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) != truth
| not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) != not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))
| not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_360,plain,
( big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))) != truth
| not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))),truth) )],[refute_0_357,refute_0_360]) ).
cnf(refute_0_362,plain,
implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))))]]) ).
cnf(refute_0_363,plain,
( implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) != implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))))
| not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) != not(truth)
| implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_364,plain,
( not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))) != not(truth)
| implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth))))))),not(truth)) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
( implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_367,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),implies(not(truth),not(truth))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_335,refute_0_367]) ).
cnf(refute_0_369,plain,
implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))]]) ).
cnf(refute_0_370,plain,
( implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) != implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)
| implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = implies(truth,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_371,plain,
( implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))) != truth
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = implies(truth,X_33) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33),implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = implies(truth,X_33),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),truth) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
( implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) != implies(truth,X_33)
| implies(truth,X_33) != X_33
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = X_33 ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))),bind(Y0,$fot(implies(truth,X_33))),bind(Z0,$fot(X_33))]]) ).
cnf(refute_0_374,plain,
( implies(truth,X_33) != X_33
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = X_33 ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33),implies(truth,X_33)) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) = X_33,
inference(resolve,[$cnf( $equal(implies(truth,X_33),X_33) )],[refute_0_85,refute_0_374]) ).
cnf(refute_0_376,plain,
implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),
introduced(tautology,[refl,[$fot(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)))]]) ).
cnf(refute_0_377,plain,
( implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))
| implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) != X_33
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,X_33) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) ),[1,1],$fot(X_33)]]) ).
cnf(refute_0_378,plain,
( implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33) != X_33
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,X_33) ),
inference(resolve,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = implies(X_33,X_33),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33),X_33) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
( implies(X_33,X_33) != big_V(truth,X_33)
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != implies(X_33,X_33)
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = big_V(truth,X_33) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)))),bind(Y0,$fot(implies(X_33,X_33))),bind(Z0,$fot(big_V(truth,X_33)))]]) ).
cnf(refute_0_381,plain,
( implies(X_33,X_33) != big_V(truth,X_33)
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = big_V(truth,X_33) ),
inference(resolve,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),implies(X_33,X_33)) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) = big_V(truth,X_33),
inference(resolve,[$cnf( $equal(implies(X_33,X_33),big_V(truth,X_33)) )],[refute_0_180,refute_0_381]) ).
cnf(refute_0_383,plain,
( implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != big_V(truth,X_33)
| implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != truth
| big_V(truth,X_33) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),truth) ),[0],$fot(big_V(truth,X_33))]]) ).
cnf(refute_0_384,plain,
( implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)) != truth
| big_V(truth,X_33) = truth ),
inference(resolve,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),big_V(truth,X_33)) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
big_V(truth,X_33) = truth,
inference(resolve,[$cnf( $equal(implies(X_33,implies(implies(not(truth),not(big_V(truth,not(big_V(truth,not(big_V(truth,not(truth)))))))),X_33)),truth) )],[refute_0_179,refute_0_384]) ).
cnf(refute_0_386,plain,
big_V(truth,not(X_6)) = truth,
inference(subst,[],[refute_0_385:[bind(X_33,$fot(not(X_6)))]]) ).
cnf(refute_0_387,plain,
implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = implies(big_V(truth,not(X_6)),big_V(X_6,truth)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(X_6)),big_V(X_6,truth)))]]) ).
cnf(refute_0_388,plain,
( big_V(truth,not(X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) != implies(big_V(truth,not(X_6)),big_V(X_6,truth))
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = implies(truth,big_V(X_6,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),implies(big_V(truth,not(X_6)),big_V(X_6,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_389,plain,
( big_V(truth,not(X_6)) != truth
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = implies(truth,big_V(X_6,truth)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),implies(big_V(truth,not(X_6)),big_V(X_6,truth))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = implies(truth,big_V(X_6,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,not(X_6)),truth) )],[refute_0_386,refute_0_389]) ).
cnf(refute_0_391,plain,
( implies(big_V(truth,not(X_6)),big_V(X_6,truth)) != implies(truth,big_V(X_6,truth))
| implies(truth,big_V(X_6,truth)) != big_V(X_6,truth)
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = big_V(X_6,truth) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,not(X_6)),big_V(X_6,truth)))),bind(Y0,$fot(implies(truth,big_V(X_6,truth)))),bind(Z0,$fot(big_V(X_6,truth)))]]) ).
cnf(refute_0_392,plain,
( implies(truth,big_V(X_6,truth)) != big_V(X_6,truth)
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = big_V(X_6,truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),implies(truth,big_V(X_6,truth))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
implies(big_V(truth,not(X_6)),big_V(X_6,truth)) = big_V(X_6,truth),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X_6,truth)),big_V(X_6,truth)) )],[refute_0_120,refute_0_392]) ).
cnf(refute_0_394,plain,
( implies(big_V(truth,not(X_6)),big_V(X_6,truth)) != big_V(X_6,truth)
| implies(big_V(truth,not(X_6)),big_V(X_6,truth)) != truth
| big_V(X_6,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),truth) ),[0],$fot(big_V(X_6,truth))]]) ).
cnf(refute_0_395,plain,
( implies(big_V(truth,not(X_6)),big_V(X_6,truth)) != truth
| big_V(X_6,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),big_V(X_6,truth)) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
big_V(X_6,truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),big_V(X_6,truth)),truth) )],[refute_0_119,refute_0_395]) ).
cnf(refute_0_397,plain,
big_V(X_32,truth) = truth,
inference(subst,[],[refute_0_396:[bind(X_6,$fot(X_32))]]) ).
cnf(refute_0_398,plain,
implies(implies(X_32,truth),truth) = big_V(X_32,truth),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_32)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_399,plain,
( big_V(X_32,truth) != truth
| implies(implies(X_32,truth),truth) != big_V(X_32,truth)
| implies(implies(X_32,truth),truth) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(X_32,truth),truth))),bind(Y0,$fot(big_V(X_32,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_400,plain,
( big_V(X_32,truth) != truth
| implies(implies(X_32,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_32,truth),truth),big_V(X_32,truth)) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
implies(implies(X_32,truth),truth) = truth,
inference(resolve,[$cnf( $equal(big_V(X_32,truth),truth) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
big_V(truth,X_6) = truth,
inference(subst,[],[refute_0_385:[bind(X_33,$fot(X_6))]]) ).
cnf(refute_0_403,plain,
implies(X_32,big_V(truth,X_6)) = implies(X_32,big_V(truth,X_6)),
introduced(tautology,[refl,[$fot(implies(X_32,big_V(truth,X_6)))]]) ).
cnf(refute_0_404,plain,
( big_V(truth,X_6) != truth
| implies(X_32,big_V(truth,X_6)) != implies(X_32,big_V(truth,X_6))
| implies(X_32,big_V(truth,X_6)) = implies(X_32,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_32,big_V(truth,X_6)),implies(X_32,big_V(truth,X_6))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_405,plain,
( big_V(truth,X_6) != truth
| implies(X_32,big_V(truth,X_6)) = implies(X_32,truth) ),
inference(resolve,[$cnf( $equal(implies(X_32,big_V(truth,X_6)),implies(X_32,big_V(truth,X_6))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
implies(X_32,big_V(truth,X_6)) = implies(X_32,truth),
inference(resolve,[$cnf( $equal(big_V(truth,X_6),truth) )],[refute_0_402,refute_0_405]) ).
cnf(refute_0_407,plain,
implies(implies(X_32,big_V(truth,X_6)),truth) = implies(implies(X_32,big_V(truth,X_6)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_32,big_V(truth,X_6)),truth))]]) ).
cnf(refute_0_408,plain,
( implies(X_32,big_V(truth,X_6)) != implies(X_32,truth)
| implies(implies(X_32,big_V(truth,X_6)),truth) != implies(implies(X_32,big_V(truth,X_6)),truth)
| implies(implies(X_32,big_V(truth,X_6)),truth) = implies(implies(X_32,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_32,big_V(truth,X_6)),truth),implies(implies(X_32,big_V(truth,X_6)),truth)) ),[1,0],$fot(implies(X_32,truth))]]) ).
cnf(refute_0_409,plain,
( implies(X_32,big_V(truth,X_6)) != implies(X_32,truth)
| implies(implies(X_32,big_V(truth,X_6)),truth) = implies(implies(X_32,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_32,big_V(truth,X_6)),truth),implies(implies(X_32,big_V(truth,X_6)),truth)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
implies(implies(X_32,big_V(truth,X_6)),truth) = implies(implies(X_32,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_32,big_V(truth,X_6)),implies(X_32,truth)) )],[refute_0_406,refute_0_409]) ).
cnf(refute_0_411,plain,
( implies(implies(X_32,big_V(truth,X_6)),truth) != implies(implies(X_32,truth),truth)
| implies(implies(X_32,truth),truth) != truth
| implies(implies(X_32,big_V(truth,X_6)),truth) = truth ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(X_32,big_V(truth,X_6)),truth))),bind(Y0,$fot(implies(implies(X_32,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_412,plain,
( implies(implies(X_32,truth),truth) != truth
| implies(implies(X_32,big_V(truth,X_6)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_32,big_V(truth,X_6)),truth),implies(implies(X_32,truth),truth)) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
implies(implies(X_32,big_V(truth,X_6)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_32,truth),truth),truth) )],[refute_0_401,refute_0_412]) ).
cnf(refute_0_414,plain,
implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)),
introduced(tautology,[refl,[$fot(implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)))]]) ).
cnf(refute_0_415,plain,
( implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth))
| implies(implies(X_32,big_V(truth,X_6)),truth) != truth
| implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)),implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_416,plain,
( implies(implies(X_32,big_V(truth,X_6)),truth) != truth
| implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth) ),
inference(resolve,[$cnf( $equal(implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)),implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_32,big_V(truth,X_6)),truth),truth) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
implies(big_V(truth,not(X_6)),X_32) = implies(big_V(truth,not(X_6)),X_32),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(X_6)),X_32))]]) ).
cnf(refute_0_419,plain,
( big_V(truth,not(X_6)) != truth
| implies(big_V(truth,not(X_6)),X_32) != implies(big_V(truth,not(X_6)),X_32)
| implies(big_V(truth,not(X_6)),X_32) = implies(truth,X_32) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_6)),X_32),implies(big_V(truth,not(X_6)),X_32)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_420,plain,
( big_V(truth,not(X_6)) != truth
| implies(big_V(truth,not(X_6)),X_32) = implies(truth,X_32) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),X_32),implies(big_V(truth,not(X_6)),X_32)) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
implies(big_V(truth,not(X_6)),X_32) = implies(truth,X_32),
inference(resolve,[$cnf( $equal(big_V(truth,not(X_6)),truth) )],[refute_0_386,refute_0_420]) ).
cnf(refute_0_422,plain,
( implies(big_V(truth,not(X_6)),X_32) != implies(truth,X_32)
| implies(truth,X_32) != X_32
| implies(big_V(truth,not(X_6)),X_32) = X_32 ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,not(X_6)),X_32))),bind(Y0,$fot(implies(truth,X_32))),bind(Z0,$fot(X_32))]]) ).
cnf(refute_0_423,plain,
( implies(truth,X_32) != X_32
| implies(big_V(truth,not(X_6)),X_32) = X_32 ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),X_32),implies(truth,X_32)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
implies(big_V(truth,not(X_6)),X_32) = X_32,
inference(resolve,[$cnf( $equal(implies(truth,X_32),X_32) )],[refute_0_268,refute_0_423]) ).
cnf(refute_0_425,plain,
implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)))]]) ).
cnf(refute_0_426,plain,
( implies(big_V(truth,not(X_6)),X_32) != X_32
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth))
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth))) ),[1,0],$fot(X_32)]]) ).
cnf(refute_0_427,plain,
( implies(big_V(truth,not(X_6)),X_32) != X_32
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_6)),X_32),X_32) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
( implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(X_32,truth)
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth))
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)))),bind(Y0,$fot(implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)))),bind(Z0,$fot(implies(X_32,truth)))]]) ).
cnf(refute_0_430,plain,
( implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(X_32,truth)
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth))) )],[refute_0_428,refute_0_429]) ).
cnf(refute_0_431,plain,
implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) = implies(X_32,truth),
inference(resolve,[$cnf( $equal(implies(X_32,implies(implies(X_32,big_V(truth,X_6)),truth)),implies(X_32,truth)) )],[refute_0_417,refute_0_430]) ).
cnf(refute_0_432,plain,
( implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) != implies(X_32,truth)
| implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) != truth
| implies(X_32,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),truth) ),[0],$fot(implies(X_32,truth))]]) ).
cnf(refute_0_433,plain,
( implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)) != truth
| implies(X_32,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),implies(X_32,truth)) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
implies(X_32,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(X_6)),X_32),implies(implies(X_32,big_V(truth,X_6)),truth)),truth) )],[refute_0_115,refute_0_433]) ).
cnf(refute_0_435,plain,
implies(X_31,truth) = truth,
inference(subst,[],[refute_0_434:[bind(X_32,$fot(X_31))]]) ).
cnf(refute_0_436,plain,
implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),
introduced(tautology,[refl,[$fot(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))))]]) ).
cnf(refute_0_437,plain,
( implies(X_31,truth) != truth
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) != implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33)))
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(truth,implies(X_33,implies(X_31,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_438,plain,
( implies(X_31,truth) != truth
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(truth,implies(X_33,implies(X_31,X_33))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33)))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(truth,implies(X_33,implies(X_31,X_33))),
inference(resolve,[$cnf( $equal(implies(X_31,truth),truth) )],[refute_0_435,refute_0_438]) ).
cnf(refute_0_440,plain,
( implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) != implies(truth,implies(X_33,implies(X_31,X_33)))
| implies(truth,implies(X_33,implies(X_31,X_33))) != implies(X_33,implies(X_31,X_33))
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(X_33,implies(X_31,X_33)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))))),bind(Y0,$fot(implies(truth,implies(X_33,implies(X_31,X_33))))),bind(Z0,$fot(implies(X_33,implies(X_31,X_33))))]]) ).
cnf(refute_0_441,plain,
( implies(truth,implies(X_33,implies(X_31,X_33))) != implies(X_33,implies(X_31,X_33))
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(X_33,implies(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),implies(truth,implies(X_33,implies(X_31,X_33)))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) = implies(X_33,implies(X_31,X_33)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_33,implies(X_31,X_33))),implies(X_33,implies(X_31,X_33))) )],[refute_0_89,refute_0_441]) ).
cnf(refute_0_443,plain,
( implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) != implies(X_33,implies(X_31,X_33))
| implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) != truth
| implies(X_33,implies(X_31,X_33)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),truth) ),[0],$fot(implies(X_33,implies(X_31,X_33)))]]) ).
cnf(refute_0_444,plain,
( implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))) != truth
| implies(X_33,implies(X_31,X_33)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),implies(X_33,implies(X_31,X_33))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
implies(X_33,implies(X_31,X_33)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_31,truth),implies(X_33,implies(X_31,X_33))),truth) )],[refute_0_88,refute_0_444]) ).
cnf(refute_0_446,plain,
implies(X,implies(X_48,X)) = truth,
inference(subst,[],[refute_0_445:[bind(X_31,$fot(X_48)),bind(X_33,$fot(X))]]) ).
cnf(refute_0_447,plain,
( big_V(X,implies(X_48,X)) != implies(implies(X,implies(X_48,X)),implies(X_48,X))
| implies(X,implies(X_48,X)) != truth
| big_V(X,implies(X_48,X)) = implies(truth,implies(X_48,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(X_48,X)),implies(implies(X,implies(X_48,X)),implies(X_48,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_448,plain,
( big_V(X,implies(X_48,X)) != implies(implies(X,implies(X_48,X)),implies(X_48,X))
| big_V(X,implies(X_48,X)) = implies(truth,implies(X_48,X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_48,X)),truth) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
big_V(X,implies(X_48,X)) = implies(truth,implies(X_48,X)),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_48,X)),implies(implies(X,implies(X_48,X)),implies(X_48,X))) )],[refute_0_83,refute_0_448]) ).
cnf(refute_0_450,plain,
implies(truth,implies(X_48,X)) = implies(X_48,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_48,X)))]]) ).
cnf(refute_0_451,plain,
( big_V(X,implies(X_48,X)) != implies(truth,implies(X_48,X))
| implies(truth,implies(X_48,X)) != implies(X_48,X)
| big_V(X,implies(X_48,X)) = implies(X_48,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,implies(X_48,X)),implies(X_48,X)) ),[0],$fot(implies(truth,implies(X_48,X)))]]) ).
cnf(refute_0_452,plain,
( big_V(X,implies(X_48,X)) != implies(truth,implies(X_48,X))
| big_V(X,implies(X_48,X)) = implies(X_48,X) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_48,X)),implies(X_48,X)) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
big_V(X,implies(X_48,X)) = implies(X_48,X),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_48,X)),implies(truth,implies(X_48,X))) )],[refute_0_449,refute_0_452]) ).
cnf(refute_0_454,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(subst,[],[refute_0_453:[bind(X,$fot(not(not(truth)))),bind(X_48,$fot(not(truth)))]]) ).
cnf(refute_0_455,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(not(truth),not(not(truth)))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),not(not(truth))) ),[0],$fot(implies(not(truth),not(not(truth))))]]) ).
cnf(refute_0_456,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),not(not(truth))) )],[refute_0_82,refute_0_456]) ).
cnf(refute_0_458,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_459,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_54,refute_0_459]) ).
cnf(refute_0_461,plain,
implies(not(truth),implies(not(not(not(truth))),not(truth))) = truth,
inference(subst,[],[refute_0_445:[bind(X_31,$fot(not(not(not(truth))))),bind(X_33,$fot(not(truth)))]]) ).
cnf(refute_0_462,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))]]) ).
cnf(refute_0_463,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_464,plain,
( implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(not(not(truth))),not(truth))),truth) )],[refute_0_461,refute_0_464]) ).
cnf(refute_0_466,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_467,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_79,refute_0_467]) ).
cnf(refute_0_469,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_470,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) )],[refute_0_460,refute_0_470]) ).
cnf(refute_0_472,plain,
implies(not(not(truth)),not(not(X_86))) = implies(not(not(truth)),not(not(X_86))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_86))))]]) ).
cnf(refute_0_473,plain,
( implies(not(not(truth)),not(not(X_86))) != implies(not(not(truth)),not(not(X_86)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_86))) = implies(truth,not(not(X_86))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_86))),implies(not(not(truth)),not(not(X_86)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_474,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_86))) = implies(truth,not(not(X_86))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_86))),implies(not(not(truth)),not(not(X_86)))) )],[refute_0_472,refute_0_473]) ).
cnf(refute_0_475,plain,
implies(not(not(truth)),not(not(X_86))) = implies(truth,not(not(X_86))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_471,refute_0_474]) ).
cnf(refute_0_476,plain,
( implies(not(not(truth)),not(not(X_86))) != implies(truth,not(not(X_86)))
| implies(truth,not(not(X_86))) != not(not(X_86))
| implies(not(not(truth)),not(not(X_86))) = not(not(X_86)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(not(truth)),not(not(X_86))))),bind(Y0,$fot(implies(truth,not(not(X_86))))),bind(Z0,$fot(not(not(X_86))))]]) ).
cnf(refute_0_477,plain,
( implies(truth,not(not(X_86))) != not(not(X_86))
| implies(not(not(truth)),not(not(X_86))) = not(not(X_86)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_86))),implies(truth,not(not(X_86)))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
implies(not(not(truth)),not(not(X_86))) = not(not(X_86)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_86))),not(not(X_86))) )],[refute_0_53,refute_0_477]) ).
cnf(refute_0_479,plain,
implies(implies(not(not(truth)),not(not(X_86))),X_86) = implies(implies(not(not(truth)),not(not(X_86))),X_86),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_86))),X_86))]]) ).
cnf(refute_0_480,plain,
( implies(implies(not(not(truth)),not(not(X_86))),X_86) != implies(implies(not(not(truth)),not(not(X_86))),X_86)
| implies(not(not(truth)),not(not(X_86))) != not(not(X_86))
| implies(implies(not(not(truth)),not(not(X_86))),X_86) = implies(not(not(X_86)),X_86) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_86))),X_86),implies(implies(not(not(truth)),not(not(X_86))),X_86)) ),[1,0],$fot(not(not(X_86)))]]) ).
cnf(refute_0_481,plain,
( implies(not(not(truth)),not(not(X_86))) != not(not(X_86))
| implies(implies(not(not(truth)),not(not(X_86))),X_86) = implies(not(not(X_86)),X_86) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_86))),X_86),implies(implies(not(not(truth)),not(not(X_86))),X_86)) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
implies(implies(not(not(truth)),not(not(X_86))),X_86) = implies(not(not(X_86)),X_86),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_86))),not(not(X_86))) )],[refute_0_478,refute_0_481]) ).
cnf(refute_0_483,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = implies(implies(not(not(truth)),not(not(X_86))),X_86),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_86))),X_86)))]]) ).
cnf(refute_0_484,plain,
( implies(implies(not(not(truth)),not(not(X_86))),X_86) != implies(not(not(X_86)),X_86)
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) != implies(implies(not(not(truth)),not(not(X_86))),X_86)
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = implies(not(not(X_86)),X_86) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)))),bind(Y0,$fot(implies(implies(not(not(truth)),not(not(X_86))),X_86))),bind(Z0,$fot(implies(not(not(X_86)),X_86)))]]) ).
cnf(refute_0_485,plain,
( implies(implies(not(not(truth)),not(not(X_86))),X_86) != implies(not(not(X_86)),X_86)
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = implies(not(not(X_86)),X_86) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)),implies(implies(not(not(truth)),not(not(X_86))),X_86)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) = implies(not(not(X_86)),X_86),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_86))),X_86),implies(not(not(X_86)),X_86)) )],[refute_0_482,refute_0_485]) ).
cnf(refute_0_487,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) != implies(not(not(X_86)),X_86)
| implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) != truth
| implies(not(not(X_86)),X_86) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)),truth) ),[0],$fot(implies(not(not(X_86)),X_86))]]) ).
cnf(refute_0_488,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)) != truth
| implies(not(not(X_86)),X_86) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)),implies(not(not(X_86)),X_86)) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
implies(not(not(X_86)),X_86) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_86))),X_86)),truth) )],[refute_0_52,refute_0_488]) ).
cnf(refute_0_490,plain,
implies(not(not(not(X_7))),not(X_7)) = truth,
inference(subst,[],[refute_0_489:[bind(X_86,$fot(not(X_7)))]]) ).
cnf(refute_0_491,plain,
( big_V(implies(X_7,not(not(X_7))),implies(not(not(not(X_7))),not(X_7))) != implies(X_7,not(not(X_7)))
| implies(not(not(not(X_7))),not(X_7)) != truth
| big_V(implies(X_7,not(not(X_7))),truth) = implies(X_7,not(not(X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_7,not(not(X_7))),implies(not(not(not(X_7))),not(X_7))),implies(X_7,not(not(X_7)))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_492,plain,
( big_V(implies(X_7,not(not(X_7))),implies(not(not(not(X_7))),not(X_7))) != implies(X_7,not(not(X_7)))
| big_V(implies(X_7,not(not(X_7))),truth) = implies(X_7,not(not(X_7))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(X_7))),not(X_7)),truth) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
big_V(implies(X_7,not(not(X_7))),truth) = implies(X_7,not(not(X_7))),
inference(resolve,[$cnf( $equal(big_V(implies(X_7,not(not(X_7))),implies(not(not(not(X_7))),not(X_7))),implies(X_7,not(not(X_7)))) )],[refute_0_29,refute_0_492]) ).
cnf(refute_0_494,plain,
big_V(implies(X_7,not(not(X_7))),truth) = truth,
inference(subst,[],[refute_0_396:[bind(X_6,$fot(implies(X_7,not(not(X_7)))))]]) ).
cnf(refute_0_495,plain,
( big_V(implies(X_7,not(not(X_7))),truth) != implies(X_7,not(not(X_7)))
| big_V(implies(X_7,not(not(X_7))),truth) != truth
| truth = implies(X_7,not(not(X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_7,not(not(X_7))),truth),implies(X_7,not(not(X_7)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_496,plain,
( big_V(implies(X_7,not(not(X_7))),truth) != implies(X_7,not(not(X_7)))
| truth = implies(X_7,not(not(X_7))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_7,not(not(X_7))),truth),truth) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
truth = implies(X_7,not(not(X_7))),
inference(resolve,[$cnf( $equal(big_V(implies(X_7,not(not(X_7))),truth),implies(X_7,not(not(X_7)))) )],[refute_0_493,refute_0_496]) ).
cnf(refute_0_498,plain,
truth = implies(X,not(not(X))),
inference(subst,[],[refute_0_497:[bind(X_7,$fot(X))]]) ).
cnf(refute_0_499,plain,
( truth != implies(X,not(not(X)))
| implies(X,not(not(X))) = truth ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X,not(not(X)))))]]) ).
cnf(refute_0_500,plain,
implies(X,not(not(X))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X,not(not(X)))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
( big_V(X,not(not(X))) != implies(implies(X,not(not(X))),not(not(X)))
| implies(X,not(not(X))) != truth
| big_V(X,not(not(X))) = implies(truth,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_502,plain,
( big_V(X,not(not(X))) != implies(implies(X,not(not(X))),not(not(X)))
| big_V(X,not(not(X))) = implies(truth,not(not(X))) ),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),truth) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
big_V(X,not(not(X))) = implies(truth,not(not(X))),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) )],[refute_0_1,refute_0_502]) ).
cnf(refute_0_504,plain,
big_V(not(not(Y)),Y) = implies(implies(not(not(Y)),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_505,plain,
implies(not(not(Y)),Y) = truth,
inference(subst,[],[refute_0_489:[bind(X_86,$fot(Y))]]) ).
cnf(refute_0_506,plain,
( big_V(not(not(Y)),Y) != implies(implies(not(not(Y)),Y),Y)
| implies(not(not(Y)),Y) != truth
| big_V(not(not(Y)),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(Y)),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_507,plain,
( big_V(not(not(Y)),Y) != implies(implies(not(not(Y)),Y),Y)
| big_V(not(not(Y)),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
big_V(not(not(Y)),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
big_V(not(not(Y)),Y) = big_V(Y,not(not(Y))),
inference(subst,[],[refute_0_20:[bind(X,$fot(Y)),bind(Y,$fot(not(not(Y))))]]) ).
cnf(refute_0_510,plain,
( big_V(not(not(Y)),Y) != big_V(Y,not(not(Y)))
| big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(Y)),Y),implies(truth,Y)) ),[0],$fot(big_V(Y,not(not(Y))))]]) ).
cnf(refute_0_511,plain,
( big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),big_V(Y,not(not(Y)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_513,plain,
( big_V(Y,not(not(Y))) != implies(truth,Y)
| implies(truth,Y) != Y
| big_V(Y,not(not(Y))) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(Y,not(not(Y))),Y) ),[0],$fot(implies(truth,Y))]]) ).
cnf(refute_0_514,plain,
( big_V(Y,not(not(Y))) != implies(truth,Y)
| big_V(Y,not(not(Y))) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
( big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,not(not(Y))),implies(truth,Y)) )],[refute_0_511,refute_0_514]) ).
cnf(refute_0_516,plain,
big_V(Y,not(not(Y))) = Y,
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),implies(truth,Y)) )],[refute_0_508,refute_0_515]) ).
cnf(refute_0_517,plain,
big_V(X,not(not(X))) = X,
inference(subst,[],[refute_0_516:[bind(Y,$fot(X))]]) ).
cnf(refute_0_518,plain,
( big_V(X,not(not(X))) != X
| big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = implies(truth,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(not(X))),implies(truth,not(not(X)))) ),[0],$fot(X)]]) ).
cnf(refute_0_519,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = implies(truth,not(not(X))) ),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),X) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
implies(truth,not(not(X))) = not(not(X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_521,plain,
( X != implies(truth,not(not(X)))
| implies(truth,not(not(X))) != not(not(X))
| X = not(not(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,not(not(X))) ),[0],$fot(implies(truth,not(not(X))))]]) ).
cnf(refute_0_522,plain,
( X != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X))),not(not(X))) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(X,implies(truth,not(not(X)))) )],[refute_0_519,refute_0_522]) ).
cnf(refute_0_524,plain,
X = not(not(X)),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(truth,not(not(X)))) )],[refute_0_503,refute_0_523]) ).
cnf(refute_0_525,plain,
X_98 = not(not(X_98)),
inference(subst,[],[refute_0_524:[bind(X,$fot(X_98))]]) ).
cnf(refute_0_526,plain,
( X_98 != not(not(X_98))
| not(not(X_98)) = X_98 ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X_98)),bind(Y0,$fot(not(not(X_98))))]]) ).
cnf(refute_0_527,plain,
not(not(X_98)) = X_98,
inference(resolve,[$cnf( $equal(X_98,not(not(X_98))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
( big_hat(not(X_98),Y) != not(big_V(not(not(X_98)),not(Y)))
| not(not(X_98)) != X_98
| big_hat(not(X_98),Y) = not(big_V(X_98,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(not(X_98),Y),not(big_V(not(not(X_98)),not(Y)))) ),[1,0,0],$fot(X_98)]]) ).
cnf(refute_0_529,plain,
( big_hat(not(X_98),Y) != not(big_V(not(not(X_98)),not(Y)))
| big_hat(not(X_98),Y) = not(big_V(X_98,not(Y))) ),
inference(resolve,[$cnf( $equal(not(not(X_98)),X_98) )],[refute_0_527,refute_0_528]) ).
cnf(refute_0_530,plain,
big_hat(not(X_98),Y) = not(big_V(X_98,not(Y))),
inference(resolve,[$cnf( $equal(big_hat(not(X_98),Y),not(big_V(not(not(X_98)),not(Y)))) )],[refute_0_0,refute_0_529]) ).
cnf(refute_0_531,plain,
big_hat(not(X_403),not(X)) = not(big_V(X_403,not(not(X)))),
inference(subst,[],[refute_0_530:[bind(Y,$fot(not(X))),bind(X_98,$fot(X_403))]]) ).
cnf(refute_0_532,plain,
( X != not(not(X))
| not(not(X)) = X ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X)),bind(Y0,$fot(not(not(X))))]]) ).
cnf(refute_0_533,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(X,not(not(X))) )],[refute_0_524,refute_0_532]) ).
cnf(refute_0_534,plain,
( big_hat(not(X_403),not(X)) != not(big_V(X_403,not(not(X))))
| not(not(X)) != X
| big_hat(not(X_403),not(X)) = not(big_V(X_403,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(not(X_403),not(X)),not(big_V(X_403,not(not(X))))) ),[1,0,1],$fot(X)]]) ).
cnf(refute_0_535,plain,
( big_hat(not(X_403),not(X)) != not(big_V(X_403,not(not(X))))
| big_hat(not(X_403),not(X)) = not(big_V(X_403,X)) ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
big_hat(not(X_403),not(X)) = not(big_V(X_403,X)),
inference(resolve,[$cnf( $equal(big_hat(not(X_403),not(X)),not(big_V(X_403,not(not(X))))) )],[refute_0_531,refute_0_535]) ).
cnf(refute_0_537,plain,
big_hat(not(x),not(y)) = not(big_V(x,y)),
inference(subst,[],[refute_0_536:[bind(X,$fot(y)),bind(X_403,$fot(x))]]) ).
cnf(refute_0_538,plain,
( big_hat(not(x),not(y)) != not(big_V(x,y))
| not(big_V(x,y)) != not(big_V(x,y))
| not(big_V(x,y)) = big_hat(not(x),not(y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(big_V(x,y)),big_hat(not(x),not(y))) ),[1],$fot(not(big_V(x,y)))]]) ).
cnf(refute_0_539,plain,
( not(big_V(x,y)) != not(big_V(x,y))
| not(big_V(x,y)) = big_hat(not(x),not(y)) ),
inference(resolve,[$cnf( $equal(big_hat(not(x),not(y)),not(big_V(x,y))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
not(big_V(x,y)) != not(big_V(x,y)),
inference(resolve,[$cnf( $equal(not(big_V(x,y)),big_hat(not(x),not(y))) )],[refute_0_539,prove_wajsberg_theorem]) ).
cnf(refute_0_541,plain,
not(big_V(x,y)) = not(big_V(x,y)),
introduced(tautology,[refl,[$fot(not(big_V(x,y)))]]) ).
cnf(refute_0_542,plain,
$false,
inference(resolve,[$cnf( $equal(not(big_V(x,y)),not(big_V(x,y))) )],[refute_0_541,refute_0_540]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL145-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n028.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 3 06:41:03 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.39/1.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.39/1.60
% 1.39/1.60 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.48/1.66
%------------------------------------------------------------------------------