TSTP Solution File: LCL146-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 12:49:58 EDT 2022
% Result : Unsatisfiable 0.42s 0.59s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 104
% Number of leaves : 122
% Syntax : Number of clauses : 466 ( 232 unt; 0 nHn; 282 RR)
% Number of literals : 805 ( 746 equ; 341 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 514 ( 21 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(partial_order_definition1,axiom,
( ~ ordered(X,Y)
| implies(X,Y) = truth ) ).
cnf(partial_order_definition2,axiom,
( implies(X,Y) != truth
| ordered(X,Y) ) ).
cnf(prove_wajsberg_theorem,negated_conjecture,
not(big_hat(x,y)) != big_V(not(x),not(y)) ).
cnf(refute_0_0,plain,
big_V(X,not(not(X))) = implies(implies(X,not(not(X))),not(not(X))),
inference(subst,[],[big_V_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_1,plain,
big_V(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X)),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_2,plain,
( big_V(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| big_V(implies(not(X),not(Y)),implies(Y,X)) = implies(truth,implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_3,plain,
( big_V(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))
| big_V(implies(not(X),not(Y)),implies(Y,X)) = implies(truth,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_2]) ).
cnf(refute_0_4,plain,
big_V(implies(not(X),not(Y)),implies(Y,X)) = implies(truth,implies(Y,X)),
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(Y)),implies(Y,X)),implies(implies(implies(not(X),not(Y)),implies(Y,X)),implies(Y,X))) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( big_V(X,Y) != implies(implies(X,Y),Y)
| implies(implies(X,Y),Y) = big_V(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(implies(implies(X,Y),Y)))]]) ).
cnf(refute_0_9,plain,
implies(implies(X,Y),Y) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(X,Y),Y)) )],[big_V_definition,refute_0_8]) ).
cnf(refute_0_10,plain,
( implies(implies(X,Y),Y) != big_V(X,Y)
| implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) ),[0],$fot(big_V(X,Y))]]) ).
cnf(refute_0_11,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),big_V(X,Y)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(implies(Y,X),X) = big_V(Y,X),
inference(subst,[],[refute_0_9:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_13,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) != big_V(Y,X)
| big_V(X,Y) = big_V(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,Y),big_V(Y,X)) ),[0],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_14,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),X),big_V(Y,X)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(Y,X),X)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
big_V(X,Y) = big_V(Y,X),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_15]) ).
cnf(refute_0_17,plain,
( big_V(X,Y) != big_V(Y,X)
| big_V(Y,X) = big_V(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(big_V(Y,X)))]]) ).
cnf(refute_0_18,plain,
big_V(Y,X) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),big_V(Y,X)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
big_V(implies(not(X),not(Y)),implies(Y,X)) = big_V(implies(Y,X),implies(not(X),not(Y))),
inference(subst,[],[refute_0_18:[bind(X,$fot(implies(Y,X))),bind(Y,$fot(implies(not(X),not(Y))))]]) ).
cnf(refute_0_20,plain,
( big_V(implies(not(X),not(Y)),implies(Y,X)) != big_V(implies(Y,X),implies(not(X),not(Y)))
| big_V(implies(not(X),not(Y)),implies(Y,X)) != implies(truth,implies(Y,X))
| big_V(implies(Y,X),implies(not(X),not(Y))) = implies(truth,implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X),not(Y)),implies(Y,X)),implies(truth,implies(Y,X))) ),[0],$fot(big_V(implies(Y,X),implies(not(X),not(Y))))]]) ).
cnf(refute_0_21,plain,
( big_V(implies(not(X),not(Y)),implies(Y,X)) != implies(truth,implies(Y,X))
| big_V(implies(Y,X),implies(not(X),not(Y))) = implies(truth,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(Y)),implies(Y,X)),big_V(implies(Y,X),implies(not(X),not(Y)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(truth,implies(Y,X)) = implies(Y,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,X)))]]) ).
cnf(refute_0_23,plain,
( big_V(implies(Y,X),implies(not(X),not(Y))) != implies(truth,implies(Y,X))
| implies(truth,implies(Y,X)) != implies(Y,X)
| big_V(implies(Y,X),implies(not(X),not(Y))) = implies(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(Y,X),implies(not(X),not(Y))),implies(Y,X)) ),[0],$fot(implies(truth,implies(Y,X)))]]) ).
cnf(refute_0_24,plain,
( big_V(implies(Y,X),implies(not(X),not(Y))) != implies(truth,implies(Y,X))
| big_V(implies(Y,X),implies(not(X),not(Y))) = implies(Y,X) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,X)),implies(Y,X)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( big_V(implies(not(X),not(Y)),implies(Y,X)) != implies(truth,implies(Y,X))
| big_V(implies(Y,X),implies(not(X),not(Y))) = implies(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(implies(Y,X),implies(not(X),not(Y))),implies(truth,implies(Y,X))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
big_V(implies(Y,X),implies(not(X),not(Y))) = implies(Y,X),
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(Y)),implies(Y,X)),implies(truth,implies(Y,X))) )],[refute_0_4,refute_0_25]) ).
cnf(refute_0_27,plain,
big_V(implies(Y,not(not(Y))),implies(not(not(not(Y))),not(Y))) = implies(Y,not(not(Y))),
inference(subst,[],[refute_0_26:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_28,plain,
( ~ ordered(truth,implies(not(not(X_77)),X_77))
| implies(truth,implies(not(not(X_77)),X_77)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(not(X_77)),X_77)))]]) ).
cnf(refute_0_29,plain,
( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) != truth
| ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(implies(X,Y))),bind(Y,$fot(implies(implies(Y,Z),implies(X,Z))))]]) ).
cnf(refute_0_30,plain,
( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) != truth
| truth != truth
| implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_31,plain,
( truth != truth
| implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[wajsberg_2,refute_0_30]) ).
cnf(refute_0_32,plain,
( truth != truth
| ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[refute_0_31,refute_0_29]) ).
cnf(refute_0_33,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_34,plain,
ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_33,refute_0_32]) ).
cnf(refute_0_35,plain,
ordered(implies(X_63,implies(not(X_65),not(truth))),implies(implies(implies(not(X_65),not(truth)),X_65),implies(X_63,X_65))),
inference(subst,[],[refute_0_34:[bind(X,$fot(X_63)),bind(Y,$fot(implies(not(X_65),not(truth)))),bind(Z,$fot(X_65))]]) ).
cnf(refute_0_36,plain,
implies(implies(not(X_3),not(truth)),implies(truth,X_3)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_3)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_37,plain,
implies(truth,X_3) = X_3,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_38,plain,
( implies(implies(not(X_3),not(truth)),implies(truth,X_3)) != truth
| implies(truth,X_3) != X_3
| implies(implies(not(X_3),not(truth)),X_3) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_3),not(truth)),implies(truth,X_3)),truth) ),[0,1],$fot(X_3)]]) ).
cnf(refute_0_39,plain,
( implies(implies(not(X_3),not(truth)),implies(truth,X_3)) != truth
| implies(implies(not(X_3),not(truth)),X_3) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_3),X_3) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(not(X_3),not(truth)),X_3) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_3),not(truth)),implies(truth,X_3)),truth) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(implies(not(X_65),not(truth)),X_65) = truth,
inference(subst,[],[refute_0_40:[bind(X_3,$fot(X_65))]]) ).
cnf(refute_0_42,plain,
( implies(implies(not(X_65),not(truth)),X_65) != truth
| ~ ordered(implies(X_63,implies(not(X_65),not(truth))),implies(implies(implies(not(X_65),not(truth)),X_65),implies(X_63,X_65)))
| ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_63,implies(not(X_65),not(truth))),implies(implies(implies(not(X_65),not(truth)),X_65),implies(X_63,X_65))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_43,plain,
( ~ ordered(implies(X_63,implies(not(X_65),not(truth))),implies(implies(implies(not(X_65),not(truth)),X_65),implies(X_63,X_65)))
| ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_65),not(truth)),X_65),truth) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65))),
inference(resolve,[$cnf( ordered(implies(X_63,implies(not(X_65),not(truth))),implies(implies(implies(not(X_65),not(truth)),X_65),implies(X_63,X_65))) )],[refute_0_35,refute_0_43]) ).
cnf(refute_0_45,plain,
implies(truth,implies(X_63,X_65)) = implies(X_63,X_65),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_63,X_65)))]]) ).
cnf(refute_0_46,plain,
( implies(truth,implies(X_63,X_65)) != implies(X_63,X_65)
| ~ ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65)))
| ordered(implies(X_63,implies(not(X_65),not(truth))),implies(X_63,X_65)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65))) ),[1],$fot(implies(X_63,X_65))]]) ).
cnf(refute_0_47,plain,
( ~ ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65)))
| ordered(implies(X_63,implies(not(X_65),not(truth))),implies(X_63,X_65)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_63,X_65)),implies(X_63,X_65)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
ordered(implies(X_63,implies(not(X_65),not(truth))),implies(X_63,X_65)),
inference(resolve,[$cnf( ordered(implies(X_63,implies(not(X_65),not(truth))),implies(truth,implies(X_63,X_65))) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
ordered(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),implies(implies(not(not(truth)),not(not(X_76))),X_76)),
inference(subst,[],[refute_0_48:[bind(X_63,$fot(implies(not(not(truth)),not(not(X_76))))),bind(X_65,$fot(X_76))]]) ).
cnf(refute_0_50,plain,
implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_76)))]]) ).
cnf(refute_0_51,plain,
( implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))) != truth
| ~ ordered(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),implies(implies(not(not(truth)),not(not(X_76))),X_76))
| ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),implies(implies(not(not(truth)),not(not(X_76))),X_76)) ),[0],$fot(truth)]]) ).
cnf(refute_0_52,plain,
( ~ ordered(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),implies(implies(not(not(truth)),not(not(X_76))),X_76))
| ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),truth) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76)),
inference(resolve,[$cnf( ordered(implies(implies(not(not(truth)),not(not(X_76))),implies(not(X_76),not(truth))),implies(implies(not(not(truth)),not(not(X_76))),X_76)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(truth,not(not(X_76))) = not(not(X_76)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_76))))]]) ).
cnf(refute_0_55,plain,
( ~ ordered(truth,not(not(truth)))
| implies(truth,not(not(truth))) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(truth)),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_56,plain,
ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),implies(not(truth),not(not(truth))))),
inference(subst,[],[refute_0_34:[bind(X,$fot(not(truth))),bind(Y,$fot(X_64)),bind(Z,$fot(not(not(truth))))]]) ).
cnf(refute_0_57,plain,
big_V(implies(X_8,Y),Y) = implies(implies(implies(X_8,Y),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(X_8,Y)))]]) ).
cnf(refute_0_58,plain,
big_V(X_8,Y) = implies(implies(X_8,Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_59,plain,
( big_V(X_8,Y) != implies(implies(X_8,Y),Y)
| implies(implies(X_8,Y),Y) = big_V(X_8,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X_8,Y))),bind(Y0,$fot(implies(implies(X_8,Y),Y)))]]) ).
cnf(refute_0_60,plain,
implies(implies(X_8,Y),Y) = big_V(X_8,Y),
inference(resolve,[$cnf( $equal(big_V(X_8,Y),implies(implies(X_8,Y),Y)) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
( big_V(implies(X_8,Y),Y) != implies(implies(implies(X_8,Y),Y),Y)
| implies(implies(X_8,Y),Y) != big_V(X_8,Y)
| big_V(implies(X_8,Y),Y) = implies(big_V(X_8,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_8,Y),Y),implies(implies(implies(X_8,Y),Y),Y)) ),[1,0],$fot(big_V(X_8,Y))]]) ).
cnf(refute_0_62,plain,
( big_V(implies(X_8,Y),Y) != implies(implies(implies(X_8,Y),Y),Y)
| big_V(implies(X_8,Y),Y) = implies(big_V(X_8,Y),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(X_8,Y),Y),big_V(X_8,Y)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
big_V(implies(X_8,Y),Y) = implies(big_V(X_8,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_8,Y),Y),implies(implies(implies(X_8,Y),Y),Y)) )],[refute_0_57,refute_0_62]) ).
cnf(refute_0_64,plain,
big_V(implies(X_8,Y),Y) = big_V(Y,implies(X_8,Y)),
inference(subst,[],[refute_0_18:[bind(X,$fot(Y)),bind(Y,$fot(implies(X_8,Y)))]]) ).
cnf(refute_0_65,plain,
( big_V(implies(X_8,Y),Y) != big_V(Y,implies(X_8,Y))
| big_V(implies(X_8,Y),Y) != implies(big_V(X_8,Y),Y)
| big_V(Y,implies(X_8,Y)) = implies(big_V(X_8,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_8,Y),Y),implies(big_V(X_8,Y),Y)) ),[0],$fot(big_V(Y,implies(X_8,Y)))]]) ).
cnf(refute_0_66,plain,
( big_V(implies(X_8,Y),Y) != implies(big_V(X_8,Y),Y)
| big_V(Y,implies(X_8,Y)) = implies(big_V(X_8,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_8,Y),Y),big_V(Y,implies(X_8,Y))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
big_V(Y,implies(X_8,Y)) = implies(big_V(X_8,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_8,Y),Y),implies(big_V(X_8,Y),Y)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(big_V(not(truth),not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_67:[bind(Y,$fot(not(not(truth)))),bind(X_8,$fot(not(truth)))]]) ).
cnf(refute_0_69,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_40:[bind(X_3,$fot(not(truth)))]]) ).
cnf(refute_0_70,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_71,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)) = big_V(not(not(truth)),not(truth)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(not(not(truth)),not(truth)))),bind(Y0,$fot(implies(implies(not(not(truth)),not(truth)),not(truth))))]]) ).
cnf(refute_0_72,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = big_V(not(not(truth)),not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(truth)),not(truth))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != big_V(not(not(truth)),not(truth))
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| big_V(not(not(truth)),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) ),[0],$fot(big_V(not(not(truth)),not(truth)))]]) ).
cnf(refute_0_74,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| big_V(not(not(truth)),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),big_V(not(not(truth)),not(truth))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_69,refute_0_74]) ).
cnf(refute_0_76,plain,
big_V(not(not(truth)),not(truth)) = big_V(not(truth),not(not(truth))),
inference(subst,[],[refute_0_18:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_77,plain,
( big_V(not(not(truth)),not(truth)) != big_V(not(truth),not(not(truth)))
| big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(big_V(not(truth),not(not(truth))))]]) ).
cnf(refute_0_78,plain,
( big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),big_V(not(truth),not(not(truth)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
big_V(not(truth),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(big_V(not(truth),not(not(truth))),not(not(truth)))
| big_V(not(truth),not(not(truth))) != truth
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$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_81,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( $equal(big_V(not(truth),not(not(truth))),truth) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(big_V(not(truth),not(not(truth))),not(not(truth)))) )],[refute_0_68,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_84,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_85,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( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(truth,not(not(truth)))) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
big_V(X,implies(X_55,X)) = implies(implies(X,implies(X_55,X)),implies(X_55,X)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(implies(X_55,X)))]]) ).
cnf(refute_0_88,plain,
implies(implies(X_29,truth),implies(implies(truth,X_31),implies(X_29,X_31))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_29)),bind(Y,$fot(truth)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_89,plain,
implies(truth,X_31) = X_31,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_90,plain,
( implies(implies(X_29,truth),implies(implies(truth,X_31),implies(X_29,X_31))) != truth
| implies(truth,X_31) != X_31
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_29,truth),implies(implies(truth,X_31),implies(X_29,X_31))),truth) ),[0,1,0],$fot(X_31)]]) ).
cnf(refute_0_91,plain,
( implies(implies(X_29,truth),implies(implies(truth,X_31),implies(X_29,X_31))) != truth
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_31),X_31) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_29,truth),implies(implies(truth,X_31),implies(X_29,X_31))),truth) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(truth,implies(X_31,implies(X_29,X_31))) = implies(X_31,implies(X_29,X_31)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_31,implies(X_29,X_31))))]]) ).
cnf(refute_0_94,plain,
implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(big_V(truth,not(Y)))),bind(Y,$fot(X_30)),bind(Z,$fot(big_V(truth,Y)))]]) ).
cnf(refute_0_95,plain,
implies(implies(not(Y),not(Y)),implies(Y,Y)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(Y))]]) ).
cnf(refute_0_96,plain,
big_V(truth,X_9) = implies(implies(truth,X_9),X_9),
inference(subst,[],[big_V_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_97,plain,
implies(truth,X_9) = X_9,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_98,plain,
( big_V(truth,X_9) != implies(implies(truth,X_9),X_9)
| implies(truth,X_9) != X_9
| big_V(truth,X_9) = implies(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_9),implies(implies(truth,X_9),X_9)) ),[1,0],$fot(X_9)]]) ).
cnf(refute_0_99,plain,
( big_V(truth,X_9) != implies(implies(truth,X_9),X_9)
| big_V(truth,X_9) = implies(X_9,X_9) ),
inference(resolve,[$cnf( $equal(implies(truth,X_9),X_9) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
big_V(truth,X_9) = implies(X_9,X_9),
inference(resolve,[$cnf( $equal(big_V(truth,X_9),implies(implies(truth,X_9),X_9)) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
big_V(truth,not(Y)) = implies(not(Y),not(Y)),
inference(subst,[],[refute_0_100:[bind(X_9,$fot(not(Y)))]]) ).
cnf(refute_0_102,plain,
( big_V(truth,not(Y)) != implies(not(Y),not(Y))
| implies(not(Y),not(Y)) = big_V(truth,not(Y)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(truth,not(Y)))),bind(Y0,$fot(implies(not(Y),not(Y))))]]) ).
cnf(refute_0_103,plain,
implies(not(Y),not(Y)) = big_V(truth,not(Y)),
inference(resolve,[$cnf( $equal(big_V(truth,not(Y)),implies(not(Y),not(Y))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( implies(implies(not(Y),not(Y)),implies(Y,Y)) != truth
| implies(not(Y),not(Y)) != big_V(truth,not(Y))
| implies(big_V(truth,not(Y)),implies(Y,Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(Y),not(Y)),implies(Y,Y)),truth) ),[0,0],$fot(big_V(truth,not(Y)))]]) ).
cnf(refute_0_105,plain,
( implies(implies(not(Y),not(Y)),implies(Y,Y)) != truth
| implies(big_V(truth,not(Y)),implies(Y,Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(Y),not(Y)),big_V(truth,not(Y))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(big_V(truth,not(Y)),implies(Y,Y)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(Y)),implies(Y,Y)),truth) )],[refute_0_95,refute_0_105]) ).
cnf(refute_0_107,plain,
( big_V(truth,X_9) != implies(X_9,X_9)
| implies(X_9,X_9) = big_V(truth,X_9) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(truth,X_9))),bind(Y0,$fot(implies(X_9,X_9)))]]) ).
cnf(refute_0_108,plain,
implies(X_9,X_9) = big_V(truth,X_9),
inference(resolve,[$cnf( $equal(big_V(truth,X_9),implies(X_9,X_9)) )],[refute_0_100,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(Y,Y) = big_V(truth,Y),
inference(subst,[],[refute_0_108:[bind(X_9,$fot(Y))]]) ).
cnf(refute_0_110,plain,
implies(big_V(truth,not(Y)),implies(Y,Y)) = implies(big_V(truth,not(Y)),implies(Y,Y)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(Y)),implies(Y,Y)))]]) ).
cnf(refute_0_111,plain,
( implies(Y,Y) != big_V(truth,Y)
| implies(big_V(truth,not(Y)),implies(Y,Y)) != implies(big_V(truth,not(Y)),implies(Y,Y))
| implies(big_V(truth,not(Y)),implies(Y,Y)) = implies(big_V(truth,not(Y)),big_V(truth,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(Y)),implies(Y,Y)),implies(big_V(truth,not(Y)),implies(Y,Y))) ),[1,1],$fot(big_V(truth,Y))]]) ).
cnf(refute_0_112,plain,
( implies(Y,Y) != big_V(truth,Y)
| implies(big_V(truth,not(Y)),implies(Y,Y)) = implies(big_V(truth,not(Y)),big_V(truth,Y)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),implies(Y,Y)),implies(big_V(truth,not(Y)),implies(Y,Y))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(big_V(truth,not(Y)),implies(Y,Y)) = implies(big_V(truth,not(Y)),big_V(truth,Y)),
inference(resolve,[$cnf( $equal(implies(Y,Y),big_V(truth,Y)) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
( implies(big_V(truth,not(Y)),implies(Y,Y)) != implies(big_V(truth,not(Y)),big_V(truth,Y))
| implies(big_V(truth,not(Y)),implies(Y,Y)) != truth
| implies(big_V(truth,not(Y)),big_V(truth,Y)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(Y)),implies(Y,Y)),truth) ),[0],$fot(implies(big_V(truth,not(Y)),big_V(truth,Y)))]]) ).
cnf(refute_0_115,plain,
( implies(big_V(truth,not(Y)),implies(Y,Y)) != truth
| implies(big_V(truth,not(Y)),big_V(truth,Y)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),implies(Y,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(big_V(truth,not(Y)),big_V(truth,Y)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),implies(Y,Y)),truth) )],[refute_0_106,refute_0_115]) ).
cnf(refute_0_117,plain,
( implies(big_V(truth,not(Y)),big_V(truth,Y)) != truth
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y)))) != truth
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_118,plain,
( implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y)))) != truth
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),big_V(truth,Y)),truth) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),implies(big_V(truth,not(Y)),big_V(truth,Y)))),truth) )],[refute_0_94,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(big_V(truth,not(X_13)),big_V(truth,X_13)) = truth,
inference(subst,[],[refute_0_116:[bind(Y,$fot(X_13))]]) ).
cnf(refute_0_121,plain,
big_V(X_13,truth) = big_V(truth,X_13),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_13)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_122,plain,
( big_V(X_13,truth) != big_V(truth,X_13)
| big_V(truth,X_13) = big_V(X_13,truth) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X_13,truth))),bind(Y0,$fot(big_V(truth,X_13)))]]) ).
cnf(refute_0_123,plain,
big_V(truth,X_13) = big_V(X_13,truth),
inference(resolve,[$cnf( $equal(big_V(X_13,truth),big_V(truth,X_13)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( big_V(truth,X_13) != big_V(X_13,truth)
| implies(big_V(truth,not(X_13)),big_V(truth,X_13)) != truth
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(truth,X_13)),truth) ),[0,1],$fot(big_V(X_13,truth))]]) ).
cnf(refute_0_125,plain,
( implies(big_V(truth,not(X_13)),big_V(truth,X_13)) != truth
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,X_13),big_V(X_13,truth)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(truth,X_13)),truth) )],[refute_0_120,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(truth,big_V(X_13,truth)) = big_V(X_13,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X_13,truth)))]]) ).
cnf(refute_0_128,plain,
implies(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))))),bind(Y,$fot(truth)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_129,plain,
implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(truth)),bind(Y,$fot(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))))]]) ).
cnf(refute_0_130,plain,
implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,implies(not(truth),not(big_V(truth,not(truth)))))) = truth,
inference(subst,[],[refute_0_116:[bind(Y,$fot(implies(not(truth),not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_131,plain,
big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) = implies(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X),not(implies(not(X),not(truth)))))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_132,plain,
implies(implies(not(X),not(implies(not(X),not(truth)))),implies(implies(not(X),not(truth)),X)) = truth,
inference(subst,[],[wajsberg_4:[bind(Y,$fot(implies(not(X),not(truth))))]]) ).
cnf(refute_0_133,plain,
implies(implies(not(X),not(truth)),X) = truth,
inference(subst,[],[refute_0_40:[bind(X_3,$fot(X))]]) ).
cnf(refute_0_134,plain,
( implies(implies(not(X),not(implies(not(X),not(truth)))),implies(implies(not(X),not(truth)),X)) != truth
| implies(implies(not(X),not(truth)),X) != truth
| implies(implies(not(X),not(implies(not(X),not(truth)))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(implies(not(X),not(truth)))),implies(implies(not(X),not(truth)),X)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_135,plain,
( implies(implies(not(X),not(implies(not(X),not(truth)))),implies(implies(not(X),not(truth)),X)) != truth
| implies(implies(not(X),not(implies(not(X),not(truth)))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(truth)),X),truth) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(implies(not(X),not(implies(not(X),not(truth)))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(implies(not(X),not(truth)))),implies(implies(not(X),not(truth)),X)),truth) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
( big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != implies(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth)
| implies(implies(not(X),not(implies(not(X),not(truth)))),truth) != truth
| big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X),not(implies(not(X),not(truth)))),truth),implies(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_138,plain,
( big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != implies(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth)
| big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(implies(not(X),not(truth)))),truth),implies(implies(implies(not(X),not(implies(not(X),not(truth)))),truth),truth)) )],[refute_0_131,refute_0_138]) ).
cnf(refute_0_140,plain,
big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) = big_V(truth,implies(not(X),not(implies(not(X),not(truth))))),
inference(subst,[],[refute_0_18:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(X),not(implies(not(X),not(truth))))))]]) ).
cnf(refute_0_141,plain,
( big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != big_V(truth,implies(not(X),not(implies(not(X),not(truth)))))
| big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != implies(truth,truth)
| big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X),not(implies(not(X),not(truth)))),truth),implies(truth,truth)) ),[0],$fot(big_V(truth,implies(not(X),not(implies(not(X),not(truth))))))]]) ).
cnf(refute_0_142,plain,
( big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != implies(truth,truth)
| big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(implies(not(X),not(truth)))),truth),big_V(truth,implies(not(X),not(implies(not(X),not(truth)))))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_144,plain,
( big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) != implies(truth,truth)
| implies(truth,truth) != truth
| big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,implies(not(X),not(implies(not(X),not(truth))))),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_145,plain,
( big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) != implies(truth,truth)
| big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
( big_V(implies(not(X),not(implies(not(X),not(truth)))),truth) != implies(truth,truth)
| big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,implies(not(X),not(implies(not(X),not(truth))))),implies(truth,truth)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
big_V(truth,implies(not(X),not(implies(not(X),not(truth))))) = truth,
inference(resolve,[$cnf( $equal(big_V(implies(not(X),not(implies(not(X),not(truth)))),truth),implies(truth,truth)) )],[refute_0_139,refute_0_146]) ).
cnf(refute_0_148,plain,
big_V(truth,implies(not(truth),not(implies(not(truth),not(truth))))) = truth,
inference(subst,[],[refute_0_147:[bind(X,$fot(truth))]]) ).
cnf(refute_0_149,plain,
big_V(truth,not(truth)) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_100:[bind(X_9,$fot(not(truth)))]]) ).
cnf(refute_0_150,plain,
( big_V(truth,not(truth)) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) = big_V(truth,not(truth)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(truth,not(truth)))),bind(Y0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_151,plain,
implies(not(truth),not(truth)) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),implies(not(truth),not(truth))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( big_V(truth,implies(not(truth),not(implies(not(truth),not(truth))))) != truth
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| big_V(truth,implies(not(truth),not(big_V(truth,not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,implies(not(truth),not(implies(not(truth),not(truth))))),truth) ),[0,1,1,0],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_153,plain,
( big_V(truth,implies(not(truth),not(implies(not(truth),not(truth))))) != truth
| big_V(truth,implies(not(truth),not(big_V(truth,not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
big_V(truth,implies(not(truth),not(big_V(truth,not(truth))))) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,implies(not(truth),not(implies(not(truth),not(truth))))),truth) )],[refute_0_148,refute_0_153]) ).
cnf(refute_0_155,plain,
( big_V(truth,implies(not(truth),not(big_V(truth,not(truth))))) != truth
| implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,implies(not(truth),not(big_V(truth,not(truth)))))) != truth
| implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,implies(not(truth),not(big_V(truth,not(truth)))))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_156,plain,
( implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,implies(not(truth),not(big_V(truth,not(truth)))))) != truth
| implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,implies(not(truth),not(big_V(truth,not(truth))))),truth) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,implies(not(truth),not(big_V(truth,not(truth)))))),truth) )],[refute_0_130,refute_0_156]) ).
cnf(refute_0_158,plain,
( implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth)) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_159,plain,
( implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth)) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth),truth) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth)),truth) )],[refute_0_129,refute_0_159]) ).
cnf(refute_0_161,plain,
( implies(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth) != truth
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_162,plain,
( implies(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != truth
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),truth) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),truth) )],[refute_0_128,refute_0_162]) ).
cnf(refute_0_164,plain,
implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)))]]) ).
cnf(refute_0_165,plain,
( implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(truth,X_31) != X_31
| implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) ),[1,0],$fot(X_31)]]) ).
cnf(refute_0_166,plain,
( implies(truth,X_31) != X_31
| implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),
inference(resolve,[$cnf( $equal(implies(truth,X_31),X_31) )],[refute_0_89,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))))]]) ).
cnf(refute_0_169,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_170,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_169]) ).
cnf(refute_0_171,plain,
( implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))))),bind(Y0,$fot(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)))),bind(Z0,$fot(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))))]]) ).
cnf(refute_0_172,plain,
( implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) )],[refute_0_167,refute_0_172]) ).
cnf(refute_0_174,plain,
( implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != truth
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),truth) ),[0],$fot(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)))]]) ).
cnf(refute_0_175,plain,
( implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) != truth
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),truth) )],[refute_0_163,refute_0_175]) ).
cnf(refute_0_177,plain,
implies(X_31,X_31) = big_V(truth,X_31),
inference(subst,[],[refute_0_108:[bind(X_9,$fot(X_31))]]) ).
cnf(refute_0_178,plain,
big_V(not(truth),truth) = implies(implies(not(truth),truth),truth),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(truth))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_179,plain,
implies(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(Y,X_31),X_31))),bind(Z,$fot(implies(Y,X_31)))]]) ).
cnf(refute_0_180,plain,
implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,X_31))),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_181,plain,
( implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31))) != truth
| implies(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31)))) != truth
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_182,plain,
( implies(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31)))) != truth
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31))),truth) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(Y,implies(Y,X_31)),implies(implies(implies(Y,X_31),X_31),implies(Y,X_31)))),truth) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
big_V(X_21,implies(X_22,X_21)) = implies(big_V(X_22,X_21),X_21),
inference(subst,[],[refute_0_67:[bind(Y,$fot(X_21)),bind(X_8,$fot(X_22))]]) ).
cnf(refute_0_185,plain,
big_V(X_21,X_22) = big_V(X_22,X_21),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_21)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_186,plain,
( big_V(X_21,X_22) != big_V(X_22,X_21)
| big_V(X_22,X_21) = big_V(X_21,X_22) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X_21,X_22))),bind(Y0,$fot(big_V(X_22,X_21)))]]) ).
cnf(refute_0_187,plain,
big_V(X_22,X_21) = big_V(X_21,X_22),
inference(resolve,[$cnf( $equal(big_V(X_21,X_22),big_V(X_22,X_21)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
( big_V(X_21,implies(X_22,X_21)) != implies(big_V(X_22,X_21),X_21)
| big_V(X_22,X_21) != big_V(X_21,X_22)
| big_V(X_21,implies(X_22,X_21)) = implies(big_V(X_21,X_22),X_21) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_21,implies(X_22,X_21)),implies(big_V(X_22,X_21),X_21)) ),[1,0],$fot(big_V(X_21,X_22))]]) ).
cnf(refute_0_189,plain,
( big_V(X_21,implies(X_22,X_21)) != implies(big_V(X_22,X_21),X_21)
| big_V(X_21,implies(X_22,X_21)) = implies(big_V(X_21,X_22),X_21) ),
inference(resolve,[$cnf( $equal(big_V(X_22,X_21),big_V(X_21,X_22)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
big_V(X_21,implies(X_22,X_21)) = implies(big_V(X_21,X_22),X_21),
inference(resolve,[$cnf( $equal(big_V(X_21,implies(X_22,X_21)),implies(big_V(X_22,X_21),X_21)) )],[refute_0_184,refute_0_189]) ).
cnf(refute_0_191,plain,
( big_V(X_21,implies(X_22,X_21)) != implies(big_V(X_21,X_22),X_21)
| implies(big_V(X_21,X_22),X_21) = big_V(X_21,implies(X_22,X_21)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(X_21,implies(X_22,X_21)))),bind(Y0,$fot(implies(big_V(X_21,X_22),X_21)))]]) ).
cnf(refute_0_192,plain,
implies(big_V(X_21,X_22),X_21) = big_V(X_21,implies(X_22,X_21)),
inference(resolve,[$cnf( $equal(big_V(X_21,implies(X_22,X_21)),implies(big_V(X_21,X_22),X_21)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(big_V(Y,X_31),Y) = big_V(Y,implies(X_31,Y)),
inference(subst,[],[refute_0_192:[bind(X_21,$fot(Y)),bind(X_22,$fot(X_31))]]) ).
cnf(refute_0_194,plain,
implies(implies(Y,X_31),X_31) = big_V(Y,X_31),
inference(subst,[],[refute_0_9:[bind(X,$fot(Y)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_195,plain,
implies(implies(implies(Y,X_31),X_31),Y) = implies(implies(implies(Y,X_31),X_31),Y),
introduced(tautology,[refl,[$fot(implies(implies(implies(Y,X_31),X_31),Y))]]) ).
cnf(refute_0_196,plain,
( implies(implies(Y,X_31),X_31) != big_V(Y,X_31)
| implies(implies(implies(Y,X_31),X_31),Y) != implies(implies(implies(Y,X_31),X_31),Y)
| implies(implies(implies(Y,X_31),X_31),Y) = implies(big_V(Y,X_31),Y) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(implies(Y,X_31),X_31),Y)) ),[1,0],$fot(big_V(Y,X_31))]]) ).
cnf(refute_0_197,plain,
( implies(implies(Y,X_31),X_31) != big_V(Y,X_31)
| implies(implies(implies(Y,X_31),X_31),Y) = implies(big_V(Y,X_31),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_31),X_31),Y),implies(implies(implies(Y,X_31),X_31),Y)) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(implies(implies(Y,X_31),X_31),Y) = implies(big_V(Y,X_31),Y),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_31),X_31),big_V(Y,X_31)) )],[refute_0_194,refute_0_197]) ).
cnf(refute_0_199,plain,
( implies(big_V(Y,X_31),Y) != big_V(Y,implies(X_31,Y))
| implies(implies(implies(Y,X_31),X_31),Y) != implies(big_V(Y,X_31),Y)
| implies(implies(implies(Y,X_31),X_31),Y) = big_V(Y,implies(X_31,Y)) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(implies(Y,X_31),X_31),Y))),bind(Y0,$fot(implies(big_V(Y,X_31),Y))),bind(Z0,$fot(big_V(Y,implies(X_31,Y))))]]) ).
cnf(refute_0_200,plain,
( implies(big_V(Y,X_31),Y) != big_V(Y,implies(X_31,Y))
| implies(implies(implies(Y,X_31),X_31),Y) = big_V(Y,implies(X_31,Y)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_31),X_31),Y),implies(big_V(Y,X_31),Y)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(implies(implies(Y,X_31),X_31),Y) = big_V(Y,implies(X_31,Y)),
inference(resolve,[$cnf( $equal(implies(big_V(Y,X_31),Y),big_V(Y,implies(X_31,Y))) )],[refute_0_193,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = implies(implies(implies(implies(Y,X_31),X_31),Y),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(Y,X_31),X_31),Y),truth))]]) ).
cnf(refute_0_203,plain,
( implies(implies(implies(Y,X_31),X_31),Y) != big_V(Y,implies(X_31,Y))
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) != implies(implies(implies(implies(Y,X_31),X_31),Y),truth)
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = implies(big_V(Y,implies(X_31,Y)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),truth),implies(implies(implies(implies(Y,X_31),X_31),Y),truth)) ),[1,0],$fot(big_V(Y,implies(X_31,Y)))]]) ).
cnf(refute_0_204,plain,
( implies(implies(implies(Y,X_31),X_31),Y) != big_V(Y,implies(X_31,Y))
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = implies(big_V(Y,implies(X_31,Y)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),truth),implies(implies(implies(implies(Y,X_31),X_31),Y),truth)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
implies(implies(implies(implies(Y,X_31),X_31),Y),truth) = implies(big_V(Y,implies(X_31,Y)),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(Y,X_31),X_31),Y),big_V(Y,implies(X_31,Y))) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( implies(implies(implies(implies(Y,X_31),X_31),Y),truth) != implies(big_V(Y,implies(X_31,Y)),truth)
| implies(implies(implies(implies(Y,X_31),X_31),Y),truth) != truth
| implies(big_V(Y,implies(X_31,Y)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),truth),truth) ),[0],$fot(implies(big_V(Y,implies(X_31,Y)),truth))]]) ).
cnf(refute_0_207,plain,
( implies(implies(implies(implies(Y,X_31),X_31),Y),truth) != truth
| implies(big_V(Y,implies(X_31,Y)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),truth),implies(big_V(Y,implies(X_31,Y)),truth)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(big_V(Y,implies(X_31,Y)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_31),X_31),Y),truth),truth) )],[refute_0_183,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(big_V(not(truth),implies(not(not(truth)),not(truth))),truth) = truth,
inference(subst,[],[refute_0_208:[bind(Y,$fot(not(truth))),bind(X_31,$fot(not(not(truth))))]]) ).
cnf(refute_0_210,plain,
big_V(implies(not(X_9),not(truth)),X_9) = implies(implies(implies(not(X_9),not(truth)),X_9),X_9),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X_9),not(truth)))),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_211,plain,
implies(implies(not(X_9),not(truth)),X_9) = truth,
inference(subst,[],[refute_0_40:[bind(X_3,$fot(X_9))]]) ).
cnf(refute_0_212,plain,
( big_V(implies(not(X_9),not(truth)),X_9) != implies(implies(implies(not(X_9),not(truth)),X_9),X_9)
| implies(implies(not(X_9),not(truth)),X_9) != truth
| big_V(implies(not(X_9),not(truth)),X_9) = implies(truth,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_9),not(truth)),X_9),implies(implies(implies(not(X_9),not(truth)),X_9),X_9)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_213,plain,
( big_V(implies(not(X_9),not(truth)),X_9) != implies(implies(implies(not(X_9),not(truth)),X_9),X_9)
| big_V(implies(not(X_9),not(truth)),X_9) = implies(truth,X_9) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_9),not(truth)),X_9),truth) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
big_V(implies(not(X_9),not(truth)),X_9) = implies(truth,X_9),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_9),not(truth)),X_9),implies(implies(implies(not(X_9),not(truth)),X_9),X_9)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
big_V(implies(not(X_9),not(truth)),X_9) = big_V(X_9,implies(not(X_9),not(truth))),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_9)),bind(Y,$fot(implies(not(X_9),not(truth))))]]) ).
cnf(refute_0_216,plain,
( big_V(implies(not(X_9),not(truth)),X_9) != big_V(X_9,implies(not(X_9),not(truth)))
| big_V(implies(not(X_9),not(truth)),X_9) != implies(truth,X_9)
| big_V(X_9,implies(not(X_9),not(truth))) = implies(truth,X_9) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_9),not(truth)),X_9),implies(truth,X_9)) ),[0],$fot(big_V(X_9,implies(not(X_9),not(truth))))]]) ).
cnf(refute_0_217,plain,
( big_V(implies(not(X_9),not(truth)),X_9) != implies(truth,X_9)
| big_V(X_9,implies(not(X_9),not(truth))) = implies(truth,X_9) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_9),not(truth)),X_9),big_V(X_9,implies(not(X_9),not(truth)))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
( big_V(X_9,implies(not(X_9),not(truth))) != implies(truth,X_9)
| implies(truth,X_9) != X_9
| big_V(X_9,implies(not(X_9),not(truth))) = X_9 ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X_9,implies(not(X_9),not(truth))),X_9) ),[0],$fot(implies(truth,X_9))]]) ).
cnf(refute_0_219,plain,
( big_V(X_9,implies(not(X_9),not(truth))) != implies(truth,X_9)
| big_V(X_9,implies(not(X_9),not(truth))) = X_9 ),
inference(resolve,[$cnf( $equal(implies(truth,X_9),X_9) )],[refute_0_97,refute_0_218]) ).
cnf(refute_0_220,plain,
( big_V(implies(not(X_9),not(truth)),X_9) != implies(truth,X_9)
| big_V(X_9,implies(not(X_9),not(truth))) = X_9 ),
inference(resolve,[$cnf( $equal(big_V(X_9,implies(not(X_9),not(truth))),implies(truth,X_9)) )],[refute_0_217,refute_0_219]) ).
cnf(refute_0_221,plain,
big_V(X_9,implies(not(X_9),not(truth))) = X_9,
inference(resolve,[$cnf( $equal(big_V(implies(not(X_9),not(truth)),X_9),implies(truth,X_9)) )],[refute_0_214,refute_0_220]) ).
cnf(refute_0_222,plain,
big_V(not(truth),implies(not(not(truth)),not(truth))) = not(truth),
inference(subst,[],[refute_0_221:[bind(X_9,$fot(not(truth)))]]) ).
cnf(refute_0_223,plain,
( big_V(not(truth),implies(not(not(truth)),not(truth))) != not(truth)
| implies(big_V(not(truth),implies(not(not(truth)),not(truth))),truth) != truth
| implies(not(truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(not(truth),implies(not(not(truth)),not(truth))),truth),truth) ),[0,0],$fot(not(truth))]]) ).
cnf(refute_0_224,plain,
( implies(big_V(not(truth),implies(not(not(truth)),not(truth))),truth) != truth
| implies(not(truth),truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(truth),implies(not(not(truth)),not(truth))),not(truth)) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
implies(not(truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(not(truth),implies(not(not(truth)),not(truth))),truth),truth) )],[refute_0_209,refute_0_224]) ).
cnf(refute_0_226,plain,
( big_V(not(truth),truth) != implies(implies(not(truth),truth),truth)
| implies(not(truth),truth) != truth
| big_V(not(truth),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(truth),truth),implies(implies(not(truth),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_227,plain,
( big_V(not(truth),truth) != implies(implies(not(truth),truth),truth)
| big_V(not(truth),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(not(truth),truth),truth) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
big_V(not(truth),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(big_V(not(truth),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_178,refute_0_227]) ).
cnf(refute_0_229,plain,
big_V(not(truth),truth) = big_V(truth,not(truth)),
inference(subst,[],[refute_0_18:[bind(X,$fot(truth)),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_230,plain,
( big_V(not(truth),truth) != big_V(truth,not(truth))
| big_V(not(truth),truth) != implies(truth,truth)
| big_V(truth,not(truth)) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(truth),truth),implies(truth,truth)) ),[0],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_231,plain,
( big_V(not(truth),truth) != implies(truth,truth)
| big_V(truth,not(truth)) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(big_V(not(truth),truth),big_V(truth,not(truth))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
( big_V(truth,not(truth)) != implies(truth,truth)
| implies(truth,truth) != truth
| big_V(truth,not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(truth,not(truth)),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_233,plain,
( big_V(truth,not(truth)) != implies(truth,truth)
| big_V(truth,not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_143,refute_0_232]) ).
cnf(refute_0_234,plain,
( big_V(not(truth),truth) != implies(truth,truth)
| big_V(truth,not(truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),implies(truth,truth)) )],[refute_0_231,refute_0_233]) ).
cnf(refute_0_235,plain,
big_V(truth,not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(not(truth),truth),implies(truth,truth)) )],[refute_0_228,refute_0_234]) ).
cnf(refute_0_236,plain,
( big_V(truth,not(truth)) != truth
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(not(truth),not(truth)) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(not(truth),not(truth)))),bind(Y0,$fot(big_V(truth,not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_237,plain,
( big_V(truth,not(truth)) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_151,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
not(big_V(truth,not(truth))) = not(big_V(truth,not(truth))),
introduced(tautology,[refl,[$fot(not(big_V(truth,not(truth))))]]) ).
cnf(refute_0_240,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_241,plain,
( big_V(truth,not(truth)) != truth
| not(big_V(truth,not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(truth))),not(big_V(truth,not(truth)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
not(big_V(truth,not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_235,refute_0_241]) ).
cnf(refute_0_243,plain,
implies(not(truth),not(big_V(truth,not(truth)))) = implies(not(truth),not(big_V(truth,not(truth)))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(big_V(truth,not(truth)))))]]) ).
cnf(refute_0_244,plain,
( implies(not(truth),not(big_V(truth,not(truth)))) != implies(not(truth),not(big_V(truth,not(truth))))
| not(big_V(truth,not(truth))) != not(truth)
| implies(not(truth),not(big_V(truth,not(truth)))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(truth)))),implies(not(truth),not(big_V(truth,not(truth))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_245,plain,
( not(big_V(truth,not(truth))) != not(truth)
| implies(not(truth),not(big_V(truth,not(truth)))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(truth)))),implies(not(truth),not(big_V(truth,not(truth))))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
implies(not(truth),not(big_V(truth,not(truth)))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(truth))),not(truth)) )],[refute_0_242,refute_0_245]) ).
cnf(refute_0_247,plain,
( implies(not(truth),not(big_V(truth,not(truth)))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(truth)))) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(not(truth),not(big_V(truth,not(truth)))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_248,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(truth)))),implies(not(truth),not(truth))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
implies(not(truth),not(big_V(truth,not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_238,refute_0_248]) ).
cnf(refute_0_250,plain,
not(implies(not(truth),not(big_V(truth,not(truth))))) = not(implies(not(truth),not(big_V(truth,not(truth))))),
introduced(tautology,[refl,[$fot(not(implies(not(truth),not(big_V(truth,not(truth))))))]]) ).
cnf(refute_0_251,plain,
( implies(not(truth),not(big_V(truth,not(truth)))) != truth
| not(implies(not(truth),not(big_V(truth,not(truth))))) != not(implies(not(truth),not(big_V(truth,not(truth)))))
| not(implies(not(truth),not(big_V(truth,not(truth))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(truth),not(big_V(truth,not(truth))))),not(implies(not(truth),not(big_V(truth,not(truth)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_252,plain,
( implies(not(truth),not(big_V(truth,not(truth)))) != truth
| not(implies(not(truth),not(big_V(truth,not(truth))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(big_V(truth,not(truth))))),not(implies(not(truth),not(big_V(truth,not(truth)))))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
not(implies(not(truth),not(big_V(truth,not(truth))))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(truth)))),truth) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),
introduced(tautology,[refl,[$fot(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))]]) ).
cnf(refute_0_255,plain,
( big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) != big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))
| not(implies(not(truth),not(big_V(truth,not(truth))))) != not(truth)
| big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_256,plain,
( not(implies(not(truth),not(big_V(truth,not(truth))))) != not(truth)
| big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(not(implies(not(truth),not(big_V(truth,not(truth))))),not(truth)) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
( big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) != big_V(truth,not(truth))
| big_V(truth,not(truth)) != truth
| big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),bind(Y0,$fot(big_V(truth,not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_259,plain,
( big_V(truth,not(truth)) != truth
| big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),big_V(truth,not(truth))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) = truth,
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_235,refute_0_259]) ).
cnf(refute_0_261,plain,
not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) = not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))),
introduced(tautology,[refl,[$fot(not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))))]]) ).
cnf(refute_0_262,plain,
( big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) != truth
| not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) != not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))
| not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_263,plain,
( big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))) != truth
| not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))),truth) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))))]]) ).
cnf(refute_0_266,plain,
( implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) != implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))))
| not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) != not(truth)
| implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_267,plain,
( not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))) != not(truth)
| implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth))))))),not(truth)) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
( implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_270,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),implies(not(truth),not(truth))) )],[refute_0_268,refute_0_269]) ).
cnf(refute_0_271,plain,
implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_238,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))]]) ).
cnf(refute_0_273,plain,
( implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) != implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)
| implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = implies(truth,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_274,plain,
( implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))) != truth
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = implies(truth,X_31) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31),implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = implies(truth,X_31),
inference(resolve,[$cnf( $equal(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),truth) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) != implies(truth,X_31)
| implies(truth,X_31) != X_31
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = X_31 ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))),bind(Y0,$fot(implies(truth,X_31))),bind(Z0,$fot(X_31))]]) ).
cnf(refute_0_277,plain,
( implies(truth,X_31) != X_31
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = X_31 ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31),implies(truth,X_31)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) = X_31,
inference(resolve,[$cnf( $equal(implies(truth,X_31),X_31) )],[refute_0_89,refute_0_277]) ).
cnf(refute_0_279,plain,
implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),
introduced(tautology,[refl,[$fot(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)))]]) ).
cnf(refute_0_280,plain,
( implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))
| implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) != X_31
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,X_31) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) ),[1,1],$fot(X_31)]]) ).
cnf(refute_0_281,plain,
( implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31) != X_31
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,X_31) ),
inference(resolve,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = implies(X_31,X_31),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31),X_31) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
( implies(X_31,X_31) != big_V(truth,X_31)
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != implies(X_31,X_31)
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = big_V(truth,X_31) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)))),bind(Y0,$fot(implies(X_31,X_31))),bind(Z0,$fot(big_V(truth,X_31)))]]) ).
cnf(refute_0_284,plain,
( implies(X_31,X_31) != big_V(truth,X_31)
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = big_V(truth,X_31) ),
inference(resolve,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),implies(X_31,X_31)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) = big_V(truth,X_31),
inference(resolve,[$cnf( $equal(implies(X_31,X_31),big_V(truth,X_31)) )],[refute_0_177,refute_0_284]) ).
cnf(refute_0_286,plain,
( implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != big_V(truth,X_31)
| implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != truth
| big_V(truth,X_31) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),truth) ),[0],$fot(big_V(truth,X_31))]]) ).
cnf(refute_0_287,plain,
( implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)) != truth
| big_V(truth,X_31) = truth ),
inference(resolve,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),big_V(truth,X_31)) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
big_V(truth,X_31) = truth,
inference(resolve,[$cnf( $equal(implies(X_31,implies(implies(not(truth),not(big_V(truth,not(implies(not(truth),not(big_V(truth,not(truth)))))))),X_31)),truth) )],[refute_0_176,refute_0_287]) ).
cnf(refute_0_289,plain,
big_V(truth,not(X_13)) = truth,
inference(subst,[],[refute_0_288:[bind(X_31,$fot(not(X_13)))]]) ).
cnf(refute_0_290,plain,
implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = implies(big_V(truth,not(X_13)),big_V(X_13,truth)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(X_13)),big_V(X_13,truth)))]]) ).
cnf(refute_0_291,plain,
( big_V(truth,not(X_13)) != truth
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) != implies(big_V(truth,not(X_13)),big_V(X_13,truth))
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = implies(truth,big_V(X_13,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),implies(big_V(truth,not(X_13)),big_V(X_13,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_292,plain,
( big_V(truth,not(X_13)) != truth
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = implies(truth,big_V(X_13,truth)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),implies(big_V(truth,not(X_13)),big_V(X_13,truth))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = implies(truth,big_V(X_13,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,not(X_13)),truth) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( implies(big_V(truth,not(X_13)),big_V(X_13,truth)) != implies(truth,big_V(X_13,truth))
| implies(truth,big_V(X_13,truth)) != big_V(X_13,truth)
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = big_V(X_13,truth) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(big_V(truth,not(X_13)),big_V(X_13,truth)))),bind(Y0,$fot(implies(truth,big_V(X_13,truth)))),bind(Z0,$fot(big_V(X_13,truth)))]]) ).
cnf(refute_0_295,plain,
( implies(truth,big_V(X_13,truth)) != big_V(X_13,truth)
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = big_V(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),implies(truth,big_V(X_13,truth))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(big_V(truth,not(X_13)),big_V(X_13,truth)) = big_V(X_13,truth),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X_13,truth)),big_V(X_13,truth)) )],[refute_0_127,refute_0_295]) ).
cnf(refute_0_297,plain,
( implies(big_V(truth,not(X_13)),big_V(X_13,truth)) != big_V(X_13,truth)
| implies(big_V(truth,not(X_13)),big_V(X_13,truth)) != truth
| big_V(X_13,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),truth) ),[0],$fot(big_V(X_13,truth))]]) ).
cnf(refute_0_298,plain,
( implies(big_V(truth,not(X_13)),big_V(X_13,truth)) != truth
| big_V(X_13,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),big_V(X_13,truth)) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
big_V(X_13,truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_13)),big_V(X_13,truth)),truth) )],[refute_0_126,refute_0_298]) ).
cnf(refute_0_300,plain,
big_V(X_30,truth) = truth,
inference(subst,[],[refute_0_299:[bind(X_13,$fot(X_30))]]) ).
cnf(refute_0_301,plain,
implies(implies(X_30,truth),truth) = big_V(X_30,truth),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_30)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_302,plain,
( big_V(X_30,truth) != truth
| implies(implies(X_30,truth),truth) != big_V(X_30,truth)
| implies(implies(X_30,truth),truth) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(X_30,truth),truth))),bind(Y0,$fot(big_V(X_30,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_303,plain,
( big_V(X_30,truth) != truth
| implies(implies(X_30,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,truth),truth),big_V(X_30,truth)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
implies(implies(X_30,truth),truth) = truth,
inference(resolve,[$cnf( $equal(big_V(X_30,truth),truth) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
big_V(truth,Y) = truth,
inference(subst,[],[refute_0_288:[bind(X_31,$fot(Y))]]) ).
cnf(refute_0_306,plain,
implies(X_30,big_V(truth,Y)) = implies(X_30,big_V(truth,Y)),
introduced(tautology,[refl,[$fot(implies(X_30,big_V(truth,Y)))]]) ).
cnf(refute_0_307,plain,
( big_V(truth,Y) != truth
| implies(X_30,big_V(truth,Y)) != implies(X_30,big_V(truth,Y))
| implies(X_30,big_V(truth,Y)) = implies(X_30,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,big_V(truth,Y)),implies(X_30,big_V(truth,Y))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_308,plain,
( big_V(truth,Y) != truth
| implies(X_30,big_V(truth,Y)) = implies(X_30,truth) ),
inference(resolve,[$cnf( $equal(implies(X_30,big_V(truth,Y)),implies(X_30,big_V(truth,Y))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(X_30,big_V(truth,Y)) = implies(X_30,truth),
inference(resolve,[$cnf( $equal(big_V(truth,Y),truth) )],[refute_0_305,refute_0_308]) ).
cnf(refute_0_310,plain,
implies(implies(X_30,big_V(truth,Y)),truth) = implies(implies(X_30,big_V(truth,Y)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_30,big_V(truth,Y)),truth))]]) ).
cnf(refute_0_311,plain,
( implies(X_30,big_V(truth,Y)) != implies(X_30,truth)
| implies(implies(X_30,big_V(truth,Y)),truth) != implies(implies(X_30,big_V(truth,Y)),truth)
| implies(implies(X_30,big_V(truth,Y)),truth) = implies(implies(X_30,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_30,big_V(truth,Y)),truth),implies(implies(X_30,big_V(truth,Y)),truth)) ),[1,0],$fot(implies(X_30,truth))]]) ).
cnf(refute_0_312,plain,
( implies(X_30,big_V(truth,Y)) != implies(X_30,truth)
| implies(implies(X_30,big_V(truth,Y)),truth) = implies(implies(X_30,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,big_V(truth,Y)),truth),implies(implies(X_30,big_V(truth,Y)),truth)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(implies(X_30,big_V(truth,Y)),truth) = implies(implies(X_30,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_30,big_V(truth,Y)),implies(X_30,truth)) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
( implies(implies(X_30,big_V(truth,Y)),truth) != implies(implies(X_30,truth),truth)
| implies(implies(X_30,truth),truth) != truth
| implies(implies(X_30,big_V(truth,Y)),truth) = truth ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(X_30,big_V(truth,Y)),truth))),bind(Y0,$fot(implies(implies(X_30,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_315,plain,
( implies(implies(X_30,truth),truth) != truth
| implies(implies(X_30,big_V(truth,Y)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_30,big_V(truth,Y)),truth),implies(implies(X_30,truth),truth)) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
implies(implies(X_30,big_V(truth,Y)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_30,truth),truth),truth) )],[refute_0_304,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)),
introduced(tautology,[refl,[$fot(implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)))]]) ).
cnf(refute_0_318,plain,
( implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) != implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth))
| implies(implies(X_30,big_V(truth,Y)),truth) != truth
| implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)),implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_319,plain,
( implies(implies(X_30,big_V(truth,Y)),truth) != truth
| implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth) ),
inference(resolve,[$cnf( $equal(implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)),implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth))) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_30,big_V(truth,Y)),truth),truth) )],[refute_0_316,refute_0_319]) ).
cnf(refute_0_321,plain,
implies(truth,X_30) = X_30,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_30))]]) ).
cnf(refute_0_322,plain,
big_V(truth,not(Y)) = truth,
inference(subst,[],[refute_0_288:[bind(X_31,$fot(not(Y)))]]) ).
cnf(refute_0_323,plain,
implies(big_V(truth,not(Y)),X_30) = implies(big_V(truth,not(Y)),X_30),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(Y)),X_30))]]) ).
cnf(refute_0_324,plain,
( big_V(truth,not(Y)) != truth
| implies(big_V(truth,not(Y)),X_30) != implies(big_V(truth,not(Y)),X_30)
| implies(big_V(truth,not(Y)),X_30) = implies(truth,X_30) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(Y)),X_30),implies(big_V(truth,not(Y)),X_30)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_325,plain,
( big_V(truth,not(Y)) != truth
| implies(big_V(truth,not(Y)),X_30) = implies(truth,X_30) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),X_30),implies(big_V(truth,not(Y)),X_30)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(big_V(truth,not(Y)),X_30) = implies(truth,X_30),
inference(resolve,[$cnf( $equal(big_V(truth,not(Y)),truth) )],[refute_0_322,refute_0_325]) ).
cnf(refute_0_327,plain,
( implies(big_V(truth,not(Y)),X_30) != implies(truth,X_30)
| implies(truth,X_30) != X_30
| implies(big_V(truth,not(Y)),X_30) = X_30 ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(big_V(truth,not(Y)),X_30))),bind(Y0,$fot(implies(truth,X_30))),bind(Z0,$fot(X_30))]]) ).
cnf(refute_0_328,plain,
( implies(truth,X_30) != X_30
| implies(big_V(truth,not(Y)),X_30) = X_30 ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),X_30),implies(truth,X_30)) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(big_V(truth,not(Y)),X_30) = X_30,
inference(resolve,[$cnf( $equal(implies(truth,X_30),X_30) )],[refute_0_321,refute_0_328]) ).
cnf(refute_0_330,plain,
implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)))]]) ).
cnf(refute_0_331,plain,
( implies(big_V(truth,not(Y)),X_30) != X_30
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) != implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth))
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth))) ),[1,0],$fot(X_30)]]) ).
cnf(refute_0_332,plain,
( implies(big_V(truth,not(Y)),X_30) != X_30
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(Y)),X_30),X_30) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
( implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) != implies(X_30,truth)
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) != implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth))
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)))),bind(Y0,$fot(implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)))),bind(Z0,$fot(implies(X_30,truth)))]]) ).
cnf(refute_0_335,plain,
( implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)) != implies(X_30,truth)
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) = implies(X_30,truth),
inference(resolve,[$cnf( $equal(implies(X_30,implies(implies(X_30,big_V(truth,Y)),truth)),implies(X_30,truth)) )],[refute_0_320,refute_0_335]) ).
cnf(refute_0_337,plain,
( implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) != implies(X_30,truth)
| implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) != truth
| implies(X_30,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),truth) ),[0],$fot(implies(X_30,truth))]]) ).
cnf(refute_0_338,plain,
( implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)) != truth
| implies(X_30,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),implies(X_30,truth)) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
implies(X_30,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(truth,not(Y)),X_30),implies(implies(X_30,big_V(truth,Y)),truth)),truth) )],[refute_0_119,refute_0_338]) ).
cnf(refute_0_340,plain,
implies(X_29,truth) = truth,
inference(subst,[],[refute_0_339:[bind(X_30,$fot(X_29))]]) ).
cnf(refute_0_341,plain,
implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),
introduced(tautology,[refl,[$fot(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))))]]) ).
cnf(refute_0_342,plain,
( implies(X_29,truth) != truth
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) != implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31)))
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(truth,implies(X_31,implies(X_29,X_31))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_343,plain,
( implies(X_29,truth) != truth
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(truth,implies(X_31,implies(X_29,X_31))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31)))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(truth,implies(X_31,implies(X_29,X_31))),
inference(resolve,[$cnf( $equal(implies(X_29,truth),truth) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
( implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) != implies(truth,implies(X_31,implies(X_29,X_31)))
| implies(truth,implies(X_31,implies(X_29,X_31))) != implies(X_31,implies(X_29,X_31))
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(X_31,implies(X_29,X_31)) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))))),bind(Y0,$fot(implies(truth,implies(X_31,implies(X_29,X_31))))),bind(Z0,$fot(implies(X_31,implies(X_29,X_31))))]]) ).
cnf(refute_0_346,plain,
( implies(truth,implies(X_31,implies(X_29,X_31))) != implies(X_31,implies(X_29,X_31))
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(X_31,implies(X_29,X_31)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),implies(truth,implies(X_31,implies(X_29,X_31)))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) = implies(X_31,implies(X_29,X_31)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_31,implies(X_29,X_31))),implies(X_31,implies(X_29,X_31))) )],[refute_0_93,refute_0_346]) ).
cnf(refute_0_348,plain,
( implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) != implies(X_31,implies(X_29,X_31))
| implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) != truth
| implies(X_31,implies(X_29,X_31)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),truth) ),[0],$fot(implies(X_31,implies(X_29,X_31)))]]) ).
cnf(refute_0_349,plain,
( implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))) != truth
| implies(X_31,implies(X_29,X_31)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),implies(X_31,implies(X_29,X_31))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
implies(X_31,implies(X_29,X_31)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_29,truth),implies(X_31,implies(X_29,X_31))),truth) )],[refute_0_92,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(X,implies(X_55,X)) = truth,
inference(subst,[],[refute_0_350:[bind(X_29,$fot(X_55)),bind(X_31,$fot(X))]]) ).
cnf(refute_0_352,plain,
( big_V(X,implies(X_55,X)) != implies(implies(X,implies(X_55,X)),implies(X_55,X))
| implies(X,implies(X_55,X)) != truth
| big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(implies(X,implies(X_55,X)),implies(X_55,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_353,plain,
( big_V(X,implies(X_55,X)) != implies(implies(X,implies(X_55,X)),implies(X_55,X))
| big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_55,X)),truth) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(implies(X,implies(X_55,X)),implies(X_55,X))) )],[refute_0_87,refute_0_353]) ).
cnf(refute_0_355,plain,
implies(truth,implies(X_55,X)) = implies(X_55,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_55,X)))]]) ).
cnf(refute_0_356,plain,
( big_V(X,implies(X_55,X)) != implies(truth,implies(X_55,X))
| implies(truth,implies(X_55,X)) != implies(X_55,X)
| big_V(X,implies(X_55,X)) = implies(X_55,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,implies(X_55,X)),implies(X_55,X)) ),[0],$fot(implies(truth,implies(X_55,X)))]]) ).
cnf(refute_0_357,plain,
( big_V(X,implies(X_55,X)) != implies(truth,implies(X_55,X))
| big_V(X,implies(X_55,X)) = implies(X_55,X) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_55,X)),implies(X_55,X)) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
big_V(X,implies(X_55,X)) = implies(X_55,X),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(truth,implies(X_55,X))) )],[refute_0_354,refute_0_357]) ).
cnf(refute_0_359,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(subst,[],[refute_0_358:[bind(X,$fot(not(not(truth)))),bind(X_55,$fot(not(truth)))]]) ).
cnf(refute_0_360,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(not(truth),not(not(truth)))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$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_361,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( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),not(not(truth))) )],[refute_0_86,refute_0_361]) ).
cnf(refute_0_363,plain,
( implies(not(truth),not(not(truth))) != not(not(truth))
| ~ ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),implies(not(truth),not(not(truth)))))
| ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),implies(not(truth),not(not(truth))))) ),[1,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_364,plain,
( ~ ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),implies(not(truth),not(not(truth)))))
| ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth)))),
inference(resolve,[$cnf( ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),implies(not(truth),not(not(truth))))) )],[refute_0_56,refute_0_364]) ).
cnf(refute_0_366,plain,
implies(implies(X_64,not(not(truth))),not(not(truth))) = big_V(X_64,not(not(truth))),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_64)),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_367,plain,
( implies(implies(X_64,not(not(truth))),not(not(truth))) != big_V(X_64,not(not(truth)))
| ~ ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth))))
| ordered(implies(not(truth),X_64),big_V(X_64,not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth)))) ),[1],$fot(big_V(X_64,not(not(truth))))]]) ).
cnf(refute_0_368,plain,
( ~ ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth))))
| ordered(implies(not(truth),X_64),big_V(X_64,not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_64,not(not(truth))),not(not(truth))),big_V(X_64,not(not(truth)))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
ordered(implies(not(truth),X_64),big_V(X_64,not(not(truth)))),
inference(resolve,[$cnf( ordered(implies(not(truth),X_64),implies(implies(X_64,not(not(truth))),not(not(truth)))) )],[refute_0_365,refute_0_368]) ).
cnf(refute_0_370,plain,
ordered(implies(not(truth),X_66),big_V(X_66,not(not(truth)))),
inference(subst,[],[refute_0_369:[bind(X_64,$fot(X_66))]]) ).
cnf(refute_0_371,plain,
big_V(not(not(truth)),X_66) = big_V(X_66,not(not(truth))),
inference(subst,[],[refute_0_16:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(X_66))]]) ).
cnf(refute_0_372,plain,
( big_V(not(not(truth)),X_66) != big_V(X_66,not(not(truth)))
| big_V(X_66,not(not(truth))) = big_V(not(not(truth)),X_66) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_V(not(not(truth)),X_66))),bind(Y0,$fot(big_V(X_66,not(not(truth)))))]]) ).
cnf(refute_0_373,plain,
big_V(X_66,not(not(truth))) = big_V(not(not(truth)),X_66),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),X_66),big_V(X_66,not(not(truth)))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
( big_V(X_66,not(not(truth))) != big_V(not(not(truth)),X_66)
| ~ ordered(implies(not(truth),X_66),big_V(X_66,not(not(truth))))
| ordered(implies(not(truth),X_66),big_V(not(not(truth)),X_66)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),X_66),big_V(X_66,not(not(truth)))) ),[1],$fot(big_V(not(not(truth)),X_66))]]) ).
cnf(refute_0_375,plain,
( ~ ordered(implies(not(truth),X_66),big_V(X_66,not(not(truth))))
| ordered(implies(not(truth),X_66),big_V(not(not(truth)),X_66)) ),
inference(resolve,[$cnf( $equal(big_V(X_66,not(not(truth))),big_V(not(not(truth)),X_66)) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
ordered(implies(not(truth),X_66),big_V(not(not(truth)),X_66)),
inference(resolve,[$cnf( ordered(implies(not(truth),X_66),big_V(X_66,not(not(truth)))) )],[refute_0_370,refute_0_375]) ).
cnf(refute_0_377,plain,
ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),big_V(not(not(truth)),implies(not(not(not(truth))),not(truth)))),
inference(subst,[],[refute_0_376:[bind(X_66,$fot(implies(not(not(not(truth))),not(truth))))]]) ).
cnf(refute_0_378,plain,
big_V(not(not(truth)),implies(not(not(not(truth))),not(truth))) = not(not(truth)),
inference(subst,[],[refute_0_221:[bind(X_9,$fot(not(not(truth))))]]) ).
cnf(refute_0_379,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(truth))) != not(not(truth))
| ~ ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),big_V(not(not(truth)),implies(not(not(not(truth))),not(truth))))
| ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),big_V(not(not(truth)),implies(not(not(not(truth))),not(truth)))) ),[1],$fot(not(not(truth)))]]) ).
cnf(refute_0_380,plain,
( ~ ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),big_V(not(not(truth)),implies(not(not(not(truth))),not(truth))))
| ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(truth))),not(not(truth))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),
inference(resolve,[$cnf( ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),big_V(not(not(truth)),implies(not(not(not(truth))),not(truth)))) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
implies(not(truth),implies(not(not(not(truth))),not(truth))) = truth,
inference(subst,[],[refute_0_350:[bind(X_29,$fot(not(not(not(truth))))),bind(X_31,$fot(not(truth)))]]) ).
cnf(refute_0_383,plain,
( implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
| ~ ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| ordered(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) ),[0],$fot(truth)]]) ).
cnf(refute_0_384,plain,
( ~ ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| ordered(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(not(not(truth))),not(truth))),truth) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
ordered(truth,not(not(truth))),
inference(resolve,[$cnf( ordered(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) )],[refute_0_381,refute_0_384]) ).
cnf(refute_0_386,plain,
implies(truth,not(not(truth))) = truth,
inference(resolve,[$cnf( ordered(truth,not(not(truth))) )],[refute_0_385,refute_0_55]) ).
cnf(refute_0_387,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(truth,not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_388,plain,
( implies(truth,not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_83,refute_0_387]) ).
cnf(refute_0_389,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),truth) )],[refute_0_386,refute_0_388]) ).
cnf(refute_0_390,plain,
implies(not(not(truth)),not(not(X_76))) = implies(not(not(truth)),not(not(X_76))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_76))))]]) ).
cnf(refute_0_391,plain,
( implies(not(not(truth)),not(not(X_76))) != implies(not(not(truth)),not(not(X_76)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_76))) = implies(truth,not(not(X_76))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_76))),implies(not(not(truth)),not(not(X_76)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_392,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_76))) = implies(truth,not(not(X_76))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_76))),implies(not(not(truth)),not(not(X_76)))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
implies(not(not(truth)),not(not(X_76))) = implies(truth,not(not(X_76))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_389,refute_0_392]) ).
cnf(refute_0_394,plain,
( implies(not(not(truth)),not(not(X_76))) != implies(truth,not(not(X_76)))
| implies(truth,not(not(X_76))) != not(not(X_76))
| implies(not(not(truth)),not(not(X_76))) = not(not(X_76)) ),
inference(subst,[],[refute_0_170:[bind(X0,$fot(implies(not(not(truth)),not(not(X_76))))),bind(Y0,$fot(implies(truth,not(not(X_76))))),bind(Z0,$fot(not(not(X_76))))]]) ).
cnf(refute_0_395,plain,
( implies(truth,not(not(X_76))) != not(not(X_76))
| implies(not(not(truth)),not(not(X_76))) = not(not(X_76)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_76))),implies(truth,not(not(X_76)))) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
implies(not(not(truth)),not(not(X_76))) = not(not(X_76)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_76))),not(not(X_76))) )],[refute_0_54,refute_0_395]) ).
cnf(refute_0_397,plain,
implies(implies(not(not(truth)),not(not(X_76))),X_76) = implies(implies(not(not(truth)),not(not(X_76))),X_76),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_76))),X_76))]]) ).
cnf(refute_0_398,plain,
( implies(implies(not(not(truth)),not(not(X_76))),X_76) != implies(implies(not(not(truth)),not(not(X_76))),X_76)
| implies(not(not(truth)),not(not(X_76))) != not(not(X_76))
| implies(implies(not(not(truth)),not(not(X_76))),X_76) = implies(not(not(X_76)),X_76) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_76))),X_76),implies(implies(not(not(truth)),not(not(X_76))),X_76)) ),[1,0],$fot(not(not(X_76)))]]) ).
cnf(refute_0_399,plain,
( implies(not(not(truth)),not(not(X_76))) != not(not(X_76))
| implies(implies(not(not(truth)),not(not(X_76))),X_76) = implies(not(not(X_76)),X_76) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_76))),X_76),implies(implies(not(not(truth)),not(not(X_76))),X_76)) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
implies(implies(not(not(truth)),not(not(X_76))),X_76) = implies(not(not(X_76)),X_76),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_76))),not(not(X_76))) )],[refute_0_396,refute_0_399]) ).
cnf(refute_0_401,plain,
( implies(implies(not(not(truth)),not(not(X_76))),X_76) != implies(not(not(X_76)),X_76)
| ~ ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76))
| ordered(truth,implies(not(not(X_76)),X_76)) ),
introduced(tautology,[equality,[$cnf( ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76)) ),[1],$fot(implies(not(not(X_76)),X_76))]]) ).
cnf(refute_0_402,plain,
( ~ ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76))
| ordered(truth,implies(not(not(X_76)),X_76)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_76))),X_76),implies(not(not(X_76)),X_76)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
ordered(truth,implies(not(not(X_76)),X_76)),
inference(resolve,[$cnf( ordered(truth,implies(implies(not(not(truth)),not(not(X_76))),X_76)) )],[refute_0_53,refute_0_402]) ).
cnf(refute_0_404,plain,
ordered(truth,implies(not(not(X_77)),X_77)),
inference(subst,[],[refute_0_403:[bind(X_76,$fot(X_77))]]) ).
cnf(refute_0_405,plain,
implies(truth,implies(not(not(X_77)),X_77)) = truth,
inference(resolve,[$cnf( ordered(truth,implies(not(not(X_77)),X_77)) )],[refute_0_404,refute_0_28]) ).
cnf(refute_0_406,plain,
implies(truth,implies(not(not(X_77)),X_77)) = implies(not(not(X_77)),X_77),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(not(X_77)),X_77)))]]) ).
cnf(refute_0_407,plain,
( implies(truth,implies(not(not(X_77)),X_77)) != implies(not(not(X_77)),X_77)
| implies(truth,implies(not(not(X_77)),X_77)) != truth
| implies(not(not(X_77)),X_77) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(not(X_77)),X_77)),truth) ),[0],$fot(implies(not(not(X_77)),X_77))]]) ).
cnf(refute_0_408,plain,
( implies(truth,implies(not(not(X_77)),X_77)) != truth
| implies(not(not(X_77)),X_77) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(not(X_77)),X_77)),implies(not(not(X_77)),X_77)) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
implies(not(not(X_77)),X_77) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(not(X_77)),X_77)),truth) )],[refute_0_405,refute_0_408]) ).
cnf(refute_0_410,plain,
implies(not(not(not(Y))),not(Y)) = truth,
inference(subst,[],[refute_0_409:[bind(X_77,$fot(not(Y)))]]) ).
cnf(refute_0_411,plain,
( big_V(implies(Y,not(not(Y))),implies(not(not(not(Y))),not(Y))) != implies(Y,not(not(Y)))
| implies(not(not(not(Y))),not(Y)) != truth
| big_V(implies(Y,not(not(Y))),truth) = implies(Y,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(Y,not(not(Y))),implies(not(not(not(Y))),not(Y))),implies(Y,not(not(Y)))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_412,plain,
( big_V(implies(Y,not(not(Y))),implies(not(not(not(Y))),not(Y))) != implies(Y,not(not(Y)))
| big_V(implies(Y,not(not(Y))),truth) = implies(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(Y)),truth) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
big_V(implies(Y,not(not(Y))),truth) = implies(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(big_V(implies(Y,not(not(Y))),implies(not(not(not(Y))),not(Y))),implies(Y,not(not(Y)))) )],[refute_0_27,refute_0_412]) ).
cnf(refute_0_414,plain,
big_V(implies(Y,not(not(Y))),truth) = truth,
inference(subst,[],[refute_0_299:[bind(X_13,$fot(implies(Y,not(not(Y)))))]]) ).
cnf(refute_0_415,plain,
( big_V(implies(Y,not(not(Y))),truth) != implies(Y,not(not(Y)))
| big_V(implies(Y,not(not(Y))),truth) != truth
| truth = implies(Y,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(Y,not(not(Y))),truth),implies(Y,not(not(Y)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_416,plain,
( big_V(implies(Y,not(not(Y))),truth) != implies(Y,not(not(Y)))
| truth = implies(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(big_V(implies(Y,not(not(Y))),truth),truth) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
truth = implies(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(big_V(implies(Y,not(not(Y))),truth),implies(Y,not(not(Y)))) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
truth = implies(X,not(not(X))),
inference(subst,[],[refute_0_417:[bind(Y,$fot(X))]]) ).
cnf(refute_0_419,plain,
( truth != implies(X,not(not(X)))
| implies(X,not(not(X))) = truth ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X,not(not(X)))))]]) ).
cnf(refute_0_420,plain,
implies(X,not(not(X))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X,not(not(X)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
( big_V(X,not(not(X))) != implies(implies(X,not(not(X))),not(not(X)))
| implies(X,not(not(X))) != truth
| big_V(X,not(not(X))) = implies(truth,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_422,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( $equal(implies(X,not(not(X))),truth) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
big_V(X,not(not(X))) = implies(truth,not(not(X))),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) )],[refute_0_0,refute_0_422]) ).
cnf(refute_0_424,plain,
big_V(not(not(Y)),Y) = implies(implies(not(not(Y)),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_425,plain,
implies(not(not(Y)),Y) = truth,
inference(subst,[],[refute_0_409:[bind(X_77,$fot(Y))]]) ).
cnf(refute_0_426,plain,
( big_V(not(not(Y)),Y) != implies(implies(not(not(Y)),Y),Y)
| implies(not(not(Y)),Y) != truth
| big_V(not(not(Y)),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(Y)),Y),implies(implies(not(not(Y)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_427,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( $equal(implies(not(not(Y)),Y),truth) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
big_V(not(not(Y)),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),implies(implies(not(not(Y)),Y),Y)) )],[refute_0_424,refute_0_427]) ).
cnf(refute_0_429,plain,
big_V(not(not(Y)),Y) = big_V(Y,not(not(Y))),
inference(subst,[],[refute_0_18:[bind(X,$fot(Y)),bind(Y,$fot(not(not(Y))))]]) ).
cnf(refute_0_430,plain,
( big_V(not(not(Y)),Y) != big_V(Y,not(not(Y)))
| big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(Y)),Y),implies(truth,Y)) ),[0],$fot(big_V(Y,not(not(Y))))]]) ).
cnf(refute_0_431,plain,
( big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),big_V(Y,not(not(Y)))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_433,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_434,plain,
( big_V(Y,not(not(Y))) != implies(truth,Y)
| big_V(Y,not(not(Y))) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
( big_V(not(not(Y)),Y) != implies(truth,Y)
| big_V(Y,not(not(Y))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,not(not(Y))),implies(truth,Y)) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
big_V(Y,not(not(Y))) = Y,
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),Y),implies(truth,Y)) )],[refute_0_428,refute_0_435]) ).
cnf(refute_0_437,plain,
big_V(X,not(not(X))) = X,
inference(subst,[],[refute_0_436:[bind(Y,$fot(X))]]) ).
cnf(refute_0_438,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_439,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = implies(truth,not(not(X))) ),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),X) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
implies(truth,not(not(X))) = not(not(X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_441,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_442,plain,
( X != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X))),not(not(X))) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(X,implies(truth,not(not(X)))) )],[refute_0_439,refute_0_442]) ).
cnf(refute_0_444,plain,
X = not(not(X)),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(truth,not(not(X)))) )],[refute_0_423,refute_0_443]) ).
cnf(refute_0_445,plain,
big_V(not(X),not(Y)) = not(not(big_V(not(X),not(Y)))),
inference(subst,[],[refute_0_444:[bind(X,$fot(big_V(not(X),not(Y))))]]) ).
cnf(refute_0_446,plain,
( big_hat(X,Y) != not(big_V(not(X),not(Y)))
| not(big_V(not(X),not(Y))) = big_hat(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(big_hat(X,Y))),bind(Y0,$fot(not(big_V(not(X),not(Y)))))]]) ).
cnf(refute_0_447,plain,
not(big_V(not(X),not(Y))) = big_hat(X,Y),
inference(resolve,[$cnf( $equal(big_hat(X,Y),not(big_V(not(X),not(Y)))) )],[big_hat_definition,refute_0_446]) ).
cnf(refute_0_448,plain,
( big_V(not(X),not(Y)) != not(not(big_V(not(X),not(Y))))
| not(big_V(not(X),not(Y))) != big_hat(X,Y)
| big_V(not(X),not(Y)) = not(big_hat(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X),not(Y)),not(not(big_V(not(X),not(Y))))) ),[1,0],$fot(big_hat(X,Y))]]) ).
cnf(refute_0_449,plain,
( big_V(not(X),not(Y)) != not(not(big_V(not(X),not(Y))))
| big_V(not(X),not(Y)) = not(big_hat(X,Y)) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X),not(Y))),big_hat(X,Y)) )],[refute_0_447,refute_0_448]) ).
cnf(refute_0_450,plain,
big_V(not(X),not(Y)) = not(big_hat(X,Y)),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(not(big_V(not(X),not(Y))))) )],[refute_0_445,refute_0_449]) ).
cnf(refute_0_451,plain,
big_V(not(x),not(y)) = not(big_hat(x,y)),
inference(subst,[],[refute_0_450:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).
cnf(refute_0_452,plain,
( big_V(not(x),not(y)) != not(big_hat(x,y))
| not(big_hat(x,y)) != not(big_hat(x,y))
| not(big_hat(x,y)) = big_V(not(x),not(y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(big_hat(x,y)),big_V(not(x),not(y))) ),[1],$fot(not(big_hat(x,y)))]]) ).
cnf(refute_0_453,plain,
( not(big_hat(x,y)) != not(big_hat(x,y))
| not(big_hat(x,y)) = big_V(not(x),not(y)) ),
inference(resolve,[$cnf( $equal(big_V(not(x),not(y)),not(big_hat(x,y))) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
not(big_hat(x,y)) != not(big_hat(x,y)),
inference(resolve,[$cnf( $equal(not(big_hat(x,y)),big_V(not(x),not(y))) )],[refute_0_453,prove_wajsberg_theorem]) ).
cnf(refute_0_455,plain,
not(big_hat(x,y)) = not(big_hat(x,y)),
introduced(tautology,[refl,[$fot(not(big_hat(x,y)))]]) ).
cnf(refute_0_456,plain,
$false,
inference(resolve,[$cnf( $equal(not(big_hat(x,y)),not(big_hat(x,y))) )],[refute_0_455,refute_0_454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL146-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 18:36:00 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.59
% 0.42/0.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.49/0.65
%------------------------------------------------------------------------------