TSTP Solution File: LCL109-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL109-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 12:49:34 EDT 2022
% Result : Timeout 289.89s 290.10s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 152
% Number of leaves : 252
% Syntax : Number of clauses : 1036 ( 515 unt; 0 nHn; 616 RR)
% Number of literals : 1789 (1741 equ; 755 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 1490 ( 40 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_mv_4,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth ).
cnf(refute_0_0,plain,
( ~ ordered(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795))
| implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)))),bind(Y,$fot(implies(X_2796,X_2795)))]]) ).
cnf(refute_0_1,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_2,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_3,plain,
( truth != truth
| implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[wajsberg_2,refute_0_2]) ).
cnf(refute_0_4,plain,
( truth != truth
| ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),truth) )],[refute_0_3,refute_0_1]) ).
cnf(refute_0_5,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_6,plain,
ordered(implies(X,Y),implies(implies(Y,Z),implies(X,Z))),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
ordered(implies(X_69,implies(X,X_71)),implies(implies(implies(X,X_71),X_71),implies(X_69,X_71))),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_69)),bind(Y,$fot(implies(X,X_71))),bind(Z,$fot(X_71))]]) ).
cnf(refute_0_8,plain,
big_V(X,X_71) = implies(implies(X,X_71),X_71),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_71))]]) ).
cnf(refute_0_9,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_10,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_11,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( big_V(X,X_71) != implies(implies(X,X_71),X_71)
| implies(implies(X,X_71),X_71) = big_V(X,X_71) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_71))),bind(Y0,$fot(implies(implies(X,X_71),X_71)))]]) ).
cnf(refute_0_13,plain,
implies(implies(X,X_71),X_71) = big_V(X,X_71),
inference(resolve,[$cnf( $equal(big_V(X,X_71),implies(implies(X,X_71),X_71)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(implies(X,X_71),X_71) != big_V(X,X_71)
| ~ ordered(implies(X_69,implies(X,X_71)),implies(implies(implies(X,X_71),X_71),implies(X_69,X_71)))
| ordered(implies(X_69,implies(X,X_71)),implies(big_V(X,X_71),implies(X_69,X_71))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_69,implies(X,X_71)),implies(implies(implies(X,X_71),X_71),implies(X_69,X_71))) ),[1,0],$fot(big_V(X,X_71))]]) ).
cnf(refute_0_15,plain,
( ~ ordered(implies(X_69,implies(X,X_71)),implies(implies(implies(X,X_71),X_71),implies(X_69,X_71)))
| ordered(implies(X_69,implies(X,X_71)),implies(big_V(X,X_71),implies(X_69,X_71))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_71),X_71),big_V(X,X_71)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
ordered(implies(X_69,implies(X,X_71)),implies(big_V(X,X_71),implies(X_69,X_71))),
inference(resolve,[$cnf( ordered(implies(X_69,implies(X,X_71)),implies(implies(implies(X,X_71),X_71),implies(X_69,X_71))) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
ordered(implies(X_890,implies(X_889,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_889)),bind(X_69,$fot(X_890)),bind(X_71,$fot(big_hat(X_889,X_462)))]]) ).
cnf(refute_0_18,plain,
big_V(not(X_298),not(X_297)) = implies(implies(not(X_298),not(X_297)),not(X_297)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(X_298))),bind(Y,$fot(not(X_297)))]]) ).
cnf(refute_0_19,plain,
big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14))),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(X_12,X_13))),bind(Y,$fot(implies(implies(X_13,X_14),implies(X_12,X_14))))]]) ).
cnf(refute_0_20,plain,
implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_21,plain,
( big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) != implies(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14)))
| implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) != truth
| big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_22,plain,
( big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) != implies(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14)))
| big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),truth) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14)))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(implies(X_13,X_14),implies(X_12,X_14)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_13,X_14),implies(X_12,X_14))))]]) ).
cnf(refute_0_25,plain,
( big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) != implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14)))
| implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))) != implies(implies(X_13,X_14),implies(X_12,X_14))
| big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(implies(X_13,X_14),implies(X_12,X_14)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14))) ),[0],$fot(implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))))]]) ).
cnf(refute_0_26,plain,
( big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) != implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14)))
| big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(implies(X_13,X_14),implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14))),implies(implies(X_13,X_14),implies(X_12,X_14))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))) = implies(implies(X_13,X_14),implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(big_V(implies(X_12,X_13),implies(implies(X_13,X_14),implies(X_12,X_14))),implies(truth,implies(implies(X_13,X_14),implies(X_12,X_14)))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))),
inference(subst,[],[refute_0_27:[bind(X_12,$fot(X_294)),bind(X_13,$fot(X_295)),bind(X_14,$fot(not(truth)))]]) ).
cnf(refute_0_29,plain,
big_V(not(X_84),not(truth)) = implies(implies(not(X_84),not(truth)),not(truth)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(X_84))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_30,plain,
big_V(X,implies(not(X),not(truth))) = implies(implies(X,implies(not(X),not(truth))),implies(not(X),not(truth))),
inference(subst,[],[big_V_definition:[bind(Y,$fot(implies(not(X),not(truth))))]]) ).
cnf(refute_0_31,plain,
big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(X_24,X_23)),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X_23),not(X_24)))),bind(Y,$fot(implies(X_24,X_23)))]]) ).
cnf(refute_0_32,plain,
implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_23)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_33,plain,
( big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(X_24,X_23))
| implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != truth
| big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = implies(truth,implies(X_24,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(X_24,X_23))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_34,plain,
( big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(X_24,X_23))
| big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = implies(truth,implies(X_24,X_23)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),truth) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = implies(truth,implies(X_24,X_23)),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(X_24,X_23))) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( big_V(X,Y) != implies(implies(X,Y),Y)
| implies(implies(X,Y),Y) = big_V(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(implies(implies(X,Y),Y)))]]) ).
cnf(refute_0_37,plain,
implies(implies(X,Y),Y) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(X,Y),Y)) )],[big_V_definition,refute_0_36]) ).
cnf(refute_0_38,plain,
( implies(implies(X,Y),Y) != big_V(X,Y)
| implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) ),[0],$fot(big_V(X,Y))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),big_V(X,Y)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(Y,X),X) = big_V(Y,X),
inference(subst,[],[refute_0_37:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_41,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) != big_V(Y,X)
| big_V(X,Y) = big_V(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,Y),big_V(Y,X)) ),[0],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_42,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),X),big_V(Y,X)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(Y,X),X)) )],[refute_0_39,refute_0_42]) ).
cnf(refute_0_44,plain,
big_V(X,Y) = big_V(Y,X),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_43]) ).
cnf(refute_0_45,plain,
( big_V(X,Y) != big_V(Y,X)
| big_V(Y,X) = big_V(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(big_V(Y,X)))]]) ).
cnf(refute_0_46,plain,
big_V(Y,X) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),big_V(Y,X)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) = big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))),
inference(subst,[],[refute_0_46:[bind(X,$fot(implies(X_24,X_23))),bind(Y,$fot(implies(not(X_23),not(X_24))))]]) ).
cnf(refute_0_48,plain,
( big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != big_V(implies(X_24,X_23),implies(not(X_23),not(X_24)))
| big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != implies(truth,implies(X_24,X_23))
| big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(truth,implies(X_24,X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(truth,implies(X_24,X_23))) ),[0],$fot(big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))))]]) ).
cnf(refute_0_49,plain,
( big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != implies(truth,implies(X_24,X_23))
| big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(truth,implies(X_24,X_23)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)),big_V(implies(X_24,X_23),implies(not(X_23),not(X_24)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
implies(truth,implies(X_24,X_23)) = implies(X_24,X_23),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_24,X_23)))]]) ).
cnf(refute_0_51,plain,
( big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) != implies(truth,implies(X_24,X_23))
| implies(truth,implies(X_24,X_23)) != implies(X_24,X_23)
| big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(X_24,X_23) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))),implies(X_24,X_23)) ),[0],$fot(implies(truth,implies(X_24,X_23)))]]) ).
cnf(refute_0_52,plain,
( big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) != implies(truth,implies(X_24,X_23))
| big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(X_24,X_23) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_24,X_23)),implies(X_24,X_23)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != implies(truth,implies(X_24,X_23))
| big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(X_24,X_23) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))),implies(truth,implies(X_24,X_23))) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
big_V(implies(X_24,X_23),implies(not(X_23),not(X_24))) = implies(X_24,X_23),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(truth,implies(X_24,X_23))) )],[refute_0_35,refute_0_53]) ).
cnf(refute_0_55,plain,
big_V(implies(X_24,implies(not(X_24),not(truth))),implies(not(implies(not(X_24),not(truth))),not(X_24))) = implies(X_24,implies(not(X_24),not(truth))),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(implies(not(X_24),not(truth))))]]) ).
cnf(refute_0_56,plain,
implies(implies(not(X_23),not(implies(X,X_23))),implies(implies(X,X_23),X_23)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_23)),bind(Y,$fot(implies(X,X_23)))]]) ).
cnf(refute_0_57,plain,
big_V(X,X_23) = implies(implies(X,X_23),X_23),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_23))]]) ).
cnf(refute_0_58,plain,
( big_V(X,X_23) != implies(implies(X,X_23),X_23)
| implies(implies(X,X_23),X_23) = big_V(X,X_23) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_23))),bind(Y0,$fot(implies(implies(X,X_23),X_23)))]]) ).
cnf(refute_0_59,plain,
implies(implies(X,X_23),X_23) = big_V(X,X_23),
inference(resolve,[$cnf( $equal(big_V(X,X_23),implies(implies(X,X_23),X_23)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( implies(implies(X,X_23),X_23) != big_V(X,X_23)
| implies(implies(not(X_23),not(implies(X,X_23))),implies(implies(X,X_23),X_23)) != truth
| implies(implies(not(X_23),not(implies(X,X_23))),big_V(X,X_23)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_23),not(implies(X,X_23))),implies(implies(X,X_23),X_23)),truth) ),[0,1],$fot(big_V(X,X_23))]]) ).
cnf(refute_0_61,plain,
( implies(implies(not(X_23),not(implies(X,X_23))),implies(implies(X,X_23),X_23)) != truth
| implies(implies(not(X_23),not(implies(X,X_23))),big_V(X,X_23)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_23),X_23),big_V(X,X_23)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(implies(not(X_23),not(implies(X,X_23))),big_V(X,X_23)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_23),not(implies(X,X_23))),implies(implies(X,X_23),X_23)),truth) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(implies(not(not(truth)),not(implies(X,not(truth)))),big_V(X,not(truth))) = truth,
inference(subst,[],[refute_0_62:[bind(X_23,$fot(not(truth)))]]) ).
cnf(refute_0_64,plain,
implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) = truth,
inference(subst,[],[refute_0_62:[bind(X,$fot(not(not(truth)))),bind(X_23,$fot(implies(not(not(not(truth))),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_65,plain,
big_V(implies(not(not(not(truth))),not(not(truth))),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(not(not(truth)))),bind(X_24,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_66,plain,
big_V(implies(not(truth),not(not(truth))),implies(not(not(not(truth))),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(not(not(truth)))),bind(X_24,$fot(not(truth)))]]) ).
cnf(refute_0_67,plain,
big_V(implies(X_3,Y),Y) = implies(implies(implies(X_3,Y),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(X_3,Y)))]]) ).
cnf(refute_0_68,plain,
big_V(X_3,Y) = implies(implies(X_3,Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_69,plain,
( big_V(X_3,Y) != implies(implies(X_3,Y),Y)
| implies(implies(X_3,Y),Y) = big_V(X_3,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_3,Y))),bind(Y0,$fot(implies(implies(X_3,Y),Y)))]]) ).
cnf(refute_0_70,plain,
implies(implies(X_3,Y),Y) = big_V(X_3,Y),
inference(resolve,[$cnf( $equal(big_V(X_3,Y),implies(implies(X_3,Y),Y)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( big_V(implies(X_3,Y),Y) != implies(implies(implies(X_3,Y),Y),Y)
| implies(implies(X_3,Y),Y) != big_V(X_3,Y)
| big_V(implies(X_3,Y),Y) = implies(big_V(X_3,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_3,Y),Y),implies(implies(implies(X_3,Y),Y),Y)) ),[1,0],$fot(big_V(X_3,Y))]]) ).
cnf(refute_0_72,plain,
( big_V(implies(X_3,Y),Y) != implies(implies(implies(X_3,Y),Y),Y)
| big_V(implies(X_3,Y),Y) = implies(big_V(X_3,Y),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(X_3,Y),Y),big_V(X_3,Y)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
big_V(implies(X_3,Y),Y) = implies(big_V(X_3,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_3,Y),Y),implies(implies(implies(X_3,Y),Y),Y)) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
big_V(implies(X_3,Y),Y) = big_V(Y,implies(X_3,Y)),
inference(subst,[],[refute_0_46:[bind(X,$fot(Y)),bind(Y,$fot(implies(X_3,Y)))]]) ).
cnf(refute_0_75,plain,
( big_V(implies(X_3,Y),Y) != big_V(Y,implies(X_3,Y))
| big_V(implies(X_3,Y),Y) != implies(big_V(X_3,Y),Y)
| big_V(Y,implies(X_3,Y)) = implies(big_V(X_3,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_3,Y),Y),implies(big_V(X_3,Y),Y)) ),[0],$fot(big_V(Y,implies(X_3,Y)))]]) ).
cnf(refute_0_76,plain,
( big_V(implies(X_3,Y),Y) != implies(big_V(X_3,Y),Y)
| big_V(Y,implies(X_3,Y)) = implies(big_V(X_3,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_3,Y),Y),big_V(Y,implies(X_3,Y))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
big_V(Y,implies(X_3,Y)) = implies(big_V(X_3,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_3,Y),Y),implies(big_V(X_3,Y),Y)) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(big_V(not(truth),not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_77:[bind(Y,$fot(not(not(truth)))),bind(X_3,$fot(not(truth)))]]) ).
cnf(refute_0_79,plain,
big_V(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(truth)),not(truth)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_80,plain,
implies(implies(not(X_23),not(truth)),implies(truth,X_23)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_23)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_81,plain,
implies(truth,X_23) = X_23,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_82,plain,
( implies(implies(not(X_23),not(truth)),implies(truth,X_23)) != truth
| implies(truth,X_23) != X_23
| implies(implies(not(X_23),not(truth)),X_23) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_23),not(truth)),implies(truth,X_23)),truth) ),[0,1],$fot(X_23)]]) ).
cnf(refute_0_83,plain,
( implies(implies(not(X_23),not(truth)),implies(truth,X_23)) != truth
| implies(implies(not(X_23),not(truth)),X_23) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_23),X_23) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
implies(implies(not(X_23),not(truth)),X_23) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_23),not(truth)),implies(truth,X_23)),truth) )],[refute_0_80,refute_0_83]) ).
cnf(refute_0_85,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_84:[bind(X_23,$fot(not(truth)))]]) ).
cnf(refute_0_86,plain,
( big_V(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(truth)),not(truth))
| implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| big_V(not(not(truth)),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(truth)),not(truth)))]]) ).
cnf(refute_0_87,plain,
( big_V(not(not(truth)),not(truth)) != implies(implies(not(not(truth)),not(truth)),not(truth))
| big_V(not(not(truth)),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(truth)),not(truth))) )],[refute_0_79,refute_0_87]) ).
cnf(refute_0_89,plain,
big_V(not(not(truth)),not(truth)) = big_V(not(truth),not(not(truth))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_90,plain,
( big_V(not(not(truth)),not(truth)) != big_V(not(truth),not(not(truth)))
| big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(big_V(not(truth),not(not(truth))))]]) ).
cnf(refute_0_91,plain,
( big_V(not(not(truth)),not(truth)) != truth
| big_V(not(truth),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),big_V(not(truth),not(not(truth)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
big_V(not(truth),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) )],[refute_0_88,refute_0_91]) ).
cnf(refute_0_93,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(big_V(not(truth),not(not(truth))),not(not(truth)))
| big_V(not(truth),not(not(truth))) != truth
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$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_94,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( $equal(big_V(not(truth),not(not(truth))),truth) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(big_V(not(truth),not(not(truth))),not(not(truth)))) )],[refute_0_78,refute_0_94]) ).
cnf(refute_0_96,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_97,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_98,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( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(truth,not(not(truth)))) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
big_V(X,implies(X_27,X)) = implies(implies(X,implies(X_27,X)),implies(X_27,X)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(implies(X_27,X)))]]) ).
cnf(refute_0_101,plain,
implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(truth)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_102,plain,
implies(truth,X_14) = X_14,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_103,plain,
( implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) != truth
| implies(truth,X_14) != X_14
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))),truth) ),[0,1,0],$fot(X_14)]]) ).
cnf(refute_0_104,plain,
( implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))),truth) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(truth,implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_107,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_108,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) != truth
| implies(truth,X_14) != X_14
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))),truth) ),[0,1,1],$fot(X_14)]]) ).
cnf(refute_0_109,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) != truth
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_102,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))),truth) )],[refute_0_107,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(implies(X_13,X_14),X_14) = big_V(X_13,X_14),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_13)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_112,plain,
implies(X_13,implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(implies(X_13,X_14),X_14)))]]) ).
cnf(refute_0_113,plain,
( implies(X_13,implies(implies(X_13,X_14),X_14)) != implies(X_13,implies(implies(X_13,X_14),X_14))
| implies(implies(X_13,X_14),X_14) != big_V(X_13,X_14)
| implies(X_13,implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(implies(X_13,X_14),X_14)),implies(X_13,implies(implies(X_13,X_14),X_14))) ),[1,1],$fot(big_V(X_13,X_14))]]) ).
cnf(refute_0_114,plain,
( implies(implies(X_13,X_14),X_14) != big_V(X_13,X_14)
| implies(X_13,implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,X_14),X_14)),implies(X_13,implies(implies(X_13,X_14),X_14))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(X_13,implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)),
inference(resolve,[$cnf( $equal(implies(implies(X_13,X_14),X_14),big_V(X_13,X_14)) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(truth,X_13) = X_13,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_117,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)))]]) ).
cnf(refute_0_118,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))
| implies(truth,X_13) != X_13
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_119,plain,
( implies(truth,X_13) != X_13
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)),
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_122,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_11,refute_0_121]) ).
cnf(refute_0_123,plain,
( implies(X_13,implies(implies(X_13,X_14),X_14)) != implies(X_13,big_V(X_13,X_14))
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != implies(X_13,implies(implies(X_13,X_14),X_14))
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)))),bind(Y0,$fot(implies(X_13,implies(implies(X_13,X_14),X_14)))),bind(Z0,$fot(implies(X_13,big_V(X_13,X_14))))]]) ).
cnf(refute_0_124,plain,
( implies(X_13,implies(implies(X_13,X_14),X_14)) != implies(X_13,big_V(X_13,X_14))
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(X_13,implies(implies(X_13,X_14),X_14))) )],[refute_0_120,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,big_V(X_13,X_14)),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,X_14),X_14)),implies(X_13,big_V(X_13,X_14))) )],[refute_0_115,refute_0_124]) ).
cnf(refute_0_126,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != implies(X_13,big_V(X_13,X_14))
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != truth
| implies(X_13,big_V(X_13,X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),truth) ),[0],$fot(implies(X_13,big_V(X_13,X_14)))]]) ).
cnf(refute_0_127,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != truth
| implies(X_13,big_V(X_13,X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(X_13,big_V(X_13,X_14))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(X_13,big_V(X_13,X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),truth) )],[refute_0_110,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(X_13,big_V(X_13,truth)) = truth,
inference(subst,[],[refute_0_128:[bind(X_14,$fot(truth))]]) ).
cnf(refute_0_130,plain,
big_V(Y,implies(Y,Y)) = implies(big_V(Y,Y),Y),
inference(subst,[],[refute_0_77:[bind(X_3,$fot(Y))]]) ).
cnf(refute_0_131,plain,
big_V(Y,Y) = implies(implies(Y,Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(Y))]]) ).
cnf(refute_0_132,plain,
big_V(truth,X_4) = implies(implies(truth,X_4),X_4),
inference(subst,[],[big_V_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_4))]]) ).
cnf(refute_0_133,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_134,plain,
( big_V(truth,X_4) != implies(implies(truth,X_4),X_4)
| implies(truth,X_4) != X_4
| big_V(truth,X_4) = implies(X_4,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_4),implies(implies(truth,X_4),X_4)) ),[1,0],$fot(X_4)]]) ).
cnf(refute_0_135,plain,
( big_V(truth,X_4) != implies(implies(truth,X_4),X_4)
| big_V(truth,X_4) = implies(X_4,X_4) ),
inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
big_V(truth,X_4) = implies(X_4,X_4),
inference(resolve,[$cnf( $equal(big_V(truth,X_4),implies(implies(truth,X_4),X_4)) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(truth,big_V(truth,X_16)) = big_V(truth,X_16),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(truth,X_16)))]]) ).
cnf(refute_0_138,plain,
implies(truth,big_V(truth,X_16)) = truth,
inference(subst,[],[refute_0_128:[bind(X_13,$fot(truth)),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_139,plain,
( implies(truth,big_V(truth,X_16)) != big_V(truth,X_16)
| implies(truth,big_V(truth,X_16)) != truth
| truth = big_V(truth,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,big_V(truth,X_16)),big_V(truth,X_16)) ),[0],$fot(truth)]]) ).
cnf(refute_0_140,plain,
( implies(truth,big_V(truth,X_16)) != big_V(truth,X_16)
| truth = big_V(truth,X_16) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_16)),truth) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
truth = big_V(truth,X_16),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_16)),big_V(truth,X_16)) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( truth != big_V(truth,X_16)
| big_V(truth,X_16) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(big_V(truth,X_16)))]]) ).
cnf(refute_0_143,plain,
big_V(truth,X_16) = truth,
inference(resolve,[$cnf( $equal(truth,big_V(truth,X_16)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
big_V(truth,X_4) = truth,
inference(subst,[],[refute_0_143:[bind(X_16,$fot(X_4))]]) ).
cnf(refute_0_145,plain,
( big_V(truth,X_4) != implies(X_4,X_4)
| big_V(truth,X_4) != truth
| truth = implies(X_4,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_4),implies(X_4,X_4)) ),[0],$fot(truth)]]) ).
cnf(refute_0_146,plain,
( big_V(truth,X_4) != implies(X_4,X_4)
| truth = implies(X_4,X_4) ),
inference(resolve,[$cnf( $equal(big_V(truth,X_4),truth) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
truth = implies(X_4,X_4),
inference(resolve,[$cnf( $equal(big_V(truth,X_4),implies(X_4,X_4)) )],[refute_0_136,refute_0_146]) ).
cnf(refute_0_148,plain,
truth = implies(Y,Y),
inference(subst,[],[refute_0_147:[bind(X_4,$fot(Y))]]) ).
cnf(refute_0_149,plain,
( truth != implies(Y,Y)
| implies(Y,Y) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(Y,Y)))]]) ).
cnf(refute_0_150,plain,
implies(Y,Y) = truth,
inference(resolve,[$cnf( $equal(truth,implies(Y,Y)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( big_V(Y,Y) != implies(implies(Y,Y),Y)
| implies(Y,Y) != truth
| big_V(Y,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,Y),implies(implies(Y,Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_152,plain,
( big_V(Y,Y) != implies(implies(Y,Y),Y)
| big_V(Y,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(Y,Y),truth) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
big_V(Y,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(Y,Y),implies(implies(Y,Y),Y)) )],[refute_0_131,refute_0_152]) ).
cnf(refute_0_154,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_155,plain,
( big_V(Y,Y) != implies(truth,Y)
| implies(truth,Y) != Y
| big_V(Y,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(Y,Y),Y) ),[0],$fot(implies(truth,Y))]]) ).
cnf(refute_0_156,plain,
( big_V(Y,Y) != implies(truth,Y)
| big_V(Y,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
big_V(Y,Y) = Y,
inference(resolve,[$cnf( $equal(big_V(Y,Y),implies(truth,Y)) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( big_V(Y,Y) != Y
| big_V(Y,implies(Y,Y)) != implies(big_V(Y,Y),Y)
| big_V(Y,implies(Y,Y)) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(Y,Y)),implies(big_V(Y,Y),Y)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_159,plain,
( big_V(Y,implies(Y,Y)) != implies(big_V(Y,Y),Y)
| big_V(Y,implies(Y,Y)) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(big_V(Y,Y),Y) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
big_V(Y,implies(Y,Y)) = implies(Y,Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(Y,Y)),implies(big_V(Y,Y),Y)) )],[refute_0_130,refute_0_159]) ).
cnf(refute_0_161,plain,
big_V(Y,implies(Y,Y)) = big_V(Y,implies(Y,Y)),
introduced(tautology,[refl,[$fot(big_V(Y,implies(Y,Y)))]]) ).
cnf(refute_0_162,plain,
( big_V(Y,implies(Y,Y)) != big_V(Y,implies(Y,Y))
| implies(Y,Y) != truth
| big_V(Y,implies(Y,Y)) = big_V(Y,truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(Y,Y)),big_V(Y,implies(Y,Y))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_163,plain,
( implies(Y,Y) != truth
| big_V(Y,implies(Y,Y)) = big_V(Y,truth) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(Y,Y)),big_V(Y,implies(Y,Y))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
big_V(Y,implies(Y,Y)) = big_V(Y,truth),
inference(resolve,[$cnf( $equal(implies(Y,Y),truth) )],[refute_0_150,refute_0_163]) ).
cnf(refute_0_165,plain,
( big_V(Y,implies(Y,Y)) != big_V(Y,truth)
| big_V(Y,implies(Y,Y)) != implies(Y,Y)
| big_V(Y,truth) = implies(Y,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(Y,Y)),implies(Y,Y)) ),[0],$fot(big_V(Y,truth))]]) ).
cnf(refute_0_166,plain,
( big_V(Y,implies(Y,Y)) != implies(Y,Y)
| big_V(Y,truth) = implies(Y,Y) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(Y,Y)),big_V(Y,truth)) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( big_V(Y,truth) != implies(Y,Y)
| implies(Y,Y) != truth
| big_V(Y,truth) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(Y,truth),truth) ),[0],$fot(implies(Y,Y))]]) ).
cnf(refute_0_168,plain,
( big_V(Y,truth) != implies(Y,Y)
| big_V(Y,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(Y,Y),truth) )],[refute_0_150,refute_0_167]) ).
cnf(refute_0_169,plain,
( big_V(Y,implies(Y,Y)) != implies(Y,Y)
| big_V(Y,truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(Y,truth),implies(Y,Y)) )],[refute_0_166,refute_0_168]) ).
cnf(refute_0_170,plain,
big_V(Y,truth) = truth,
inference(resolve,[$cnf( $equal(big_V(Y,implies(Y,Y)),implies(Y,Y)) )],[refute_0_160,refute_0_169]) ).
cnf(refute_0_171,plain,
big_V(X_13,truth) = truth,
inference(subst,[],[refute_0_170:[bind(Y,$fot(X_13))]]) ).
cnf(refute_0_172,plain,
( big_V(X_13,truth) != truth
| implies(X_13,big_V(X_13,truth)) != truth
| implies(X_13,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,big_V(X_13,truth)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_173,plain,
( implies(X_13,big_V(X_13,truth)) != truth
| implies(X_13,truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(X_13,truth),truth) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(X_13,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_13,big_V(X_13,truth)),truth) )],[refute_0_129,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(X_12,truth) = truth,
inference(subst,[],[refute_0_174:[bind(X_13,$fot(X_12))]]) ).
cnf(refute_0_176,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),
introduced(tautology,[refl,[$fot(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_177,plain,
( implies(X_12,truth) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_178,plain,
( implies(X_12,truth) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(implies(X_12,truth),truth) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(truth,implies(X_14,implies(X_12,X_14)))
| implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))))),bind(Y0,$fot(implies(truth,implies(X_14,implies(X_12,X_14))))),bind(Z0,$fot(implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_181,plain,
( implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(truth,implies(X_14,implies(X_12,X_14)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_14,implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_106,refute_0_181]) ).
cnf(refute_0_183,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),truth) ),[0],$fot(implies(X_14,implies(X_12,X_14)))]]) ).
cnf(refute_0_184,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(X_14,implies(X_12,X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),truth) )],[refute_0_105,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(X,implies(X_27,X)) = truth,
inference(subst,[],[refute_0_185:[bind(X_12,$fot(X_27)),bind(X_14,$fot(X))]]) ).
cnf(refute_0_187,plain,
( big_V(X,implies(X_27,X)) != implies(implies(X,implies(X_27,X)),implies(X_27,X))
| implies(X,implies(X_27,X)) != truth
| big_V(X,implies(X_27,X)) = implies(truth,implies(X_27,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(X_27,X)),implies(implies(X,implies(X_27,X)),implies(X_27,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_188,plain,
( big_V(X,implies(X_27,X)) != implies(implies(X,implies(X_27,X)),implies(X_27,X))
| big_V(X,implies(X_27,X)) = implies(truth,implies(X_27,X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_27,X)),truth) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
big_V(X,implies(X_27,X)) = implies(truth,implies(X_27,X)),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_27,X)),implies(implies(X,implies(X_27,X)),implies(X_27,X))) )],[refute_0_100,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(truth,implies(X_27,X)) = implies(X_27,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_27,X)))]]) ).
cnf(refute_0_191,plain,
( big_V(X,implies(X_27,X)) != implies(truth,implies(X_27,X))
| implies(truth,implies(X_27,X)) != implies(X_27,X)
| big_V(X,implies(X_27,X)) = implies(X_27,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,implies(X_27,X)),implies(X_27,X)) ),[0],$fot(implies(truth,implies(X_27,X)))]]) ).
cnf(refute_0_192,plain,
( big_V(X,implies(X_27,X)) != implies(truth,implies(X_27,X))
| big_V(X,implies(X_27,X)) = implies(X_27,X) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_27,X)),implies(X_27,X)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
big_V(X,implies(X_27,X)) = implies(X_27,X),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_27,X)),implies(truth,implies(X_27,X))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
big_V(not(not(truth)),implies(not(truth),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(subst,[],[refute_0_193:[bind(X,$fot(not(not(truth)))),bind(X_27,$fot(not(truth)))]]) ).
cnf(refute_0_195,plain,
( big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != implies(not(truth),not(not(truth)))
| big_V(not(not(truth)),implies(not(truth),not(not(truth)))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$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_196,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( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),implies(not(truth),not(not(truth)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(truth),not(not(truth)))),not(not(truth))) )],[refute_0_99,refute_0_196]) ).
cnf(refute_0_198,plain,
( big_V(implies(not(truth),not(not(truth))),implies(not(not(not(truth))),not(not(truth)))) != implies(not(truth),not(not(truth)))
| implies(not(truth),not(not(truth))) != not(not(truth))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) = implies(not(truth),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),not(not(truth))),implies(not(not(not(truth))),not(not(truth)))),implies(not(truth),not(not(truth)))) ),[0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_199,plain,
( big_V(implies(not(truth),not(not(truth))),implies(not(not(not(truth))),not(not(truth)))) != implies(not(truth),not(not(truth)))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) = implies(not(truth),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) = implies(not(truth),not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),not(not(truth))),implies(not(not(not(truth))),not(not(truth)))),implies(not(truth),not(not(truth)))) )],[refute_0_66,refute_0_199]) ).
cnf(refute_0_201,plain,
big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) = implies(not(not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_193:[bind(X,$fot(not(not(truth)))),bind(X_27,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_202,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) != implies(not(not(not(truth))),not(not(truth)))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) != implies(not(truth),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) = implies(not(truth),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))),implies(not(truth),not(not(truth)))) ),[0],$fot(implies(not(not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_203,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) != implies(not(truth),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) = implies(not(truth),not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))),implies(not(not(not(truth))),not(not(truth)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
( implies(not(not(not(truth))),not(not(truth))) != implies(not(truth),not(not(truth)))
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(not(not(not(truth))),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) ),[0],$fot(implies(not(truth),not(not(truth))))]]) ).
cnf(refute_0_205,plain,
( implies(not(not(not(truth))),not(not(truth))) != implies(not(truth),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_197,refute_0_204]) ).
cnf(refute_0_206,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))) != implies(not(truth),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) )],[refute_0_203,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(not(not(not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(truth)))),implies(not(truth),not(not(truth)))) )],[refute_0_200,refute_0_206]) ).
cnf(refute_0_208,plain,
( big_V(implies(not(not(not(truth))),not(not(truth))),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(not(truth))),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) != not(not(truth))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(not(truth))),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(not(not(truth))),not(not(truth))),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(not(truth))),not(not(truth)))) ),[0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_209,plain,
( big_V(implies(not(not(not(truth))),not(not(truth))),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(not(truth))),not(not(truth)))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(not(truth))),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(not(truth))),not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(not(not(not(truth))),not(not(truth))),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(not(truth))),not(not(truth)))) )],[refute_0_65,refute_0_209]) ).
cnf(refute_0_211,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(not(truth))),not(not(truth)))
| implies(not(not(not(truth))),not(not(truth))) != not(not(truth))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),not(not(truth))) ),[0],$fot(implies(not(not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_212,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(not(truth))),not(not(truth)))
| big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_207,refute_0_211]) ).
cnf(refute_0_213,plain,
big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(not(truth))),not(not(truth)))) )],[refute_0_210,refute_0_212]) ).
cnf(refute_0_214,plain,
( big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != not(not(truth))
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) != truth
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_215,plain,
( implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) != truth
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),not(not(truth))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),big_V(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),truth) )],[refute_0_64,refute_0_215]) ).
cnf(refute_0_217,plain,
big_V(Y,implies(X_3,Y)) = implies(X_3,Y),
inference(subst,[],[refute_0_193:[bind(X,$fot(Y)),bind(X_27,$fot(X_3))]]) ).
cnf(refute_0_218,plain,
( big_V(Y,implies(X_3,Y)) != implies(X_3,Y)
| big_V(Y,implies(X_3,Y)) != implies(big_V(X_3,Y),Y)
| implies(X_3,Y) = implies(big_V(X_3,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(X_3,Y)),implies(big_V(X_3,Y),Y)) ),[0],$fot(implies(X_3,Y))]]) ).
cnf(refute_0_219,plain,
( big_V(Y,implies(X_3,Y)) != implies(big_V(X_3,Y),Y)
| implies(X_3,Y) = implies(big_V(X_3,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_3,Y)),implies(X_3,Y)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
implies(X_3,Y) = implies(big_V(X_3,Y),Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_3,Y)),implies(big_V(X_3,Y),Y)) )],[refute_0_77,refute_0_219]) ).
cnf(refute_0_221,plain,
implies(not(not(not(truth))),not(not(not(not(truth))))) = implies(big_V(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth))))),
inference(subst,[],[refute_0_220:[bind(Y,$fot(not(not(not(not(truth)))))),bind(X_3,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_222,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(not(not(truth)),not(not(not(truth))))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(not(truth))))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_223,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(big_V(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[refute_0_220:[bind(Y,$fot(not(not(not(truth))))),bind(X_3,$fot(not(not(truth))))]]) ).
cnf(refute_0_224,plain,
implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_225,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_226,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_197,refute_0_225]) ).
cnf(refute_0_227,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_224,refute_0_226]) ).
cnf(refute_0_228,plain,
big_V(not(not(not(truth))),not(not(truth))) = big_V(not(not(truth)),not(not(not(truth)))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_229,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = big_V(not(not(not(truth))),not(not(truth))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(truth))))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_230,plain,
( big_V(not(not(not(truth))),not(not(truth))) != big_V(not(not(truth)),not(not(not(truth))))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != big_V(not(not(not(truth))),not(not(truth)))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = big_V(not(not(truth)),not(not(not(truth)))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))))),bind(Y0,$fot(big_V(not(not(not(truth))),not(not(truth))))),bind(Z0,$fot(big_V(not(not(truth)),not(not(not(truth))))))]]) ).
cnf(refute_0_231,plain,
( big_V(not(not(not(truth))),not(not(truth))) != big_V(not(not(truth)),not(not(not(truth))))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = big_V(not(not(truth)),not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),big_V(not(not(not(truth))),not(not(truth)))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) = big_V(not(not(truth)),not(not(not(truth)))),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),not(not(truth))),big_V(not(not(truth)),not(not(not(truth))))) )],[refute_0_228,refute_0_231]) ).
cnf(refute_0_233,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != big_V(not(not(truth)),not(not(not(truth))))
| implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != truth
| big_V(not(not(truth)),not(not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),truth) ),[0],$fot(big_V(not(not(truth)),not(not(not(truth)))))]]) ).
cnf(refute_0_234,plain,
( implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) != truth
| big_V(not(not(truth)),not(not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),big_V(not(not(truth)),not(not(not(truth))))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
big_V(not(not(truth)),not(not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(truth))),not(not(truth))),truth) )],[refute_0_227,refute_0_234]) ).
cnf(refute_0_236,plain,
( big_V(not(not(truth)),not(not(not(truth)))) != truth
| implies(not(not(truth)),not(not(not(truth)))) != implies(big_V(not(not(truth)),not(not(not(truth)))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(big_V(not(not(truth)),not(not(not(truth)))),not(not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_237,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(big_V(not(not(truth)),not(not(not(truth)))),not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(not(not(truth)))),truth) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(not(not(truth)),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(big_V(not(not(truth)),not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_223,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(truth,not(not(not(truth)))) = not(not(not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_240,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(truth,not(not(not(truth)))) != not(not(not(truth)))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) ),[0],$fot(implies(truth,not(not(not(truth)))))]]) ).
cnf(refute_0_241,plain,
( implies(not(not(truth)),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
implies(not(not(truth)),not(not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),implies(truth,not(not(not(truth))))) )],[refute_0_238,refute_0_241]) ).
cnf(refute_0_243,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(not(not(truth)),not(not(not(truth))))) != truth
| implies(not(not(truth)),not(not(not(truth)))) != not(not(not(truth)))
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(not(not(truth)),not(not(not(truth))))),truth) ),[0,1],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_244,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(not(not(truth)),not(not(not(truth))))) != truth
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),implies(not(not(truth)),not(not(not(truth))))),truth) )],[refute_0_222,refute_0_244]) ).
cnf(refute_0_246,plain,
big_V(not(not(not(not(truth)))),not(not(not(truth)))) = big_V(not(not(not(truth))),not(not(not(not(truth))))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(not(not(truth))))),bind(Y,$fot(not(not(not(not(truth))))))]]) ).
cnf(refute_0_247,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = big_V(not(not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[refute_0_37:[bind(X,$fot(not(not(not(not(truth)))))),bind(Y,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_248,plain,
( big_V(not(not(not(not(truth)))),not(not(not(truth)))) != big_V(not(not(not(truth))),not(not(not(not(truth)))))
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != big_V(not(not(not(not(truth)))),not(not(not(truth))))
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = big_V(not(not(not(truth))),not(not(not(not(truth))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))))),bind(Y0,$fot(big_V(not(not(not(not(truth)))),not(not(not(truth)))))),bind(Z0,$fot(big_V(not(not(not(truth))),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_249,plain,
( big_V(not(not(not(not(truth)))),not(not(not(truth)))) != big_V(not(not(not(truth))),not(not(not(not(truth)))))
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = big_V(not(not(not(truth))),not(not(not(not(truth))))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),big_V(not(not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) = big_V(not(not(not(truth))),not(not(not(not(truth))))),
inference(resolve,[$cnf( $equal(big_V(not(not(not(not(truth)))),not(not(not(truth)))),big_V(not(not(not(truth))),not(not(not(not(truth)))))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != big_V(not(not(not(truth))),not(not(not(not(truth)))))
| implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != truth
| big_V(not(not(not(truth))),not(not(not(not(truth))))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),truth) ),[0],$fot(big_V(not(not(not(truth))),not(not(not(not(truth))))))]]) ).
cnf(refute_0_252,plain,
( implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))) != truth
| big_V(not(not(not(truth))),not(not(not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),big_V(not(not(not(truth))),not(not(not(not(truth)))))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
big_V(not(not(not(truth))),not(not(not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(truth)))),not(not(not(truth)))),not(not(not(truth)))),truth) )],[refute_0_245,refute_0_252]) ).
cnf(refute_0_254,plain,
( big_V(not(not(not(truth))),not(not(not(not(truth))))) != truth
| implies(not(not(not(truth))),not(not(not(not(truth))))) != implies(big_V(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth)))))
| implies(not(not(not(truth))),not(not(not(not(truth))))) = implies(truth,not(not(not(not(truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(big_V(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth)))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_255,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != implies(big_V(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth)))))
| implies(not(not(not(truth))),not(not(not(not(truth))))) = implies(truth,not(not(not(not(truth))))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),not(not(not(not(truth))))),truth) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
implies(not(not(not(truth))),not(not(not(not(truth))))) = implies(truth,not(not(not(not(truth))))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(big_V(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth)))))) )],[refute_0_221,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(truth,not(not(not(not(truth))))) = not(not(not(not(truth)))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(not(not(truth))))))]]) ).
cnf(refute_0_258,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != implies(truth,not(not(not(not(truth)))))
| implies(truth,not(not(not(not(truth))))) != not(not(not(not(truth))))
| implies(not(not(not(truth))),not(not(not(not(truth))))) = not(not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth))))) ),[0],$fot(implies(truth,not(not(not(not(truth))))))]]) ).
cnf(refute_0_259,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != implies(truth,not(not(not(not(truth)))))
| implies(not(not(not(truth))),not(not(not(not(truth))))) = not(not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(not(truth))))),not(not(not(not(truth))))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
implies(not(not(not(truth))),not(not(not(not(truth))))) = not(not(not(not(truth)))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(truth,not(not(not(not(truth)))))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_262,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))
| implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(truth)),not(not(not(not(truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) ),[1,1],$fot(not(not(not(not(truth)))))]]) ).
cnf(refute_0_263,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(truth)),not(not(not(not(truth))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) = implies(not(not(truth)),not(not(not(not(truth))))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth))))) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) = not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),
introduced(tautology,[refl,[$fot(not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))]]) ).
cnf(refute_0_266,plain,
( implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(truth)),not(not(not(not(truth)))))
| not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) != not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))
| not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) = not(implies(not(not(truth)),not(not(not(not(truth)))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) ),[1,0],$fot(implies(not(not(truth)),not(not(not(not(truth))))))]]) ).
cnf(refute_0_267,plain,
( implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))) != implies(not(not(truth)),not(not(not(not(truth)))))
| not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) = not(implies(not(not(truth)),not(not(not(not(truth)))))) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) = not(implies(not(not(truth)),not(not(not(not(truth)))))),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))),implies(not(not(truth)),not(not(not(not(truth)))))) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),
introduced(tautology,[refl,[$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))))]]) ).
cnf(refute_0_270,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))
| not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) != not(implies(not(not(truth)),not(not(not(not(truth))))))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))) ),[1,1],$fot(not(implies(not(not(truth)),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_271,plain,
( not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))) != not(implies(not(not(truth)),not(not(not(not(truth))))))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
not(implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(implies(not(not(not(truth))),not(not(not(not(truth)))))),
introduced(tautology,[refl,[$fot(not(implies(not(not(not(truth))),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_274,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| not(implies(not(not(not(truth))),not(not(not(not(truth)))))) != not(implies(not(not(not(truth))),not(not(not(not(truth))))))
| not(implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(not(not(not(truth))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(not(truth))),not(not(not(not(truth))))))) ),[1,0],$fot(not(not(not(not(truth)))))]]) ).
cnf(refute_0_275,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| not(implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(not(not(not(truth))))) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(not(truth))),not(not(not(not(truth))))))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
not(implies(not(not(not(truth))),not(not(not(not(truth)))))) = not(not(not(not(not(truth))))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth))))) )],[refute_0_260,refute_0_275]) ).
cnf(refute_0_277,plain,
implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),
introduced(tautology,[refl,[$fot(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))))]]) ).
cnf(refute_0_278,plain,
( implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))
| not(implies(not(not(not(truth))),not(not(not(not(truth)))))) != not(not(not(not(not(truth)))))
| implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))) ),[1,0],$fot(not(not(not(not(not(truth))))))]]) ).
cnf(refute_0_279,plain,
( not(implies(not(not(not(truth))),not(not(not(not(truth)))))) != not(not(not(not(not(truth)))))
| implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),
inference(resolve,[$cnf( $equal(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(not(not(not(not(truth)))))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
( implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))))),bind(Y0,$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))))),bind(Z0,$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))))]]) ).
cnf(refute_0_282,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth))))))))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))) )],[refute_0_272,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))))]]) ).
cnf(refute_0_285,plain,
( implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) != implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth)))
| implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth)))) ),[1,0],$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))))]]) ).
cnf(refute_0_286,plain,
( implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) = implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))) )],[refute_0_283,refute_0_286]) ).
cnf(refute_0_288,plain,
( implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) != implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth)))
| implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) != truth
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),truth) ),[0],$fot(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))))]]) ).
cnf(refute_0_289,plain,
( implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))) != truth
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth)))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(implies(not(not(not(truth))),not(not(not(not(truth)))))),not(implies(not(not(truth)),implies(not(not(not(truth))),not(not(not(not(truth)))))))),not(not(truth))),truth) )],[refute_0_216,refute_0_289]) ).
cnf(refute_0_291,plain,
( truth != implies(X_4,X_4)
| implies(X_4,X_4) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_4,X_4)))]]) ).
cnf(refute_0_292,plain,
implies(X_4,X_4) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_4,X_4)) )],[refute_0_147,refute_0_291]) ).
cnf(refute_0_293,plain,
implies(not(truth),not(truth)) = truth,
inference(subst,[],[refute_0_292:[bind(X_4,$fot(not(truth)))]]) ).
cnf(refute_0_294,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(subst,[],[refute_0_292:[bind(X_4,$fot(not(not(truth))))]]) ).
cnf(refute_0_295,plain,
big_V(implies(not(not(truth)),not(truth)),implies(not(not(truth)),not(not(not(truth))))) = implies(not(not(truth)),not(truth)),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(not(truth))),bind(X_24,$fot(not(not(truth))))]]) ).
cnf(refute_0_296,plain,
( big_V(implies(not(not(truth)),not(truth)),implies(not(not(truth)),not(not(not(truth))))) != implies(not(not(truth)),not(truth))
| implies(not(not(truth)),not(not(not(truth)))) != not(not(not(truth)))
| big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) = implies(not(not(truth)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(not(truth)),not(truth)),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(truth))) ),[0,1],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_297,plain,
( big_V(implies(not(not(truth)),not(truth)),implies(not(not(truth)),not(not(not(truth))))) != implies(not(not(truth)),not(truth))
| big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) = implies(not(not(truth)),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_242,refute_0_296]) ).
cnf(refute_0_298,plain,
big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) = implies(not(not(truth)),not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(not(not(truth)),not(truth)),implies(not(not(truth)),not(not(not(truth))))),implies(not(not(truth)),not(truth))) )],[refute_0_295,refute_0_297]) ).
cnf(refute_0_299,plain,
big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) = big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(not(not(truth))))),bind(Y,$fot(implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_300,plain,
( big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) != big_V(not(not(not(truth))),implies(not(not(truth)),not(truth)))
| big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) != implies(not(not(truth)),not(truth))
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(truth)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) ),[0],$fot(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_301,plain,
( big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))) != implies(not(not(truth)),not(truth))
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(truth)),not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))),big_V(not(not(not(truth))),implies(not(not(truth)),not(truth)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = implies(not(not(truth)),not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(not(not(truth)),not(truth)),not(not(not(truth)))),implies(not(not(truth)),not(truth))) )],[refute_0_298,refute_0_301]) ).
cnf(refute_0_303,plain,
big_V(not(truth),not(not(not(truth)))) = implies(implies(not(truth),not(not(not(truth)))),not(not(not(truth)))),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_304,plain,
big_V(implies(not(truth),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(truth)))) = implies(not(truth),not(not(not(truth)))),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(not(not(not(truth))))),bind(X_24,$fot(not(truth)))]]) ).
cnf(refute_0_305,plain,
implies(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(not(not(not(truth))),not(not(truth)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_306,plain,
( implies(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(not(not(not(truth))),not(not(truth)))) != truth
| implies(not(not(not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(not(not(not(truth))),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_307,plain,
( implies(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(not(not(not(truth))),not(not(truth)))) != truth
| implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_207,refute_0_306]) ).
cnf(refute_0_308,plain,
implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),implies(not(not(not(truth))),not(not(truth)))),truth) )],[refute_0_305,refute_0_307]) ).
cnf(refute_0_309,plain,
implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))))]]) ).
cnf(refute_0_310,plain,
( implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) != implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth)))
| implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = implies(not(not(not(not(truth)))),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth)))) ),[1,0],$fot(not(not(not(not(truth)))))]]) ).
cnf(refute_0_311,plain,
( implies(not(not(not(truth))),not(not(not(not(truth))))) != not(not(not(not(truth))))
| implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = implies(not(not(not(not(truth)))),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth)))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) = implies(not(not(not(not(truth)))),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(not(not(truth))))) )],[refute_0_260,refute_0_311]) ).
cnf(refute_0_313,plain,
( implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) != implies(not(not(not(not(truth)))),not(not(truth)))
| implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) != truth
| implies(not(not(not(not(truth)))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),truth) ),[0],$fot(implies(not(not(not(not(truth)))),not(not(truth))))]]) ).
cnf(refute_0_314,plain,
( implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))) != truth
| implies(not(not(not(not(truth)))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),implies(not(not(not(not(truth)))),not(not(truth)))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
implies(not(not(not(not(truth)))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(not(not(not(truth))))),not(not(truth))),truth) )],[refute_0_308,refute_0_314]) ).
cnf(refute_0_316,plain,
( big_V(implies(not(truth),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(truth)))) != implies(not(truth),not(not(not(truth))))
| implies(not(not(not(not(truth)))),not(not(truth))) != truth
| big_V(implies(not(truth),not(not(not(truth)))),truth) = implies(not(truth),not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(truth)))),implies(not(truth),not(not(not(truth))))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_317,plain,
( big_V(implies(not(truth),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(truth)))) != implies(not(truth),not(not(not(truth))))
| big_V(implies(not(truth),not(not(not(truth)))),truth) = implies(not(truth),not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(truth)))),not(not(truth))),truth) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
big_V(implies(not(truth),not(not(not(truth)))),truth) = implies(not(truth),not(not(not(truth)))),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),not(not(not(truth)))),implies(not(not(not(not(truth)))),not(not(truth)))),implies(not(truth),not(not(not(truth))))) )],[refute_0_304,refute_0_317]) ).
cnf(refute_0_319,plain,
big_V(implies(not(truth),not(not(not(truth)))),truth) = truth,
inference(subst,[],[refute_0_170:[bind(Y,$fot(implies(not(truth),not(not(not(truth))))))]]) ).
cnf(refute_0_320,plain,
( big_V(implies(not(truth),not(not(not(truth)))),truth) != implies(not(truth),not(not(not(truth))))
| big_V(implies(not(truth),not(not(not(truth)))),truth) != truth
| truth = implies(not(truth),not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),not(not(not(truth)))),truth),implies(not(truth),not(not(not(truth))))) ),[0],$fot(truth)]]) ).
cnf(refute_0_321,plain,
( big_V(implies(not(truth),not(not(not(truth)))),truth) != implies(not(truth),not(not(not(truth))))
| truth = implies(not(truth),not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),not(not(not(truth)))),truth),truth) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
truth = implies(not(truth),not(not(not(truth)))),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),not(not(not(truth)))),truth),implies(not(truth),not(not(not(truth))))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( truth != implies(not(truth),not(not(not(truth))))
| implies(not(truth),not(not(not(truth)))) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(not(truth),not(not(not(truth))))))]]) ).
cnf(refute_0_324,plain,
implies(not(truth),not(not(not(truth)))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(not(truth),not(not(not(truth))))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
( big_V(not(truth),not(not(not(truth)))) != implies(implies(not(truth),not(not(not(truth)))),not(not(not(truth))))
| implies(not(truth),not(not(not(truth)))) != truth
| big_V(not(truth),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(truth),not(not(not(truth)))),implies(implies(not(truth),not(not(not(truth)))),not(not(not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_326,plain,
( big_V(not(truth),not(not(not(truth)))) != implies(implies(not(truth),not(not(not(truth)))),not(not(not(truth))))
| big_V(not(truth),not(not(not(truth)))) = implies(truth,not(not(not(truth)))) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(not(truth)))),truth) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
big_V(not(truth),not(not(not(truth)))) = implies(truth,not(not(not(truth)))),
inference(resolve,[$cnf( $equal(big_V(not(truth),not(not(not(truth)))),implies(implies(not(truth),not(not(not(truth)))),not(not(not(truth))))) )],[refute_0_303,refute_0_326]) ).
cnf(refute_0_328,plain,
( big_V(not(truth),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| implies(truth,not(not(not(truth)))) != not(not(not(truth)))
| big_V(not(truth),not(not(not(truth)))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(truth),not(not(not(truth)))),not(not(not(truth)))) ),[0],$fot(implies(truth,not(not(not(truth)))))]]) ).
cnf(refute_0_329,plain,
( big_V(not(truth),not(not(not(truth)))) != implies(truth,not(not(not(truth))))
| big_V(not(truth),not(not(not(truth)))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_239,refute_0_328]) ).
cnf(refute_0_330,plain,
big_V(not(truth),not(not(not(truth)))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(truth),not(not(not(truth)))),implies(truth,not(not(not(truth))))) )],[refute_0_327,refute_0_329]) ).
cnf(refute_0_331,plain,
big_V(not(not(not(truth))),not(truth)) = big_V(not(truth),not(not(not(truth)))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(truth))),bind(Y,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_332,plain,
( big_V(not(not(not(truth))),not(truth)) != big_V(not(truth),not(not(not(truth))))
| big_V(not(truth),not(not(not(truth)))) != not(not(not(truth)))
| big_V(not(not(not(truth))),not(truth)) = not(not(not(truth))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(not(not(not(truth))),not(truth)))),bind(Y0,$fot(big_V(not(truth),not(not(not(truth)))))),bind(Z0,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_333,plain,
( big_V(not(truth),not(not(not(truth)))) != not(not(not(truth)))
| big_V(not(not(not(truth))),not(truth)) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),not(truth)),big_V(not(truth),not(not(not(truth))))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
big_V(not(not(not(truth))),not(truth)) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(truth),not(not(not(truth)))),not(not(not(truth)))) )],[refute_0_330,refute_0_333]) ).
cnf(refute_0_335,plain,
big_V(implies(not(Y),not(truth)),Y) = implies(implies(implies(not(Y),not(truth)),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(Y),not(truth))))]]) ).
cnf(refute_0_336,plain,
implies(implies(not(Y),not(truth)),Y) = truth,
inference(subst,[],[refute_0_84:[bind(X_23,$fot(Y))]]) ).
cnf(refute_0_337,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(implies(implies(not(Y),not(truth)),Y),Y)
| implies(implies(not(Y),not(truth)),Y) != truth
| big_V(implies(not(Y),not(truth)),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(implies(implies(not(Y),not(truth)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_338,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(implies(implies(not(Y),not(truth)),Y),Y)
| big_V(implies(not(Y),not(truth)),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(implies(not(Y),not(truth)),Y),truth) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
big_V(implies(not(Y),not(truth)),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(implies(implies(not(Y),not(truth)),Y),Y)) )],[refute_0_335,refute_0_338]) ).
cnf(refute_0_340,plain,
big_V(implies(not(Y),not(truth)),Y) = big_V(Y,implies(not(Y),not(truth))),
inference(subst,[],[refute_0_46:[bind(X,$fot(Y)),bind(Y,$fot(implies(not(Y),not(truth))))]]) ).
cnf(refute_0_341,plain,
( big_V(implies(not(Y),not(truth)),Y) != big_V(Y,implies(not(Y),not(truth)))
| big_V(implies(not(Y),not(truth)),Y) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(truth,Y)) ),[0],$fot(big_V(Y,implies(not(Y),not(truth))))]]) ).
cnf(refute_0_342,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),big_V(Y,implies(not(Y),not(truth)))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
( big_V(Y,implies(not(Y),not(truth))) != implies(truth,Y)
| implies(truth,Y) != Y
| big_V(Y,implies(not(Y),not(truth))) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(Y,implies(not(Y),not(truth))),Y) ),[0],$fot(implies(truth,Y))]]) ).
cnf(refute_0_344,plain,
( big_V(Y,implies(not(Y),not(truth))) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_154,refute_0_343]) ).
cnf(refute_0_345,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),implies(truth,Y)) )],[refute_0_342,refute_0_344]) ).
cnf(refute_0_346,plain,
big_V(Y,implies(not(Y),not(truth))) = Y,
inference(resolve,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(truth,Y)) )],[refute_0_339,refute_0_345]) ).
cnf(refute_0_347,plain,
big_V(not(truth),implies(not(not(truth)),not(truth))) = not(truth),
inference(subst,[],[refute_0_346:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_348,plain,
big_V(not(truth),implies(not(not(truth)),not(truth))) = implies(not(not(truth)),not(truth)),
inference(subst,[],[refute_0_193:[bind(X,$fot(not(truth))),bind(X_27,$fot(not(not(truth))))]]) ).
cnf(refute_0_349,plain,
( big_V(not(truth),implies(not(not(truth)),not(truth))) != implies(not(not(truth)),not(truth))
| big_V(not(truth),implies(not(not(truth)),not(truth))) != not(truth)
| implies(not(not(truth)),not(truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(truth),implies(not(not(truth)),not(truth))),not(truth)) ),[0],$fot(implies(not(not(truth)),not(truth)))]]) ).
cnf(refute_0_350,plain,
( big_V(not(truth),implies(not(not(truth)),not(truth))) != not(truth)
| implies(not(not(truth)),not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(big_V(not(truth),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(not(not(truth)),not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(big_V(not(truth),implies(not(not(truth)),not(truth))),not(truth)) )],[refute_0_347,refute_0_350]) ).
cnf(refute_0_352,plain,
big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),
introduced(tautology,[refl,[$fot(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_353,plain,
( big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != big_V(not(not(not(truth))),implies(not(not(truth)),not(truth)))
| implies(not(not(truth)),not(truth)) != not(truth)
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = big_V(not(not(not(truth))),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),big_V(not(not(not(truth))),implies(not(not(truth)),not(truth)))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_354,plain,
( implies(not(not(truth)),not(truth)) != not(truth)
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = big_V(not(not(not(truth))),not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),big_V(not(not(not(truth))),implies(not(not(truth)),not(truth)))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = big_V(not(not(not(truth))),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),not(truth)) )],[refute_0_351,refute_0_354]) ).
cnf(refute_0_356,plain,
( big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != big_V(not(not(not(truth))),not(truth))
| big_V(not(not(not(truth))),not(truth)) != not(not(not(truth)))
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = not(not(not(truth))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))))),bind(Y0,$fot(big_V(not(not(not(truth))),not(truth)))),bind(Z0,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_357,plain,
( big_V(not(not(not(truth))),not(truth)) != not(not(not(truth)))
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),big_V(not(not(not(truth))),not(truth))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),not(truth)),not(not(not(truth)))) )],[refute_0_334,refute_0_357]) ).
cnf(refute_0_359,plain,
( big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != implies(not(not(truth)),not(truth))
| big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != not(not(not(truth)))
| not(not(not(truth))) = implies(not(not(truth)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) ),[0],$fot(not(not(not(truth))))]]) ).
cnf(refute_0_360,plain,
( big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != implies(not(not(truth)),not(truth))
| not(not(not(truth))) = implies(not(not(truth)),not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),not(not(not(truth)))) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
( implies(not(not(truth)),not(truth)) != not(truth)
| not(not(not(truth))) != implies(not(not(truth)),not(truth))
| not(not(not(truth))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(truth))),implies(not(not(truth)),not(truth))) ),[1],$fot(not(truth))]]) ).
cnf(refute_0_362,plain,
( not(not(not(truth))) != implies(not(not(truth)),not(truth))
| not(not(not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(truth)),not(truth)) )],[refute_0_351,refute_0_361]) ).
cnf(refute_0_363,plain,
( big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))) != implies(not(not(truth)),not(truth))
| not(not(not(truth))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(not(not(truth))),implies(not(not(truth)),not(truth))) )],[refute_0_360,refute_0_362]) ).
cnf(refute_0_364,plain,
not(not(not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(big_V(not(not(not(truth))),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) )],[refute_0_302,refute_0_363]) ).
cnf(refute_0_365,plain,
not(not(not(not(truth)))) = not(not(not(not(truth)))),
introduced(tautology,[refl,[$fot(not(not(not(not(truth)))))]]) ).
cnf(refute_0_366,plain,
( not(not(not(not(truth)))) != not(not(not(not(truth))))
| not(not(not(truth))) != not(truth)
| not(not(not(not(truth)))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(not(truth)))),not(not(not(not(truth))))) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_367,plain,
( not(not(not(truth))) != not(truth)
| not(not(not(not(truth)))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(not(not(not(not(truth)))),not(not(not(not(truth))))) )],[refute_0_365,refute_0_366]) ).
cnf(refute_0_368,plain,
not(not(not(not(truth)))) = not(not(truth)),
inference(resolve,[$cnf( $equal(not(not(not(truth))),not(truth)) )],[refute_0_364,refute_0_367]) ).
cnf(refute_0_369,plain,
implies(not(not(truth)),not(not(not(not(truth))))) = implies(not(not(truth)),not(not(not(not(truth))))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(not(not(truth))))))]]) ).
cnf(refute_0_370,plain,
( implies(not(not(truth)),not(not(not(not(truth))))) != implies(not(not(truth)),not(not(not(not(truth)))))
| not(not(not(not(truth)))) != not(not(truth))
| implies(not(not(truth)),not(not(not(not(truth))))) = implies(not(not(truth)),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(not(not(truth))))),implies(not(not(truth)),not(not(not(not(truth)))))) ),[1,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_371,plain,
( not(not(not(not(truth)))) != not(not(truth))
| implies(not(not(truth)),not(not(not(not(truth))))) = implies(not(not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(not(truth))))),implies(not(not(truth)),not(not(not(not(truth)))))) )],[refute_0_369,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(not(not(truth)),not(not(not(not(truth))))) = implies(not(not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(not(not(not(not(truth)))),not(not(truth))) )],[refute_0_368,refute_0_371]) ).
cnf(refute_0_373,plain,
( implies(not(not(truth)),not(not(not(not(truth))))) != implies(not(not(truth)),not(not(truth)))
| implies(not(not(truth)),not(not(truth))) != truth
| implies(not(not(truth)),not(not(not(not(truth))))) = truth ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(not(truth)),not(not(not(not(truth))))))),bind(Y0,$fot(implies(not(not(truth)),not(not(truth))))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_374,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| implies(not(not(truth)),not(not(not(not(truth))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(not(truth))))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
implies(not(not(truth)),not(not(not(not(truth))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_294,refute_0_374]) ).
cnf(refute_0_376,plain,
not(implies(not(not(truth)),not(not(not(not(truth)))))) = not(implies(not(not(truth)),not(not(not(not(truth)))))),
introduced(tautology,[refl,[$fot(not(implies(not(not(truth)),not(not(not(not(truth)))))))]]) ).
cnf(refute_0_377,plain,
( implies(not(not(truth)),not(not(not(not(truth))))) != truth
| not(implies(not(not(truth)),not(not(not(not(truth)))))) != not(implies(not(not(truth)),not(not(not(not(truth))))))
| not(implies(not(not(truth)),not(not(not(not(truth)))))) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(not(not(truth)),not(not(not(not(truth)))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_378,plain,
( implies(not(not(truth)),not(not(not(not(truth))))) != truth
| not(implies(not(not(truth)),not(not(not(not(truth)))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(not(not(truth)))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
not(implies(not(not(truth)),not(not(not(not(truth)))))) = not(truth),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(not(not(truth))))),truth) )],[refute_0_375,refute_0_378]) ).
cnf(refute_0_380,plain,
implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))),
introduced(tautology,[refl,[$fot(implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))))]]) ).
cnf(refute_0_381,plain,
( implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| not(implies(not(not(truth)),not(not(not(not(truth)))))) != not(truth)
| implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth)))))))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_382,plain,
( not(implies(not(not(truth)),not(not(not(not(truth)))))) != not(truth)
| implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth)))))))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(not(implies(not(not(truth)),not(not(not(not(truth)))))),not(truth)) )],[refute_0_379,refute_0_382]) ).
cnf(refute_0_384,plain,
not(not(not(not(not(truth))))) = not(not(not(not(not(truth))))),
introduced(tautology,[refl,[$fot(not(not(not(not(not(truth))))))]]) ).
cnf(refute_0_385,plain,
( not(not(not(not(not(truth))))) != not(not(not(not(not(truth)))))
| not(not(not(not(truth)))) != not(not(truth))
| not(not(not(not(not(truth))))) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(not(not(not(truth))))),not(not(not(not(not(truth)))))) ),[1,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_386,plain,
( not(not(not(not(truth)))) != not(not(truth))
| not(not(not(not(not(truth))))) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(not(not(not(not(not(truth))))),not(not(not(not(not(truth)))))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
not(not(not(not(not(truth))))) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(not(not(not(not(truth)))),not(not(truth))) )],[refute_0_368,refute_0_386]) ).
cnf(refute_0_388,plain,
( not(not(not(not(not(truth))))) != not(not(not(truth)))
| not(not(not(truth))) != not(truth)
| not(not(not(not(not(truth))))) = not(truth) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(not(not(not(not(not(truth))))))),bind(Y0,$fot(not(not(not(truth))))),bind(Z0,$fot(not(truth)))]]) ).
cnf(refute_0_389,plain,
( not(not(not(truth))) != not(truth)
| not(not(not(not(not(truth))))) = not(truth) ),
inference(resolve,[$cnf( $equal(not(not(not(not(not(truth))))),not(not(not(truth)))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
not(not(not(not(not(truth))))) = not(truth),
inference(resolve,[$cnf( $equal(not(not(not(truth))),not(truth)) )],[refute_0_364,refute_0_389]) ).
cnf(refute_0_391,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),
introduced(tautology,[refl,[$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))))]]) ).
cnf(refute_0_392,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| not(not(not(not(not(truth))))) != not(truth)
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_393,plain,
( not(not(not(not(not(truth))))) != not(truth)
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth)))))))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))),
inference(resolve,[$cnf( $equal(not(not(not(not(not(truth))))),not(truth)) )],[refute_0_390,refute_0_393]) ).
cnf(refute_0_395,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth)))))))
| implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(truth),not(truth))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))))),bind(Y0,$fot(implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_396,plain,
( implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(truth),not(truth))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth)))))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(truth),not(truth))) )],[refute_0_383,refute_0_396]) ).
cnf(refute_0_398,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != truth
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = truth ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_399,plain,
( implies(not(truth),not(truth)) != truth
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),implies(not(truth),not(truth))) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_293,refute_0_399]) ).
cnf(refute_0_401,plain,
implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))))]]) ).
cnf(refute_0_402,plain,
( implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) != implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth)))
| implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) != truth
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_403,plain,
( implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))) != truth
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth)))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),truth) )],[refute_0_400,refute_0_403]) ).
cnf(refute_0_405,plain,
( implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_406,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_96,refute_0_406]) ).
cnf(refute_0_408,plain,
( implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) != not(not(truth))
| implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_409,plain,
( implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),not(not(truth))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(not(not(truth))))),not(implies(not(not(truth)),not(not(not(not(truth))))))),not(not(truth))),truth) )],[refute_0_290,refute_0_409]) ).
cnf(refute_0_411,plain,
( implies(implies(not(not(truth)),not(implies(X,not(truth)))),big_V(X,not(truth))) != truth
| not(not(truth)) != truth
| implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(X,not(truth)))),big_V(X,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_412,plain,
( implies(implies(not(not(truth)),not(implies(X,not(truth)))),big_V(X,not(truth))) != truth
| implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(implies(X,not(truth)))),big_V(X,not(truth))),truth) )],[refute_0_63,refute_0_412]) ).
cnf(refute_0_414,plain,
implies(truth,not(implies(X,not(truth)))) = not(implies(X,not(truth))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(implies(X,not(truth)))))]]) ).
cnf(refute_0_415,plain,
implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))))]]) ).
cnf(refute_0_416,plain,
( implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) != implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth)))
| implies(truth,not(implies(X,not(truth)))) != not(implies(X,not(truth)))
| implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),big_V(X,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth)))) ),[1,0],$fot(not(implies(X,not(truth))))]]) ).
cnf(refute_0_417,plain,
( implies(truth,not(implies(X,not(truth)))) != not(implies(X,not(truth)))
| implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),big_V(X,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth)))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),big_V(X,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(implies(X,not(truth)))),not(implies(X,not(truth)))) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
( implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) != implies(not(implies(X,not(truth))),big_V(X,not(truth)))
| implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) != truth
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),truth) ),[0],$fot(implies(not(implies(X,not(truth))),big_V(X,not(truth))))]]) ).
cnf(refute_0_420,plain,
( implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))) != truth
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),implies(not(implies(X,not(truth))),big_V(X,not(truth)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
implies(not(implies(X,not(truth))),big_V(X,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(implies(X,not(truth)))),big_V(X,not(truth))),truth) )],[refute_0_413,refute_0_420]) ).
cnf(refute_0_422,plain,
big_V(X,not(truth)) = big_V(not(truth),X),
inference(subst,[],[refute_0_44:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_423,plain,
big_V(not(truth),Y) = implies(implies(not(truth),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_424,plain,
big_V(implies(not(truth),X_23),implies(not(X_23),not(not(truth)))) = implies(not(truth),X_23),
inference(subst,[],[refute_0_54:[bind(X_24,$fot(not(truth)))]]) ).
cnf(refute_0_425,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),not(not(truth)))) != implies(not(truth),X_23)
| not(not(truth)) != truth
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = implies(not(truth),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),not(not(truth)))),implies(not(truth),X_23)) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_426,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),not(not(truth)))) != implies(not(truth),X_23)
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = implies(not(truth),X_23) ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_410,refute_0_425]) ).
cnf(refute_0_427,plain,
big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = implies(not(truth),X_23),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),not(not(truth)))),implies(not(truth),X_23)) )],[refute_0_424,refute_0_426]) ).
cnf(refute_0_428,plain,
big_V(implies(not(truth),X_23),truth) = truth,
inference(subst,[],[refute_0_170:[bind(Y,$fot(implies(not(truth),X_23)))]]) ).
cnf(refute_0_429,plain,
implies(not(X_23),truth) = truth,
inference(subst,[],[refute_0_174:[bind(X_13,$fot(not(X_23)))]]) ).
cnf(refute_0_430,plain,
big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = big_V(implies(not(truth),X_23),implies(not(X_23),truth)),
introduced(tautology,[refl,[$fot(big_V(implies(not(truth),X_23),implies(not(X_23),truth)))]]) ).
cnf(refute_0_431,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),truth)) != big_V(implies(not(truth),X_23),implies(not(X_23),truth))
| implies(not(X_23),truth) != truth
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = big_V(implies(not(truth),X_23),truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),big_V(implies(not(truth),X_23),implies(not(X_23),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_432,plain,
( implies(not(X_23),truth) != truth
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = big_V(implies(not(truth),X_23),truth) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),big_V(implies(not(truth),X_23),implies(not(X_23),truth))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = big_V(implies(not(truth),X_23),truth),
inference(resolve,[$cnf( $equal(implies(not(X_23),truth),truth) )],[refute_0_429,refute_0_432]) ).
cnf(refute_0_434,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),truth)) != big_V(implies(not(truth),X_23),truth)
| big_V(implies(not(truth),X_23),truth) != truth
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = truth ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(implies(not(truth),X_23),implies(not(X_23),truth)))),bind(Y0,$fot(big_V(implies(not(truth),X_23),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_435,plain,
( big_V(implies(not(truth),X_23),truth) != truth
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),big_V(implies(not(truth),X_23),truth)) )],[refute_0_433,refute_0_434]) ).
cnf(refute_0_436,plain,
big_V(implies(not(truth),X_23),implies(not(X_23),truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),truth),truth) )],[refute_0_428,refute_0_435]) ).
cnf(refute_0_437,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),truth)) != implies(not(truth),X_23)
| big_V(implies(not(truth),X_23),implies(not(X_23),truth)) != truth
| truth = implies(not(truth),X_23) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),implies(not(truth),X_23)) ),[0],$fot(truth)]]) ).
cnf(refute_0_438,plain,
( big_V(implies(not(truth),X_23),implies(not(X_23),truth)) != implies(not(truth),X_23)
| truth = implies(not(truth),X_23) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),truth) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
truth = implies(not(truth),X_23),
inference(resolve,[$cnf( $equal(big_V(implies(not(truth),X_23),implies(not(X_23),truth)),implies(not(truth),X_23)) )],[refute_0_427,refute_0_438]) ).
cnf(refute_0_440,plain,
truth = implies(not(truth),Y),
inference(subst,[],[refute_0_439:[bind(X_23,$fot(Y))]]) ).
cnf(refute_0_441,plain,
( truth != implies(not(truth),Y)
| implies(not(truth),Y) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(not(truth),Y)))]]) ).
cnf(refute_0_442,plain,
implies(not(truth),Y) = truth,
inference(resolve,[$cnf( $equal(truth,implies(not(truth),Y)) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
( big_V(not(truth),Y) != implies(implies(not(truth),Y),Y)
| implies(not(truth),Y) != truth
| big_V(not(truth),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(truth),Y),implies(implies(not(truth),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_444,plain,
( big_V(not(truth),Y) != implies(implies(not(truth),Y),Y)
| big_V(not(truth),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(not(truth),Y),truth) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
big_V(not(truth),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(not(truth),Y),implies(implies(not(truth),Y),Y)) )],[refute_0_423,refute_0_444]) ).
cnf(refute_0_446,plain,
( big_V(not(truth),Y) != implies(truth,Y)
| implies(truth,Y) != Y
| big_V(not(truth),Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(truth),Y),Y) ),[0],$fot(implies(truth,Y))]]) ).
cnf(refute_0_447,plain,
( big_V(not(truth),Y) != implies(truth,Y)
| big_V(not(truth),Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_154,refute_0_446]) ).
cnf(refute_0_448,plain,
big_V(not(truth),Y) = Y,
inference(resolve,[$cnf( $equal(big_V(not(truth),Y),implies(truth,Y)) )],[refute_0_445,refute_0_447]) ).
cnf(refute_0_449,plain,
big_V(not(truth),X) = X,
inference(subst,[],[refute_0_448:[bind(Y,$fot(X))]]) ).
cnf(refute_0_450,plain,
( big_V(X,not(truth)) != big_V(not(truth),X)
| big_V(not(truth),X) != X
| big_V(X,not(truth)) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,not(truth)),X) ),[0],$fot(big_V(not(truth),X))]]) ).
cnf(refute_0_451,plain,
( big_V(X,not(truth)) != big_V(not(truth),X)
| big_V(X,not(truth)) = X ),
inference(resolve,[$cnf( $equal(big_V(not(truth),X),X) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
big_V(X,not(truth)) = X,
inference(resolve,[$cnf( $equal(big_V(X,not(truth)),big_V(not(truth),X)) )],[refute_0_422,refute_0_451]) ).
cnf(refute_0_453,plain,
implies(not(implies(X,not(truth))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),big_V(X,not(truth))),
introduced(tautology,[refl,[$fot(implies(not(implies(X,not(truth))),big_V(X,not(truth))))]]) ).
cnf(refute_0_454,plain,
( big_V(X,not(truth)) != X
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) != implies(not(implies(X,not(truth))),big_V(X,not(truth)))
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X,not(truth))),big_V(X,not(truth))),implies(not(implies(X,not(truth))),big_V(X,not(truth)))) ),[1,1],$fot(X)]]) ).
cnf(refute_0_455,plain,
( big_V(X,not(truth)) != X
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),X) ),
inference(resolve,[$cnf( $equal(implies(not(implies(X,not(truth))),big_V(X,not(truth))),implies(not(implies(X,not(truth))),big_V(X,not(truth)))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
implies(not(implies(X,not(truth))),big_V(X,not(truth))) = implies(not(implies(X,not(truth))),X),
inference(resolve,[$cnf( $equal(big_V(X,not(truth)),X) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
( implies(not(implies(X,not(truth))),big_V(X,not(truth))) != implies(not(implies(X,not(truth))),X)
| implies(not(implies(X,not(truth))),big_V(X,not(truth))) != truth
| implies(not(implies(X,not(truth))),X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(implies(X,not(truth))),big_V(X,not(truth))),truth) ),[0],$fot(implies(not(implies(X,not(truth))),X))]]) ).
cnf(refute_0_458,plain,
( implies(not(implies(X,not(truth))),big_V(X,not(truth))) != truth
| implies(not(implies(X,not(truth))),X) = truth ),
inference(resolve,[$cnf( $equal(implies(not(implies(X,not(truth))),big_V(X,not(truth))),implies(not(implies(X,not(truth))),X)) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(not(implies(X,not(truth))),X) = truth,
inference(resolve,[$cnf( $equal(implies(not(implies(X,not(truth))),big_V(X,not(truth))),truth) )],[refute_0_421,refute_0_458]) ).
cnf(refute_0_460,plain,
implies(not(implies(not(X_24),not(truth))),not(X_24)) = truth,
inference(subst,[],[refute_0_459:[bind(X,$fot(not(X_24)))]]) ).
cnf(refute_0_461,plain,
( big_V(implies(X_24,implies(not(X_24),not(truth))),implies(not(implies(not(X_24),not(truth))),not(X_24))) != implies(X_24,implies(not(X_24),not(truth)))
| implies(not(implies(not(X_24),not(truth))),not(X_24)) != truth
| big_V(implies(X_24,implies(not(X_24),not(truth))),truth) = implies(X_24,implies(not(X_24),not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_24,implies(not(X_24),not(truth))),implies(not(implies(not(X_24),not(truth))),not(X_24))),implies(X_24,implies(not(X_24),not(truth)))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_462,plain,
( big_V(implies(X_24,implies(not(X_24),not(truth))),implies(not(implies(not(X_24),not(truth))),not(X_24))) != implies(X_24,implies(not(X_24),not(truth)))
| big_V(implies(X_24,implies(not(X_24),not(truth))),truth) = implies(X_24,implies(not(X_24),not(truth))) ),
inference(resolve,[$cnf( $equal(implies(not(implies(not(X_24),not(truth))),not(X_24)),truth) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
big_V(implies(X_24,implies(not(X_24),not(truth))),truth) = implies(X_24,implies(not(X_24),not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,implies(not(X_24),not(truth))),implies(not(implies(not(X_24),not(truth))),not(X_24))),implies(X_24,implies(not(X_24),not(truth)))) )],[refute_0_55,refute_0_462]) ).
cnf(refute_0_464,plain,
big_V(implies(X_24,implies(not(X_24),not(truth))),truth) = truth,
inference(subst,[],[refute_0_170:[bind(Y,$fot(implies(X_24,implies(not(X_24),not(truth)))))]]) ).
cnf(refute_0_465,plain,
( big_V(implies(X_24,implies(not(X_24),not(truth))),truth) != implies(X_24,implies(not(X_24),not(truth)))
| big_V(implies(X_24,implies(not(X_24),not(truth))),truth) != truth
| truth = implies(X_24,implies(not(X_24),not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_24,implies(not(X_24),not(truth))),truth),implies(X_24,implies(not(X_24),not(truth)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_466,plain,
( big_V(implies(X_24,implies(not(X_24),not(truth))),truth) != implies(X_24,implies(not(X_24),not(truth)))
| truth = implies(X_24,implies(not(X_24),not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,implies(not(X_24),not(truth))),truth),truth) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
truth = implies(X_24,implies(not(X_24),not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,implies(not(X_24),not(truth))),truth),implies(X_24,implies(not(X_24),not(truth)))) )],[refute_0_463,refute_0_466]) ).
cnf(refute_0_468,plain,
truth = implies(X,implies(not(X),not(truth))),
inference(subst,[],[refute_0_467:[bind(X_24,$fot(X))]]) ).
cnf(refute_0_469,plain,
( truth != implies(X,implies(not(X),not(truth)))
| implies(X,implies(not(X),not(truth))) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X,implies(not(X),not(truth)))))]]) ).
cnf(refute_0_470,plain,
implies(X,implies(not(X),not(truth))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X,implies(not(X),not(truth)))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
( big_V(X,implies(not(X),not(truth))) != implies(implies(X,implies(not(X),not(truth))),implies(not(X),not(truth)))
| implies(X,implies(not(X),not(truth))) != truth
| big_V(X,implies(not(X),not(truth))) = implies(truth,implies(not(X),not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(not(X),not(truth))),implies(implies(X,implies(not(X),not(truth))),implies(not(X),not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_472,plain,
( big_V(X,implies(not(X),not(truth))) != implies(implies(X,implies(not(X),not(truth))),implies(not(X),not(truth)))
| big_V(X,implies(not(X),not(truth))) = implies(truth,implies(not(X),not(truth))) ),
inference(resolve,[$cnf( $equal(implies(X,implies(not(X),not(truth))),truth) )],[refute_0_470,refute_0_471]) ).
cnf(refute_0_473,plain,
big_V(X,implies(not(X),not(truth))) = implies(truth,implies(not(X),not(truth))),
inference(resolve,[$cnf( $equal(big_V(X,implies(not(X),not(truth))),implies(implies(X,implies(not(X),not(truth))),implies(not(X),not(truth)))) )],[refute_0_30,refute_0_472]) ).
cnf(refute_0_474,plain,
big_V(X,implies(not(X),not(truth))) = X,
inference(subst,[],[refute_0_346:[bind(Y,$fot(X))]]) ).
cnf(refute_0_475,plain,
( big_V(X,implies(not(X),not(truth))) != X
| big_V(X,implies(not(X),not(truth))) != implies(truth,implies(not(X),not(truth)))
| X = implies(truth,implies(not(X),not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(not(X),not(truth))),implies(truth,implies(not(X),not(truth)))) ),[0],$fot(X)]]) ).
cnf(refute_0_476,plain,
( big_V(X,implies(not(X),not(truth))) != implies(truth,implies(not(X),not(truth)))
| X = implies(truth,implies(not(X),not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(X,implies(not(X),not(truth))),X) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
implies(truth,implies(not(X),not(truth))) = implies(not(X),not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X),not(truth))))]]) ).
cnf(refute_0_478,plain,
( X != implies(truth,implies(not(X),not(truth)))
| implies(truth,implies(not(X),not(truth))) != implies(not(X),not(truth))
| X = implies(not(X),not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,implies(not(X),not(truth))) ),[0],$fot(implies(truth,implies(not(X),not(truth))))]]) ).
cnf(refute_0_479,plain,
( X != implies(truth,implies(not(X),not(truth)))
| X = implies(not(X),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X),not(truth))),implies(not(X),not(truth))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
( big_V(X,implies(not(X),not(truth))) != implies(truth,implies(not(X),not(truth)))
| X = implies(not(X),not(truth)) ),
inference(resolve,[$cnf( $equal(X,implies(truth,implies(not(X),not(truth)))) )],[refute_0_476,refute_0_479]) ).
cnf(refute_0_481,plain,
X = implies(not(X),not(truth)),
inference(resolve,[$cnf( $equal(big_V(X,implies(not(X),not(truth))),implies(truth,implies(not(X),not(truth)))) )],[refute_0_473,refute_0_480]) ).
cnf(refute_0_482,plain,
X_84 = implies(not(X_84),not(truth)),
inference(subst,[],[refute_0_481:[bind(X,$fot(X_84))]]) ).
cnf(refute_0_483,plain,
( X_84 != implies(not(X_84),not(truth))
| implies(not(X_84),not(truth)) = X_84 ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X_84)),bind(Y0,$fot(implies(not(X_84),not(truth))))]]) ).
cnf(refute_0_484,plain,
implies(not(X_84),not(truth)) = X_84,
inference(resolve,[$cnf( $equal(X_84,implies(not(X_84),not(truth))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
( big_V(not(X_84),not(truth)) != implies(implies(not(X_84),not(truth)),not(truth))
| implies(not(X_84),not(truth)) != X_84
| big_V(not(X_84),not(truth)) = implies(X_84,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_84),not(truth)),implies(implies(not(X_84),not(truth)),not(truth))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_486,plain,
( big_V(not(X_84),not(truth)) != implies(implies(not(X_84),not(truth)),not(truth))
| big_V(not(X_84),not(truth)) = implies(X_84,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(X_84),not(truth)),X_84) )],[refute_0_484,refute_0_485]) ).
cnf(refute_0_487,plain,
big_V(not(X_84),not(truth)) = implies(X_84,not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(X_84),not(truth)),implies(implies(not(X_84),not(truth)),not(truth))) )],[refute_0_29,refute_0_486]) ).
cnf(refute_0_488,plain,
big_V(not(X_84),not(truth)) = not(X_84),
inference(subst,[],[refute_0_452:[bind(X,$fot(not(X_84)))]]) ).
cnf(refute_0_489,plain,
( big_V(not(X_84),not(truth)) != implies(X_84,not(truth))
| big_V(not(X_84),not(truth)) != not(X_84)
| not(X_84) = implies(X_84,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_84),not(truth)),implies(X_84,not(truth))) ),[0],$fot(not(X_84))]]) ).
cnf(refute_0_490,plain,
( big_V(not(X_84),not(truth)) != implies(X_84,not(truth))
| not(X_84) = implies(X_84,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(not(X_84),not(truth)),not(X_84)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
not(X_84) = implies(X_84,not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(X_84),not(truth)),implies(X_84,not(truth))) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
not(X_294) = implies(X_294,not(truth)),
inference(subst,[],[refute_0_491:[bind(X_84,$fot(X_294))]]) ).
cnf(refute_0_493,plain,
( not(X_294) != implies(X_294,not(truth))
| implies(X_294,not(truth)) = not(X_294) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_294))),bind(Y0,$fot(implies(X_294,not(truth))))]]) ).
cnf(refute_0_494,plain,
implies(X_294,not(truth)) = not(X_294),
inference(resolve,[$cnf( $equal(not(X_294),implies(X_294,not(truth))) )],[refute_0_492,refute_0_493]) ).
cnf(refute_0_495,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(X_294,not(truth)) != not(X_294)
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) ),[0,1,1],$fot(not(X_294))]]) ).
cnf(refute_0_496,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(X_294,not(truth)),not(X_294)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) )],[refute_0_28,refute_0_496]) ).
cnf(refute_0_498,plain,
big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))) = implies(X_294,X_295),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(X_295)),bind(X_24,$fot(X_294))]]) ).
cnf(refute_0_499,plain,
( not(X_84) != implies(X_84,not(truth))
| implies(X_84,not(truth)) = not(X_84) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_84))),bind(Y0,$fot(implies(X_84,not(truth))))]]) ).
cnf(refute_0_500,plain,
implies(X_84,not(truth)) = not(X_84),
inference(resolve,[$cnf( $equal(not(X_84),implies(X_84,not(truth))) )],[refute_0_491,refute_0_499]) ).
cnf(refute_0_501,plain,
implies(X_295,not(truth)) = not(X_295),
inference(subst,[],[refute_0_500:[bind(X_84,$fot(X_295))]]) ).
cnf(refute_0_502,plain,
implies(implies(X_295,not(truth)),not(X_294)) = implies(implies(X_295,not(truth)),not(X_294)),
introduced(tautology,[refl,[$fot(implies(implies(X_295,not(truth)),not(X_294)))]]) ).
cnf(refute_0_503,plain,
( implies(X_295,not(truth)) != not(X_295)
| implies(implies(X_295,not(truth)),not(X_294)) != implies(implies(X_295,not(truth)),not(X_294))
| implies(implies(X_295,not(truth)),not(X_294)) = implies(not(X_295),not(X_294)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_295,not(truth)),not(X_294)),implies(implies(X_295,not(truth)),not(X_294))) ),[1,0],$fot(not(X_295))]]) ).
cnf(refute_0_504,plain,
( implies(X_295,not(truth)) != not(X_295)
| implies(implies(X_295,not(truth)),not(X_294)) = implies(not(X_295),not(X_294)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_295,not(truth)),not(X_294)),implies(implies(X_295,not(truth)),not(X_294))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
implies(implies(X_295,not(truth)),not(X_294)) = implies(not(X_295),not(X_294)),
inference(resolve,[$cnf( $equal(implies(X_295,not(truth)),not(X_295)) )],[refute_0_501,refute_0_504]) ).
cnf(refute_0_506,plain,
big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),
introduced(tautology,[refl,[$fot(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))))]]) ).
cnf(refute_0_507,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294)))
| implies(implies(X_295,not(truth)),not(X_294)) != implies(not(X_295),not(X_294))
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294)))) ),[1,1],$fot(implies(not(X_295),not(X_294)))]]) ).
cnf(refute_0_508,plain,
( implies(implies(X_295,not(truth)),not(X_294)) != implies(not(X_295),not(X_294))
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294)))) )],[refute_0_506,refute_0_507]) ).
cnf(refute_0_509,plain,
big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))),
inference(resolve,[$cnf( $equal(implies(implies(X_295,not(truth)),not(X_294)),implies(not(X_295),not(X_294))) )],[refute_0_505,refute_0_508]) ).
cnf(refute_0_510,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != big_V(implies(X_294,X_295),implies(not(X_295),not(X_294)))
| big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))) != implies(X_294,X_295)
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(X_294,X_295) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))))),bind(Y0,$fot(big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))))),bind(Z0,$fot(implies(X_294,X_295)))]]) ).
cnf(refute_0_511,plain,
( big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))) != implies(X_294,X_295)
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(X_294,X_295) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),big_V(implies(X_294,X_295),implies(not(X_295),not(X_294)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) = implies(X_294,X_295),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(not(X_295),not(X_294))),implies(X_294,X_295)) )],[refute_0_498,refute_0_511]) ).
cnf(refute_0_513,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != implies(X_294,X_295)
| big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(X_294,X_295) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) ),[0],$fot(implies(X_294,X_295))]]) ).
cnf(refute_0_514,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(X_294,X_295) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),implies(X_294,X_295)) )],[refute_0_512,refute_0_513]) ).
cnf(refute_0_515,plain,
implies(not(X_295),implies(X_294,not(truth))) = implies(not(X_295),implies(X_294,not(truth))),
introduced(tautology,[refl,[$fot(implies(not(X_295),implies(X_294,not(truth))))]]) ).
cnf(refute_0_516,plain,
( implies(X_294,not(truth)) != not(X_294)
| implies(not(X_295),implies(X_294,not(truth))) != implies(not(X_295),implies(X_294,not(truth)))
| implies(not(X_295),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_295),implies(X_294,not(truth))),implies(not(X_295),implies(X_294,not(truth)))) ),[1,1],$fot(not(X_294))]]) ).
cnf(refute_0_517,plain,
( implies(X_294,not(truth)) != not(X_294)
| implies(not(X_295),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)) ),
inference(resolve,[$cnf( $equal(implies(not(X_295),implies(X_294,not(truth))),implies(not(X_295),implies(X_294,not(truth)))) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
implies(not(X_295),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)),
inference(resolve,[$cnf( $equal(implies(X_294,not(truth)),not(X_294)) )],[refute_0_494,refute_0_517]) ).
cnf(refute_0_519,plain,
implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(implies(X_295,not(truth)),implies(X_294,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(X_295,not(truth)),implies(X_294,not(truth))))]]) ).
cnf(refute_0_520,plain,
( implies(X_295,not(truth)) != not(X_295)
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),implies(X_294,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_295,not(truth)),implies(X_294,not(truth))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) ),[1,0],$fot(not(X_295))]]) ).
cnf(refute_0_521,plain,
( implies(X_295,not(truth)) != not(X_295)
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),implies(X_294,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_295,not(truth)),implies(X_294,not(truth))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),implies(X_294,not(truth))),
inference(resolve,[$cnf( $equal(implies(X_295,not(truth)),not(X_295)) )],[refute_0_501,refute_0_521]) ).
cnf(refute_0_523,plain,
( implies(implies(X_295,not(truth)),implies(X_294,not(truth))) != implies(not(X_295),implies(X_294,not(truth)))
| implies(not(X_295),implies(X_294,not(truth))) != implies(not(X_295),not(X_294))
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(X_295,not(truth)),implies(X_294,not(truth))))),bind(Y0,$fot(implies(not(X_295),implies(X_294,not(truth))))),bind(Z0,$fot(implies(not(X_295),not(X_294))))]]) ).
cnf(refute_0_524,plain,
( implies(not(X_295),implies(X_294,not(truth))) != implies(not(X_295),not(X_294))
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_295,not(truth)),implies(X_294,not(truth))),implies(not(X_295),implies(X_294,not(truth)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
implies(implies(X_295,not(truth)),implies(X_294,not(truth))) = implies(not(X_295),not(X_294)),
inference(resolve,[$cnf( $equal(implies(not(X_295),implies(X_294,not(truth))),implies(not(X_295),not(X_294))) )],[refute_0_518,refute_0_524]) ).
cnf(refute_0_526,plain,
( implies(X_294,X_295) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(implies(X_295,not(truth)),implies(X_294,not(truth))) != implies(not(X_295),not(X_294))
| implies(X_294,X_295) = implies(not(X_295),not(X_294)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_294,X_295),implies(not(X_295),not(X_294))) ),[0],$fot(implies(implies(X_295,not(truth)),implies(X_294,not(truth))))]]) ).
cnf(refute_0_527,plain,
( implies(X_294,X_295) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(X_294,X_295) = implies(not(X_295),not(X_294)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_295,not(truth)),implies(X_294,not(truth))),implies(not(X_295),not(X_294))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
( big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))) != implies(implies(X_295,not(truth)),implies(X_294,not(truth)))
| implies(X_294,X_295) = implies(not(X_295),not(X_294)) ),
inference(resolve,[$cnf( $equal(implies(X_294,X_295),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) )],[refute_0_514,refute_0_527]) ).
cnf(refute_0_529,plain,
implies(X_294,X_295) = implies(not(X_295),not(X_294)),
inference(resolve,[$cnf( $equal(big_V(implies(X_294,X_295),implies(implies(X_295,not(truth)),not(X_294))),implies(implies(X_295,not(truth)),implies(X_294,not(truth)))) )],[refute_0_497,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(X_297,X_298) = implies(not(X_298),not(X_297)),
inference(subst,[],[refute_0_529:[bind(X_294,$fot(X_297)),bind(X_295,$fot(X_298))]]) ).
cnf(refute_0_531,plain,
( implies(X_297,X_298) != implies(not(X_298),not(X_297))
| implies(not(X_298),not(X_297)) = implies(X_297,X_298) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_297,X_298))),bind(Y0,$fot(implies(not(X_298),not(X_297))))]]) ).
cnf(refute_0_532,plain,
implies(not(X_298),not(X_297)) = implies(X_297,X_298),
inference(resolve,[$cnf( $equal(implies(X_297,X_298),implies(not(X_298),not(X_297))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
( big_V(not(X_298),not(X_297)) != implies(implies(not(X_298),not(X_297)),not(X_297))
| implies(not(X_298),not(X_297)) != implies(X_297,X_298)
| big_V(not(X_298),not(X_297)) = implies(implies(X_297,X_298),not(X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_298),not(X_297)),implies(implies(not(X_298),not(X_297)),not(X_297))) ),[1,0],$fot(implies(X_297,X_298))]]) ).
cnf(refute_0_534,plain,
( big_V(not(X_298),not(X_297)) != implies(implies(not(X_298),not(X_297)),not(X_297))
| big_V(not(X_298),not(X_297)) = implies(implies(X_297,X_298),not(X_297)) ),
inference(resolve,[$cnf( $equal(implies(not(X_298),not(X_297)),implies(X_297,X_298)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
big_V(not(X_298),not(X_297)) = implies(implies(X_297,X_298),not(X_297)),
inference(resolve,[$cnf( $equal(big_V(not(X_298),not(X_297)),implies(implies(not(X_298),not(X_297)),not(X_297))) )],[refute_0_18,refute_0_534]) ).
cnf(refute_0_536,plain,
big_V(not(X),not(Y)) = implies(not(big_V(not(X),not(Y))),not(truth)),
inference(subst,[],[refute_0_481:[bind(X,$fot(big_V(not(X),not(Y))))]]) ).
cnf(refute_0_537,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_11:[bind(X0,$fot(big_hat(X,Y))),bind(Y0,$fot(not(big_V(not(X),not(Y)))))]]) ).
cnf(refute_0_538,plain,
not(big_V(not(X),not(Y))) = big_hat(X,Y),
inference(resolve,[$cnf( $equal(big_hat(X,Y),not(big_V(not(X),not(Y)))) )],[big_hat_definition,refute_0_537]) ).
cnf(refute_0_539,plain,
( big_V(not(X),not(Y)) != implies(not(big_V(not(X),not(Y))),not(truth))
| not(big_V(not(X),not(Y))) != big_hat(X,Y)
| big_V(not(X),not(Y)) = implies(big_hat(X,Y),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X),not(Y)),implies(not(big_V(not(X),not(Y))),not(truth))) ),[1,0],$fot(big_hat(X,Y))]]) ).
cnf(refute_0_540,plain,
( big_V(not(X),not(Y)) != implies(not(big_V(not(X),not(Y))),not(truth))
| big_V(not(X),not(Y)) = implies(big_hat(X,Y),not(truth)) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X),not(Y))),big_hat(X,Y)) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
big_V(not(X),not(Y)) = implies(big_hat(X,Y),not(truth)),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),implies(not(big_V(not(X),not(Y))),not(truth))) )],[refute_0_536,refute_0_540]) ).
cnf(refute_0_542,plain,
implies(big_hat(X,Y),not(truth)) = not(big_hat(X,Y)),
inference(subst,[],[refute_0_500:[bind(X_84,$fot(big_hat(X,Y)))]]) ).
cnf(refute_0_543,plain,
( big_V(not(X),not(Y)) != implies(big_hat(X,Y),not(truth))
| implies(big_hat(X,Y),not(truth)) != not(big_hat(X,Y))
| big_V(not(X),not(Y)) = not(big_hat(X,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) ),[0],$fot(implies(big_hat(X,Y),not(truth)))]]) ).
cnf(refute_0_544,plain,
( big_V(not(X),not(Y)) != implies(big_hat(X,Y),not(truth))
| big_V(not(X),not(Y)) = not(big_hat(X,Y)) ),
inference(resolve,[$cnf( $equal(implies(big_hat(X,Y),not(truth)),not(big_hat(X,Y))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
big_V(not(X),not(Y)) = not(big_hat(X,Y)),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),implies(big_hat(X,Y),not(truth))) )],[refute_0_541,refute_0_544]) ).
cnf(refute_0_546,plain,
big_V(not(X_298),not(X_297)) = not(big_hat(X_298,X_297)),
inference(subst,[],[refute_0_545:[bind(X,$fot(X_298)),bind(Y,$fot(X_297))]]) ).
cnf(refute_0_547,plain,
( big_V(not(X_298),not(X_297)) != implies(implies(X_297,X_298),not(X_297))
| big_V(not(X_298),not(X_297)) != not(big_hat(X_298,X_297))
| not(big_hat(X_298,X_297)) = implies(implies(X_297,X_298),not(X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_298),not(X_297)),implies(implies(X_297,X_298),not(X_297))) ),[0],$fot(not(big_hat(X_298,X_297)))]]) ).
cnf(refute_0_548,plain,
( big_V(not(X_298),not(X_297)) != implies(implies(X_297,X_298),not(X_297))
| not(big_hat(X_298,X_297)) = implies(implies(X_297,X_298),not(X_297)) ),
inference(resolve,[$cnf( $equal(big_V(not(X_298),not(X_297)),not(big_hat(X_298,X_297))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
not(big_hat(X_298,X_297)) = implies(implies(X_297,X_298),not(X_297)),
inference(resolve,[$cnf( $equal(big_V(not(X_298),not(X_297)),implies(implies(X_297,X_298),not(X_297))) )],[refute_0_535,refute_0_548]) ).
cnf(refute_0_550,plain,
implies(X_297,not(X_84)) = implies(not(not(X_84)),not(X_297)),
inference(subst,[],[refute_0_529:[bind(X_294,$fot(X_297)),bind(X_295,$fot(not(X_84)))]]) ).
cnf(refute_0_551,plain,
big_V(implies(X_24,not(truth)),implies(not(not(truth)),not(X_24))) = implies(X_24,not(truth)),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(not(truth)))]]) ).
cnf(refute_0_552,plain,
( big_V(implies(X_24,not(truth)),implies(not(not(truth)),not(X_24))) != implies(X_24,not(truth))
| not(not(truth)) != truth
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = implies(X_24,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(not(not(truth)),not(X_24))),implies(X_24,not(truth))) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_553,plain,
( big_V(implies(X_24,not(truth)),implies(not(not(truth)),not(X_24))) != implies(X_24,not(truth))
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = implies(X_24,not(truth)) ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_410,refute_0_552]) ).
cnf(refute_0_554,plain,
big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = implies(X_24,not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(not(not(truth)),not(X_24))),implies(X_24,not(truth))) )],[refute_0_551,refute_0_553]) ).
cnf(refute_0_555,plain,
big_V(implies(X_24,not(truth)),not(X_24)) = big_V(not(X_24),implies(X_24,not(truth))),
inference(subst,[],[refute_0_46:[bind(X,$fot(not(X_24))),bind(Y,$fot(implies(X_24,not(truth))))]]) ).
cnf(refute_0_556,plain,
implies(truth,not(X_24)) = not(X_24),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_24)))]]) ).
cnf(refute_0_557,plain,
big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),
introduced(tautology,[refl,[$fot(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))))]]) ).
cnf(refute_0_558,plain,
( big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) != big_V(implies(X_24,not(truth)),implies(truth,not(X_24)))
| implies(truth,not(X_24)) != not(X_24)
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(implies(X_24,not(truth)),not(X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),big_V(implies(X_24,not(truth)),implies(truth,not(X_24)))) ),[1,1],$fot(not(X_24))]]) ).
cnf(refute_0_559,plain,
( implies(truth,not(X_24)) != not(X_24)
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(implies(X_24,not(truth)),not(X_24)) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),big_V(implies(X_24,not(truth)),implies(truth,not(X_24)))) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(implies(X_24,not(truth)),not(X_24)),
inference(resolve,[$cnf( $equal(implies(truth,not(X_24)),not(X_24)) )],[refute_0_556,refute_0_559]) ).
cnf(refute_0_561,plain,
( big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) != big_V(implies(X_24,not(truth)),not(X_24))
| big_V(implies(X_24,not(truth)),not(X_24)) != big_V(not(X_24),implies(X_24,not(truth)))
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(not(X_24),implies(X_24,not(truth))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))))),bind(Y0,$fot(big_V(implies(X_24,not(truth)),not(X_24)))),bind(Z0,$fot(big_V(not(X_24),implies(X_24,not(truth)))))]]) ).
cnf(refute_0_562,plain,
( big_V(implies(X_24,not(truth)),not(X_24)) != big_V(not(X_24),implies(X_24,not(truth)))
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(not(X_24),implies(X_24,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),big_V(implies(X_24,not(truth)),not(X_24))) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) = big_V(not(X_24),implies(X_24,not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),not(X_24)),big_V(not(X_24),implies(X_24,not(truth)))) )],[refute_0_555,refute_0_562]) ).
cnf(refute_0_564,plain,
( big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) != big_V(not(X_24),implies(X_24,not(truth)))
| big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) != implies(X_24,not(truth))
| big_V(not(X_24),implies(X_24,not(truth))) = implies(X_24,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),implies(X_24,not(truth))) ),[0],$fot(big_V(not(X_24),implies(X_24,not(truth))))]]) ).
cnf(refute_0_565,plain,
( big_V(implies(X_24,not(truth)),implies(truth,not(X_24))) != implies(X_24,not(truth))
| big_V(not(X_24),implies(X_24,not(truth))) = implies(X_24,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),big_V(not(X_24),implies(X_24,not(truth)))) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
big_V(not(X_24),implies(X_24,not(truth))) = implies(X_24,not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(X_24,not(truth)),implies(truth,not(X_24))),implies(X_24,not(truth))) )],[refute_0_554,refute_0_565]) ).
cnf(refute_0_567,plain,
big_V(not(not(X_84)),implies(not(X_84),not(truth))) = implies(not(X_84),not(truth)),
inference(subst,[],[refute_0_566:[bind(X_24,$fot(not(X_84)))]]) ).
cnf(refute_0_568,plain,
( big_V(not(not(X_84)),implies(not(X_84),not(truth))) != implies(not(X_84),not(truth))
| implies(not(X_84),not(truth)) != X_84
| big_V(not(not(X_84)),implies(not(X_84),not(truth))) = X_84 ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),X_84) ),[0],$fot(implies(not(X_84),not(truth)))]]) ).
cnf(refute_0_569,plain,
( big_V(not(not(X_84)),implies(not(X_84),not(truth))) != implies(not(X_84),not(truth))
| big_V(not(not(X_84)),implies(not(X_84),not(truth))) = X_84 ),
inference(resolve,[$cnf( $equal(implies(not(X_84),not(truth)),X_84) )],[refute_0_484,refute_0_568]) ).
cnf(refute_0_570,plain,
big_V(not(not(X_84)),implies(not(X_84),not(truth))) = X_84,
inference(resolve,[$cnf( $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),implies(not(X_84),not(truth))) )],[refute_0_567,refute_0_569]) ).
cnf(refute_0_571,plain,
implies(not(X_84),not(truth)) = not(not(X_84)),
inference(subst,[],[refute_0_500:[bind(X_84,$fot(not(X_84)))]]) ).
cnf(refute_0_572,plain,
( big_V(not(not(X_84)),implies(not(X_84),not(truth))) != implies(not(X_84),not(truth))
| implies(not(X_84),not(truth)) != not(not(X_84))
| big_V(not(not(X_84)),implies(not(X_84),not(truth))) = not(not(X_84)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(not(not(X_84)),implies(not(X_84),not(truth))))),bind(Y0,$fot(implies(not(X_84),not(truth)))),bind(Z0,$fot(not(not(X_84))))]]) ).
cnf(refute_0_573,plain,
( implies(not(X_84),not(truth)) != not(not(X_84))
| big_V(not(not(X_84)),implies(not(X_84),not(truth))) = not(not(X_84)) ),
inference(resolve,[$cnf( $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),implies(not(X_84),not(truth))) )],[refute_0_567,refute_0_572]) ).
cnf(refute_0_574,plain,
big_V(not(not(X_84)),implies(not(X_84),not(truth))) = not(not(X_84)),
inference(resolve,[$cnf( $equal(implies(not(X_84),not(truth)),not(not(X_84))) )],[refute_0_571,refute_0_573]) ).
cnf(refute_0_575,plain,
( big_V(not(not(X_84)),implies(not(X_84),not(truth))) != X_84
| big_V(not(not(X_84)),implies(not(X_84),not(truth))) != not(not(X_84))
| not(not(X_84)) = X_84 ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),X_84) ),[0],$fot(not(not(X_84)))]]) ).
cnf(refute_0_576,plain,
( big_V(not(not(X_84)),implies(not(X_84),not(truth))) != X_84
| not(not(X_84)) = X_84 ),
inference(resolve,[$cnf( $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),not(not(X_84))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
not(not(X_84)) = X_84,
inference(resolve,[$cnf( $equal(big_V(not(not(X_84)),implies(not(X_84),not(truth))),X_84) )],[refute_0_570,refute_0_576]) ).
cnf(refute_0_578,plain,
( implies(X_297,not(X_84)) != implies(not(not(X_84)),not(X_297))
| not(not(X_84)) != X_84
| implies(X_297,not(X_84)) = implies(X_84,not(X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_297,not(X_84)),implies(not(not(X_84)),not(X_297))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_579,plain,
( implies(X_297,not(X_84)) != implies(not(not(X_84)),not(X_297))
| implies(X_297,not(X_84)) = implies(X_84,not(X_297)) ),
inference(resolve,[$cnf( $equal(not(not(X_84)),X_84) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
implies(X_297,not(X_84)) = implies(X_84,not(X_297)),
inference(resolve,[$cnf( $equal(implies(X_297,not(X_84)),implies(not(not(X_84)),not(X_297))) )],[refute_0_550,refute_0_579]) ).
cnf(refute_0_581,plain,
( implies(X_297,not(X_84)) != implies(X_84,not(X_297))
| implies(X_84,not(X_297)) = implies(X_297,not(X_84)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_297,not(X_84)))),bind(Y0,$fot(implies(X_84,not(X_297))))]]) ).
cnf(refute_0_582,plain,
implies(X_84,not(X_297)) = implies(X_297,not(X_84)),
inference(resolve,[$cnf( $equal(implies(X_297,not(X_84)),implies(X_84,not(X_297))) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
implies(implies(X_297,X_298),not(X_297)) = implies(X_297,not(implies(X_297,X_298))),
inference(subst,[],[refute_0_582:[bind(X_84,$fot(implies(X_297,X_298)))]]) ).
cnf(refute_0_584,plain,
( implies(implies(X_297,X_298),not(X_297)) != implies(X_297,not(implies(X_297,X_298)))
| not(big_hat(X_298,X_297)) != implies(implies(X_297,X_298),not(X_297))
| not(big_hat(X_298,X_297)) = implies(X_297,not(implies(X_297,X_298))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(X_298,X_297)),implies(implies(X_297,X_298),not(X_297))) ),[1],$fot(implies(X_297,not(implies(X_297,X_298))))]]) ).
cnf(refute_0_585,plain,
( not(big_hat(X_298,X_297)) != implies(implies(X_297,X_298),not(X_297))
| not(big_hat(X_298,X_297)) = implies(X_297,not(implies(X_297,X_298))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_297,X_298),not(X_297)),implies(X_297,not(implies(X_297,X_298)))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
not(big_hat(X_298,X_297)) = implies(X_297,not(implies(X_297,X_298))),
inference(resolve,[$cnf( $equal(not(big_hat(X_298,X_297)),implies(implies(X_297,X_298),not(X_297))) )],[refute_0_549,refute_0_585]) ).
cnf(refute_0_587,plain,
not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,not(implies(X_297,not(implies(X_297,X_351))))),
inference(subst,[],[refute_0_586:[bind(X_298,$fot(not(implies(X_297,X_351))))]]) ).
cnf(refute_0_588,plain,
not(big_hat(X_351,X_297)) = implies(X_297,not(implies(X_297,X_351))),
inference(subst,[],[refute_0_586:[bind(X_298,$fot(X_351))]]) ).
cnf(refute_0_589,plain,
( not(big_hat(X_351,X_297)) != implies(X_297,not(implies(X_297,X_351)))
| implies(X_297,not(implies(X_297,X_351))) = not(big_hat(X_351,X_297)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_351,X_297)))),bind(Y0,$fot(implies(X_297,not(implies(X_297,X_351)))))]]) ).
cnf(refute_0_590,plain,
implies(X_297,not(implies(X_297,X_351))) = not(big_hat(X_351,X_297)),
inference(resolve,[$cnf( $equal(not(big_hat(X_351,X_297)),implies(X_297,not(implies(X_297,X_351)))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
( implies(X_297,not(implies(X_297,X_351))) != not(big_hat(X_351,X_297))
| not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,not(implies(X_297,not(implies(X_297,X_351)))))
| not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,not(not(big_hat(X_351,X_297)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),implies(X_297,not(implies(X_297,not(implies(X_297,X_351)))))) ),[1,1,0],$fot(not(big_hat(X_351,X_297)))]]) ).
cnf(refute_0_592,plain,
( not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,not(implies(X_297,not(implies(X_297,X_351)))))
| not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,not(not(big_hat(X_351,X_297)))) ),
inference(resolve,[$cnf( $equal(implies(X_297,not(implies(X_297,X_351))),not(big_hat(X_351,X_297))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,not(not(big_hat(X_351,X_297)))),
inference(resolve,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),implies(X_297,not(implies(X_297,not(implies(X_297,X_351)))))) )],[refute_0_587,refute_0_592]) ).
cnf(refute_0_594,plain,
big_V(not(X_114),implies(X_114,X_115)) = implies(implies(not(X_114),implies(X_114,X_115)),implies(X_114,X_115)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(X_114))),bind(Y,$fot(implies(X_114,X_115)))]]) ).
cnf(refute_0_595,plain,
implies(implies(X,not(truth)),implies(implies(not(truth),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_596,plain,
truth = implies(not(truth),Z),
inference(subst,[],[refute_0_439:[bind(X_23,$fot(Z))]]) ).
cnf(refute_0_597,plain,
( truth != implies(not(truth),Z)
| implies(not(truth),Z) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(not(truth),Z)))]]) ).
cnf(refute_0_598,plain,
implies(not(truth),Z) = truth,
inference(resolve,[$cnf( $equal(truth,implies(not(truth),Z)) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
( implies(implies(X,not(truth)),implies(implies(not(truth),Z),implies(X,Z))) != truth
| implies(not(truth),Z) != truth
| implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),implies(implies(not(truth),Z),implies(X,Z))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_600,plain,
( implies(implies(X,not(truth)),implies(implies(not(truth),Z),implies(X,Z))) != truth
| implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),Z),truth) )],[refute_0_598,refute_0_599]) ).
cnf(refute_0_601,plain,
implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(implies(not(truth),Z),implies(X,Z))),truth) )],[refute_0_595,refute_0_600]) ).
cnf(refute_0_602,plain,
implies(truth,implies(X,Z)) = implies(X,Z),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X,Z)))]]) ).
cnf(refute_0_603,plain,
implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = implies(implies(X,not(truth)),implies(truth,implies(X,Z))),
introduced(tautology,[refl,[$fot(implies(implies(X,not(truth)),implies(truth,implies(X,Z))))]]) ).
cnf(refute_0_604,plain,
( implies(implies(X,not(truth)),implies(truth,implies(X,Z))) != implies(implies(X,not(truth)),implies(truth,implies(X,Z)))
| implies(truth,implies(X,Z)) != implies(X,Z)
| implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = implies(implies(X,not(truth)),implies(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),implies(truth,implies(X,Z))),implies(implies(X,not(truth)),implies(truth,implies(X,Z)))) ),[1,1],$fot(implies(X,Z))]]) ).
cnf(refute_0_605,plain,
( implies(truth,implies(X,Z)) != implies(X,Z)
| implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = implies(implies(X,not(truth)),implies(X,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(truth,implies(X,Z))),implies(implies(X,not(truth)),implies(truth,implies(X,Z)))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
implies(implies(X,not(truth)),implies(truth,implies(X,Z))) = implies(implies(X,not(truth)),implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X,Z)),implies(X,Z)) )],[refute_0_602,refute_0_605]) ).
cnf(refute_0_607,plain,
( implies(implies(X,not(truth)),implies(truth,implies(X,Z))) != implies(implies(X,not(truth)),implies(X,Z))
| implies(implies(X,not(truth)),implies(truth,implies(X,Z))) != truth
| implies(implies(X,not(truth)),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),implies(truth,implies(X,Z))),truth) ),[0],$fot(implies(implies(X,not(truth)),implies(X,Z)))]]) ).
cnf(refute_0_608,plain,
( implies(implies(X,not(truth)),implies(truth,implies(X,Z))) != truth
| implies(implies(X,not(truth)),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(truth,implies(X,Z))),implies(implies(X,not(truth)),implies(X,Z))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
implies(implies(X,not(truth)),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(truth,implies(X,Z))),truth) )],[refute_0_601,refute_0_608]) ).
cnf(refute_0_610,plain,
implies(X,not(truth)) = not(X),
inference(subst,[],[refute_0_500:[bind(X_84,$fot(X))]]) ).
cnf(refute_0_611,plain,
implies(implies(X,not(truth)),implies(X,Z)) = implies(implies(X,not(truth)),implies(X,Z)),
introduced(tautology,[refl,[$fot(implies(implies(X,not(truth)),implies(X,Z)))]]) ).
cnf(refute_0_612,plain,
( implies(X,not(truth)) != not(X)
| implies(implies(X,not(truth)),implies(X,Z)) != implies(implies(X,not(truth)),implies(X,Z))
| implies(implies(X,not(truth)),implies(X,Z)) = implies(not(X),implies(X,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),implies(X,Z)),implies(implies(X,not(truth)),implies(X,Z))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_613,plain,
( implies(X,not(truth)) != not(X)
| implies(implies(X,not(truth)),implies(X,Z)) = implies(not(X),implies(X,Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(X,Z)),implies(implies(X,not(truth)),implies(X,Z))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
implies(implies(X,not(truth)),implies(X,Z)) = implies(not(X),implies(X,Z)),
inference(resolve,[$cnf( $equal(implies(X,not(truth)),not(X)) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
( implies(implies(X,not(truth)),implies(X,Z)) != implies(not(X),implies(X,Z))
| implies(implies(X,not(truth)),implies(X,Z)) != truth
| implies(not(X),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,not(truth)),implies(X,Z)),truth) ),[0],$fot(implies(not(X),implies(X,Z)))]]) ).
cnf(refute_0_616,plain,
( implies(implies(X,not(truth)),implies(X,Z)) != truth
| implies(not(X),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(X,Z)),implies(not(X),implies(X,Z))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
implies(not(X),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,not(truth)),implies(X,Z)),truth) )],[refute_0_609,refute_0_616]) ).
cnf(refute_0_618,plain,
implies(not(X_114),implies(X_114,X_115)) = truth,
inference(subst,[],[refute_0_617:[bind(X,$fot(X_114)),bind(Z,$fot(X_115))]]) ).
cnf(refute_0_619,plain,
( big_V(not(X_114),implies(X_114,X_115)) != implies(implies(not(X_114),implies(X_114,X_115)),implies(X_114,X_115))
| implies(not(X_114),implies(X_114,X_115)) != truth
| big_V(not(X_114),implies(X_114,X_115)) = implies(truth,implies(X_114,X_115)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_114),implies(X_114,X_115)),implies(implies(not(X_114),implies(X_114,X_115)),implies(X_114,X_115))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_620,plain,
( big_V(not(X_114),implies(X_114,X_115)) != implies(implies(not(X_114),implies(X_114,X_115)),implies(X_114,X_115))
| big_V(not(X_114),implies(X_114,X_115)) = implies(truth,implies(X_114,X_115)) ),
inference(resolve,[$cnf( $equal(implies(not(X_114),implies(X_114,X_115)),truth) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
big_V(not(X_114),implies(X_114,X_115)) = implies(truth,implies(X_114,X_115)),
inference(resolve,[$cnf( $equal(big_V(not(X_114),implies(X_114,X_115)),implies(implies(not(X_114),implies(X_114,X_115)),implies(X_114,X_115))) )],[refute_0_594,refute_0_620]) ).
cnf(refute_0_622,plain,
implies(truth,implies(X_114,X_115)) = implies(X_114,X_115),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_114,X_115)))]]) ).
cnf(refute_0_623,plain,
( big_V(not(X_114),implies(X_114,X_115)) != implies(truth,implies(X_114,X_115))
| implies(truth,implies(X_114,X_115)) != implies(X_114,X_115)
| big_V(not(X_114),implies(X_114,X_115)) = implies(X_114,X_115) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(not(X_114),implies(X_114,X_115)),implies(X_114,X_115)) ),[0],$fot(implies(truth,implies(X_114,X_115)))]]) ).
cnf(refute_0_624,plain,
( big_V(not(X_114),implies(X_114,X_115)) != implies(truth,implies(X_114,X_115))
| big_V(not(X_114),implies(X_114,X_115)) = implies(X_114,X_115) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_114,X_115)),implies(X_114,X_115)) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
big_V(not(X_114),implies(X_114,X_115)) = implies(X_114,X_115),
inference(resolve,[$cnf( $equal(big_V(not(X_114),implies(X_114,X_115)),implies(truth,implies(X_114,X_115))) )],[refute_0_621,refute_0_624]) ).
cnf(refute_0_626,plain,
big_V(not(X_297),implies(X_297,X_351)) = implies(X_297,X_351),
inference(subst,[],[refute_0_625:[bind(X_114,$fot(X_297)),bind(X_115,$fot(X_351))]]) ).
cnf(refute_0_627,plain,
big_V(implies(implies(X,X_29),X_29),implies(not(X_29),not(implies(X,X_29)))) = implies(implies(X,X_29),X_29),
inference(subst,[],[refute_0_54:[bind(X_23,$fot(X_29)),bind(X_24,$fot(implies(X,X_29)))]]) ).
cnf(refute_0_628,plain,
big_V(X,X_29) = implies(implies(X,X_29),X_29),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_29))]]) ).
cnf(refute_0_629,plain,
( big_V(X,X_29) != implies(implies(X,X_29),X_29)
| implies(implies(X,X_29),X_29) = big_V(X,X_29) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_29))),bind(Y0,$fot(implies(implies(X,X_29),X_29)))]]) ).
cnf(refute_0_630,plain,
implies(implies(X,X_29),X_29) = big_V(X,X_29),
inference(resolve,[$cnf( $equal(big_V(X,X_29),implies(implies(X,X_29),X_29)) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
( big_V(implies(implies(X,X_29),X_29),implies(not(X_29),not(implies(X,X_29)))) != implies(implies(X,X_29),X_29)
| implies(implies(X,X_29),X_29) != big_V(X,X_29)
| big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = implies(implies(X,X_29),X_29) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(implies(X,X_29),X_29),implies(not(X_29),not(implies(X,X_29)))),implies(implies(X,X_29),X_29)) ),[0,0],$fot(big_V(X,X_29))]]) ).
cnf(refute_0_632,plain,
( big_V(implies(implies(X,X_29),X_29),implies(not(X_29),not(implies(X,X_29)))) != implies(implies(X,X_29),X_29)
| big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = implies(implies(X,X_29),X_29) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_29),X_29),big_V(X,X_29)) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = implies(implies(X,X_29),X_29),
inference(resolve,[$cnf( $equal(big_V(implies(implies(X,X_29),X_29),implies(not(X_29),not(implies(X,X_29)))),implies(implies(X,X_29),X_29)) )],[refute_0_627,refute_0_632]) ).
cnf(refute_0_634,plain,
( big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) != implies(implies(X,X_29),X_29)
| implies(implies(X,X_29),X_29) != big_V(X,X_29)
| big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = big_V(X,X_29) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))),big_V(X,X_29)) ),[0],$fot(implies(implies(X,X_29),X_29))]]) ).
cnf(refute_0_635,plain,
( big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) != implies(implies(X,X_29),X_29)
| big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = big_V(X,X_29) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_29),X_29),big_V(X,X_29)) )],[refute_0_630,refute_0_634]) ).
cnf(refute_0_636,plain,
big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))) = big_V(X,X_29),
inference(resolve,[$cnf( $equal(big_V(big_V(X,X_29),implies(not(X_29),not(implies(X,X_29)))),implies(implies(X,X_29),X_29)) )],[refute_0_633,refute_0_635]) ).
cnf(refute_0_637,plain,
big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(big_V(X_101,X_7),X_101)))) = big_V(big_V(X_101,X_7),X_101),
inference(subst,[],[refute_0_636:[bind(X,$fot(big_V(X_101,X_7))),bind(X_29,$fot(X_101))]]) ).
cnf(refute_0_638,plain,
big_V(X_6,implies(X_7,X_6)) = implies(big_V(X_7,X_6),X_6),
inference(subst,[],[refute_0_77:[bind(Y,$fot(X_6)),bind(X_3,$fot(X_7))]]) ).
cnf(refute_0_639,plain,
big_V(X_6,X_7) = big_V(X_7,X_6),
inference(subst,[],[refute_0_44:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_640,plain,
( big_V(X_6,X_7) != big_V(X_7,X_6)
| big_V(X_7,X_6) = big_V(X_6,X_7) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_6,X_7))),bind(Y0,$fot(big_V(X_7,X_6)))]]) ).
cnf(refute_0_641,plain,
big_V(X_7,X_6) = big_V(X_6,X_7),
inference(resolve,[$cnf( $equal(big_V(X_6,X_7),big_V(X_7,X_6)) )],[refute_0_639,refute_0_640]) ).
cnf(refute_0_642,plain,
( big_V(X_6,implies(X_7,X_6)) != implies(big_V(X_7,X_6),X_6)
| big_V(X_7,X_6) != big_V(X_6,X_7)
| big_V(X_6,implies(X_7,X_6)) = implies(big_V(X_6,X_7),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_6,implies(X_7,X_6)),implies(big_V(X_7,X_6),X_6)) ),[1,0],$fot(big_V(X_6,X_7))]]) ).
cnf(refute_0_643,plain,
( big_V(X_6,implies(X_7,X_6)) != implies(big_V(X_7,X_6),X_6)
| big_V(X_6,implies(X_7,X_6)) = implies(big_V(X_6,X_7),X_6) ),
inference(resolve,[$cnf( $equal(big_V(X_7,X_6),big_V(X_6,X_7)) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
big_V(X_6,implies(X_7,X_6)) = implies(big_V(X_6,X_7),X_6),
inference(resolve,[$cnf( $equal(big_V(X_6,implies(X_7,X_6)),implies(big_V(X_7,X_6),X_6)) )],[refute_0_638,refute_0_643]) ).
cnf(refute_0_645,plain,
big_V(X_6,implies(X_7,X_6)) = implies(X_7,X_6),
inference(subst,[],[refute_0_193:[bind(X,$fot(X_6)),bind(X_27,$fot(X_7))]]) ).
cnf(refute_0_646,plain,
( big_V(X_6,implies(X_7,X_6)) != implies(X_7,X_6)
| big_V(X_6,implies(X_7,X_6)) != implies(big_V(X_6,X_7),X_6)
| implies(X_7,X_6) = implies(big_V(X_6,X_7),X_6) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_6,implies(X_7,X_6)),implies(big_V(X_6,X_7),X_6)) ),[0],$fot(implies(X_7,X_6))]]) ).
cnf(refute_0_647,plain,
( big_V(X_6,implies(X_7,X_6)) != implies(big_V(X_6,X_7),X_6)
| implies(X_7,X_6) = implies(big_V(X_6,X_7),X_6) ),
inference(resolve,[$cnf( $equal(big_V(X_6,implies(X_7,X_6)),implies(X_7,X_6)) )],[refute_0_645,refute_0_646]) ).
cnf(refute_0_648,plain,
implies(X_7,X_6) = implies(big_V(X_6,X_7),X_6),
inference(resolve,[$cnf( $equal(big_V(X_6,implies(X_7,X_6)),implies(big_V(X_6,X_7),X_6)) )],[refute_0_644,refute_0_647]) ).
cnf(refute_0_649,plain,
implies(X_7,X_101) = implies(big_V(X_101,X_7),X_101),
inference(subst,[],[refute_0_648:[bind(X_6,$fot(X_101))]]) ).
cnf(refute_0_650,plain,
( implies(X_7,X_101) != implies(big_V(X_101,X_7),X_101)
| implies(big_V(X_101,X_7),X_101) = implies(X_7,X_101) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_7,X_101))),bind(Y0,$fot(implies(big_V(X_101,X_7),X_101)))]]) ).
cnf(refute_0_651,plain,
implies(big_V(X_101,X_7),X_101) = implies(X_7,X_101),
inference(resolve,[$cnf( $equal(implies(X_7,X_101),implies(big_V(X_101,X_7),X_101)) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
( big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(big_V(X_101,X_7),X_101)))) != big_V(big_V(X_101,X_7),X_101)
| implies(big_V(X_101,X_7),X_101) != implies(X_7,X_101)
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),X_101) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(big_V(X_101,X_7),X_101)))),big_V(big_V(X_101,X_7),X_101)) ),[0,1,1,0],$fot(implies(X_7,X_101))]]) ).
cnf(refute_0_653,plain,
( big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(big_V(X_101,X_7),X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),X_101) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_101,X_7),X_101),implies(X_7,X_101)) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),X_101),
inference(resolve,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(big_V(X_101,X_7),X_101)))),big_V(big_V(X_101,X_7),X_101)) )],[refute_0_637,refute_0_653]) ).
cnf(refute_0_655,plain,
big_V(X,big_V(X,X_16)) = implies(implies(X,big_V(X,X_16)),big_V(X,X_16)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(big_V(X,X_16)))]]) ).
cnf(refute_0_656,plain,
implies(X,big_V(X,X_16)) = truth,
inference(subst,[],[refute_0_128:[bind(X_13,$fot(X)),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_657,plain,
( big_V(X,big_V(X,X_16)) != implies(implies(X,big_V(X,X_16)),big_V(X,X_16))
| implies(X,big_V(X,X_16)) != truth
| big_V(X,big_V(X,X_16)) = implies(truth,big_V(X,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_V(X,X_16)),implies(implies(X,big_V(X,X_16)),big_V(X,X_16))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_658,plain,
( big_V(X,big_V(X,X_16)) != implies(implies(X,big_V(X,X_16)),big_V(X,X_16))
| big_V(X,big_V(X,X_16)) = implies(truth,big_V(X,X_16)) ),
inference(resolve,[$cnf( $equal(implies(X,big_V(X,X_16)),truth) )],[refute_0_656,refute_0_657]) ).
cnf(refute_0_659,plain,
big_V(X,big_V(X,X_16)) = implies(truth,big_V(X,X_16)),
inference(resolve,[$cnf( $equal(big_V(X,big_V(X,X_16)),implies(implies(X,big_V(X,X_16)),big_V(X,X_16))) )],[refute_0_655,refute_0_658]) ).
cnf(refute_0_660,plain,
implies(truth,big_V(X,X_16)) = big_V(X,X_16),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X,X_16)))]]) ).
cnf(refute_0_661,plain,
( big_V(X,big_V(X,X_16)) != implies(truth,big_V(X,X_16))
| implies(truth,big_V(X,X_16)) != big_V(X,X_16)
| big_V(X,big_V(X,X_16)) = big_V(X,X_16) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,big_V(X,X_16)),big_V(X,X_16)) ),[0],$fot(implies(truth,big_V(X,X_16)))]]) ).
cnf(refute_0_662,plain,
( big_V(X,big_V(X,X_16)) != implies(truth,big_V(X,X_16))
| big_V(X,big_V(X,X_16)) = big_V(X,X_16) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X,X_16)),big_V(X,X_16)) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
big_V(X,big_V(X,X_16)) = big_V(X,X_16),
inference(resolve,[$cnf( $equal(big_V(X,big_V(X,X_16)),implies(truth,big_V(X,X_16))) )],[refute_0_659,refute_0_662]) ).
cnf(refute_0_664,plain,
big_V(X_101,big_V(X_101,X_7)) = big_V(X_101,X_7),
inference(subst,[],[refute_0_663:[bind(X,$fot(X_101)),bind(X_16,$fot(X_7))]]) ).
cnf(refute_0_665,plain,
big_V(big_V(X_101,X_7),X_101) = big_V(X_101,big_V(X_101,X_7)),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_101)),bind(Y,$fot(big_V(X_101,X_7)))]]) ).
cnf(refute_0_666,plain,
( big_V(X_101,big_V(X_101,X_7)) != big_V(X_101,X_7)
| big_V(big_V(X_101,X_7),X_101) != big_V(X_101,big_V(X_101,X_7))
| big_V(big_V(X_101,X_7),X_101) = big_V(X_101,X_7) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(big_V(X_101,X_7),X_101))),bind(Y0,$fot(big_V(X_101,big_V(X_101,X_7)))),bind(Z0,$fot(big_V(X_101,X_7)))]]) ).
cnf(refute_0_667,plain,
( big_V(X_101,big_V(X_101,X_7)) != big_V(X_101,X_7)
| big_V(big_V(X_101,X_7),X_101) = big_V(X_101,X_7) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_101,X_7),X_101),big_V(X_101,big_V(X_101,X_7))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
big_V(big_V(X_101,X_7),X_101) = big_V(X_101,X_7),
inference(resolve,[$cnf( $equal(big_V(X_101,big_V(X_101,X_7)),big_V(X_101,X_7)) )],[refute_0_664,refute_0_667]) ).
cnf(refute_0_669,plain,
big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),
introduced(tautology,[refl,[$fot(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))))]]) ).
cnf(refute_0_670,plain,
( big_V(big_V(X_101,X_7),X_101) != big_V(X_101,X_7)
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101))))
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101))))) ),[1,0],$fot(big_V(X_101,X_7))]]) ).
cnf(refute_0_671,plain,
( big_V(big_V(X_101,X_7),X_101) != big_V(X_101,X_7)
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) ),
inference(resolve,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101))))) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))),
inference(resolve,[$cnf( $equal(big_V(big_V(X_101,X_7),X_101),big_V(X_101,X_7)) )],[refute_0_668,refute_0_671]) ).
cnf(refute_0_673,plain,
( big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101))))
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),X_101) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(X_101,X_7),X_101)) ),[0],$fot(big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))))]]) ).
cnf(refute_0_674,plain,
( big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(big_V(X_101,X_7),X_101) ),
inference(resolve,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101))))) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
( big_V(big_V(X_101,X_7),X_101) != big_V(X_101,X_7)
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(X_101,X_7) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(X_101,X_7),X_101)) ),[1],$fot(big_V(X_101,X_7))]]) ).
cnf(refute_0_676,plain,
( big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(X_101,X_7) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_101,X_7),X_101),big_V(X_101,X_7)) )],[refute_0_668,refute_0_675]) ).
cnf(refute_0_677,plain,
( big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))) != big_V(big_V(X_101,X_7),X_101)
| big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(X_101,X_7) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(X_101,X_7),X_101)) )],[refute_0_674,refute_0_676]) ).
cnf(refute_0_678,plain,
big_V(big_V(X_101,X_7),implies(not(X_101),not(implies(X_7,X_101)))) = big_V(X_101,X_7),
inference(resolve,[$cnf( $equal(big_V(big_V(big_V(X_101,X_7),X_101),implies(not(X_101),not(implies(X_7,X_101)))),big_V(big_V(X_101,X_7),X_101)) )],[refute_0_654,refute_0_677]) ).
cnf(refute_0_679,plain,
big_V(big_V(not(X_84),X_154),implies(not(not(X_84)),not(implies(X_154,not(X_84))))) = big_V(not(X_84),X_154),
inference(subst,[],[refute_0_678:[bind(X_101,$fot(not(X_84))),bind(X_7,$fot(X_154))]]) ).
cnf(refute_0_680,plain,
( big_V(big_V(not(X_84),X_154),implies(not(not(X_84)),not(implies(X_154,not(X_84))))) != big_V(not(X_84),X_154)
| not(not(X_84)) != X_84
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(not(X_84),X_154) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(not(not(X_84)),not(implies(X_154,not(X_84))))),big_V(not(X_84),X_154)) ),[0,1,0],$fot(X_84)]]) ).
cnf(refute_0_681,plain,
( big_V(big_V(not(X_84),X_154),implies(not(not(X_84)),not(implies(X_154,not(X_84))))) != big_V(not(X_84),X_154)
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(not(X_84),X_154) ),
inference(resolve,[$cnf( $equal(not(not(X_84)),X_84) )],[refute_0_577,refute_0_680]) ).
cnf(refute_0_682,plain,
big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(not(X_84),X_154),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(not(not(X_84)),not(implies(X_154,not(X_84))))),big_V(not(X_84),X_154)) )],[refute_0_679,refute_0_681]) ).
cnf(refute_0_683,plain,
big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = implies(implies(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201)),
inference(subst,[],[big_V_definition:[bind(X,$fot(big_V(X_201,X_202))),bind(Y,$fot(big_V(X_202,X_201)))]]) ).
cnf(refute_0_684,plain,
implies(implies(X,big_V(Z,X_81)),implies(implies(big_V(Z,X_81),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(big_V(Z,X_81)))]]) ).
cnf(refute_0_685,plain,
implies(X_81,Z) = implies(big_V(Z,X_81),Z),
inference(subst,[],[refute_0_648:[bind(X_6,$fot(Z)),bind(X_7,$fot(X_81))]]) ).
cnf(refute_0_686,plain,
( implies(X_81,Z) != implies(big_V(Z,X_81),Z)
| implies(big_V(Z,X_81),Z) = implies(X_81,Z) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_81,Z))),bind(Y0,$fot(implies(big_V(Z,X_81),Z)))]]) ).
cnf(refute_0_687,plain,
implies(big_V(Z,X_81),Z) = implies(X_81,Z),
inference(resolve,[$cnf( $equal(implies(X_81,Z),implies(big_V(Z,X_81),Z)) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
( implies(big_V(Z,X_81),Z) != implies(X_81,Z)
| implies(implies(X,big_V(Z,X_81)),implies(implies(big_V(Z,X_81),Z),implies(X,Z))) != truth
| implies(implies(X,big_V(Z,X_81)),implies(implies(X_81,Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,big_V(Z,X_81)),implies(implies(big_V(Z,X_81),Z),implies(X,Z))),truth) ),[0,1,0],$fot(implies(X_81,Z))]]) ).
cnf(refute_0_689,plain,
( implies(implies(X,big_V(Z,X_81)),implies(implies(big_V(Z,X_81),Z),implies(X,Z))) != truth
| implies(implies(X,big_V(Z,X_81)),implies(implies(X_81,Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(Z,X_81),Z),implies(X_81,Z)) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
implies(implies(X,big_V(Z,X_81)),implies(implies(X_81,Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,big_V(Z,X_81)),implies(implies(big_V(Z,X_81),Z),implies(X,Z))),truth) )],[refute_0_684,refute_0_689]) ).
cnf(refute_0_691,plain,
implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),implies(truth,X_199))) = truth,
inference(subst,[],[refute_0_690:[bind(X,$fot(truth)),bind(Z,$fot(X_199)),bind(X_81,$fot(X_200))]]) ).
cnf(refute_0_692,plain,
implies(truth,X_199) = X_199,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_199))]]) ).
cnf(refute_0_693,plain,
( implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),implies(truth,X_199))) != truth
| implies(truth,X_199) != X_199
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),implies(truth,X_199))),truth) ),[0,1,1],$fot(X_199)]]) ).
cnf(refute_0_694,plain,
( implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),implies(truth,X_199))) != truth
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_199),X_199) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),implies(truth,X_199))),truth) )],[refute_0_691,refute_0_694]) ).
cnf(refute_0_696,plain,
implies(implies(X_200,X_199),X_199) = big_V(X_200,X_199),
inference(subst,[],[refute_0_37:[bind(X,$fot(X_200)),bind(Y,$fot(X_199))]]) ).
cnf(refute_0_697,plain,
implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)),
introduced(tautology,[refl,[$fot(implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)))]]) ).
cnf(refute_0_698,plain,
( implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) != implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199))
| implies(implies(X_200,X_199),X_199) != big_V(X_200,X_199)
| implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)),implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199))) ),[1,1],$fot(big_V(X_200,X_199))]]) ).
cnf(refute_0_699,plain,
( implies(implies(X_200,X_199),X_199) != big_V(X_200,X_199)
| implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)),implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199))) )],[refute_0_697,refute_0_698]) ).
cnf(refute_0_700,plain,
implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)),
inference(resolve,[$cnf( $equal(implies(implies(X_200,X_199),X_199),big_V(X_200,X_199)) )],[refute_0_696,refute_0_699]) ).
cnf(refute_0_701,plain,
implies(truth,big_V(X_199,X_200)) = big_V(X_199,X_200),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X_199,X_200)))]]) ).
cnf(refute_0_702,plain,
implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),
introduced(tautology,[refl,[$fot(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)))]]) ).
cnf(refute_0_703,plain,
( implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) != implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199))
| implies(truth,big_V(X_199,X_200)) != big_V(X_199,X_200)
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199))) ),[1,0],$fot(big_V(X_199,X_200))]]) ).
cnf(refute_0_704,plain,
( implies(truth,big_V(X_199,X_200)) != big_V(X_199,X_200)
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X_199,X_200)),big_V(X_199,X_200)) )],[refute_0_701,refute_0_704]) ).
cnf(refute_0_706,plain,
( implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) != implies(big_V(X_199,X_200),big_V(X_200,X_199))
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) != implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199))
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)))),bind(Y0,$fot(implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)))),bind(Z0,$fot(implies(big_V(X_199,X_200),big_V(X_200,X_199))))]]) ).
cnf(refute_0_707,plain,
( implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)) != implies(big_V(X_199,X_200),big_V(X_200,X_199))
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199))) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) = implies(big_V(X_199,X_200),big_V(X_200,X_199)),
inference(resolve,[$cnf( $equal(implies(big_V(X_199,X_200),implies(implies(X_200,X_199),X_199)),implies(big_V(X_199,X_200),big_V(X_200,X_199))) )],[refute_0_700,refute_0_707]) ).
cnf(refute_0_709,plain,
( implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) != implies(big_V(X_199,X_200),big_V(X_200,X_199))
| implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) != truth
| implies(big_V(X_199,X_200),big_V(X_200,X_199)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),truth) ),[0],$fot(implies(big_V(X_199,X_200),big_V(X_200,X_199)))]]) ).
cnf(refute_0_710,plain,
( implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)) != truth
| implies(big_V(X_199,X_200),big_V(X_200,X_199)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),implies(big_V(X_199,X_200),big_V(X_200,X_199))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
implies(big_V(X_199,X_200),big_V(X_200,X_199)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,big_V(X_199,X_200)),implies(implies(X_200,X_199),X_199)),truth) )],[refute_0_695,refute_0_710]) ).
cnf(refute_0_712,plain,
implies(big_V(X_201,X_202),big_V(X_202,X_201)) = truth,
inference(subst,[],[refute_0_711:[bind(X_199,$fot(X_201)),bind(X_200,$fot(X_202))]]) ).
cnf(refute_0_713,plain,
( big_V(big_V(X_201,X_202),big_V(X_202,X_201)) != implies(implies(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201))
| implies(big_V(X_201,X_202),big_V(X_202,X_201)) != truth
| big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = implies(truth,big_V(X_202,X_201)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(X_201,X_202),big_V(X_202,X_201)),implies(implies(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_714,plain,
( big_V(big_V(X_201,X_202),big_V(X_202,X_201)) != implies(implies(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201))
| big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = implies(truth,big_V(X_202,X_201)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_201,X_202),big_V(X_202,X_201)),truth) )],[refute_0_712,refute_0_713]) ).
cnf(refute_0_715,plain,
big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = implies(truth,big_V(X_202,X_201)),
inference(resolve,[$cnf( $equal(big_V(big_V(X_201,X_202),big_V(X_202,X_201)),implies(implies(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201))) )],[refute_0_683,refute_0_714]) ).
cnf(refute_0_716,plain,
implies(truth,big_V(X_202,X_201)) = big_V(X_202,X_201),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X_202,X_201)))]]) ).
cnf(refute_0_717,plain,
( big_V(big_V(X_201,X_202),big_V(X_202,X_201)) != implies(truth,big_V(X_202,X_201))
| implies(truth,big_V(X_202,X_201)) != big_V(X_202,X_201)
| big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = big_V(X_202,X_201) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(big_V(X_201,X_202),big_V(X_202,X_201)),big_V(X_202,X_201)) ),[0],$fot(implies(truth,big_V(X_202,X_201)))]]) ).
cnf(refute_0_718,plain,
( big_V(big_V(X_201,X_202),big_V(X_202,X_201)) != implies(truth,big_V(X_202,X_201))
| big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = big_V(X_202,X_201) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X_202,X_201)),big_V(X_202,X_201)) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
big_V(big_V(X_201,X_202),big_V(X_202,X_201)) = big_V(X_202,X_201),
inference(resolve,[$cnf( $equal(big_V(big_V(X_201,X_202),big_V(X_202,X_201)),implies(truth,big_V(X_202,X_201))) )],[refute_0_715,refute_0_718]) ).
cnf(refute_0_720,plain,
big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))) = big_V(X_154,not(X_84)),
inference(subst,[],[refute_0_719:[bind(X_201,$fot(not(X_84))),bind(X_202,$fot(X_154))]]) ).
cnf(refute_0_721,plain,
big_V(X,not(X_304)) = implies(implies(X,not(X_304)),not(X_304)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(not(X_304)))]]) ).
cnf(refute_0_722,plain,
implies(implies(X,not(X_304)),not(X_304)) = implies(X_304,not(implies(X,not(X_304)))),
inference(subst,[],[refute_0_580:[bind(X_297,$fot(implies(X,not(X_304)))),bind(X_84,$fot(X_304))]]) ).
cnf(refute_0_723,plain,
( big_V(X,not(X_304)) != implies(implies(X,not(X_304)),not(X_304))
| implies(implies(X,not(X_304)),not(X_304)) != implies(X_304,not(implies(X,not(X_304))))
| big_V(X,not(X_304)) = implies(X_304,not(implies(X,not(X_304)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,not(X_304)),implies(X_304,not(implies(X,not(X_304))))) ),[0],$fot(implies(implies(X,not(X_304)),not(X_304)))]]) ).
cnf(refute_0_724,plain,
( big_V(X,not(X_304)) != implies(implies(X,not(X_304)),not(X_304))
| big_V(X,not(X_304)) = implies(X_304,not(implies(X,not(X_304)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X,not(X_304)),not(X_304)),implies(X_304,not(implies(X,not(X_304))))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
big_V(X,not(X_304)) = implies(X_304,not(implies(X,not(X_304)))),
inference(resolve,[$cnf( $equal(big_V(X,not(X_304)),implies(implies(X,not(X_304)),not(X_304))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( big_V(X,not(X_304)) != implies(X_304,not(implies(X,not(X_304))))
| implies(X_304,not(implies(X,not(X_304)))) = big_V(X,not(X_304)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,not(X_304)))),bind(Y0,$fot(implies(X_304,not(implies(X,not(X_304))))))]]) ).
cnf(refute_0_727,plain,
implies(X_304,not(implies(X,not(X_304)))) = big_V(X,not(X_304)),
inference(resolve,[$cnf( $equal(big_V(X,not(X_304)),implies(X_304,not(implies(X,not(X_304))))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
implies(X_84,not(implies(X_154,not(X_84)))) = big_V(X_154,not(X_84)),
inference(subst,[],[refute_0_727:[bind(X,$fot(X_154)),bind(X_304,$fot(X_84))]]) ).
cnf(refute_0_729,plain,
big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),
introduced(tautology,[refl,[$fot(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))))]]) ).
cnf(refute_0_730,plain,
( big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) != big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84)))))
| implies(X_84,not(implies(X_154,not(X_84)))) != big_V(X_154,not(X_84))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84)))))) ),[1,1],$fot(big_V(X_154,not(X_84)))]]) ).
cnf(refute_0_731,plain,
( implies(X_84,not(implies(X_154,not(X_84)))) != big_V(X_154,not(X_84))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))) ),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84)))))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))),
inference(resolve,[$cnf( $equal(implies(X_84,not(implies(X_154,not(X_84)))),big_V(X_154,not(X_84))) )],[refute_0_728,refute_0_731]) ).
cnf(refute_0_733,plain,
( big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))) != big_V(X_154,not(X_84))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) != big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84)))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(X_154,not(X_84)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))))),bind(Y0,$fot(big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))))),bind(Z0,$fot(big_V(X_154,not(X_84))))]]) ).
cnf(refute_0_734,plain,
( big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))) != big_V(X_154,not(X_84))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(X_154,not(X_84)) ),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84)))) )],[refute_0_732,refute_0_733]) ).
cnf(refute_0_735,plain,
big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) = big_V(X_154,not(X_84)),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),big_V(X_154,not(X_84))),big_V(X_154,not(X_84))) )],[refute_0_720,refute_0_734]) ).
cnf(refute_0_736,plain,
( big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) != big_V(X_154,not(X_84))
| big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) != big_V(not(X_84),X_154)
| big_V(X_154,not(X_84)) = big_V(not(X_84),X_154) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(not(X_84),X_154)) ),[0],$fot(big_V(X_154,not(X_84)))]]) ).
cnf(refute_0_737,plain,
( big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))) != big_V(not(X_84),X_154)
| big_V(X_154,not(X_84)) = big_V(not(X_84),X_154) ),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(X_154,not(X_84))) )],[refute_0_735,refute_0_736]) ).
cnf(refute_0_738,plain,
big_V(X_154,not(X_84)) = big_V(not(X_84),X_154),
inference(resolve,[$cnf( $equal(big_V(big_V(not(X_84),X_154),implies(X_84,not(implies(X_154,not(X_84))))),big_V(not(X_84),X_154)) )],[refute_0_682,refute_0_737]) ).
cnf(refute_0_739,plain,
big_V(implies(X_297,X_351),not(X_297)) = big_V(not(X_297),implies(X_297,X_351)),
inference(subst,[],[refute_0_738:[bind(X_154,$fot(implies(X_297,X_351))),bind(X_84,$fot(X_297))]]) ).
cnf(refute_0_740,plain,
( big_V(implies(X_297,X_351),not(X_297)) != big_V(not(X_297),implies(X_297,X_351))
| big_V(not(X_297),implies(X_297,X_351)) != implies(X_297,X_351)
| big_V(implies(X_297,X_351),not(X_297)) = implies(X_297,X_351) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(big_V(implies(X_297,X_351),not(X_297)))),bind(Y0,$fot(big_V(not(X_297),implies(X_297,X_351)))),bind(Z0,$fot(implies(X_297,X_351)))]]) ).
cnf(refute_0_741,plain,
( big_V(not(X_297),implies(X_297,X_351)) != implies(X_297,X_351)
| big_V(implies(X_297,X_351),not(X_297)) = implies(X_297,X_351) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_297,X_351),not(X_297)),big_V(not(X_297),implies(X_297,X_351))) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
big_V(implies(X_297,X_351),not(X_297)) = implies(X_297,X_351),
inference(resolve,[$cnf( $equal(big_V(not(X_297),implies(X_297,X_351)),implies(X_297,X_351)) )],[refute_0_626,refute_0_741]) ).
cnf(refute_0_743,plain,
implies(X,not(X_304)) = implies(X_304,not(X)),
inference(subst,[],[refute_0_580:[bind(X_297,$fot(X)),bind(X_84,$fot(X_304))]]) ).
cnf(refute_0_744,plain,
( big_V(X,not(X_304)) != implies(implies(X,not(X_304)),not(X_304))
| implies(X,not(X_304)) != implies(X_304,not(X))
| big_V(X,not(X_304)) = implies(implies(X_304,not(X)),not(X_304)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(X_304)),implies(implies(X,not(X_304)),not(X_304))) ),[1,0],$fot(implies(X_304,not(X)))]]) ).
cnf(refute_0_745,plain,
( big_V(X,not(X_304)) != implies(implies(X,not(X_304)),not(X_304))
| big_V(X,not(X_304)) = implies(implies(X_304,not(X)),not(X_304)) ),
inference(resolve,[$cnf( $equal(implies(X,not(X_304)),implies(X_304,not(X))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
big_V(X,not(X_304)) = implies(implies(X_304,not(X)),not(X_304)),
inference(resolve,[$cnf( $equal(big_V(X,not(X_304)),implies(implies(X,not(X_304)),not(X_304))) )],[refute_0_721,refute_0_745]) ).
cnf(refute_0_747,plain,
( not(big_hat(X_298,X_297)) != implies(X_297,not(implies(X_297,X_298)))
| implies(X_297,not(implies(X_297,X_298))) = not(big_hat(X_298,X_297)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_298,X_297)))),bind(Y0,$fot(implies(X_297,not(implies(X_297,X_298)))))]]) ).
cnf(refute_0_748,plain,
implies(X_297,not(implies(X_297,X_298))) = not(big_hat(X_298,X_297)),
inference(resolve,[$cnf( $equal(not(big_hat(X_298,X_297)),implies(X_297,not(implies(X_297,X_298)))) )],[refute_0_586,refute_0_747]) ).
cnf(refute_0_749,plain,
implies(X_304,not(implies(X_304,not(X)))) = not(big_hat(not(X),X_304)),
inference(subst,[],[refute_0_748:[bind(X_297,$fot(X_304)),bind(X_298,$fot(not(X)))]]) ).
cnf(refute_0_750,plain,
implies(implies(X_304,not(X)),not(X_304)) = implies(X_304,not(implies(X_304,not(X)))),
inference(subst,[],[refute_0_582:[bind(X_297,$fot(X_304)),bind(X_84,$fot(implies(X_304,not(X))))]]) ).
cnf(refute_0_751,plain,
( implies(X_304,not(implies(X_304,not(X)))) != not(big_hat(not(X),X_304))
| implies(implies(X_304,not(X)),not(X_304)) != implies(X_304,not(implies(X_304,not(X))))
| implies(implies(X_304,not(X)),not(X_304)) = not(big_hat(not(X),X_304)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(implies(X_304,not(X)),not(X_304)))),bind(Y0,$fot(implies(X_304,not(implies(X_304,not(X)))))),bind(Z0,$fot(not(big_hat(not(X),X_304))))]]) ).
cnf(refute_0_752,plain,
( implies(X_304,not(implies(X_304,not(X)))) != not(big_hat(not(X),X_304))
| implies(implies(X_304,not(X)),not(X_304)) = not(big_hat(not(X),X_304)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_304,not(X)),not(X_304)),implies(X_304,not(implies(X_304,not(X))))) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
implies(implies(X_304,not(X)),not(X_304)) = not(big_hat(not(X),X_304)),
inference(resolve,[$cnf( $equal(implies(X_304,not(implies(X_304,not(X)))),not(big_hat(not(X),X_304))) )],[refute_0_749,refute_0_752]) ).
cnf(refute_0_754,plain,
( big_V(X,not(X_304)) != implies(implies(X_304,not(X)),not(X_304))
| implies(implies(X_304,not(X)),not(X_304)) != not(big_hat(not(X),X_304))
| big_V(X,not(X_304)) = not(big_hat(not(X),X_304)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,not(X_304)),not(big_hat(not(X),X_304))) ),[0],$fot(implies(implies(X_304,not(X)),not(X_304)))]]) ).
cnf(refute_0_755,plain,
( big_V(X,not(X_304)) != implies(implies(X_304,not(X)),not(X_304))
| big_V(X,not(X_304)) = not(big_hat(not(X),X_304)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_304,not(X)),not(X_304)),not(big_hat(not(X),X_304))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
big_V(X,not(X_304)) = not(big_hat(not(X),X_304)),
inference(resolve,[$cnf( $equal(big_V(X,not(X_304)),implies(implies(X_304,not(X)),not(X_304))) )],[refute_0_746,refute_0_755]) ).
cnf(refute_0_757,plain,
( big_V(X,not(X_304)) != not(big_hat(not(X),X_304))
| not(big_hat(not(X),X_304)) = big_V(X,not(X_304)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,not(X_304)))),bind(Y0,$fot(not(big_hat(not(X),X_304))))]]) ).
cnf(refute_0_758,plain,
not(big_hat(not(X),X_304)) = big_V(X,not(X_304)),
inference(resolve,[$cnf( $equal(big_V(X,not(X_304)),not(big_hat(not(X),X_304))) )],[refute_0_756,refute_0_757]) ).
cnf(refute_0_759,plain,
not(big_hat(not(implies(X_297,X_351)),X_297)) = big_V(implies(X_297,X_351),not(X_297)),
inference(subst,[],[refute_0_758:[bind(X,$fot(implies(X_297,X_351))),bind(X_304,$fot(X_297))]]) ).
cnf(refute_0_760,plain,
( big_V(implies(X_297,X_351),not(X_297)) != implies(X_297,X_351)
| not(big_hat(not(implies(X_297,X_351)),X_297)) != big_V(implies(X_297,X_351),not(X_297))
| not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,X_351) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(not(big_hat(not(implies(X_297,X_351)),X_297)))),bind(Y0,$fot(big_V(implies(X_297,X_351),not(X_297)))),bind(Z0,$fot(implies(X_297,X_351)))]]) ).
cnf(refute_0_761,plain,
( big_V(implies(X_297,X_351),not(X_297)) != implies(X_297,X_351)
| not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,X_351) ),
inference(resolve,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),big_V(implies(X_297,X_351),not(X_297))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
not(big_hat(not(implies(X_297,X_351)),X_297)) = implies(X_297,X_351),
inference(resolve,[$cnf( $equal(big_V(implies(X_297,X_351),not(X_297)),implies(X_297,X_351)) )],[refute_0_742,refute_0_761]) ).
cnf(refute_0_763,plain,
( not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,X_351)
| not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,not(not(big_hat(X_351,X_297))))
| implies(X_297,X_351) = implies(X_297,not(not(big_hat(X_351,X_297)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),implies(X_297,not(not(big_hat(X_351,X_297))))) ),[0],$fot(implies(X_297,X_351))]]) ).
cnf(refute_0_764,plain,
( not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,not(not(big_hat(X_351,X_297))))
| implies(X_297,X_351) = implies(X_297,not(not(big_hat(X_351,X_297)))) ),
inference(resolve,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),implies(X_297,X_351)) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
not(not(big_hat(X_351,X_297))) = big_hat(X_351,X_297),
inference(subst,[],[refute_0_577:[bind(X_84,$fot(big_hat(X_351,X_297)))]]) ).
cnf(refute_0_766,plain,
implies(X_297,not(not(big_hat(X_351,X_297)))) = implies(X_297,not(not(big_hat(X_351,X_297)))),
introduced(tautology,[refl,[$fot(implies(X_297,not(not(big_hat(X_351,X_297)))))]]) ).
cnf(refute_0_767,plain,
( implies(X_297,not(not(big_hat(X_351,X_297)))) != implies(X_297,not(not(big_hat(X_351,X_297))))
| not(not(big_hat(X_351,X_297))) != big_hat(X_351,X_297)
| implies(X_297,not(not(big_hat(X_351,X_297)))) = implies(X_297,big_hat(X_351,X_297)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_297,not(not(big_hat(X_351,X_297)))),implies(X_297,not(not(big_hat(X_351,X_297))))) ),[1,1],$fot(big_hat(X_351,X_297))]]) ).
cnf(refute_0_768,plain,
( not(not(big_hat(X_351,X_297))) != big_hat(X_351,X_297)
| implies(X_297,not(not(big_hat(X_351,X_297)))) = implies(X_297,big_hat(X_351,X_297)) ),
inference(resolve,[$cnf( $equal(implies(X_297,not(not(big_hat(X_351,X_297)))),implies(X_297,not(not(big_hat(X_351,X_297))))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
implies(X_297,not(not(big_hat(X_351,X_297)))) = implies(X_297,big_hat(X_351,X_297)),
inference(resolve,[$cnf( $equal(not(not(big_hat(X_351,X_297))),big_hat(X_351,X_297)) )],[refute_0_765,refute_0_768]) ).
cnf(refute_0_770,plain,
( implies(X_297,X_351) != implies(X_297,not(not(big_hat(X_351,X_297))))
| implies(X_297,not(not(big_hat(X_351,X_297)))) != implies(X_297,big_hat(X_351,X_297))
| implies(X_297,X_351) = implies(X_297,big_hat(X_351,X_297)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_297,X_351),implies(X_297,big_hat(X_351,X_297))) ),[0],$fot(implies(X_297,not(not(big_hat(X_351,X_297)))))]]) ).
cnf(refute_0_771,plain,
( implies(X_297,X_351) != implies(X_297,not(not(big_hat(X_351,X_297))))
| implies(X_297,X_351) = implies(X_297,big_hat(X_351,X_297)) ),
inference(resolve,[$cnf( $equal(implies(X_297,not(not(big_hat(X_351,X_297)))),implies(X_297,big_hat(X_351,X_297))) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
( not(big_hat(not(implies(X_297,X_351)),X_297)) != implies(X_297,not(not(big_hat(X_351,X_297))))
| implies(X_297,X_351) = implies(X_297,big_hat(X_351,X_297)) ),
inference(resolve,[$cnf( $equal(implies(X_297,X_351),implies(X_297,not(not(big_hat(X_351,X_297))))) )],[refute_0_764,refute_0_771]) ).
cnf(refute_0_773,plain,
implies(X_297,X_351) = implies(X_297,big_hat(X_351,X_297)),
inference(resolve,[$cnf( $equal(not(big_hat(not(implies(X_297,X_351)),X_297)),implies(X_297,not(not(big_hat(X_351,X_297))))) )],[refute_0_593,refute_0_772]) ).
cnf(refute_0_774,plain,
implies(X_461,X_462) = implies(X_461,big_hat(X_462,X_461)),
inference(subst,[],[refute_0_773:[bind(X_297,$fot(X_461)),bind(X_351,$fot(X_462))]]) ).
cnf(refute_0_775,plain,
big_hat(X_8,X_9) = not(big_V(not(X_8),not(X_9))),
inference(subst,[],[big_hat_definition:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_776,plain,
big_V(not(X_9),not(X_8)) = big_V(not(X_8),not(X_9)),
inference(subst,[],[refute_0_44:[bind(X,$fot(not(X_9))),bind(Y,$fot(not(X_8)))]]) ).
cnf(refute_0_777,plain,
( big_V(not(X_9),not(X_8)) != big_V(not(X_8),not(X_9))
| big_V(not(X_8),not(X_9)) = big_V(not(X_9),not(X_8)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(not(X_9),not(X_8)))),bind(Y0,$fot(big_V(not(X_8),not(X_9))))]]) ).
cnf(refute_0_778,plain,
big_V(not(X_8),not(X_9)) = big_V(not(X_9),not(X_8)),
inference(resolve,[$cnf( $equal(big_V(not(X_9),not(X_8)),big_V(not(X_8),not(X_9))) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
( big_V(not(X_8),not(X_9)) != big_V(not(X_9),not(X_8))
| big_hat(X_8,X_9) != not(big_V(not(X_8),not(X_9)))
| big_hat(X_8,X_9) = not(big_V(not(X_9),not(X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X_8,X_9),not(big_V(not(X_8),not(X_9)))) ),[1,0],$fot(big_V(not(X_9),not(X_8)))]]) ).
cnf(refute_0_780,plain,
( big_hat(X_8,X_9) != not(big_V(not(X_8),not(X_9)))
| big_hat(X_8,X_9) = not(big_V(not(X_9),not(X_8))) ),
inference(resolve,[$cnf( $equal(big_V(not(X_8),not(X_9)),big_V(not(X_9),not(X_8))) )],[refute_0_778,refute_0_779]) ).
cnf(refute_0_781,plain,
big_hat(X_8,X_9) = not(big_V(not(X_9),not(X_8))),
inference(resolve,[$cnf( $equal(big_hat(X_8,X_9),not(big_V(not(X_8),not(X_9)))) )],[refute_0_775,refute_0_780]) ).
cnf(refute_0_782,plain,
not(big_V(not(X_9),not(X_8))) = big_hat(X_9,X_8),
inference(subst,[],[refute_0_538:[bind(X,$fot(X_9)),bind(Y,$fot(X_8))]]) ).
cnf(refute_0_783,plain,
( big_hat(X_8,X_9) != not(big_V(not(X_9),not(X_8)))
| not(big_V(not(X_9),not(X_8))) != big_hat(X_9,X_8)
| big_hat(X_8,X_9) = big_hat(X_9,X_8) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(X_8,X_9),big_hat(X_9,X_8)) ),[0],$fot(not(big_V(not(X_9),not(X_8))))]]) ).
cnf(refute_0_784,plain,
( big_hat(X_8,X_9) != not(big_V(not(X_9),not(X_8)))
| big_hat(X_8,X_9) = big_hat(X_9,X_8) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X_9),not(X_8))),big_hat(X_9,X_8)) )],[refute_0_782,refute_0_783]) ).
cnf(refute_0_785,plain,
big_hat(X_8,X_9) = big_hat(X_9,X_8),
inference(resolve,[$cnf( $equal(big_hat(X_8,X_9),not(big_V(not(X_9),not(X_8)))) )],[refute_0_781,refute_0_784]) ).
cnf(refute_0_786,plain,
big_hat(X_461,X_462) = big_hat(X_462,X_461),
inference(subst,[],[refute_0_785:[bind(X_8,$fot(X_461)),bind(X_9,$fot(X_462))]]) ).
cnf(refute_0_787,plain,
( big_hat(X_461,X_462) != big_hat(X_462,X_461)
| big_hat(X_462,X_461) = big_hat(X_461,X_462) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X_461,X_462))),bind(Y0,$fot(big_hat(X_462,X_461)))]]) ).
cnf(refute_0_788,plain,
big_hat(X_462,X_461) = big_hat(X_461,X_462),
inference(resolve,[$cnf( $equal(big_hat(X_461,X_462),big_hat(X_462,X_461)) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
( big_hat(X_462,X_461) != big_hat(X_461,X_462)
| implies(X_461,X_462) != implies(X_461,big_hat(X_462,X_461))
| implies(X_461,X_462) = implies(X_461,big_hat(X_461,X_462)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_461,X_462),implies(X_461,big_hat(X_462,X_461))) ),[1,1],$fot(big_hat(X_461,X_462))]]) ).
cnf(refute_0_790,plain,
( implies(X_461,X_462) != implies(X_461,big_hat(X_462,X_461))
| implies(X_461,X_462) = implies(X_461,big_hat(X_461,X_462)) ),
inference(resolve,[$cnf( $equal(big_hat(X_462,X_461),big_hat(X_461,X_462)) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
implies(X_461,X_462) = implies(X_461,big_hat(X_461,X_462)),
inference(resolve,[$cnf( $equal(implies(X_461,X_462),implies(X_461,big_hat(X_462,X_461))) )],[refute_0_774,refute_0_790]) ).
cnf(refute_0_792,plain,
implies(X_889,X_462) = implies(X_889,big_hat(X_889,X_462)),
inference(subst,[],[refute_0_791:[bind(X_461,$fot(X_889))]]) ).
cnf(refute_0_793,plain,
( implies(X_889,X_462) != implies(X_889,big_hat(X_889,X_462))
| implies(X_889,big_hat(X_889,X_462)) = implies(X_889,X_462) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_889,X_462))),bind(Y0,$fot(implies(X_889,big_hat(X_889,X_462))))]]) ).
cnf(refute_0_794,plain,
implies(X_889,big_hat(X_889,X_462)) = implies(X_889,X_462),
inference(resolve,[$cnf( $equal(implies(X_889,X_462),implies(X_889,big_hat(X_889,X_462))) )],[refute_0_792,refute_0_793]) ).
cnf(refute_0_795,plain,
( implies(X_889,big_hat(X_889,X_462)) != implies(X_889,X_462)
| ~ ordered(implies(X_890,implies(X_889,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))))
| ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_890,implies(X_889,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) ),[0,1],$fot(implies(X_889,X_462))]]) ).
cnf(refute_0_796,plain,
( ~ ordered(implies(X_890,implies(X_889,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))))
| ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) ),
inference(resolve,[$cnf( $equal(implies(X_889,big_hat(X_889,X_462)),implies(X_889,X_462)) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))),
inference(resolve,[$cnf( ordered(implies(X_890,implies(X_889,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) )],[refute_0_17,refute_0_796]) ).
cnf(refute_0_798,plain,
not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = implies(not(X_283),not(implies(not(X_283),implies(implies(not(X_16),X_283),X_16)))),
inference(subst,[],[refute_0_586:[bind(X_297,$fot(not(X_283))),bind(X_298,$fot(implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_799,plain,
implies(implies(X,big_V(X,X_16)),implies(implies(big_V(X,X_16),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(big_V(X,X_16)))]]) ).
cnf(refute_0_800,plain,
( implies(X,big_V(X,X_16)) != truth
| implies(implies(X,big_V(X,X_16)),implies(implies(big_V(X,X_16),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,big_V(X,X_16)),implies(implies(big_V(X,X_16),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_801,plain,
( implies(implies(X,big_V(X,X_16)),implies(implies(big_V(X,X_16),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(X,big_V(X,X_16)),truth) )],[refute_0_656,refute_0_800]) ).
cnf(refute_0_802,plain,
implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,big_V(X,X_16)),implies(implies(big_V(X,X_16),Z),implies(X,Z))),truth) )],[refute_0_799,refute_0_801]) ).
cnf(refute_0_803,plain,
implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) = implies(implies(big_V(X,X_16),Z),implies(X,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(big_V(X,X_16),Z),implies(X,Z))))]]) ).
cnf(refute_0_804,plain,
( implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) != implies(implies(big_V(X,X_16),Z),implies(X,Z))
| implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) != truth
| implies(implies(big_V(X,X_16),Z),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(big_V(X,X_16),Z),implies(X,Z)))]]) ).
cnf(refute_0_805,plain,
( implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))) != truth
| implies(implies(big_V(X,X_16),Z),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))),implies(implies(big_V(X,X_16),Z),implies(X,Z))) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
implies(implies(big_V(X,X_16),Z),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(big_V(X,X_16),Z),implies(X,Z))),truth) )],[refute_0_802,refute_0_805]) ).
cnf(refute_0_807,plain,
implies(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) = truth,
inference(subst,[],[refute_0_806:[bind(X,$fot(not(X_283))),bind(Z,$fot(implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_808,plain,
implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_23),not(X_24)))),bind(Y,$fot(implies(X_24,X_23)))]]) ).
cnf(refute_0_809,plain,
( implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) != truth
| implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)) != truth
| implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_810,plain,
( implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) != truth
| implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),truth) )],[refute_0_32,refute_0_809]) ).
cnf(refute_0_811,plain,
implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_23),not(X_24)),implies(X_24,X_23)),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))),truth) )],[refute_0_808,refute_0_810]) ).
cnf(refute_0_812,plain,
implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) = implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))))]]) ).
cnf(refute_0_813,plain,
( implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) != implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))
| implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) != truth
| implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))),truth) ),[0],$fot(implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z)))]]) ).
cnf(refute_0_814,plain,
( implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) != truth
| implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))),implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))) )],[refute_0_812,refute_0_813]) ).
cnf(refute_0_815,plain,
implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_24,X_23),Z),implies(implies(not(X_23),not(X_24)),Z))),truth) )],[refute_0_811,refute_0_814]) ).
cnf(refute_0_816,plain,
implies(implies(implies(X_106,X_104),X_104),implies(implies(not(X_104),not(X_106)),X_104)) = truth,
inference(subst,[],[refute_0_815:[bind(Z,$fot(X_104)),bind(X_23,$fot(X_104)),bind(X_24,$fot(X_106))]]) ).
cnf(refute_0_817,plain,
big_V(X_106,X_104) = implies(implies(X_106,X_104),X_104),
inference(subst,[],[big_V_definition:[bind(X,$fot(X_106)),bind(Y,$fot(X_104))]]) ).
cnf(refute_0_818,plain,
( big_V(X_106,X_104) != implies(implies(X_106,X_104),X_104)
| implies(implies(X_106,X_104),X_104) = big_V(X_106,X_104) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_106,X_104))),bind(Y0,$fot(implies(implies(X_106,X_104),X_104)))]]) ).
cnf(refute_0_819,plain,
implies(implies(X_106,X_104),X_104) = big_V(X_106,X_104),
inference(resolve,[$cnf( $equal(big_V(X_106,X_104),implies(implies(X_106,X_104),X_104)) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
( implies(implies(X_106,X_104),X_104) != big_V(X_106,X_104)
| implies(implies(implies(X_106,X_104),X_104),implies(implies(not(X_104),not(X_106)),X_104)) != truth
| implies(big_V(X_106,X_104),implies(implies(not(X_104),not(X_106)),X_104)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_106,X_104),X_104),implies(implies(not(X_104),not(X_106)),X_104)),truth) ),[0,0],$fot(big_V(X_106,X_104))]]) ).
cnf(refute_0_821,plain,
( implies(implies(implies(X_106,X_104),X_104),implies(implies(not(X_104),not(X_106)),X_104)) != truth
| implies(big_V(X_106,X_104),implies(implies(not(X_104),not(X_106)),X_104)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_106,X_104),X_104),big_V(X_106,X_104)) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
implies(big_V(X_106,X_104),implies(implies(not(X_104),not(X_106)),X_104)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_106,X_104),X_104),implies(implies(not(X_104),not(X_106)),X_104)),truth) )],[refute_0_816,refute_0_821]) ).
cnf(refute_0_823,plain,
implies(big_V(not(X_84),X_109),implies(implies(not(X_109),not(not(X_84))),X_109)) = truth,
inference(subst,[],[refute_0_822:[bind(X_104,$fot(X_109)),bind(X_106,$fot(not(X_84)))]]) ).
cnf(refute_0_824,plain,
( implies(big_V(not(X_84),X_109),implies(implies(not(X_109),not(not(X_84))),X_109)) != truth
| not(not(X_84)) != X_84
| implies(big_V(not(X_84),X_109),implies(implies(not(X_109),X_84),X_109)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(not(X_84),X_109),implies(implies(not(X_109),not(not(X_84))),X_109)),truth) ),[0,1,0,1],$fot(X_84)]]) ).
cnf(refute_0_825,plain,
( implies(big_V(not(X_84),X_109),implies(implies(not(X_109),not(not(X_84))),X_109)) != truth
| implies(big_V(not(X_84),X_109),implies(implies(not(X_109),X_84),X_109)) = truth ),
inference(resolve,[$cnf( $equal(not(not(X_84)),X_84) )],[refute_0_577,refute_0_824]) ).
cnf(refute_0_826,plain,
implies(big_V(not(X_84),X_109),implies(implies(not(X_109),X_84),X_109)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(not(X_84),X_109),implies(implies(not(X_109),not(not(X_84))),X_109)),truth) )],[refute_0_823,refute_0_825]) ).
cnf(refute_0_827,plain,
implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)) = truth,
inference(subst,[],[refute_0_826:[bind(X_109,$fot(X_16)),bind(X_84,$fot(X_283))]]) ).
cnf(refute_0_828,plain,
( implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)) != truth
| implies(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) != truth
| implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_829,plain,
( implies(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) != truth
| implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),truth) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(big_V(not(X_283),X_16),implies(implies(not(X_16),X_283),X_16)),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))),truth) )],[refute_0_807,refute_0_829]) ).
cnf(refute_0_831,plain,
implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) = implies(not(X_283),implies(implies(not(X_16),X_283),X_16)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(X_283),implies(implies(not(X_16),X_283),X_16))))]]) ).
cnf(refute_0_832,plain,
( implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) != implies(not(X_283),implies(implies(not(X_16),X_283),X_16))
| implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) != truth
| implies(not(X_283),implies(implies(not(X_16),X_283),X_16)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))),truth) ),[0],$fot(implies(not(X_283),implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_833,plain,
( implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) != truth
| implies(not(X_283),implies(implies(not(X_16),X_283),X_16)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))),implies(not(X_283),implies(implies(not(X_16),X_283),X_16))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
implies(not(X_283),implies(implies(not(X_16),X_283),X_16)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(X_283),implies(implies(not(X_16),X_283),X_16))),truth) )],[refute_0_830,refute_0_833]) ).
cnf(refute_0_835,plain,
( implies(not(X_283),implies(implies(not(X_16),X_283),X_16)) != truth
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != implies(not(X_283),not(implies(not(X_283),implies(implies(not(X_16),X_283),X_16))))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = implies(not(X_283),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),implies(not(X_283),not(implies(not(X_283),implies(implies(not(X_16),X_283),X_16))))) ),[1,1,0],$fot(truth)]]) ).
cnf(refute_0_836,plain,
( not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != implies(not(X_283),not(implies(not(X_283),implies(implies(not(X_16),X_283),X_16))))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = implies(not(X_283),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(X_283),implies(implies(not(X_16),X_283),X_16)),truth) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = implies(not(X_283),not(truth)),
inference(resolve,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),implies(not(X_283),not(implies(not(X_283),implies(implies(not(X_16),X_283),X_16))))) )],[refute_0_798,refute_0_836]) ).
cnf(refute_0_838,plain,
not(not(big_hat(X_283,not(X_16)))) = big_hat(X_283,not(X_16)),
inference(subst,[],[refute_0_577:[bind(X_84,$fot(big_hat(X_283,not(X_16))))]]) ).
cnf(refute_0_839,plain,
implies(implies(not(X_295),X_351),X_295) = implies(not(X_295),not(implies(not(X_295),X_351))),
inference(subst,[],[refute_0_529:[bind(X_294,$fot(implies(not(X_295),X_351)))]]) ).
cnf(refute_0_840,plain,
not(big_hat(X_351,not(X_295))) = implies(not(X_295),not(implies(not(X_295),X_351))),
inference(subst,[],[refute_0_586:[bind(X_297,$fot(not(X_295))),bind(X_298,$fot(X_351))]]) ).
cnf(refute_0_841,plain,
( not(big_hat(X_351,not(X_295))) != implies(not(X_295),not(implies(not(X_295),X_351)))
| implies(not(X_295),not(implies(not(X_295),X_351))) = not(big_hat(X_351,not(X_295))) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_351,not(X_295))))),bind(Y0,$fot(implies(not(X_295),not(implies(not(X_295),X_351)))))]]) ).
cnf(refute_0_842,plain,
implies(not(X_295),not(implies(not(X_295),X_351))) = not(big_hat(X_351,not(X_295))),
inference(resolve,[$cnf( $equal(not(big_hat(X_351,not(X_295))),implies(not(X_295),not(implies(not(X_295),X_351)))) )],[refute_0_840,refute_0_841]) ).
cnf(refute_0_843,plain,
( implies(implies(not(X_295),X_351),X_295) != implies(not(X_295),not(implies(not(X_295),X_351)))
| implies(not(X_295),not(implies(not(X_295),X_351))) != not(big_hat(X_351,not(X_295)))
| implies(implies(not(X_295),X_351),X_295) = not(big_hat(X_351,not(X_295))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(not(X_295),X_351),X_295),not(big_hat(X_351,not(X_295)))) ),[0],$fot(implies(not(X_295),not(implies(not(X_295),X_351))))]]) ).
cnf(refute_0_844,plain,
( implies(implies(not(X_295),X_351),X_295) != implies(not(X_295),not(implies(not(X_295),X_351)))
| implies(implies(not(X_295),X_351),X_295) = not(big_hat(X_351,not(X_295))) ),
inference(resolve,[$cnf( $equal(implies(not(X_295),not(implies(not(X_295),X_351))),not(big_hat(X_351,not(X_295)))) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
implies(implies(not(X_295),X_351),X_295) = not(big_hat(X_351,not(X_295))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_295),X_351),X_295),implies(not(X_295),not(implies(not(X_295),X_351)))) )],[refute_0_839,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(implies(not(X_16),X_283),X_16) = not(big_hat(X_283,not(X_16))),
inference(subst,[],[refute_0_845:[bind(X_295,$fot(X_16)),bind(X_351,$fot(X_283))]]) ).
cnf(refute_0_847,plain,
not(implies(implies(not(X_16),X_283),X_16)) = not(implies(implies(not(X_16),X_283),X_16)),
introduced(tautology,[refl,[$fot(not(implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_848,plain,
( implies(implies(not(X_16),X_283),X_16) != not(big_hat(X_283,not(X_16)))
| not(implies(implies(not(X_16),X_283),X_16)) != not(implies(implies(not(X_16),X_283),X_16))
| not(implies(implies(not(X_16),X_283),X_16)) = not(not(big_hat(X_283,not(X_16)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(implies(not(X_16),X_283),X_16)),not(implies(implies(not(X_16),X_283),X_16))) ),[1,0],$fot(not(big_hat(X_283,not(X_16))))]]) ).
cnf(refute_0_849,plain,
( implies(implies(not(X_16),X_283),X_16) != not(big_hat(X_283,not(X_16)))
| not(implies(implies(not(X_16),X_283),X_16)) = not(not(big_hat(X_283,not(X_16)))) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(X_16),X_283),X_16)),not(implies(implies(not(X_16),X_283),X_16))) )],[refute_0_847,refute_0_848]) ).
cnf(refute_0_850,plain,
not(implies(implies(not(X_16),X_283),X_16)) = not(not(big_hat(X_283,not(X_16)))),
inference(resolve,[$cnf( $equal(implies(implies(not(X_16),X_283),X_16),not(big_hat(X_283,not(X_16)))) )],[refute_0_846,refute_0_849]) ).
cnf(refute_0_851,plain,
( not(implies(implies(not(X_16),X_283),X_16)) != not(not(big_hat(X_283,not(X_16))))
| not(not(big_hat(X_283,not(X_16)))) != big_hat(X_283,not(X_16))
| not(implies(implies(not(X_16),X_283),X_16)) = big_hat(X_283,not(X_16)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(not(implies(implies(not(X_16),X_283),X_16)))),bind(Y0,$fot(not(not(big_hat(X_283,not(X_16)))))),bind(Z0,$fot(big_hat(X_283,not(X_16))))]]) ).
cnf(refute_0_852,plain,
( not(not(big_hat(X_283,not(X_16)))) != big_hat(X_283,not(X_16))
| not(implies(implies(not(X_16),X_283),X_16)) = big_hat(X_283,not(X_16)) ),
inference(resolve,[$cnf( $equal(not(implies(implies(not(X_16),X_283),X_16)),not(not(big_hat(X_283,not(X_16))))) )],[refute_0_850,refute_0_851]) ).
cnf(refute_0_853,plain,
not(implies(implies(not(X_16),X_283),X_16)) = big_hat(X_283,not(X_16)),
inference(resolve,[$cnf( $equal(not(not(big_hat(X_283,not(X_16)))),big_hat(X_283,not(X_16))) )],[refute_0_838,refute_0_852]) ).
cnf(refute_0_854,plain,
big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) = big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),
introduced(tautology,[refl,[$fot(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))))]]) ).
cnf(refute_0_855,plain,
( big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) != big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))
| not(implies(implies(not(X_16),X_283),X_16)) != big_hat(X_283,not(X_16))
| big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) = big_V(X_283,big_hat(X_283,not(X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))) ),[1,1],$fot(big_hat(X_283,not(X_16)))]]) ).
cnf(refute_0_856,plain,
( not(implies(implies(not(X_16),X_283),X_16)) != big_hat(X_283,not(X_16))
| big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) = big_V(X_283,big_hat(X_283,not(X_16))) ),
inference(resolve,[$cnf( $equal(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) = big_V(X_283,big_hat(X_283,not(X_16))),
inference(resolve,[$cnf( $equal(not(implies(implies(not(X_16),X_283),X_16)),big_hat(X_283,not(X_16))) )],[refute_0_853,refute_0_856]) ).
cnf(refute_0_858,plain,
not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))) = big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),
inference(subst,[],[refute_0_758:[bind(X,$fot(X_283)),bind(X_304,$fot(implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_859,plain,
big_hat(truth,Y) = not(big_V(not(truth),not(Y))),
inference(subst,[],[big_hat_definition:[bind(X,$fot(truth))]]) ).
cnf(refute_0_860,plain,
big_V(not(truth),not(Y)) = not(Y),
inference(subst,[],[refute_0_448:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_861,plain,
( big_V(not(truth),not(Y)) != not(Y)
| big_hat(truth,Y) != not(big_V(not(truth),not(Y)))
| big_hat(truth,Y) = not(not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(truth,Y),not(big_V(not(truth),not(Y)))) ),[1,0],$fot(not(Y))]]) ).
cnf(refute_0_862,plain,
( big_hat(truth,Y) != not(big_V(not(truth),not(Y)))
| big_hat(truth,Y) = not(not(Y)) ),
inference(resolve,[$cnf( $equal(big_V(not(truth),not(Y)),not(Y)) )],[refute_0_860,refute_0_861]) ).
cnf(refute_0_863,plain,
big_hat(truth,Y) = not(not(Y)),
inference(resolve,[$cnf( $equal(big_hat(truth,Y),not(big_V(not(truth),not(Y)))) )],[refute_0_859,refute_0_862]) ).
cnf(refute_0_864,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_577:[bind(X_84,$fot(Y))]]) ).
cnf(refute_0_865,plain,
( big_hat(truth,Y) != not(not(Y))
| not(not(Y)) != Y
| big_hat(truth,Y) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(truth,Y),Y) ),[0],$fot(not(not(Y)))]]) ).
cnf(refute_0_866,plain,
( big_hat(truth,Y) != not(not(Y))
| big_hat(truth,Y) = Y ),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_864,refute_0_865]) ).
cnf(refute_0_867,plain,
big_hat(truth,Y) = Y,
inference(resolve,[$cnf( $equal(big_hat(truth,Y),not(not(Y))) )],[refute_0_863,refute_0_866]) ).
cnf(refute_0_868,plain,
big_hat(truth,not(big_hat(X_234,X_233))) = not(big_hat(X_234,X_233)),
inference(subst,[],[refute_0_867:[bind(Y,$fot(not(big_hat(X_234,X_233))))]]) ).
cnf(refute_0_869,plain,
big_hat(X,big_V(not(X_8),not(X_9))) = not(big_V(not(X),not(big_V(not(X_8),not(X_9))))),
inference(subst,[],[big_hat_definition:[bind(Y,$fot(big_V(not(X_8),not(X_9))))]]) ).
cnf(refute_0_870,plain,
( big_hat(X_8,X_9) != not(big_V(not(X_8),not(X_9)))
| not(big_V(not(X_8),not(X_9))) = big_hat(X_8,X_9) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X_8,X_9))),bind(Y0,$fot(not(big_V(not(X_8),not(X_9)))))]]) ).
cnf(refute_0_871,plain,
not(big_V(not(X_8),not(X_9))) = big_hat(X_8,X_9),
inference(resolve,[$cnf( $equal(big_hat(X_8,X_9),not(big_V(not(X_8),not(X_9)))) )],[refute_0_775,refute_0_870]) ).
cnf(refute_0_872,plain,
( big_hat(X,big_V(not(X_8),not(X_9))) != not(big_V(not(X),not(big_V(not(X_8),not(X_9)))))
| not(big_V(not(X_8),not(X_9))) != big_hat(X_8,X_9)
| big_hat(X,big_V(not(X_8),not(X_9))) = not(big_V(not(X),big_hat(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),not(big_V(not(X),not(big_V(not(X_8),not(X_9)))))) ),[1,0,1],$fot(big_hat(X_8,X_9))]]) ).
cnf(refute_0_873,plain,
( big_hat(X,big_V(not(X_8),not(X_9))) != not(big_V(not(X),not(big_V(not(X_8),not(X_9)))))
| big_hat(X,big_V(not(X_8),not(X_9))) = not(big_V(not(X),big_hat(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X_8),not(X_9))),big_hat(X_8,X_9)) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
big_hat(X,big_V(not(X_8),not(X_9))) = not(big_V(not(X),big_hat(X_8,X_9))),
inference(resolve,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),not(big_V(not(X),not(big_V(not(X_8),not(X_9)))))) )],[refute_0_869,refute_0_873]) ).
cnf(refute_0_875,plain,
big_hat(X_39,big_V(not(X_40),not(X_41))) = not(big_V(not(X_39),big_hat(X_40,X_41))),
inference(subst,[],[refute_0_874:[bind(X,$fot(X_39)),bind(X_8,$fot(X_40)),bind(X_9,$fot(X_41))]]) ).
cnf(refute_0_876,plain,
big_V(not(X_41),not(X_40)) = big_V(not(X_40),not(X_41)),
inference(subst,[],[refute_0_44:[bind(X,$fot(not(X_41))),bind(Y,$fot(not(X_40)))]]) ).
cnf(refute_0_877,plain,
( big_V(not(X_41),not(X_40)) != big_V(not(X_40),not(X_41))
| big_V(not(X_40),not(X_41)) = big_V(not(X_41),not(X_40)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(not(X_41),not(X_40)))),bind(Y0,$fot(big_V(not(X_40),not(X_41))))]]) ).
cnf(refute_0_878,plain,
big_V(not(X_40),not(X_41)) = big_V(not(X_41),not(X_40)),
inference(resolve,[$cnf( $equal(big_V(not(X_41),not(X_40)),big_V(not(X_40),not(X_41))) )],[refute_0_876,refute_0_877]) ).
cnf(refute_0_879,plain,
( big_V(not(X_40),not(X_41)) != big_V(not(X_41),not(X_40))
| big_hat(X_39,big_V(not(X_40),not(X_41))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,big_V(not(X_41),not(X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X_39,big_V(not(X_40),not(X_41))),not(big_V(not(X_39),big_hat(X_40,X_41)))) ),[0,1],$fot(big_V(not(X_41),not(X_40)))]]) ).
cnf(refute_0_880,plain,
( big_hat(X_39,big_V(not(X_40),not(X_41))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,big_V(not(X_41),not(X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(big_V(not(X_40),not(X_41)),big_V(not(X_41),not(X_40))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
big_hat(X_39,big_V(not(X_41),not(X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))),
inference(resolve,[$cnf( $equal(big_hat(X_39,big_V(not(X_40),not(X_41))),not(big_V(not(X_39),big_hat(X_40,X_41)))) )],[refute_0_875,refute_0_880]) ).
cnf(refute_0_882,plain,
big_hat(X_39,big_V(not(X_41),not(X_40))) = not(big_V(not(X_39),big_hat(X_41,X_40))),
inference(subst,[],[refute_0_874:[bind(X,$fot(X_39)),bind(X_8,$fot(X_41)),bind(X_9,$fot(X_40))]]) ).
cnf(refute_0_883,plain,
( big_hat(X_39,big_V(not(X_41),not(X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,big_V(not(X_41),not(X_40))) != not(big_V(not(X_39),big_hat(X_41,X_40)))
| not(big_V(not(X_39),big_hat(X_41,X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X_39,big_V(not(X_41),not(X_40))),not(big_V(not(X_39),big_hat(X_40,X_41)))) ),[0],$fot(not(big_V(not(X_39),big_hat(X_41,X_40))))]]) ).
cnf(refute_0_884,plain,
( big_hat(X_39,big_V(not(X_41),not(X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| not(big_V(not(X_39),big_hat(X_41,X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(big_hat(X_39,big_V(not(X_41),not(X_40))),not(big_V(not(X_39),big_hat(X_41,X_40)))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
not(big_V(not(X_39),big_hat(X_41,X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))),
inference(resolve,[$cnf( $equal(big_hat(X_39,big_V(not(X_41),not(X_40))),not(big_V(not(X_39),big_hat(X_40,X_41)))) )],[refute_0_881,refute_0_884]) ).
cnf(refute_0_886,plain,
big_V(not(X_8),not(X_9)) = not(big_hat(X_8,X_9)),
inference(subst,[],[refute_0_545:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_887,plain,
big_hat(X,big_V(not(X_8),not(X_9))) = big_hat(X,big_V(not(X_8),not(X_9))),
introduced(tautology,[refl,[$fot(big_hat(X,big_V(not(X_8),not(X_9))))]]) ).
cnf(refute_0_888,plain,
( big_V(not(X_8),not(X_9)) != not(big_hat(X_8,X_9))
| big_hat(X,big_V(not(X_8),not(X_9))) != big_hat(X,big_V(not(X_8),not(X_9)))
| big_hat(X,big_V(not(X_8),not(X_9))) = big_hat(X,not(big_hat(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),big_hat(X,big_V(not(X_8),not(X_9)))) ),[1,1],$fot(not(big_hat(X_8,X_9)))]]) ).
cnf(refute_0_889,plain,
( big_V(not(X_8),not(X_9)) != not(big_hat(X_8,X_9))
| big_hat(X,big_V(not(X_8),not(X_9))) = big_hat(X,not(big_hat(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),big_hat(X,big_V(not(X_8),not(X_9)))) )],[refute_0_887,refute_0_888]) ).
cnf(refute_0_890,plain,
big_hat(X,big_V(not(X_8),not(X_9))) = big_hat(X,not(big_hat(X_8,X_9))),
inference(resolve,[$cnf( $equal(big_V(not(X_8),not(X_9)),not(big_hat(X_8,X_9))) )],[refute_0_886,refute_0_889]) ).
cnf(refute_0_891,plain,
( big_hat(X,big_V(not(X_8),not(X_9))) != big_hat(X,not(big_hat(X_8,X_9)))
| big_hat(X,big_V(not(X_8),not(X_9))) != not(big_V(not(X),big_hat(X_8,X_9)))
| big_hat(X,not(big_hat(X_8,X_9))) = not(big_V(not(X),big_hat(X_8,X_9))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),not(big_V(not(X),big_hat(X_8,X_9)))) ),[0],$fot(big_hat(X,not(big_hat(X_8,X_9))))]]) ).
cnf(refute_0_892,plain,
( big_hat(X,big_V(not(X_8),not(X_9))) != not(big_V(not(X),big_hat(X_8,X_9)))
| big_hat(X,not(big_hat(X_8,X_9))) = not(big_V(not(X),big_hat(X_8,X_9))) ),
inference(resolve,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),big_hat(X,not(big_hat(X_8,X_9)))) )],[refute_0_890,refute_0_891]) ).
cnf(refute_0_893,plain,
big_hat(X,not(big_hat(X_8,X_9))) = not(big_V(not(X),big_hat(X_8,X_9))),
inference(resolve,[$cnf( $equal(big_hat(X,big_V(not(X_8),not(X_9))),not(big_V(not(X),big_hat(X_8,X_9)))) )],[refute_0_874,refute_0_892]) ).
cnf(refute_0_894,plain,
( big_hat(X,not(big_hat(X_8,X_9))) != not(big_V(not(X),big_hat(X_8,X_9)))
| not(big_V(not(X),big_hat(X_8,X_9))) = big_hat(X,not(big_hat(X_8,X_9))) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X,not(big_hat(X_8,X_9))))),bind(Y0,$fot(not(big_V(not(X),big_hat(X_8,X_9)))))]]) ).
cnf(refute_0_895,plain,
not(big_V(not(X),big_hat(X_8,X_9))) = big_hat(X,not(big_hat(X_8,X_9))),
inference(resolve,[$cnf( $equal(big_hat(X,not(big_hat(X_8,X_9))),not(big_V(not(X),big_hat(X_8,X_9)))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
not(big_V(not(X_39),big_hat(X_41,X_40))) = big_hat(X_39,not(big_hat(X_41,X_40))),
inference(subst,[],[refute_0_895:[bind(X,$fot(X_39)),bind(X_8,$fot(X_41)),bind(X_9,$fot(X_40))]]) ).
cnf(refute_0_897,plain,
( not(big_V(not(X_39),big_hat(X_41,X_40))) != big_hat(X_39,not(big_hat(X_41,X_40)))
| not(big_V(not(X_39),big_hat(X_41,X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,not(big_hat(X_41,X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(not(X_39),big_hat(X_41,X_40))),not(big_V(not(X_39),big_hat(X_40,X_41)))) ),[0],$fot(big_hat(X_39,not(big_hat(X_41,X_40))))]]) ).
cnf(refute_0_898,plain,
( not(big_V(not(X_39),big_hat(X_41,X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,not(big_hat(X_41,X_40))) = not(big_V(not(X_39),big_hat(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X_39),big_hat(X_41,X_40))),big_hat(X_39,not(big_hat(X_41,X_40)))) )],[refute_0_896,refute_0_897]) ).
cnf(refute_0_899,plain,
not(big_V(not(X_39),big_hat(X_40,X_41))) = big_hat(X_39,not(big_hat(X_40,X_41))),
inference(subst,[],[refute_0_895:[bind(X,$fot(X_39)),bind(X_8,$fot(X_40)),bind(X_9,$fot(X_41))]]) ).
cnf(refute_0_900,plain,
( big_hat(X_39,not(big_hat(X_41,X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| not(big_V(not(X_39),big_hat(X_40,X_41))) != big_hat(X_39,not(big_hat(X_40,X_41)))
| big_hat(X_39,not(big_hat(X_41,X_40))) = big_hat(X_39,not(big_hat(X_40,X_41))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(X_39,not(big_hat(X_41,X_40))),big_hat(X_39,not(big_hat(X_40,X_41)))) ),[0],$fot(not(big_V(not(X_39),big_hat(X_40,X_41))))]]) ).
cnf(refute_0_901,plain,
( big_hat(X_39,not(big_hat(X_41,X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,not(big_hat(X_41,X_40))) = big_hat(X_39,not(big_hat(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X_39),big_hat(X_40,X_41))),big_hat(X_39,not(big_hat(X_40,X_41)))) )],[refute_0_899,refute_0_900]) ).
cnf(refute_0_902,plain,
( not(big_V(not(X_39),big_hat(X_41,X_40))) != not(big_V(not(X_39),big_hat(X_40,X_41)))
| big_hat(X_39,not(big_hat(X_41,X_40))) = big_hat(X_39,not(big_hat(X_40,X_41))) ),
inference(resolve,[$cnf( $equal(big_hat(X_39,not(big_hat(X_41,X_40))),not(big_V(not(X_39),big_hat(X_40,X_41)))) )],[refute_0_898,refute_0_901]) ).
cnf(refute_0_903,plain,
big_hat(X_39,not(big_hat(X_41,X_40))) = big_hat(X_39,not(big_hat(X_40,X_41))),
inference(resolve,[$cnf( $equal(not(big_V(not(X_39),big_hat(X_41,X_40))),not(big_V(not(X_39),big_hat(X_40,X_41)))) )],[refute_0_885,refute_0_902]) ).
cnf(refute_0_904,plain,
big_hat(truth,not(big_hat(X_234,X_233))) = big_hat(truth,not(big_hat(X_233,X_234))),
inference(subst,[],[refute_0_903:[bind(X_39,$fot(truth)),bind(X_40,$fot(X_233)),bind(X_41,$fot(X_234))]]) ).
cnf(refute_0_905,plain,
( big_hat(truth,not(big_hat(X_234,X_233))) != big_hat(truth,not(big_hat(X_233,X_234)))
| big_hat(truth,not(big_hat(X_234,X_233))) != not(big_hat(X_234,X_233))
| big_hat(truth,not(big_hat(X_233,X_234))) = not(big_hat(X_234,X_233)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(truth,not(big_hat(X_234,X_233))),not(big_hat(X_234,X_233))) ),[0],$fot(big_hat(truth,not(big_hat(X_233,X_234))))]]) ).
cnf(refute_0_906,plain,
( big_hat(truth,not(big_hat(X_234,X_233))) != not(big_hat(X_234,X_233))
| big_hat(truth,not(big_hat(X_233,X_234))) = not(big_hat(X_234,X_233)) ),
inference(resolve,[$cnf( $equal(big_hat(truth,not(big_hat(X_234,X_233))),big_hat(truth,not(big_hat(X_233,X_234)))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
big_hat(truth,not(big_hat(X_233,X_234))) = not(big_hat(X_234,X_233)),
inference(resolve,[$cnf( $equal(big_hat(truth,not(big_hat(X_234,X_233))),not(big_hat(X_234,X_233))) )],[refute_0_868,refute_0_906]) ).
cnf(refute_0_908,plain,
big_hat(truth,not(big_hat(X_233,X_234))) = not(big_hat(X_233,X_234)),
inference(subst,[],[refute_0_867:[bind(Y,$fot(not(big_hat(X_233,X_234))))]]) ).
cnf(refute_0_909,plain,
( big_hat(truth,not(big_hat(X_233,X_234))) != not(big_hat(X_233,X_234))
| big_hat(truth,not(big_hat(X_233,X_234))) != not(big_hat(X_234,X_233))
| not(big_hat(X_233,X_234)) = not(big_hat(X_234,X_233)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(truth,not(big_hat(X_233,X_234))),not(big_hat(X_234,X_233))) ),[0],$fot(not(big_hat(X_233,X_234)))]]) ).
cnf(refute_0_910,plain,
( big_hat(truth,not(big_hat(X_233,X_234))) != not(big_hat(X_234,X_233))
| not(big_hat(X_233,X_234)) = not(big_hat(X_234,X_233)) ),
inference(resolve,[$cnf( $equal(big_hat(truth,not(big_hat(X_233,X_234))),not(big_hat(X_233,X_234))) )],[refute_0_908,refute_0_909]) ).
cnf(refute_0_911,plain,
not(big_hat(X_233,X_234)) = not(big_hat(X_234,X_233)),
inference(resolve,[$cnf( $equal(big_hat(truth,not(big_hat(X_233,X_234))),not(big_hat(X_234,X_233))) )],[refute_0_907,refute_0_910]) ).
cnf(refute_0_912,plain,
( not(big_hat(X_233,X_234)) != not(big_hat(X_234,X_233))
| not(big_hat(X_234,X_233)) = not(big_hat(X_233,X_234)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_233,X_234)))),bind(Y0,$fot(not(big_hat(X_234,X_233))))]]) ).
cnf(refute_0_913,plain,
not(big_hat(X_234,X_233)) = not(big_hat(X_233,X_234)),
inference(resolve,[$cnf( $equal(not(big_hat(X_233,X_234)),not(big_hat(X_234,X_233))) )],[refute_0_911,refute_0_912]) ).
cnf(refute_0_914,plain,
not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))),
inference(subst,[],[refute_0_913:[bind(X_233,$fot(not(X_283))),bind(X_234,$fot(implies(implies(not(X_16),X_283),X_16)))]]) ).
cnf(refute_0_915,plain,
( not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16)))
| not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))) != big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))))),bind(Y0,$fot(not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))))),bind(Z0,$fot(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))))]]) ).
cnf(refute_0_916,plain,
( not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))) != big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) ),
inference(resolve,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16)))) )],[refute_0_914,refute_0_915]) ).
cnf(refute_0_917,plain,
not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),
inference(resolve,[$cnf( $equal(not(big_hat(not(X_283),implies(implies(not(X_16),X_283),X_16))),big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))) )],[refute_0_858,refute_0_916]) ).
cnf(refute_0_918,plain,
( big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) != big_V(X_283,big_hat(X_283,not(X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,big_hat(X_283,not(X_16))) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))))),bind(Y0,$fot(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))))),bind(Z0,$fot(big_V(X_283,big_hat(X_283,not(X_16)))))]]) ).
cnf(refute_0_919,plain,
( big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))) != big_V(X_283,big_hat(X_283,not(X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,big_hat(X_283,not(X_16))) ),
inference(resolve,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),big_V(X_283,not(implies(implies(not(X_16),X_283),X_16)))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) = big_V(X_283,big_hat(X_283,not(X_16))),
inference(resolve,[$cnf( $equal(big_V(X_283,not(implies(implies(not(X_16),X_283),X_16))),big_V(X_283,big_hat(X_283,not(X_16)))) )],[refute_0_857,refute_0_919]) ).
cnf(refute_0_921,plain,
( not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != big_V(X_283,big_hat(X_283,not(X_16)))
| not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != implies(not(X_283),not(truth))
| big_V(X_283,big_hat(X_283,not(X_16))) = implies(not(X_283),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),implies(not(X_283),not(truth))) ),[0],$fot(big_V(X_283,big_hat(X_283,not(X_16))))]]) ).
cnf(refute_0_922,plain,
( not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != implies(not(X_283),not(truth))
| big_V(X_283,big_hat(X_283,not(X_16))) = implies(not(X_283),not(truth)) ),
inference(resolve,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),big_V(X_283,big_hat(X_283,not(X_16)))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
not(not(X_283)) = X_283,
inference(subst,[],[refute_0_577:[bind(X_84,$fot(X_283))]]) ).
cnf(refute_0_924,plain,
implies(truth,not(not(X_283))) = not(not(X_283)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_283))))]]) ).
cnf(refute_0_925,plain,
( implies(truth,not(not(X_283))) != not(not(X_283))
| not(not(X_283)) != X_283
| implies(truth,not(not(X_283))) = X_283 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(truth,not(not(X_283))))),bind(Y0,$fot(not(not(X_283)))),bind(Z0,$fot(X_283))]]) ).
cnf(refute_0_926,plain,
( not(not(X_283)) != X_283
| implies(truth,not(not(X_283))) = X_283 ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_283))),not(not(X_283))) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
implies(truth,not(not(X_283))) = X_283,
inference(resolve,[$cnf( $equal(not(not(X_283)),X_283) )],[refute_0_923,refute_0_926]) ).
cnf(refute_0_928,plain,
implies(not(X_283),not(truth)) = implies(truth,not(not(X_283))),
inference(subst,[],[refute_0_582:[bind(X_297,$fot(truth)),bind(X_84,$fot(not(X_283)))]]) ).
cnf(refute_0_929,plain,
( implies(not(X_283),not(truth)) != implies(truth,not(not(X_283)))
| implies(truth,not(not(X_283))) != X_283
| implies(not(X_283),not(truth)) = X_283 ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(X_283),not(truth)))),bind(Y0,$fot(implies(truth,not(not(X_283))))),bind(Z0,$fot(X_283))]]) ).
cnf(refute_0_930,plain,
( implies(truth,not(not(X_283))) != X_283
| implies(not(X_283),not(truth)) = X_283 ),
inference(resolve,[$cnf( $equal(implies(not(X_283),not(truth)),implies(truth,not(not(X_283)))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
implies(not(X_283),not(truth)) = X_283,
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_283))),X_283) )],[refute_0_927,refute_0_930]) ).
cnf(refute_0_932,plain,
( big_V(X_283,big_hat(X_283,not(X_16))) != implies(not(X_283),not(truth))
| implies(not(X_283),not(truth)) != X_283
| big_V(X_283,big_hat(X_283,not(X_16))) = X_283 ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X_283,big_hat(X_283,not(X_16))),X_283) ),[0],$fot(implies(not(X_283),not(truth)))]]) ).
cnf(refute_0_933,plain,
( big_V(X_283,big_hat(X_283,not(X_16))) != implies(not(X_283),not(truth))
| big_V(X_283,big_hat(X_283,not(X_16))) = X_283 ),
inference(resolve,[$cnf( $equal(implies(not(X_283),not(truth)),X_283) )],[refute_0_931,refute_0_932]) ).
cnf(refute_0_934,plain,
( not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))) != implies(not(X_283),not(truth))
| big_V(X_283,big_hat(X_283,not(X_16))) = X_283 ),
inference(resolve,[$cnf( $equal(big_V(X_283,big_hat(X_283,not(X_16))),implies(not(X_283),not(truth))) )],[refute_0_922,refute_0_933]) ).
cnf(refute_0_935,plain,
big_V(X_283,big_hat(X_283,not(X_16))) = X_283,
inference(resolve,[$cnf( $equal(not(big_hat(implies(implies(not(X_16),X_283),X_16),not(X_283))),implies(not(X_283),not(truth))) )],[refute_0_837,refute_0_934]) ).
cnf(refute_0_936,plain,
big_V(X_367,big_hat(X_367,not(not(X_84)))) = X_367,
inference(subst,[],[refute_0_935:[bind(X_16,$fot(not(X_84))),bind(X_283,$fot(X_367))]]) ).
cnf(refute_0_937,plain,
( big_V(X_367,big_hat(X_367,not(not(X_84)))) != X_367
| not(not(X_84)) != X_84
| big_V(X_367,big_hat(X_367,X_84)) = X_367 ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_367,big_hat(X_367,not(not(X_84)))),X_367) ),[0,1,1],$fot(X_84)]]) ).
cnf(refute_0_938,plain,
( big_V(X_367,big_hat(X_367,not(not(X_84)))) != X_367
| big_V(X_367,big_hat(X_367,X_84)) = X_367 ),
inference(resolve,[$cnf( $equal(not(not(X_84)),X_84) )],[refute_0_577,refute_0_937]) ).
cnf(refute_0_939,plain,
big_V(X_367,big_hat(X_367,X_84)) = X_367,
inference(resolve,[$cnf( $equal(big_V(X_367,big_hat(X_367,not(not(X_84)))),X_367) )],[refute_0_936,refute_0_938]) ).
cnf(refute_0_940,plain,
big_V(X_889,big_hat(X_889,X_462)) = X_889,
inference(subst,[],[refute_0_939:[bind(X_367,$fot(X_889)),bind(X_84,$fot(X_462))]]) ).
cnf(refute_0_941,plain,
implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) = implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))),
introduced(tautology,[refl,[$fot(implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))))]]) ).
cnf(refute_0_942,plain,
( big_V(X_889,big_hat(X_889,X_462)) != X_889
| implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) != implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))
| implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) = implies(X_889,implies(X_890,big_hat(X_889,X_462))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) ),[1,0],$fot(X_889)]]) ).
cnf(refute_0_943,plain,
( big_V(X_889,big_hat(X_889,X_462)) != X_889
| implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) = implies(X_889,implies(X_890,big_hat(X_889,X_462))) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) = implies(X_889,implies(X_890,big_hat(X_889,X_462))),
inference(resolve,[$cnf( $equal(big_V(X_889,big_hat(X_889,X_462)),X_889) )],[refute_0_940,refute_0_943]) ).
cnf(refute_0_945,plain,
( implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))) != implies(X_889,implies(X_890,big_hat(X_889,X_462)))
| ~ ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))))
| ordered(implies(X_890,implies(X_889,X_462)),implies(X_889,implies(X_890,big_hat(X_889,X_462)))) ),
introduced(tautology,[equality,[$cnf( ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) ),[1],$fot(implies(X_889,implies(X_890,big_hat(X_889,X_462))))]]) ).
cnf(refute_0_946,plain,
( ~ ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))))
| ordered(implies(X_890,implies(X_889,X_462)),implies(X_889,implies(X_890,big_hat(X_889,X_462)))) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462))),implies(X_889,implies(X_890,big_hat(X_889,X_462)))) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
ordered(implies(X_890,implies(X_889,X_462)),implies(X_889,implies(X_890,big_hat(X_889,X_462)))),
inference(resolve,[$cnf( ordered(implies(X_890,implies(X_889,X_462)),implies(big_V(X_889,big_hat(X_889,X_462)),implies(X_890,big_hat(X_889,X_462)))) )],[refute_0_797,refute_0_946]) ).
cnf(refute_0_948,plain,
ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,implies(implies(X_892,X_893),big_hat(X_893,X_892)))),
inference(subst,[],[refute_0_947:[bind(X_462,$fot(X_892)),bind(X_889,$fot(X_893)),bind(X_890,$fot(implies(X_892,X_893)))]]) ).
cnf(refute_0_949,plain,
big_V(X,not(implies(X,X_351))) = implies(implies(X,not(implies(X,X_351))),not(implies(X,X_351))),
inference(subst,[],[big_V_definition:[bind(Y,$fot(not(implies(X,X_351))))]]) ).
cnf(refute_0_950,plain,
not(big_hat(X_351,X)) = implies(X,not(implies(X,X_351))),
inference(subst,[],[refute_0_586:[bind(X_297,$fot(X)),bind(X_298,$fot(X_351))]]) ).
cnf(refute_0_951,plain,
( not(big_hat(X_351,X)) != implies(X,not(implies(X,X_351)))
| implies(X,not(implies(X,X_351))) = not(big_hat(X_351,X)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_351,X)))),bind(Y0,$fot(implies(X,not(implies(X,X_351)))))]]) ).
cnf(refute_0_952,plain,
implies(X,not(implies(X,X_351))) = not(big_hat(X_351,X)),
inference(resolve,[$cnf( $equal(not(big_hat(X_351,X)),implies(X,not(implies(X,X_351)))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
( big_V(X,not(implies(X,X_351))) != implies(implies(X,not(implies(X,X_351))),not(implies(X,X_351)))
| implies(X,not(implies(X,X_351))) != not(big_hat(X_351,X))
| big_V(X,not(implies(X,X_351))) = implies(not(big_hat(X_351,X)),not(implies(X,X_351))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(implies(X,X_351))),implies(implies(X,not(implies(X,X_351))),not(implies(X,X_351)))) ),[1,0],$fot(not(big_hat(X_351,X)))]]) ).
cnf(refute_0_954,plain,
( big_V(X,not(implies(X,X_351))) != implies(implies(X,not(implies(X,X_351))),not(implies(X,X_351)))
| big_V(X,not(implies(X,X_351))) = implies(not(big_hat(X_351,X)),not(implies(X,X_351))) ),
inference(resolve,[$cnf( $equal(implies(X,not(implies(X,X_351))),not(big_hat(X_351,X))) )],[refute_0_952,refute_0_953]) ).
cnf(refute_0_955,plain,
big_V(X,not(implies(X,X_351))) = implies(not(big_hat(X_351,X)),not(implies(X,X_351))),
inference(resolve,[$cnf( $equal(big_V(X,not(implies(X,X_351))),implies(implies(X,not(implies(X,X_351))),not(implies(X,X_351)))) )],[refute_0_949,refute_0_954]) ).
cnf(refute_0_956,plain,
big_V(not(big_V(not(Y),X_162)),Y) = implies(implies(not(big_V(not(Y),X_162)),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(big_V(not(Y),X_162))))]]) ).
cnf(refute_0_957,plain,
( ~ ordered(truth,implies(not(big_V(not(X_161),X_160)),X_161))
| implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(big_V(not(X_161),X_160)),X_161)))]]) ).
cnf(refute_0_958,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| ordered(implies(not(X),not(Y)),implies(Y,X)) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(implies(not(X),not(Y)))),bind(Y,$fot(implies(Y,X)))]]) ).
cnf(refute_0_959,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| truth != truth
| implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_960,plain,
( truth != truth
| implies(implies(not(X),not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_959]) ).
cnf(refute_0_961,plain,
( truth != truth
| ordered(implies(not(X),not(Y)),implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[refute_0_960,refute_0_958]) ).
cnf(refute_0_962,plain,
ordered(implies(not(X),not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_5,refute_0_961]) ).
cnf(refute_0_963,plain,
ordered(implies(not(X_96),not(not(X_84))),implies(not(X_84),X_96)),
inference(subst,[],[refute_0_962:[bind(X,$fot(X_96)),bind(Y,$fot(not(X_84)))]]) ).
cnf(refute_0_964,plain,
( not(not(X_84)) != X_84
| ~ ordered(implies(not(X_96),not(not(X_84))),implies(not(X_84),X_96))
| ordered(implies(not(X_96),X_84),implies(not(X_84),X_96)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(X_96),not(not(X_84))),implies(not(X_84),X_96)) ),[0,1],$fot(X_84)]]) ).
cnf(refute_0_965,plain,
( ~ ordered(implies(not(X_96),not(not(X_84))),implies(not(X_84),X_96))
| ordered(implies(not(X_96),X_84),implies(not(X_84),X_96)) ),
inference(resolve,[$cnf( $equal(not(not(X_84)),X_84) )],[refute_0_577,refute_0_964]) ).
cnf(refute_0_966,plain,
ordered(implies(not(X_96),X_84),implies(not(X_84),X_96)),
inference(resolve,[$cnf( ordered(implies(not(X_96),not(not(X_84))),implies(not(X_84),X_96)) )],[refute_0_963,refute_0_965]) ).
cnf(refute_0_967,plain,
ordered(implies(not(X_159),big_V(not(X_159),X_14)),implies(not(big_V(not(X_159),X_14)),X_159)),
inference(subst,[],[refute_0_966:[bind(X_84,$fot(big_V(not(X_159),X_14))),bind(X_96,$fot(X_159))]]) ).
cnf(refute_0_968,plain,
implies(not(X_159),big_V(not(X_159),X_14)) = truth,
inference(subst,[],[refute_0_128:[bind(X_13,$fot(not(X_159)))]]) ).
cnf(refute_0_969,plain,
( implies(not(X_159),big_V(not(X_159),X_14)) != truth
| ~ ordered(implies(not(X_159),big_V(not(X_159),X_14)),implies(not(big_V(not(X_159),X_14)),X_159))
| ordered(truth,implies(not(big_V(not(X_159),X_14)),X_159)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(X_159),big_V(not(X_159),X_14)),implies(not(big_V(not(X_159),X_14)),X_159)) ),[0],$fot(truth)]]) ).
cnf(refute_0_970,plain,
( ~ ordered(implies(not(X_159),big_V(not(X_159),X_14)),implies(not(big_V(not(X_159),X_14)),X_159))
| ordered(truth,implies(not(big_V(not(X_159),X_14)),X_159)) ),
inference(resolve,[$cnf( $equal(implies(not(X_159),big_V(not(X_159),X_14)),truth) )],[refute_0_968,refute_0_969]) ).
cnf(refute_0_971,plain,
ordered(truth,implies(not(big_V(not(X_159),X_14)),X_159)),
inference(resolve,[$cnf( ordered(implies(not(X_159),big_V(not(X_159),X_14)),implies(not(big_V(not(X_159),X_14)),X_159)) )],[refute_0_967,refute_0_970]) ).
cnf(refute_0_972,plain,
ordered(truth,implies(not(big_V(not(X_161),X_160)),X_161)),
inference(subst,[],[refute_0_971:[bind(X_14,$fot(X_160)),bind(X_159,$fot(X_161))]]) ).
cnf(refute_0_973,plain,
implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) = truth,
inference(resolve,[$cnf( ordered(truth,implies(not(big_V(not(X_161),X_160)),X_161)) )],[refute_0_972,refute_0_957]) ).
cnf(refute_0_974,plain,
implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) = implies(not(big_V(not(X_161),X_160)),X_161),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(big_V(not(X_161),X_160)),X_161)))]]) ).
cnf(refute_0_975,plain,
( implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) != implies(not(big_V(not(X_161),X_160)),X_161)
| implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) != truth
| implies(not(big_V(not(X_161),X_160)),X_161) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)),truth) ),[0],$fot(implies(not(big_V(not(X_161),X_160)),X_161))]]) ).
cnf(refute_0_976,plain,
( implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)) != truth
| implies(not(big_V(not(X_161),X_160)),X_161) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)),implies(not(big_V(not(X_161),X_160)),X_161)) )],[refute_0_974,refute_0_975]) ).
cnf(refute_0_977,plain,
implies(not(big_V(not(X_161),X_160)),X_161) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(big_V(not(X_161),X_160)),X_161)),truth) )],[refute_0_973,refute_0_976]) ).
cnf(refute_0_978,plain,
implies(not(big_V(not(Y),X_162)),Y) = truth,
inference(subst,[],[refute_0_977:[bind(X_160,$fot(X_162)),bind(X_161,$fot(Y))]]) ).
cnf(refute_0_979,plain,
( big_V(not(big_V(not(Y),X_162)),Y) != implies(implies(not(big_V(not(Y),X_162)),Y),Y)
| implies(not(big_V(not(Y),X_162)),Y) != truth
| big_V(not(big_V(not(Y),X_162)),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(big_V(not(Y),X_162)),Y),implies(implies(not(big_V(not(Y),X_162)),Y),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_980,plain,
( big_V(not(big_V(not(Y),X_162)),Y) != implies(implies(not(big_V(not(Y),X_162)),Y),Y)
| big_V(not(big_V(not(Y),X_162)),Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(implies(not(big_V(not(Y),X_162)),Y),truth) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
big_V(not(big_V(not(Y),X_162)),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(not(big_V(not(Y),X_162)),Y),implies(implies(not(big_V(not(Y),X_162)),Y),Y)) )],[refute_0_956,refute_0_980]) ).
cnf(refute_0_982,plain,
big_V(not(big_V(not(Y),X_162)),Y) = big_V(Y,not(big_V(not(Y),X_162))),
inference(subst,[],[refute_0_46:[bind(X,$fot(Y)),bind(Y,$fot(not(big_V(not(Y),X_162))))]]) ).
cnf(refute_0_983,plain,
( big_V(not(big_V(not(Y),X_162)),Y) != big_V(Y,not(big_V(not(Y),X_162)))
| big_V(not(big_V(not(Y),X_162)),Y) != implies(truth,Y)
| big_V(Y,not(big_V(not(Y),X_162))) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(big_V(not(Y),X_162)),Y),implies(truth,Y)) ),[0],$fot(big_V(Y,not(big_V(not(Y),X_162))))]]) ).
cnf(refute_0_984,plain,
( big_V(not(big_V(not(Y),X_162)),Y) != implies(truth,Y)
| big_V(Y,not(big_V(not(Y),X_162))) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(big_V(not(big_V(not(Y),X_162)),Y),big_V(Y,not(big_V(not(Y),X_162)))) )],[refute_0_982,refute_0_983]) ).
cnf(refute_0_985,plain,
( big_V(Y,not(big_V(not(Y),X_162))) != implies(truth,Y)
| implies(truth,Y) != Y
| big_V(Y,not(big_V(not(Y),X_162))) = Y ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(Y,not(big_V(not(Y),X_162))),Y) ),[0],$fot(implies(truth,Y))]]) ).
cnf(refute_0_986,plain,
( big_V(Y,not(big_V(not(Y),X_162))) != implies(truth,Y)
| big_V(Y,not(big_V(not(Y),X_162))) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_154,refute_0_985]) ).
cnf(refute_0_987,plain,
( big_V(not(big_V(not(Y),X_162)),Y) != implies(truth,Y)
| big_V(Y,not(big_V(not(Y),X_162))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,not(big_V(not(Y),X_162))),implies(truth,Y)) )],[refute_0_984,refute_0_986]) ).
cnf(refute_0_988,plain,
big_V(Y,not(big_V(not(Y),X_162))) = Y,
inference(resolve,[$cnf( $equal(big_V(not(big_V(not(Y),X_162)),Y),implies(truth,Y)) )],[refute_0_981,refute_0_987]) ).
cnf(refute_0_989,plain,
big_V(Y,not(big_V(not(Y),implies(Y,X_189)))) = Y,
inference(subst,[],[refute_0_988:[bind(X_162,$fot(implies(Y,X_189)))]]) ).
cnf(refute_0_990,plain,
big_V(not(Y),implies(Y,X_189)) = implies(Y,X_189),
inference(subst,[],[refute_0_625:[bind(X_114,$fot(Y)),bind(X_115,$fot(X_189))]]) ).
cnf(refute_0_991,plain,
( big_V(Y,not(big_V(not(Y),implies(Y,X_189)))) != Y
| big_V(not(Y),implies(Y,X_189)) != implies(Y,X_189)
| big_V(Y,not(implies(Y,X_189))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,not(big_V(not(Y),implies(Y,X_189)))),Y) ),[0,1,0],$fot(implies(Y,X_189))]]) ).
cnf(refute_0_992,plain,
( big_V(Y,not(big_V(not(Y),implies(Y,X_189)))) != Y
| big_V(Y,not(implies(Y,X_189))) = Y ),
inference(resolve,[$cnf( $equal(big_V(not(Y),implies(Y,X_189)),implies(Y,X_189)) )],[refute_0_990,refute_0_991]) ).
cnf(refute_0_993,plain,
big_V(Y,not(implies(Y,X_189))) = Y,
inference(resolve,[$cnf( $equal(big_V(Y,not(big_V(not(Y),implies(Y,X_189)))),Y) )],[refute_0_989,refute_0_992]) ).
cnf(refute_0_994,plain,
big_V(X,not(implies(X,X_351))) = X,
inference(subst,[],[refute_0_993:[bind(Y,$fot(X)),bind(X_189,$fot(X_351))]]) ).
cnf(refute_0_995,plain,
( big_V(X,not(implies(X,X_351))) != X
| big_V(X,not(implies(X,X_351))) != implies(not(big_hat(X_351,X)),not(implies(X,X_351)))
| X = implies(not(big_hat(X_351,X)),not(implies(X,X_351))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(implies(X,X_351))),implies(not(big_hat(X_351,X)),not(implies(X,X_351)))) ),[0],$fot(X)]]) ).
cnf(refute_0_996,plain,
( big_V(X,not(implies(X,X_351))) != implies(not(big_hat(X_351,X)),not(implies(X,X_351)))
| X = implies(not(big_hat(X_351,X)),not(implies(X,X_351))) ),
inference(resolve,[$cnf( $equal(big_V(X,not(implies(X,X_351))),X) )],[refute_0_994,refute_0_995]) ).
cnf(refute_0_997,plain,
not(not(big_hat(X_351,X))) = big_hat(X_351,X),
inference(subst,[],[refute_0_577:[bind(X_84,$fot(big_hat(X_351,X)))]]) ).
cnf(refute_0_998,plain,
implies(implies(X,X_351),not(not(big_hat(X_351,X)))) = implies(implies(X,X_351),not(not(big_hat(X_351,X)))),
introduced(tautology,[refl,[$fot(implies(implies(X,X_351),not(not(big_hat(X_351,X)))))]]) ).
cnf(refute_0_999,plain,
( implies(implies(X,X_351),not(not(big_hat(X_351,X)))) != implies(implies(X,X_351),not(not(big_hat(X_351,X))))
| not(not(big_hat(X_351,X))) != big_hat(X_351,X)
| implies(implies(X,X_351),not(not(big_hat(X_351,X)))) = implies(implies(X,X_351),big_hat(X_351,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X_351),not(not(big_hat(X_351,X)))),implies(implies(X,X_351),not(not(big_hat(X_351,X))))) ),[1,1],$fot(big_hat(X_351,X))]]) ).
cnf(refute_0_1000,plain,
( not(not(big_hat(X_351,X))) != big_hat(X_351,X)
| implies(implies(X,X_351),not(not(big_hat(X_351,X)))) = implies(implies(X,X_351),big_hat(X_351,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_351),not(not(big_hat(X_351,X)))),implies(implies(X,X_351),not(not(big_hat(X_351,X))))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
implies(implies(X,X_351),not(not(big_hat(X_351,X)))) = implies(implies(X,X_351),big_hat(X_351,X)),
inference(resolve,[$cnf( $equal(not(not(big_hat(X_351,X))),big_hat(X_351,X)) )],[refute_0_997,refute_0_1000]) ).
cnf(refute_0_1002,plain,
implies(not(big_hat(X_351,X)),not(implies(X,X_351))) = implies(implies(X,X_351),not(not(big_hat(X_351,X)))),
inference(subst,[],[refute_0_582:[bind(X_297,$fot(implies(X,X_351))),bind(X_84,$fot(not(big_hat(X_351,X))))]]) ).
cnf(refute_0_1003,plain,
( implies(implies(X,X_351),not(not(big_hat(X_351,X)))) != implies(implies(X,X_351),big_hat(X_351,X))
| implies(not(big_hat(X_351,X)),not(implies(X,X_351))) != implies(implies(X,X_351),not(not(big_hat(X_351,X))))
| implies(not(big_hat(X_351,X)),not(implies(X,X_351))) = implies(implies(X,X_351),big_hat(X_351,X)) ),
inference(subst,[],[refute_0_122:[bind(X0,$fot(implies(not(big_hat(X_351,X)),not(implies(X,X_351))))),bind(Y0,$fot(implies(implies(X,X_351),not(not(big_hat(X_351,X)))))),bind(Z0,$fot(implies(implies(X,X_351),big_hat(X_351,X))))]]) ).
cnf(refute_0_1004,plain,
( implies(implies(X,X_351),not(not(big_hat(X_351,X)))) != implies(implies(X,X_351),big_hat(X_351,X))
| implies(not(big_hat(X_351,X)),not(implies(X,X_351))) = implies(implies(X,X_351),big_hat(X_351,X)) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(X_351,X)),not(implies(X,X_351))),implies(implies(X,X_351),not(not(big_hat(X_351,X))))) )],[refute_0_1002,refute_0_1003]) ).
cnf(refute_0_1005,plain,
implies(not(big_hat(X_351,X)),not(implies(X,X_351))) = implies(implies(X,X_351),big_hat(X_351,X)),
inference(resolve,[$cnf( $equal(implies(implies(X,X_351),not(not(big_hat(X_351,X)))),implies(implies(X,X_351),big_hat(X_351,X))) )],[refute_0_1001,refute_0_1004]) ).
cnf(refute_0_1006,plain,
( X != implies(not(big_hat(X_351,X)),not(implies(X,X_351)))
| implies(not(big_hat(X_351,X)),not(implies(X,X_351))) != implies(implies(X,X_351),big_hat(X_351,X))
| X = implies(implies(X,X_351),big_hat(X_351,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,implies(implies(X,X_351),big_hat(X_351,X))) ),[0],$fot(implies(not(big_hat(X_351,X)),not(implies(X,X_351))))]]) ).
cnf(refute_0_1007,plain,
( X != implies(not(big_hat(X_351,X)),not(implies(X,X_351)))
| X = implies(implies(X,X_351),big_hat(X_351,X)) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(X_351,X)),not(implies(X,X_351))),implies(implies(X,X_351),big_hat(X_351,X))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
( big_V(X,not(implies(X,X_351))) != implies(not(big_hat(X_351,X)),not(implies(X,X_351)))
| X = implies(implies(X,X_351),big_hat(X_351,X)) ),
inference(resolve,[$cnf( $equal(X,implies(not(big_hat(X_351,X)),not(implies(X,X_351)))) )],[refute_0_996,refute_0_1007]) ).
cnf(refute_0_1009,plain,
X = implies(implies(X,X_351),big_hat(X_351,X)),
inference(resolve,[$cnf( $equal(big_V(X,not(implies(X,X_351))),implies(not(big_hat(X_351,X)),not(implies(X,X_351)))) )],[refute_0_955,refute_0_1008]) ).
cnf(refute_0_1010,plain,
X_892 = implies(implies(X_892,X_893),big_hat(X_893,X_892)),
inference(subst,[],[refute_0_1009:[bind(X,$fot(X_892)),bind(X_351,$fot(X_893))]]) ).
cnf(refute_0_1011,plain,
( X_892 != implies(implies(X_892,X_893),big_hat(X_893,X_892))
| implies(implies(X_892,X_893),big_hat(X_893,X_892)) = X_892 ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X_892)),bind(Y0,$fot(implies(implies(X_892,X_893),big_hat(X_893,X_892))))]]) ).
cnf(refute_0_1012,plain,
implies(implies(X_892,X_893),big_hat(X_893,X_892)) = X_892,
inference(resolve,[$cnf( $equal(X_892,implies(implies(X_892,X_893),big_hat(X_893,X_892))) )],[refute_0_1010,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( implies(implies(X_892,X_893),big_hat(X_893,X_892)) != X_892
| ~ ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,implies(implies(X_892,X_893),big_hat(X_893,X_892))))
| ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,X_892)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,implies(implies(X_892,X_893),big_hat(X_893,X_892)))) ),[1,1],$fot(X_892)]]) ).
cnf(refute_0_1014,plain,
( ~ ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,implies(implies(X_892,X_893),big_hat(X_893,X_892))))
| ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,X_892)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_892,X_893),big_hat(X_893,X_892)),X_892) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,X_892)),
inference(resolve,[$cnf( ordered(implies(implies(X_892,X_893),implies(X_893,X_892)),implies(X_893,implies(implies(X_892,X_893),big_hat(X_893,X_892)))) )],[refute_0_948,refute_0_1014]) ).
cnf(refute_0_1016,plain,
ordered(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)),
inference(subst,[],[refute_0_1015:[bind(X_892,$fot(X_2795)),bind(X_893,$fot(X_2796))]]) ).
cnf(refute_0_1017,plain,
implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) = truth,
inference(resolve,[$cnf( ordered(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) )],[refute_0_1016,refute_0_0]) ).
cnf(refute_0_1018,plain,
implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) = big_V(implies(X_2795,X_2796),implies(X_2796,X_2795)),
inference(subst,[],[refute_0_37:[bind(X,$fot(implies(X_2795,X_2796))),bind(Y,$fot(implies(X_2796,X_2795)))]]) ).
cnf(refute_0_1019,plain,
( implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) != big_V(implies(X_2795,X_2796),implies(X_2796,X_2795))
| implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) != truth
| big_V(implies(X_2795,X_2796),implies(X_2796,X_2795)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)),truth) ),[0],$fot(big_V(implies(X_2795,X_2796),implies(X_2796,X_2795)))]]) ).
cnf(refute_0_1020,plain,
( implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)) != truth
| big_V(implies(X_2795,X_2796),implies(X_2796,X_2795)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)),big_V(implies(X_2795,X_2796),implies(X_2796,X_2795))) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
big_V(implies(X_2795,X_2796),implies(X_2796,X_2795)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2795,X_2796),implies(X_2796,X_2795)),implies(X_2796,X_2795)),truth) )],[refute_0_1017,refute_0_1020]) ).
cnf(refute_0_1022,plain,
big_V(implies(x,y),implies(y,x)) = truth,
inference(subst,[],[refute_0_1021:[bind(X_2795,$fot(x)),bind(X_2796,$fot(y))]]) ).
cnf(refute_0_1023,plain,
( big_V(implies(x,y),implies(y,x)) != truth
| truth != truth
| big_V(implies(x,y),implies(y,x)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(x,y),implies(y,x)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_1024,plain,
( truth != truth
| big_V(implies(x,y),implies(y,x)) = truth ),
inference(resolve,[$cnf( $equal(big_V(implies(x,y),implies(y,x)),truth) )],[refute_0_1022,refute_0_1023]) ).
cnf(refute_0_1025,plain,
truth != truth,
inference(resolve,[$cnf( $equal(big_V(implies(x,y),implies(y,x)),truth) )],[refute_0_1024,prove_mv_4]) ).
cnf(refute_0_1026,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_5,refute_0_1025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL109-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 4 21:23:42 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 289.89/290.10 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 289.89/290.10
% 289.89/290.10 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 289.99/290.19
%------------------------------------------------------------------------------