TSTP Solution File: LCL109-5 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 12:49:35 EDT 2022
% Result : Unsatisfiable 9.04s 9.24s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 131
% Number of leaves : 230
% Syntax : Number of clauses : 1002 ( 514 unt; 0 nHn; 520 RR)
% Number of literals : 1702 (1683 equ; 702 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 1899 ( 147 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(lemma_1,axiom,
( ~ ordered(X,Y)
| ordered(implies(X,Z),implies(Y,Z)) ) ).
cnf(lemma_4,axiom,
not(big_V(X,Y)) = big_hat(not(X),not(Y)) ).
cnf(lemma_5,axiom,
not(big_hat(X,Y)) = big_V(not(X),not(Y)) ).
cnf(lemma_6,axiom,
implies(big_V(X,Y),Z) = big_hat(implies(X,Z),implies(Y,Z)) ).
cnf(lemma_7,axiom,
implies(X,big_hat(Y,Z)) = big_hat(implies(X,Y),implies(X,Z)) ).
cnf(prove_mv_4,negated_conjecture,
big_V(implies(x,y),implies(y,x)) != truth ).
cnf(refute_0_0,plain,
big_V(X,big_hat(X,X_84)) = implies(implies(X,big_hat(X,X_84)),big_hat(X,X_84)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(big_hat(X,X_84)))]]) ).
cnf(refute_0_1,plain,
implies(X_79,big_hat(X_79,X_80)) = big_hat(implies(X_79,X_79),implies(X_79,X_80)),
inference(subst,[],[lemma_7:[bind(X,$fot(X_79)),bind(Y,$fot(X_79)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_2,plain,
big_V(truth,X_2) = implies(implies(truth,X_2),X_2),
inference(subst,[],[big_V_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_3,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_4,plain,
( big_V(truth,X_2) != implies(implies(truth,X_2),X_2)
| implies(truth,X_2) != X_2
| big_V(truth,X_2) = implies(X_2,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_2),implies(implies(truth,X_2),X_2)) ),[1,0],$fot(X_2)]]) ).
cnf(refute_0_5,plain,
( big_V(truth,X_2) != implies(implies(truth,X_2),X_2)
| big_V(truth,X_2) = implies(X_2,X_2) ),
inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
big_V(truth,X_2) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),implies(implies(truth,X_2),X_2)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(implies(not(X_22),not(X_22)),implies(X_22,X_22)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_22)),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_8,plain,
big_V(truth,X_22) = implies(X_22,X_22),
inference(subst,[],[refute_0_6:[bind(X_2,$fot(X_22))]]) ).
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( $equal(X0,X0) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( big_V(truth,X_22) != implies(X_22,X_22)
| implies(X_22,X_22) = big_V(truth,X_22) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(truth,X_22))),bind(Y0,$fot(implies(X_22,X_22)))]]) ).
cnf(refute_0_13,plain,
implies(X_22,X_22) = big_V(truth,X_22),
inference(resolve,[$cnf( $equal(big_V(truth,X_22),implies(X_22,X_22)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(X_22,X_22) != big_V(truth,X_22)
| implies(implies(not(X_22),not(X_22)),implies(X_22,X_22)) != truth
| implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),implies(X_22,X_22)),truth) ),[0,1],$fot(big_V(truth,X_22))]]) ).
cnf(refute_0_15,plain,
( implies(implies(not(X_22),not(X_22)),implies(X_22,X_22)) != truth
| implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_22,X_22),big_V(truth,X_22)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),implies(X_22,X_22)),truth) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
( big_V(truth,X_2) != implies(X_2,X_2)
| implies(X_2,X_2) = big_V(truth,X_2) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(truth,X_2))),bind(Y0,$fot(implies(X_2,X_2)))]]) ).
cnf(refute_0_18,plain,
implies(X_2,X_2) = big_V(truth,X_2),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),implies(X_2,X_2)) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(not(X_22),not(X_22)) = big_V(truth,not(X_22)),
inference(subst,[],[refute_0_18:[bind(X_2,$fot(not(X_22)))]]) ).
cnf(refute_0_20,plain,
implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)))]]) ).
cnf(refute_0_21,plain,
( implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) != implies(implies(not(X_22),not(X_22)),big_V(truth,X_22))
| implies(not(X_22),not(X_22)) != big_V(truth,not(X_22))
| implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = implies(big_V(truth,not(X_22)),big_V(truth,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),implies(implies(not(X_22),not(X_22)),big_V(truth,X_22))) ),[1,0],$fot(big_V(truth,not(X_22)))]]) ).
cnf(refute_0_22,plain,
( implies(not(X_22),not(X_22)) != big_V(truth,not(X_22))
| implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = implies(big_V(truth,not(X_22)),big_V(truth,X_22)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),implies(implies(not(X_22),not(X_22)),big_V(truth,X_22))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) = implies(big_V(truth,not(X_22)),big_V(truth,X_22)),
inference(resolve,[$cnf( $equal(implies(not(X_22),not(X_22)),big_V(truth,not(X_22))) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
( implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) != implies(big_V(truth,not(X_22)),big_V(truth,X_22))
| implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) != truth
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),truth) ),[0],$fot(implies(big_V(truth,not(X_22)),big_V(truth,X_22)))]]) ).
cnf(refute_0_25,plain,
( implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)) != truth
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),implies(big_V(truth,not(X_22)),big_V(truth,X_22))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(X_22)),big_V(truth,X_22)),truth) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(truth,big_V(truth,X_22)) = big_V(truth,X_22),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(truth,X_22)))]]) ).
cnf(refute_0_28,plain,
implies(implies(not(X_22),not(truth)),implies(truth,X_22)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_22)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_29,plain,
implies(truth,X_22) = X_22,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_30,plain,
( implies(implies(not(X_22),not(truth)),implies(truth,X_22)) != truth
| implies(truth,X_22) != X_22
| implies(implies(not(X_22),not(truth)),X_22) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(truth)),implies(truth,X_22)),truth) ),[0,1],$fot(X_22)]]) ).
cnf(refute_0_31,plain,
( implies(implies(not(X_22),not(truth)),implies(truth,X_22)) != truth
| implies(implies(not(X_22),not(truth)),X_22) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_22),X_22) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(implies(not(X_22),not(truth)),X_22) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),implies(truth,X_22)),truth) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
big_V(implies(not(Y),not(truth)),Y) = implies(implies(implies(not(Y),not(truth)),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(Y),not(truth))))]]) ).
cnf(refute_0_34,plain,
implies(implies(not(Y),not(truth)),Y) = truth,
inference(subst,[],[refute_0_32:[bind(X_22,$fot(Y))]]) ).
cnf(refute_0_35,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(implies(implies(not(Y),not(truth)),Y),Y)
| implies(implies(not(Y),not(truth)),Y) != truth
| big_V(implies(not(Y),not(truth)),Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$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_36,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( $equal(implies(implies(not(Y),not(truth)),Y),truth) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
big_V(implies(not(Y),not(truth)),Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(implies(implies(not(Y),not(truth)),Y),Y)) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( big_V(X,Y) != implies(implies(X,Y),Y)
| implies(implies(X,Y),Y) = big_V(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(implies(implies(X,Y),Y)))]]) ).
cnf(refute_0_39,plain,
implies(implies(X,Y),Y) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(X,Y),Y)) )],[big_V_definition,refute_0_38]) ).
cnf(refute_0_40,plain,
( implies(implies(X,Y),Y) != big_V(X,Y)
| implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) ),[0],$fot(big_V(X,Y))]]) ).
cnf(refute_0_41,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = implies(implies(Y,X),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),big_V(X,Y)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(implies(Y,X),X) = big_V(Y,X),
inference(subst,[],[refute_0_39:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_43,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) != big_V(Y,X)
| big_V(X,Y) = big_V(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,Y),big_V(Y,X)) ),[0],$fot(implies(implies(Y,X),X))]]) ).
cnf(refute_0_44,plain,
( big_V(X,Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X),X),big_V(Y,X)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| big_V(X,Y) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(X,Y),implies(implies(Y,X),X)) )],[refute_0_41,refute_0_44]) ).
cnf(refute_0_46,plain,
big_V(X,Y) = big_V(Y,X),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_45]) ).
cnf(refute_0_47,plain,
( big_V(X,Y) != big_V(Y,X)
| big_V(Y,X) = big_V(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,Y))),bind(Y0,$fot(big_V(Y,X)))]]) ).
cnf(refute_0_48,plain,
big_V(Y,X) = big_V(X,Y),
inference(resolve,[$cnf( $equal(big_V(X,Y),big_V(Y,X)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
big_V(implies(not(Y),not(truth)),Y) = big_V(Y,implies(not(Y),not(truth))),
inference(subst,[],[refute_0_48:[bind(X,$fot(Y)),bind(Y,$fot(implies(not(Y),not(truth))))]]) ).
cnf(refute_0_50,plain,
( big_V(implies(not(Y),not(truth)),Y) != big_V(Y,implies(not(Y),not(truth)))
| big_V(implies(not(Y),not(truth)),Y) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = implies(truth,Y) ),
introduced(tautology,[equality,[$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_51,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( $equal(big_V(implies(not(Y),not(truth)),Y),big_V(Y,implies(not(Y),not(truth)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_53,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_54,plain,
( big_V(Y,implies(not(Y),not(truth))) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( big_V(implies(not(Y),not(truth)),Y) != implies(truth,Y)
| big_V(Y,implies(not(Y),not(truth))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),implies(truth,Y)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
big_V(Y,implies(not(Y),not(truth))) = Y,
inference(resolve,[$cnf( $equal(big_V(implies(not(Y),not(truth)),Y),implies(truth,Y)) )],[refute_0_37,refute_0_55]) ).
cnf(refute_0_57,plain,
big_V(not(not(X_33)),implies(not(not(not(X_33))),not(truth))) = not(not(X_33)),
inference(subst,[],[refute_0_56:[bind(Y,$fot(not(not(X_33))))]]) ).
cnf(refute_0_58,plain,
( not(big_hat(X,Y)) != big_V(not(X),not(Y))
| big_V(not(X),not(Y)) = not(big_hat(X,Y)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X,Y)))),bind(Y0,$fot(big_V(not(X),not(Y))))]]) ).
cnf(refute_0_59,plain,
big_V(not(X),not(Y)) = not(big_hat(X,Y)),
inference(resolve,[$cnf( $equal(not(big_hat(X,Y)),big_V(not(X),not(Y))) )],[lemma_5,refute_0_58]) ).
cnf(refute_0_60,plain,
not(big_V(not(X),not(Y))) = not(big_V(not(X),not(Y))),
introduced(tautology,[refl,[$fot(not(big_V(not(X),not(Y))))]]) ).
cnf(refute_0_61,plain,
( big_V(not(X),not(Y)) != not(big_hat(X,Y))
| not(big_V(not(X),not(Y))) != not(big_V(not(X),not(Y)))
| not(big_V(not(X),not(Y))) = not(not(big_hat(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(not(X),not(Y))),not(big_V(not(X),not(Y)))) ),[1,0],$fot(not(big_hat(X,Y)))]]) ).
cnf(refute_0_62,plain,
( big_V(not(X),not(Y)) != not(big_hat(X,Y))
| not(big_V(not(X),not(Y))) = not(not(big_hat(X,Y))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X),not(Y))),not(big_V(not(X),not(Y)))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
not(big_V(not(X),not(Y))) = not(not(big_hat(X,Y))),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( big_hat(X,Y) != not(big_V(not(X),not(Y)))
| not(big_V(not(X),not(Y))) != not(not(big_hat(X,Y)))
| big_hat(X,Y) = not(not(big_hat(X,Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(X,Y),not(not(big_hat(X,Y)))) ),[0],$fot(not(big_V(not(X),not(Y))))]]) ).
cnf(refute_0_65,plain,
( big_hat(X,Y) != not(big_V(not(X),not(Y)))
| big_hat(X,Y) = not(not(big_hat(X,Y))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(X),not(Y))),not(not(big_hat(X,Y)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
big_hat(X,Y) = not(not(big_hat(X,Y))),
inference(resolve,[$cnf( $equal(big_hat(X,Y),not(big_V(not(X),not(Y)))) )],[big_hat_definition,refute_0_65]) ).
cnf(refute_0_67,plain,
big_hat(not(X_8),not(X_9)) = not(not(big_hat(not(X_8),not(X_9)))),
inference(subst,[],[refute_0_66:[bind(X,$fot(not(X_8))),bind(Y,$fot(not(X_9)))]]) ).
cnf(refute_0_68,plain,
not(big_V(X_8,X_9)) = big_hat(not(X_8),not(X_9)),
inference(subst,[],[lemma_4:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_69,plain,
( not(big_V(X_8,X_9)) != big_hat(not(X_8),not(X_9))
| big_hat(not(X_8),not(X_9)) = not(big_V(X_8,X_9)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_V(X_8,X_9)))),bind(Y0,$fot(big_hat(not(X_8),not(X_9))))]]) ).
cnf(refute_0_70,plain,
big_hat(not(X_8),not(X_9)) = not(big_V(X_8,X_9)),
inference(resolve,[$cnf( $equal(not(big_V(X_8,X_9)),big_hat(not(X_8),not(X_9))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( big_hat(not(X_8),not(X_9)) != not(big_V(X_8,X_9))
| big_hat(not(X_8),not(X_9)) != not(not(big_hat(not(X_8),not(X_9))))
| big_hat(not(X_8),not(X_9)) = not(not(not(big_V(X_8,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(not(big_hat(not(X_8),not(X_9))))) ),[1,0,0],$fot(not(big_V(X_8,X_9)))]]) ).
cnf(refute_0_72,plain,
( big_hat(not(X_8),not(X_9)) != not(not(big_hat(not(X_8),not(X_9))))
| big_hat(not(X_8),not(X_9)) = not(not(not(big_V(X_8,X_9)))) ),
inference(resolve,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(big_V(X_8,X_9))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
big_hat(not(X_8),not(X_9)) = not(not(not(big_V(X_8,X_9)))),
inference(resolve,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(not(big_hat(not(X_8),not(X_9))))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
( big_hat(not(X_8),not(X_9)) != not(big_V(X_8,X_9))
| big_hat(not(X_8),not(X_9)) != not(not(not(big_V(X_8,X_9))))
| not(big_V(X_8,X_9)) = not(not(not(big_V(X_8,X_9)))) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(not(not(big_V(X_8,X_9))))) ),[0],$fot(not(big_V(X_8,X_9)))]]) ).
cnf(refute_0_75,plain,
( big_hat(not(X_8),not(X_9)) != not(not(not(big_V(X_8,X_9))))
| not(big_V(X_8,X_9)) = not(not(not(big_V(X_8,X_9)))) ),
inference(resolve,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(big_V(X_8,X_9))) )],[refute_0_70,refute_0_74]) ).
cnf(refute_0_76,plain,
not(big_V(X_8,X_9)) = not(not(not(big_V(X_8,X_9)))),
inference(resolve,[$cnf( $equal(big_hat(not(X_8),not(X_9)),not(not(not(big_V(X_8,X_9))))) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
not(big_V(X_8,implies(not(X_8),not(truth)))) = not(not(not(big_V(X_8,implies(not(X_8),not(truth)))))),
inference(subst,[],[refute_0_76:[bind(X_9,$fot(implies(not(X_8),not(truth))))]]) ).
cnf(refute_0_78,plain,
big_V(X_8,implies(not(X_8),not(truth))) = X_8,
inference(subst,[],[refute_0_56:[bind(Y,$fot(X_8))]]) ).
cnf(refute_0_79,plain,
( big_V(X_8,implies(not(X_8),not(truth))) != X_8
| not(big_V(X_8,implies(not(X_8),not(truth)))) != not(not(not(big_V(X_8,implies(not(X_8),not(truth))))))
| not(big_V(X_8,implies(not(X_8),not(truth)))) = not(not(not(X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(not(not(big_V(X_8,implies(not(X_8),not(truth))))))) ),[1,0,0,0],$fot(X_8)]]) ).
cnf(refute_0_80,plain,
( not(big_V(X_8,implies(not(X_8),not(truth)))) != not(not(not(big_V(X_8,implies(not(X_8),not(truth))))))
| not(big_V(X_8,implies(not(X_8),not(truth)))) = not(not(not(X_8))) ),
inference(resolve,[$cnf( $equal(big_V(X_8,implies(not(X_8),not(truth))),X_8) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
not(big_V(X_8,implies(not(X_8),not(truth)))) = not(not(not(X_8))),
inference(resolve,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(not(not(big_V(X_8,implies(not(X_8),not(truth))))))) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
not(big_V(X_8,implies(not(X_8),not(truth)))) = not(big_V(X_8,implies(not(X_8),not(truth)))),
introduced(tautology,[refl,[$fot(not(big_V(X_8,implies(not(X_8),not(truth)))))]]) ).
cnf(refute_0_83,plain,
( big_V(X_8,implies(not(X_8),not(truth))) != X_8
| not(big_V(X_8,implies(not(X_8),not(truth)))) != not(big_V(X_8,implies(not(X_8),not(truth))))
| not(big_V(X_8,implies(not(X_8),not(truth)))) = not(X_8) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(big_V(X_8,implies(not(X_8),not(truth))))) ),[1,0],$fot(X_8)]]) ).
cnf(refute_0_84,plain,
( big_V(X_8,implies(not(X_8),not(truth))) != X_8
| not(big_V(X_8,implies(not(X_8),not(truth)))) = not(X_8) ),
inference(resolve,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(big_V(X_8,implies(not(X_8),not(truth))))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
not(big_V(X_8,implies(not(X_8),not(truth)))) = not(X_8),
inference(resolve,[$cnf( $equal(big_V(X_8,implies(not(X_8),not(truth))),X_8) )],[refute_0_78,refute_0_84]) ).
cnf(refute_0_86,plain,
( not(big_V(X_8,implies(not(X_8),not(truth)))) != not(X_8)
| not(big_V(X_8,implies(not(X_8),not(truth)))) != not(not(not(X_8)))
| not(X_8) = not(not(not(X_8))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(not(not(X_8)))) ),[0],$fot(not(X_8))]]) ).
cnf(refute_0_87,plain,
( not(big_V(X_8,implies(not(X_8),not(truth)))) != not(not(not(X_8)))
| not(X_8) = not(not(not(X_8))) ),
inference(resolve,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(X_8)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
not(X_8) = not(not(not(X_8))),
inference(resolve,[$cnf( $equal(not(big_V(X_8,implies(not(X_8),not(truth)))),not(not(not(X_8)))) )],[refute_0_81,refute_0_87]) ).
cnf(refute_0_89,plain,
not(X_33) = not(not(not(X_33))),
inference(subst,[],[refute_0_88:[bind(X_8,$fot(X_33))]]) ).
cnf(refute_0_90,plain,
( not(X_33) != not(not(not(X_33)))
| not(not(not(X_33))) = not(X_33) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_33))),bind(Y0,$fot(not(not(not(X_33)))))]]) ).
cnf(refute_0_91,plain,
not(not(not(X_33))) = not(X_33),
inference(resolve,[$cnf( $equal(not(X_33),not(not(not(X_33)))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
( big_V(not(not(X_33)),implies(not(not(not(X_33))),not(truth))) != not(not(X_33))
| not(not(not(X_33))) != not(X_33)
| big_V(not(not(X_33)),implies(not(X_33),not(truth))) = not(not(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(X_33)),implies(not(not(not(X_33))),not(truth))),not(not(X_33))) ),[0,1,0],$fot(not(X_33))]]) ).
cnf(refute_0_93,plain,
( big_V(not(not(X_33)),implies(not(not(not(X_33))),not(truth))) != not(not(X_33))
| big_V(not(not(X_33)),implies(not(X_33),not(truth))) = not(not(X_33)) ),
inference(resolve,[$cnf( $equal(not(not(not(X_33))),not(X_33)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
big_V(not(not(X_33)),implies(not(X_33),not(truth))) = not(not(X_33)),
inference(resolve,[$cnf( $equal(big_V(not(not(X_33)),implies(not(not(not(X_33))),not(truth))),not(not(X_33))) )],[refute_0_57,refute_0_93]) ).
cnf(refute_0_95,plain,
big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = implies(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(X_23,X_22)),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(not(X_22),not(X_23)))),bind(Y,$fot(implies(X_23,X_22)))]]) ).
cnf(refute_0_96,plain,
implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_22)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_97,plain,
( big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != implies(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(X_23,X_22))
| implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != truth
| big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = implies(truth,implies(X_23,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(X_23,X_22))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_98,plain,
( big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != implies(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(X_23,X_22))
| big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = implies(truth,implies(X_23,X_22)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),truth) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = implies(truth,implies(X_23,X_22)),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(implies(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(X_23,X_22))) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) = big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))),
inference(subst,[],[refute_0_48:[bind(X,$fot(implies(X_23,X_22))),bind(Y,$fot(implies(not(X_22),not(X_23))))]]) ).
cnf(refute_0_101,plain,
( big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != big_V(implies(X_23,X_22),implies(not(X_22),not(X_23)))
| big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != implies(truth,implies(X_23,X_22))
| big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(truth,implies(X_23,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(truth,implies(X_23,X_22))) ),[0],$fot(big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))))]]) ).
cnf(refute_0_102,plain,
( big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != implies(truth,implies(X_23,X_22))
| big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(truth,implies(X_23,X_22)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)),big_V(implies(X_23,X_22),implies(not(X_22),not(X_23)))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
implies(truth,implies(X_23,X_22)) = implies(X_23,X_22),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_23,X_22)))]]) ).
cnf(refute_0_104,plain,
( big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) != implies(truth,implies(X_23,X_22))
| implies(truth,implies(X_23,X_22)) != implies(X_23,X_22)
| big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(X_23,X_22) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))),implies(X_23,X_22)) ),[0],$fot(implies(truth,implies(X_23,X_22)))]]) ).
cnf(refute_0_105,plain,
( big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) != implies(truth,implies(X_23,X_22))
| big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(X_23,X_22) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_23,X_22)),implies(X_23,X_22)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
( big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)) != implies(truth,implies(X_23,X_22))
| big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(X_23,X_22) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))),implies(truth,implies(X_23,X_22))) )],[refute_0_102,refute_0_105]) ).
cnf(refute_0_107,plain,
big_V(implies(X_23,X_22),implies(not(X_22),not(X_23))) = implies(X_23,X_22),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_22),not(X_23)),implies(X_23,X_22)),implies(truth,implies(X_23,X_22))) )],[refute_0_99,refute_0_106]) ).
cnf(refute_0_108,plain,
big_V(implies(X_36,not(truth)),implies(not(not(truth)),not(X_36))) = implies(X_36,not(truth)),
inference(subst,[],[refute_0_107:[bind(X_22,$fot(not(truth))),bind(X_23,$fot(X_36))]]) ).
cnf(refute_0_109,plain,
implies(implies(not(not(not(truth))),not(truth)),not(not(truth))) = truth,
inference(subst,[],[refute_0_32:[bind(X_22,$fot(not(not(truth))))]]) ).
cnf(refute_0_110,plain,
not(big_V(truth,truth)) = not(not(not(big_V(truth,truth)))),
inference(subst,[],[refute_0_76:[bind(X_8,$fot(truth)),bind(X_9,$fot(truth))]]) ).
cnf(refute_0_111,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_112,plain,
big_V(truth,truth) = implies(truth,truth),
inference(subst,[],[refute_0_6:[bind(X_2,$fot(truth))]]) ).
cnf(refute_0_113,plain,
( big_V(truth,truth) != implies(truth,truth)
| implies(truth,truth) = big_V(truth,truth) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(truth,truth))),bind(Y0,$fot(implies(truth,truth)))]]) ).
cnf(refute_0_114,plain,
implies(truth,truth) = big_V(truth,truth),
inference(resolve,[$cnf( $equal(big_V(truth,truth),implies(truth,truth)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( implies(truth,truth) != big_V(truth,truth)
| implies(truth,truth) != truth
| big_V(truth,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,truth),truth) ),[0],$fot(big_V(truth,truth))]]) ).
cnf(refute_0_116,plain,
( implies(truth,truth) != truth
| big_V(truth,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),big_V(truth,truth)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
big_V(truth,truth) = truth,
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
( big_V(truth,truth) != truth
| not(big_V(truth,truth)) != not(not(not(big_V(truth,truth))))
| not(big_V(truth,truth)) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,truth)),not(not(not(big_V(truth,truth))))) ),[1,0,0,0],$fot(truth)]]) ).
cnf(refute_0_119,plain,
( not(big_V(truth,truth)) != not(not(not(big_V(truth,truth))))
| not(big_V(truth,truth)) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(truth,truth),truth) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
not(big_V(truth,truth)) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(not(big_V(truth,truth)),not(not(not(big_V(truth,truth))))) )],[refute_0_110,refute_0_119]) ).
cnf(refute_0_121,plain,
not(big_V(truth,truth)) = not(big_V(truth,truth)),
introduced(tautology,[refl,[$fot(not(big_V(truth,truth)))]]) ).
cnf(refute_0_122,plain,
( big_V(truth,truth) != truth
| not(big_V(truth,truth)) != not(big_V(truth,truth))
| not(big_V(truth,truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,truth)),not(big_V(truth,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_123,plain,
( big_V(truth,truth) != truth
| not(big_V(truth,truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,truth)),not(big_V(truth,truth))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
not(big_V(truth,truth)) = not(truth),
inference(resolve,[$cnf( $equal(big_V(truth,truth),truth) )],[refute_0_117,refute_0_123]) ).
cnf(refute_0_125,plain,
( not(big_V(truth,truth)) != not(not(not(truth)))
| not(big_V(truth,truth)) != not(truth)
| not(truth) = not(not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(truth,truth)),not(not(not(truth)))) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_126,plain,
( not(big_V(truth,truth)) != not(not(not(truth)))
| not(truth) = not(not(not(truth))) ),
inference(resolve,[$cnf( $equal(not(big_V(truth,truth)),not(truth)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
not(truth) = not(not(not(truth))),
inference(resolve,[$cnf( $equal(not(big_V(truth,truth)),not(not(not(truth)))) )],[refute_0_120,refute_0_126]) ).
cnf(refute_0_128,plain,
( not(truth) != not(not(not(truth)))
| not(not(not(truth))) = not(truth) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(truth))),bind(Y0,$fot(not(not(not(truth)))))]]) ).
cnf(refute_0_129,plain,
not(not(not(truth))) = not(truth),
inference(resolve,[$cnf( $equal(not(truth),not(not(not(truth)))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
( implies(implies(not(not(not(truth))),not(truth)),not(not(truth))) != truth
| not(not(not(truth))) != not(truth)
| implies(implies(not(truth),not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),not(not(truth))),truth) ),[0,0,0],$fot(not(truth))]]) ).
cnf(refute_0_131,plain,
( implies(implies(not(not(not(truth))),not(truth)),not(not(truth))) != truth
| implies(implies(not(truth),not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(not(not(truth))),not(truth)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(not(truth),not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(truth))),not(truth)),not(not(truth))),truth) )],[refute_0_109,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(not(truth),not(truth)) = big_V(truth,not(truth)),
inference(subst,[],[refute_0_18:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_134,plain,
implies(implies(not(truth),not(truth)),not(not(truth))) = implies(implies(not(truth),not(truth)),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),not(truth)),not(not(truth))))]]) ).
cnf(refute_0_135,plain,
( implies(implies(not(truth),not(truth)),not(not(truth))) != implies(implies(not(truth),not(truth)),not(not(truth)))
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(implies(not(truth),not(truth)),not(not(truth))) = implies(big_V(truth,not(truth)),not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),not(not(truth))),implies(implies(not(truth),not(truth)),not(not(truth)))) ),[1,0],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_136,plain,
( implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(implies(not(truth),not(truth)),not(not(truth))) = implies(big_V(truth,not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),not(not(truth))),implies(implies(not(truth),not(truth)),not(not(truth)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(implies(not(truth),not(truth)),not(not(truth))) = implies(big_V(truth,not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( implies(implies(not(truth),not(truth)),not(not(truth))) != implies(big_V(truth,not(truth)),not(not(truth)))
| implies(implies(not(truth),not(truth)),not(not(truth))) != truth
| implies(big_V(truth,not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),not(truth)),not(not(truth))),truth) ),[0],$fot(implies(big_V(truth,not(truth)),not(not(truth))))]]) ).
cnf(refute_0_139,plain,
( implies(implies(not(truth),not(truth)),not(not(truth))) != truth
| implies(big_V(truth,not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),not(not(truth))),implies(big_V(truth,not(truth)),not(not(truth)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(big_V(truth,not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),not(truth)),not(not(truth))),truth) )],[refute_0_132,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_142,plain,
implies(implies(not(big_hat(truth,not(truth))),not(truth)),big_hat(truth,not(truth))) = truth,
inference(subst,[],[refute_0_32:[bind(X_22,$fot(big_hat(truth,not(truth))))]]) ).
cnf(refute_0_143,plain,
big_V(not(not(truth)),not(truth)) = implies(implies(not(not(truth)),not(truth)),not(truth)),
inference(subst,[],[big_V_definition:[bind(X,$fot(not(not(truth)))),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_144,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_32:[bind(X_22,$fot(not(truth)))]]) ).
cnf(refute_0_145,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_146,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( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
big_V(not(not(truth)),not(truth)) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),implies(implies(not(not(truth)),not(truth)),not(truth))) )],[refute_0_143,refute_0_146]) ).
cnf(refute_0_148,plain,
big_V(X_8,X_9) = big_V(X_9,X_8),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_8)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_149,plain,
( big_V(X_8,X_9) != big_V(X_9,X_8)
| not(big_V(X_8,X_9)) != not(not(not(big_V(X_8,X_9))))
| not(big_V(X_8,X_9)) = not(not(not(big_V(X_9,X_8)))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(X_8,X_9)),not(not(not(big_V(X_8,X_9))))) ),[1,0,0,0],$fot(big_V(X_9,X_8))]]) ).
cnf(refute_0_150,plain,
( not(big_V(X_8,X_9)) != not(not(not(big_V(X_8,X_9))))
| not(big_V(X_8,X_9)) = not(not(not(big_V(X_9,X_8)))) ),
inference(resolve,[$cnf( $equal(big_V(X_8,X_9),big_V(X_9,X_8)) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
not(big_V(X_8,X_9)) = not(not(not(big_V(X_9,X_8)))),
inference(resolve,[$cnf( $equal(not(big_V(X_8,X_9)),not(not(not(big_V(X_8,X_9))))) )],[refute_0_76,refute_0_150]) ).
cnf(refute_0_152,plain,
( not(big_V(X_8,X_9)) != not(not(not(big_V(X_8,X_9))))
| not(not(not(big_V(X_8,X_9)))) = not(big_V(X_8,X_9)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_V(X_8,X_9)))),bind(Y0,$fot(not(not(not(big_V(X_8,X_9))))))]]) ).
cnf(refute_0_153,plain,
not(not(not(big_V(X_8,X_9)))) = not(big_V(X_8,X_9)),
inference(resolve,[$cnf( $equal(not(big_V(X_8,X_9)),not(not(not(big_V(X_8,X_9))))) )],[refute_0_76,refute_0_152]) ).
cnf(refute_0_154,plain,
not(not(not(big_V(X_9,X_8)))) = not(big_V(X_9,X_8)),
inference(subst,[],[refute_0_153:[bind(X_8,$fot(X_9)),bind(X_9,$fot(X_8))]]) ).
cnf(refute_0_155,plain,
( not(big_V(X_8,X_9)) != not(not(not(big_V(X_9,X_8))))
| not(not(not(big_V(X_9,X_8)))) != not(big_V(X_9,X_8))
| not(big_V(X_8,X_9)) = not(big_V(X_9,X_8)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(not(big_V(X_8,X_9)),not(big_V(X_9,X_8))) ),[0],$fot(not(not(not(big_V(X_9,X_8)))))]]) ).
cnf(refute_0_156,plain,
( not(big_V(X_8,X_9)) != not(not(not(big_V(X_9,X_8))))
| not(big_V(X_8,X_9)) = not(big_V(X_9,X_8)) ),
inference(resolve,[$cnf( $equal(not(not(not(big_V(X_9,X_8)))),not(big_V(X_9,X_8))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
not(big_V(X_8,X_9)) = not(big_V(X_9,X_8)),
inference(resolve,[$cnf( $equal(not(big_V(X_8,X_9)),not(not(not(big_V(X_9,X_8))))) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
not(big_V(not(X),not(Y))) = not(big_V(not(Y),not(X))),
inference(subst,[],[refute_0_157:[bind(X_8,$fot(not(X))),bind(X_9,$fot(not(Y)))]]) ).
cnf(refute_0_159,plain,
( big_V(not(X),not(Y)) != not(big_hat(X,Y))
| not(big_V(not(X),not(Y))) != not(big_V(not(Y),not(X)))
| not(not(big_hat(X,Y))) = not(big_V(not(Y),not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(not(X),not(Y))),not(big_V(not(Y),not(X)))) ),[0,0],$fot(not(big_hat(X,Y)))]]) ).
cnf(refute_0_160,plain,
( not(big_V(not(X),not(Y))) != not(big_V(not(Y),not(X)))
| not(not(big_hat(X,Y))) = not(big_V(not(Y),not(X))) ),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) )],[refute_0_59,refute_0_159]) ).
cnf(refute_0_161,plain,
not(not(big_hat(X,Y))) = not(big_V(not(Y),not(X))),
inference(resolve,[$cnf( $equal(not(big_V(not(X),not(Y))),not(big_V(not(Y),not(X)))) )],[refute_0_158,refute_0_160]) ).
cnf(refute_0_162,plain,
( big_hat(X,Y) != not(not(big_hat(X,Y)))
| not(not(big_hat(X,Y))) = big_hat(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X,Y))),bind(Y0,$fot(not(not(big_hat(X,Y)))))]]) ).
cnf(refute_0_163,plain,
not(not(big_hat(X,Y))) = big_hat(X,Y),
inference(resolve,[$cnf( $equal(big_hat(X,Y),not(not(big_hat(X,Y)))) )],[refute_0_66,refute_0_162]) ).
cnf(refute_0_164,plain,
( not(not(big_hat(X,Y))) != big_hat(X,Y)
| not(not(big_hat(X,Y))) != not(big_V(not(Y),not(X)))
| big_hat(X,Y) = not(big_V(not(Y),not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(big_hat(X,Y))),not(big_V(not(Y),not(X)))) ),[0],$fot(big_hat(X,Y))]]) ).
cnf(refute_0_165,plain,
( not(not(big_hat(X,Y))) != not(big_V(not(Y),not(X)))
| big_hat(X,Y) = not(big_V(not(Y),not(X))) ),
inference(resolve,[$cnf( $equal(not(not(big_hat(X,Y))),big_hat(X,Y)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
not(not(big_hat(Y,X))) = big_hat(Y,X),
inference(subst,[],[refute_0_163:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_167,plain,
big_V(not(Y),not(X)) = not(big_hat(Y,X)),
inference(subst,[],[refute_0_59:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_168,plain,
not(big_V(not(Y),not(X))) = not(big_V(not(Y),not(X))),
introduced(tautology,[refl,[$fot(not(big_V(not(Y),not(X))))]]) ).
cnf(refute_0_169,plain,
( big_V(not(Y),not(X)) != not(big_hat(Y,X))
| not(big_V(not(Y),not(X))) != not(big_V(not(Y),not(X)))
| not(big_V(not(Y),not(X))) = not(not(big_hat(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_V(not(Y),not(X))),not(big_V(not(Y),not(X)))) ),[1,0],$fot(not(big_hat(Y,X)))]]) ).
cnf(refute_0_170,plain,
( big_V(not(Y),not(X)) != not(big_hat(Y,X))
| not(big_V(not(Y),not(X))) = not(not(big_hat(Y,X))) ),
inference(resolve,[$cnf( $equal(not(big_V(not(Y),not(X))),not(big_V(not(Y),not(X)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
not(big_V(not(Y),not(X))) = not(not(big_hat(Y,X))),
inference(resolve,[$cnf( $equal(big_V(not(Y),not(X)),not(big_hat(Y,X))) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_173,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_11,refute_0_172]) ).
cnf(refute_0_174,plain,
( not(big_V(not(Y),not(X))) != not(not(big_hat(Y,X)))
| not(not(big_hat(Y,X))) != big_hat(Y,X)
| not(big_V(not(Y),not(X))) = big_hat(Y,X) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(not(big_V(not(Y),not(X))))),bind(Y0,$fot(not(not(big_hat(Y,X))))),bind(Z0,$fot(big_hat(Y,X)))]]) ).
cnf(refute_0_175,plain,
( not(not(big_hat(Y,X))) != big_hat(Y,X)
| not(big_V(not(Y),not(X))) = big_hat(Y,X) ),
inference(resolve,[$cnf( $equal(not(big_V(not(Y),not(X))),not(not(big_hat(Y,X)))) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
not(big_V(not(Y),not(X))) = big_hat(Y,X),
inference(resolve,[$cnf( $equal(not(not(big_hat(Y,X))),big_hat(Y,X)) )],[refute_0_166,refute_0_175]) ).
cnf(refute_0_177,plain,
( big_hat(X,Y) != not(big_V(not(Y),not(X)))
| not(big_V(not(Y),not(X))) != big_hat(Y,X)
| big_hat(X,Y) = big_hat(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(X,Y),big_hat(Y,X)) ),[0],$fot(not(big_V(not(Y),not(X))))]]) ).
cnf(refute_0_178,plain,
( big_hat(X,Y) != not(big_V(not(Y),not(X)))
| big_hat(X,Y) = big_hat(Y,X) ),
inference(resolve,[$cnf( $equal(not(big_V(not(Y),not(X))),big_hat(Y,X)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( not(not(big_hat(X,Y))) != not(big_V(not(Y),not(X)))
| big_hat(X,Y) = big_hat(Y,X) ),
inference(resolve,[$cnf( $equal(big_hat(X,Y),not(big_V(not(Y),not(X)))) )],[refute_0_165,refute_0_178]) ).
cnf(refute_0_180,plain,
big_hat(X,Y) = big_hat(Y,X),
inference(resolve,[$cnf( $equal(not(not(big_hat(X,Y))),not(big_V(not(Y),not(X)))) )],[refute_0_161,refute_0_179]) ).
cnf(refute_0_181,plain,
( big_hat(X,Y) != big_hat(Y,X)
| not(big_hat(X,Y)) != big_V(not(X),not(Y))
| not(big_hat(Y,X)) = big_V(not(X),not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(X,Y)),big_V(not(X),not(Y))) ),[0,0],$fot(big_hat(Y,X))]]) ).
cnf(refute_0_182,plain,
( not(big_hat(X,Y)) != big_V(not(X),not(Y))
| not(big_hat(Y,X)) = big_V(not(X),not(Y)) ),
inference(resolve,[$cnf( $equal(big_hat(X,Y),big_hat(Y,X)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
not(big_hat(Y,X)) = big_V(not(X),not(Y)),
inference(resolve,[$cnf( $equal(not(big_hat(X,Y)),big_V(not(X),not(Y))) )],[lemma_5,refute_0_182]) ).
cnf(refute_0_184,plain,
( big_V(not(X),not(Y)) != not(big_hat(X,Y))
| not(big_hat(Y,X)) != big_V(not(X),not(Y))
| not(big_hat(Y,X)) = not(big_hat(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(Y,X)),big_V(not(X),not(Y))) ),[1],$fot(not(big_hat(X,Y)))]]) ).
cnf(refute_0_185,plain,
( not(big_hat(Y,X)) != big_V(not(X),not(Y))
| not(big_hat(Y,X)) = not(big_hat(X,Y)) ),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) )],[refute_0_59,refute_0_184]) ).
cnf(refute_0_186,plain,
not(big_hat(Y,X)) = not(big_hat(X,Y)),
inference(resolve,[$cnf( $equal(not(big_hat(Y,X)),big_V(not(X),not(Y))) )],[refute_0_183,refute_0_185]) ).
cnf(refute_0_187,plain,
( not(big_hat(Y,X)) != not(big_hat(X,Y))
| not(big_hat(X,Y)) = not(big_hat(Y,X)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(Y,X)))),bind(Y0,$fot(not(big_hat(X,Y))))]]) ).
cnf(refute_0_188,plain,
not(big_hat(X,Y)) = not(big_hat(Y,X)),
inference(resolve,[$cnf( $equal(not(big_hat(Y,X)),not(big_hat(X,Y))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
not(big_hat(not(truth),truth)) = not(big_hat(truth,not(truth))),
inference(subst,[],[refute_0_188:[bind(X,$fot(not(truth))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_190,plain,
big_V(not(not(truth)),not(truth)) = not(big_hat(not(truth),truth)),
inference(subst,[],[refute_0_59:[bind(X,$fot(not(truth))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_191,plain,
( big_V(not(not(truth)),not(truth)) != not(big_hat(not(truth),truth))
| not(big_hat(not(truth),truth)) != not(big_hat(truth,not(truth)))
| big_V(not(not(truth)),not(truth)) = not(big_hat(truth,not(truth))) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(not(not(truth)),not(truth)))),bind(Y0,$fot(not(big_hat(not(truth),truth)))),bind(Z0,$fot(not(big_hat(truth,not(truth)))))]]) ).
cnf(refute_0_192,plain,
( not(big_hat(not(truth),truth)) != not(big_hat(truth,not(truth)))
| big_V(not(not(truth)),not(truth)) = not(big_hat(truth,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),not(big_hat(not(truth),truth))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
big_V(not(not(truth)),not(truth)) = not(big_hat(truth,not(truth))),
inference(resolve,[$cnf( $equal(not(big_hat(not(truth),truth)),not(big_hat(truth,not(truth)))) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( big_V(not(not(truth)),not(truth)) != not(big_hat(truth,not(truth)))
| big_V(not(not(truth)),not(truth)) != truth
| not(big_hat(truth,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) ),[0],$fot(not(big_hat(truth,not(truth))))]]) ).
cnf(refute_0_195,plain,
( big_V(not(not(truth)),not(truth)) != truth
| not(big_hat(truth,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),not(big_hat(truth,not(truth)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
not(big_hat(truth,not(truth))) = truth,
inference(resolve,[$cnf( $equal(big_V(not(not(truth)),not(truth)),truth) )],[refute_0_147,refute_0_195]) ).
cnf(refute_0_197,plain,
( implies(implies(not(big_hat(truth,not(truth))),not(truth)),big_hat(truth,not(truth))) != truth
| not(big_hat(truth,not(truth))) != truth
| implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(big_hat(truth,not(truth))),not(truth)),big_hat(truth,not(truth))),truth) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_198,plain,
( implies(implies(not(big_hat(truth,not(truth))),not(truth)),big_hat(truth,not(truth))) != truth
| implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(not(big_hat(truth,not(truth))),truth) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(big_hat(truth,not(truth))),not(truth)),big_hat(truth,not(truth))),truth) )],[refute_0_142,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(truth,not(truth)) = not(truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(truth)))]]) ).
cnf(refute_0_201,plain,
implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = implies(implies(truth,not(truth)),big_hat(truth,not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(truth,not(truth)),big_hat(truth,not(truth))))]]) ).
cnf(refute_0_202,plain,
( implies(implies(truth,not(truth)),big_hat(truth,not(truth))) != implies(implies(truth,not(truth)),big_hat(truth,not(truth)))
| implies(truth,not(truth)) != not(truth)
| implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = implies(not(truth),big_hat(truth,not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(truth)),big_hat(truth,not(truth))),implies(implies(truth,not(truth)),big_hat(truth,not(truth)))) ),[1,0],$fot(not(truth))]]) ).
cnf(refute_0_203,plain,
( implies(truth,not(truth)) != not(truth)
| implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = implies(not(truth),big_hat(truth,not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(truth)),big_hat(truth,not(truth))),implies(implies(truth,not(truth)),big_hat(truth,not(truth)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(truth,not(truth)),big_hat(truth,not(truth))) = implies(not(truth),big_hat(truth,not(truth))),
inference(resolve,[$cnf( $equal(implies(truth,not(truth)),not(truth)) )],[refute_0_200,refute_0_203]) ).
cnf(refute_0_205,plain,
( implies(implies(truth,not(truth)),big_hat(truth,not(truth))) != implies(not(truth),big_hat(truth,not(truth)))
| implies(implies(truth,not(truth)),big_hat(truth,not(truth))) != truth
| implies(not(truth),big_hat(truth,not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(truth)),big_hat(truth,not(truth))),truth) ),[0],$fot(implies(not(truth),big_hat(truth,not(truth))))]]) ).
cnf(refute_0_206,plain,
( implies(implies(truth,not(truth)),big_hat(truth,not(truth))) != truth
| implies(not(truth),big_hat(truth,not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(truth)),big_hat(truth,not(truth))),implies(not(truth),big_hat(truth,not(truth)))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(not(truth),big_hat(truth,not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(truth)),big_hat(truth,not(truth))),truth) )],[refute_0_199,refute_0_206]) ).
cnf(refute_0_208,plain,
big_hat(truth,not(truth)) = not(not(big_hat(truth,not(truth)))),
inference(subst,[],[refute_0_66:[bind(X,$fot(truth)),bind(Y,$fot(not(truth)))]]) ).
cnf(refute_0_209,plain,
( big_hat(truth,not(truth)) != not(not(big_hat(truth,not(truth))))
| not(big_hat(truth,not(truth))) != truth
| big_hat(truth,not(truth)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(truth,not(truth)),not(not(big_hat(truth,not(truth))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_210,plain,
( big_hat(truth,not(truth)) != not(not(big_hat(truth,not(truth))))
| big_hat(truth,not(truth)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(big_hat(truth,not(truth))),truth) )],[refute_0_196,refute_0_209]) ).
cnf(refute_0_211,plain,
big_hat(truth,not(truth)) = not(truth),
inference(resolve,[$cnf( $equal(big_hat(truth,not(truth)),not(not(big_hat(truth,not(truth))))) )],[refute_0_208,refute_0_210]) ).
cnf(refute_0_212,plain,
implies(not(truth),big_hat(truth,not(truth))) = implies(not(truth),big_hat(truth,not(truth))),
introduced(tautology,[refl,[$fot(implies(not(truth),big_hat(truth,not(truth))))]]) ).
cnf(refute_0_213,plain,
( big_hat(truth,not(truth)) != not(truth)
| implies(not(truth),big_hat(truth,not(truth))) != implies(not(truth),big_hat(truth,not(truth)))
| implies(not(truth),big_hat(truth,not(truth))) = implies(not(truth),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),implies(not(truth),big_hat(truth,not(truth)))) ),[1,1],$fot(not(truth))]]) ).
cnf(refute_0_214,plain,
( big_hat(truth,not(truth)) != not(truth)
| implies(not(truth),big_hat(truth,not(truth))) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),implies(not(truth),big_hat(truth,not(truth)))) )],[refute_0_212,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(not(truth),big_hat(truth,not(truth))) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(big_hat(truth,not(truth)),not(truth)) )],[refute_0_211,refute_0_214]) ).
cnf(refute_0_216,plain,
( implies(not(truth),big_hat(truth,not(truth))) != implies(not(truth),not(truth))
| implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(not(truth),big_hat(truth,not(truth))) = big_V(truth,not(truth)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(truth),big_hat(truth,not(truth))))),bind(Y0,$fot(implies(not(truth),not(truth)))),bind(Z0,$fot(big_V(truth,not(truth))))]]) ).
cnf(refute_0_217,plain,
( implies(not(truth),not(truth)) != big_V(truth,not(truth))
| implies(not(truth),big_hat(truth,not(truth))) = big_V(truth,not(truth)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),implies(not(truth),not(truth))) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
implies(not(truth),big_hat(truth,not(truth))) = big_V(truth,not(truth)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),big_V(truth,not(truth))) )],[refute_0_133,refute_0_217]) ).
cnf(refute_0_219,plain,
( implies(not(truth),big_hat(truth,not(truth))) != big_V(truth,not(truth))
| implies(not(truth),big_hat(truth,not(truth))) != truth
| big_V(truth,not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),truth) ),[0],$fot(big_V(truth,not(truth)))]]) ).
cnf(refute_0_220,plain,
( implies(not(truth),big_hat(truth,not(truth))) != truth
| big_V(truth,not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),big_V(truth,not(truth))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
big_V(truth,not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(not(truth),big_hat(truth,not(truth))),truth) )],[refute_0_207,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(big_V(truth,not(truth)),not(not(truth))) = implies(big_V(truth,not(truth)),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(truth)),not(not(truth))))]]) ).
cnf(refute_0_223,plain,
( big_V(truth,not(truth)) != truth
| implies(big_V(truth,not(truth)),not(not(truth))) != implies(big_V(truth,not(truth)),not(not(truth)))
| implies(big_V(truth,not(truth)),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),implies(big_V(truth,not(truth)),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_224,plain,
( big_V(truth,not(truth)) != truth
| implies(big_V(truth,not(truth)),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),implies(big_V(truth,not(truth)),not(not(truth)))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
implies(big_V(truth,not(truth)),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(big_V(truth,not(truth)),truth) )],[refute_0_221,refute_0_224]) ).
cnf(refute_0_226,plain,
( implies(big_V(truth,not(truth)),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(big_V(truth,not(truth)),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,not(truth)),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_227,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(big_V(truth,not(truth)),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
implies(big_V(truth,not(truth)),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_141,refute_0_227]) ).
cnf(refute_0_229,plain,
( implies(big_V(truth,not(truth)),not(not(truth))) != not(not(truth))
| implies(big_V(truth,not(truth)),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_230,plain,
( implies(big_V(truth,not(truth)),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),not(not(truth))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(truth)),not(not(truth))),truth) )],[refute_0_140,refute_0_230]) ).
cnf(refute_0_232,plain,
( big_V(implies(X_36,not(truth)),implies(not(not(truth)),not(X_36))) != implies(X_36,not(truth))
| not(not(truth)) != truth
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = implies(X_36,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(not(not(truth)),not(X_36))),implies(X_36,not(truth))) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_233,plain,
( big_V(implies(X_36,not(truth)),implies(not(not(truth)),not(X_36))) != implies(X_36,not(truth))
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = implies(X_36,not(truth)) ),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = implies(X_36,not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(not(not(truth)),not(X_36))),implies(X_36,not(truth))) )],[refute_0_108,refute_0_233]) ).
cnf(refute_0_235,plain,
big_V(implies(X_36,not(truth)),not(X_36)) = big_V(not(X_36),implies(X_36,not(truth))),
inference(subst,[],[refute_0_48:[bind(X,$fot(not(X_36))),bind(Y,$fot(implies(X_36,not(truth))))]]) ).
cnf(refute_0_236,plain,
implies(truth,not(X_36)) = not(X_36),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X_36)))]]) ).
cnf(refute_0_237,plain,
big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),
introduced(tautology,[refl,[$fot(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))))]]) ).
cnf(refute_0_238,plain,
( big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) != big_V(implies(X_36,not(truth)),implies(truth,not(X_36)))
| implies(truth,not(X_36)) != not(X_36)
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(implies(X_36,not(truth)),not(X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),big_V(implies(X_36,not(truth)),implies(truth,not(X_36)))) ),[1,1],$fot(not(X_36))]]) ).
cnf(refute_0_239,plain,
( implies(truth,not(X_36)) != not(X_36)
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(implies(X_36,not(truth)),not(X_36)) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),big_V(implies(X_36,not(truth)),implies(truth,not(X_36)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(implies(X_36,not(truth)),not(X_36)),
inference(resolve,[$cnf( $equal(implies(truth,not(X_36)),not(X_36)) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) != big_V(implies(X_36,not(truth)),not(X_36))
| big_V(implies(X_36,not(truth)),not(X_36)) != big_V(not(X_36),implies(X_36,not(truth)))
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(not(X_36),implies(X_36,not(truth))) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))))),bind(Y0,$fot(big_V(implies(X_36,not(truth)),not(X_36)))),bind(Z0,$fot(big_V(not(X_36),implies(X_36,not(truth)))))]]) ).
cnf(refute_0_242,plain,
( big_V(implies(X_36,not(truth)),not(X_36)) != big_V(not(X_36),implies(X_36,not(truth)))
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(not(X_36),implies(X_36,not(truth))) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),big_V(implies(X_36,not(truth)),not(X_36))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) = big_V(not(X_36),implies(X_36,not(truth))),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),not(X_36)),big_V(not(X_36),implies(X_36,not(truth)))) )],[refute_0_235,refute_0_242]) ).
cnf(refute_0_244,plain,
( big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) != big_V(not(X_36),implies(X_36,not(truth)))
| big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) != implies(X_36,not(truth))
| big_V(not(X_36),implies(X_36,not(truth))) = implies(X_36,not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),implies(X_36,not(truth))) ),[0],$fot(big_V(not(X_36),implies(X_36,not(truth))))]]) ).
cnf(refute_0_245,plain,
( big_V(implies(X_36,not(truth)),implies(truth,not(X_36))) != implies(X_36,not(truth))
| big_V(not(X_36),implies(X_36,not(truth))) = implies(X_36,not(truth)) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),big_V(not(X_36),implies(X_36,not(truth)))) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
big_V(not(X_36),implies(X_36,not(truth))) = implies(X_36,not(truth)),
inference(resolve,[$cnf( $equal(big_V(implies(X_36,not(truth)),implies(truth,not(X_36))),implies(X_36,not(truth))) )],[refute_0_234,refute_0_245]) ).
cnf(refute_0_247,plain,
big_V(not(not(X_33)),implies(not(X_33),not(truth))) = implies(not(X_33),not(truth)),
inference(subst,[],[refute_0_246:[bind(X_36,$fot(not(X_33)))]]) ).
cnf(refute_0_248,plain,
( big_V(not(not(X_33)),implies(not(X_33),not(truth))) != implies(not(X_33),not(truth))
| big_V(not(not(X_33)),implies(not(X_33),not(truth))) != not(not(X_33))
| implies(not(X_33),not(truth)) = not(not(X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(X_33)),implies(not(X_33),not(truth))),not(not(X_33))) ),[0],$fot(implies(not(X_33),not(truth)))]]) ).
cnf(refute_0_249,plain,
( big_V(not(not(X_33)),implies(not(X_33),not(truth))) != not(not(X_33))
| implies(not(X_33),not(truth)) = not(not(X_33)) ),
inference(resolve,[$cnf( $equal(big_V(not(not(X_33)),implies(not(X_33),not(truth))),implies(not(X_33),not(truth))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
implies(not(X_33),not(truth)) = not(not(X_33)),
inference(resolve,[$cnf( $equal(big_V(not(not(X_33)),implies(not(X_33),not(truth))),not(not(X_33))) )],[refute_0_94,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(not(X_22),not(truth)) = not(not(X_22)),
inference(subst,[],[refute_0_250:[bind(X_33,$fot(X_22))]]) ).
cnf(refute_0_252,plain,
implies(implies(not(X_22),not(truth)),X_22) = implies(implies(not(X_22),not(truth)),X_22),
introduced(tautology,[refl,[$fot(implies(implies(not(X_22),not(truth)),X_22))]]) ).
cnf(refute_0_253,plain,
( implies(implies(not(X_22),not(truth)),X_22) != implies(implies(not(X_22),not(truth)),X_22)
| implies(not(X_22),not(truth)) != not(not(X_22))
| implies(implies(not(X_22),not(truth)),X_22) = implies(not(not(X_22)),X_22) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(truth)),X_22),implies(implies(not(X_22),not(truth)),X_22)) ),[1,0],$fot(not(not(X_22)))]]) ).
cnf(refute_0_254,plain,
( implies(not(X_22),not(truth)) != not(not(X_22))
| implies(implies(not(X_22),not(truth)),X_22) = implies(not(not(X_22)),X_22) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),X_22),implies(implies(not(X_22),not(truth)),X_22)) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(implies(not(X_22),not(truth)),X_22) = implies(not(not(X_22)),X_22),
inference(resolve,[$cnf( $equal(implies(not(X_22),not(truth)),not(not(X_22))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
( implies(implies(not(X_22),not(truth)),X_22) != implies(not(not(X_22)),X_22)
| implies(implies(not(X_22),not(truth)),X_22) != truth
| implies(not(not(X_22)),X_22) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_22),not(truth)),X_22),truth) ),[0],$fot(implies(not(not(X_22)),X_22))]]) ).
cnf(refute_0_257,plain,
( implies(implies(not(X_22),not(truth)),X_22) != truth
| implies(not(not(X_22)),X_22) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),X_22),implies(not(not(X_22)),X_22)) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(not(not(X_22)),X_22) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_22),not(truth)),X_22),truth) )],[refute_0_32,refute_0_257]) ).
cnf(refute_0_259,plain,
implies(not(not(not(X_8))),not(X_8)) = truth,
inference(subst,[],[refute_0_258:[bind(X_22,$fot(not(X_8)))]]) ).
cnf(refute_0_260,plain,
( not(X_8) != not(not(not(X_8)))
| not(not(not(X_8))) = not(X_8) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_8))),bind(Y0,$fot(not(not(not(X_8)))))]]) ).
cnf(refute_0_261,plain,
not(not(not(X_8))) = not(X_8),
inference(resolve,[$cnf( $equal(not(X_8),not(not(not(X_8)))) )],[refute_0_88,refute_0_260]) ).
cnf(refute_0_262,plain,
( implies(not(not(not(X_8))),not(X_8)) != truth
| not(not(not(X_8))) != not(X_8)
| implies(not(X_8),not(X_8)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(not(X_8))),not(X_8)),truth) ),[0,0],$fot(not(X_8))]]) ).
cnf(refute_0_263,plain,
( implies(not(not(not(X_8))),not(X_8)) != truth
| implies(not(X_8),not(X_8)) = truth ),
inference(resolve,[$cnf( $equal(not(not(not(X_8))),not(X_8)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(not(X_8),not(X_8)) = truth,
inference(resolve,[$cnf( $equal(implies(not(not(not(X_8))),not(X_8)),truth) )],[refute_0_259,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(not(X_8),not(X_8)) = big_V(truth,not(X_8)),
inference(subst,[],[refute_0_18:[bind(X_2,$fot(not(X_8)))]]) ).
cnf(refute_0_266,plain,
( implies(not(X_8),not(X_8)) != big_V(truth,not(X_8))
| implies(not(X_8),not(X_8)) != truth
| big_V(truth,not(X_8)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_8),not(X_8)),truth) ),[0],$fot(big_V(truth,not(X_8)))]]) ).
cnf(refute_0_267,plain,
( implies(not(X_8),not(X_8)) != truth
| big_V(truth,not(X_8)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_8),not(X_8)),big_V(truth,not(X_8))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
big_V(truth,not(X_8)) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_8),not(X_8)),truth) )],[refute_0_264,refute_0_267]) ).
cnf(refute_0_269,plain,
big_V(truth,not(X_22)) = truth,
inference(subst,[],[refute_0_268:[bind(X_8,$fot(X_22))]]) ).
cnf(refute_0_270,plain,
implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = implies(big_V(truth,not(X_22)),big_V(truth,X_22)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(X_22)),big_V(truth,X_22)))]]) ).
cnf(refute_0_271,plain,
( big_V(truth,not(X_22)) != truth
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) != implies(big_V(truth,not(X_22)),big_V(truth,X_22))
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = implies(truth,big_V(truth,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),implies(big_V(truth,not(X_22)),big_V(truth,X_22))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_272,plain,
( big_V(truth,not(X_22)) != truth
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = implies(truth,big_V(truth,X_22)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),implies(big_V(truth,not(X_22)),big_V(truth,X_22))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = implies(truth,big_V(truth,X_22)),
inference(resolve,[$cnf( $equal(big_V(truth,not(X_22)),truth) )],[refute_0_269,refute_0_272]) ).
cnf(refute_0_274,plain,
( implies(big_V(truth,not(X_22)),big_V(truth,X_22)) != implies(truth,big_V(truth,X_22))
| implies(truth,big_V(truth,X_22)) != big_V(truth,X_22)
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = big_V(truth,X_22) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,not(X_22)),big_V(truth,X_22)))),bind(Y0,$fot(implies(truth,big_V(truth,X_22)))),bind(Z0,$fot(big_V(truth,X_22)))]]) ).
cnf(refute_0_275,plain,
( implies(truth,big_V(truth,X_22)) != big_V(truth,X_22)
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = big_V(truth,X_22) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),implies(truth,big_V(truth,X_22))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
implies(big_V(truth,not(X_22)),big_V(truth,X_22)) = big_V(truth,X_22),
inference(resolve,[$cnf( $equal(implies(truth,big_V(truth,X_22)),big_V(truth,X_22)) )],[refute_0_27,refute_0_275]) ).
cnf(refute_0_277,plain,
( implies(big_V(truth,not(X_22)),big_V(truth,X_22)) != big_V(truth,X_22)
| implies(big_V(truth,not(X_22)),big_V(truth,X_22)) != truth
| big_V(truth,X_22) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),truth) ),[0],$fot(big_V(truth,X_22))]]) ).
cnf(refute_0_278,plain,
( implies(big_V(truth,not(X_22)),big_V(truth,X_22)) != truth
| big_V(truth,X_22) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),big_V(truth,X_22)) )],[refute_0_276,refute_0_277]) ).
cnf(refute_0_279,plain,
big_V(truth,X_22) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_22)),big_V(truth,X_22)),truth) )],[refute_0_26,refute_0_278]) ).
cnf(refute_0_280,plain,
big_V(truth,X_2) = truth,
inference(subst,[],[refute_0_279:[bind(X_22,$fot(X_2))]]) ).
cnf(refute_0_281,plain,
( big_V(truth,X_2) != implies(X_2,X_2)
| big_V(truth,X_2) != truth
| truth = implies(X_2,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(truth,X_2),implies(X_2,X_2)) ),[0],$fot(truth)]]) ).
cnf(refute_0_282,plain,
( big_V(truth,X_2) != implies(X_2,X_2)
| truth = implies(X_2,X_2) ),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),truth) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
truth = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(big_V(truth,X_2),implies(X_2,X_2)) )],[refute_0_6,refute_0_282]) ).
cnf(refute_0_284,plain,
truth = implies(X_79,X_79),
inference(subst,[],[refute_0_283:[bind(X_2,$fot(X_79))]]) ).
cnf(refute_0_285,plain,
( truth != implies(X_79,X_79)
| implies(X_79,X_79) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_79,X_79)))]]) ).
cnf(refute_0_286,plain,
implies(X_79,X_79) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_79,X_79)) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
( implies(X_79,X_79) != truth
| implies(X_79,big_hat(X_79,X_80)) != big_hat(implies(X_79,X_79),implies(X_79,X_80))
| implies(X_79,big_hat(X_79,X_80)) = big_hat(truth,implies(X_79,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_79,big_hat(X_79,X_80)),big_hat(implies(X_79,X_79),implies(X_79,X_80))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_288,plain,
( implies(X_79,big_hat(X_79,X_80)) != big_hat(implies(X_79,X_79),implies(X_79,X_80))
| implies(X_79,big_hat(X_79,X_80)) = big_hat(truth,implies(X_79,X_80)) ),
inference(resolve,[$cnf( $equal(implies(X_79,X_79),truth) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
implies(X_79,big_hat(X_79,X_80)) = big_hat(truth,implies(X_79,X_80)),
inference(resolve,[$cnf( $equal(implies(X_79,big_hat(X_79,X_80)),big_hat(implies(X_79,X_79),implies(X_79,X_80))) )],[refute_0_1,refute_0_288]) ).
cnf(refute_0_290,plain,
implies(big_V(X_59,X_61),X_61) = big_hat(implies(X_59,X_61),implies(X_61,X_61)),
inference(subst,[],[lemma_6:[bind(X,$fot(X_59)),bind(Y,$fot(X_61)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_291,plain,
truth = implies(X_61,X_61),
inference(subst,[],[refute_0_283:[bind(X_2,$fot(X_61))]]) ).
cnf(refute_0_292,plain,
( truth != implies(X_61,X_61)
| implies(X_61,X_61) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_61,X_61)))]]) ).
cnf(refute_0_293,plain,
implies(X_61,X_61) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_61,X_61)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
( implies(X_61,X_61) != truth
| implies(big_V(X_59,X_61),X_61) != big_hat(implies(X_59,X_61),implies(X_61,X_61))
| implies(big_V(X_59,X_61),X_61) = big_hat(implies(X_59,X_61),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,X_61),X_61),big_hat(implies(X_59,X_61),implies(X_61,X_61))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_295,plain,
( implies(big_V(X_59,X_61),X_61) != big_hat(implies(X_59,X_61),implies(X_61,X_61))
| implies(big_V(X_59,X_61),X_61) = big_hat(implies(X_59,X_61),truth) ),
inference(resolve,[$cnf( $equal(implies(X_61,X_61),truth) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
implies(big_V(X_59,X_61),X_61) = big_hat(implies(X_59,X_61),truth),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_61),X_61),big_hat(implies(X_59,X_61),implies(X_61,X_61))) )],[refute_0_290,refute_0_295]) ).
cnf(refute_0_297,plain,
big_V(implies(X_1,Y),Y) = implies(implies(implies(X_1,Y),Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(implies(X_1,Y)))]]) ).
cnf(refute_0_298,plain,
big_V(X_1,Y) = implies(implies(X_1,Y),Y),
inference(subst,[],[big_V_definition:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_299,plain,
( big_V(X_1,Y) != implies(implies(X_1,Y),Y)
| implies(implies(X_1,Y),Y) = big_V(X_1,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_1,Y))),bind(Y0,$fot(implies(implies(X_1,Y),Y)))]]) ).
cnf(refute_0_300,plain,
implies(implies(X_1,Y),Y) = big_V(X_1,Y),
inference(resolve,[$cnf( $equal(big_V(X_1,Y),implies(implies(X_1,Y),Y)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
( big_V(implies(X_1,Y),Y) != implies(implies(implies(X_1,Y),Y),Y)
| implies(implies(X_1,Y),Y) != big_V(X_1,Y)
| big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(implies(implies(X_1,Y),Y),Y)) ),[1,0],$fot(big_V(X_1,Y))]]) ).
cnf(refute_0_302,plain,
( big_V(implies(X_1,Y),Y) != implies(implies(implies(X_1,Y),Y),Y)
| big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1,Y),Y),big_V(X_1,Y)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
big_V(implies(X_1,Y),Y) = implies(big_V(X_1,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(implies(implies(X_1,Y),Y),Y)) )],[refute_0_297,refute_0_302]) ).
cnf(refute_0_304,plain,
big_V(implies(X_1,Y),Y) = big_V(Y,implies(X_1,Y)),
inference(subst,[],[refute_0_48:[bind(X,$fot(Y)),bind(Y,$fot(implies(X_1,Y)))]]) ).
cnf(refute_0_305,plain,
( big_V(implies(X_1,Y),Y) != big_V(Y,implies(X_1,Y))
| big_V(implies(X_1,Y),Y) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(big_V(X_1,Y),Y)) ),[0],$fot(big_V(Y,implies(X_1,Y)))]]) ).
cnf(refute_0_306,plain,
( big_V(implies(X_1,Y),Y) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),big_V(Y,implies(X_1,Y))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
big_V(Y,implies(X_1,Y)) = implies(big_V(X_1,Y),Y),
inference(resolve,[$cnf( $equal(big_V(implies(X_1,Y),Y),implies(big_V(X_1,Y),Y)) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
big_V(X,implies(X_55,X)) = implies(implies(X,implies(X_55,X)),implies(X_55,X)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(implies(X_55,X)))]]) ).
cnf(refute_0_309,plain,
implies(implies(X_47,truth),implies(implies(truth,X_49),implies(X_47,X_49))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_47)),bind(Y,$fot(truth)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_310,plain,
implies(truth,X_49) = X_49,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_49))]]) ).
cnf(refute_0_311,plain,
( implies(implies(X_47,truth),implies(implies(truth,X_49),implies(X_47,X_49))) != truth
| implies(truth,X_49) != X_49
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,truth),implies(implies(truth,X_49),implies(X_47,X_49))),truth) ),[0,1,0],$fot(X_49)]]) ).
cnf(refute_0_312,plain,
( implies(implies(X_47,truth),implies(implies(truth,X_49),implies(X_47,X_49))) != truth
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_49),X_49) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_47,truth),implies(implies(truth,X_49),implies(X_47,X_49))),truth) )],[refute_0_309,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(truth,implies(X_49,implies(X_47,X_49))) = implies(X_49,implies(X_47,X_49)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_49,implies(X_47,X_49))))]]) ).
cnf(refute_0_315,plain,
implies(implies(truth,X_48),implies(implies(X_48,X_49),implies(truth,X_49))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_316,plain,
( implies(implies(truth,X_48),implies(implies(X_48,X_49),implies(truth,X_49))) != truth
| implies(truth,X_49) != X_49
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),implies(truth,X_49))),truth) ),[0,1,1],$fot(X_49)]]) ).
cnf(refute_0_317,plain,
( implies(implies(truth,X_48),implies(implies(X_48,X_49),implies(truth,X_49))) != truth
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_49),X_49) )],[refute_0_310,refute_0_316]) ).
cnf(refute_0_318,plain,
implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),implies(truth,X_49))),truth) )],[refute_0_315,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(implies(X_48,X_49),X_49) = big_V(X_48,X_49),
inference(subst,[],[refute_0_39:[bind(X,$fot(X_48)),bind(Y,$fot(X_49))]]) ).
cnf(refute_0_320,plain,
implies(X_48,implies(implies(X_48,X_49),X_49)) = implies(X_48,implies(implies(X_48,X_49),X_49)),
introduced(tautology,[refl,[$fot(implies(X_48,implies(implies(X_48,X_49),X_49)))]]) ).
cnf(refute_0_321,plain,
( implies(X_48,implies(implies(X_48,X_49),X_49)) != implies(X_48,implies(implies(X_48,X_49),X_49))
| implies(implies(X_48,X_49),X_49) != big_V(X_48,X_49)
| implies(X_48,implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_48,implies(implies(X_48,X_49),X_49)),implies(X_48,implies(implies(X_48,X_49),X_49))) ),[1,1],$fot(big_V(X_48,X_49))]]) ).
cnf(refute_0_322,plain,
( implies(implies(X_48,X_49),X_49) != big_V(X_48,X_49)
| implies(X_48,implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(implies(X_48,implies(implies(X_48,X_49),X_49)),implies(X_48,implies(implies(X_48,X_49),X_49))) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
implies(X_48,implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)),
inference(resolve,[$cnf( $equal(implies(implies(X_48,X_49),X_49),big_V(X_48,X_49)) )],[refute_0_319,refute_0_322]) ).
cnf(refute_0_324,plain,
implies(truth,X_48) = X_48,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_325,plain,
implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)))]]) ).
cnf(refute_0_326,plain,
( implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) != implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49))
| implies(truth,X_48) != X_48
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,implies(implies(X_48,X_49),X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49))) ),[1,0],$fot(X_48)]]) ).
cnf(refute_0_327,plain,
( implies(truth,X_48) != X_48
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,implies(implies(X_48,X_49),X_49)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49))) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,implies(implies(X_48,X_49),X_49)),
inference(resolve,[$cnf( $equal(implies(truth,X_48),X_48) )],[refute_0_324,refute_0_327]) ).
cnf(refute_0_329,plain,
( implies(X_48,implies(implies(X_48,X_49),X_49)) != implies(X_48,big_V(X_48,X_49))
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) != implies(X_48,implies(implies(X_48,X_49),X_49))
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)))),bind(Y0,$fot(implies(X_48,implies(implies(X_48,X_49),X_49)))),bind(Z0,$fot(implies(X_48,big_V(X_48,X_49))))]]) ).
cnf(refute_0_330,plain,
( implies(X_48,implies(implies(X_48,X_49),X_49)) != implies(X_48,big_V(X_48,X_49))
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),implies(X_48,implies(implies(X_48,X_49),X_49))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) = implies(X_48,big_V(X_48,X_49)),
inference(resolve,[$cnf( $equal(implies(X_48,implies(implies(X_48,X_49),X_49)),implies(X_48,big_V(X_48,X_49))) )],[refute_0_323,refute_0_330]) ).
cnf(refute_0_332,plain,
( implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) != implies(X_48,big_V(X_48,X_49))
| implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) != truth
| implies(X_48,big_V(X_48,X_49)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),truth) ),[0],$fot(implies(X_48,big_V(X_48,X_49)))]]) ).
cnf(refute_0_333,plain,
( implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)) != truth
| implies(X_48,big_V(X_48,X_49)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),implies(X_48,big_V(X_48,X_49))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
implies(X_48,big_V(X_48,X_49)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_48),implies(implies(X_48,X_49),X_49)),truth) )],[refute_0_318,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(X_50,big_V(X_50,truth)) = truth,
inference(subst,[],[refute_0_334:[bind(X_48,$fot(X_50)),bind(X_49,$fot(truth))]]) ).
cnf(refute_0_336,plain,
implies(big_V(truth,not(X_26)),big_V(truth,X_26)) = truth,
inference(subst,[],[refute_0_26:[bind(X_22,$fot(X_26))]]) ).
cnf(refute_0_337,plain,
big_V(X_26,truth) = big_V(truth,X_26),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_26)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_338,plain,
( big_V(X_26,truth) != big_V(truth,X_26)
| big_V(truth,X_26) = big_V(X_26,truth) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_26,truth))),bind(Y0,$fot(big_V(truth,X_26)))]]) ).
cnf(refute_0_339,plain,
big_V(truth,X_26) = big_V(X_26,truth),
inference(resolve,[$cnf( $equal(big_V(X_26,truth),big_V(truth,X_26)) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( big_V(truth,X_26) != big_V(X_26,truth)
| implies(big_V(truth,not(X_26)),big_V(truth,X_26)) != truth
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(truth,X_26)),truth) ),[0,1],$fot(big_V(X_26,truth))]]) ).
cnf(refute_0_341,plain,
( implies(big_V(truth,not(X_26)),big_V(truth,X_26)) != truth
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = truth ),
inference(resolve,[$cnf( $equal(big_V(truth,X_26),big_V(X_26,truth)) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(truth,X_26)),truth) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
implies(truth,big_V(X_26,truth)) = big_V(X_26,truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X_26,truth)))]]) ).
cnf(refute_0_344,plain,
big_V(truth,not(X_26)) = truth,
inference(subst,[],[refute_0_268:[bind(X_8,$fot(X_26))]]) ).
cnf(refute_0_345,plain,
implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = implies(big_V(truth,not(X_26)),big_V(X_26,truth)),
introduced(tautology,[refl,[$fot(implies(big_V(truth,not(X_26)),big_V(X_26,truth)))]]) ).
cnf(refute_0_346,plain,
( big_V(truth,not(X_26)) != truth
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) != implies(big_V(truth,not(X_26)),big_V(X_26,truth))
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = implies(truth,big_V(X_26,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),implies(big_V(truth,not(X_26)),big_V(X_26,truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_347,plain,
( big_V(truth,not(X_26)) != truth
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = implies(truth,big_V(X_26,truth)) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),implies(big_V(truth,not(X_26)),big_V(X_26,truth))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = implies(truth,big_V(X_26,truth)),
inference(resolve,[$cnf( $equal(big_V(truth,not(X_26)),truth) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
( implies(big_V(truth,not(X_26)),big_V(X_26,truth)) != implies(truth,big_V(X_26,truth))
| implies(truth,big_V(X_26,truth)) != big_V(X_26,truth)
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = big_V(X_26,truth) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(truth,not(X_26)),big_V(X_26,truth)))),bind(Y0,$fot(implies(truth,big_V(X_26,truth)))),bind(Z0,$fot(big_V(X_26,truth)))]]) ).
cnf(refute_0_350,plain,
( implies(truth,big_V(X_26,truth)) != big_V(X_26,truth)
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = big_V(X_26,truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),implies(truth,big_V(X_26,truth))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
implies(big_V(truth,not(X_26)),big_V(X_26,truth)) = big_V(X_26,truth),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X_26,truth)),big_V(X_26,truth)) )],[refute_0_343,refute_0_350]) ).
cnf(refute_0_352,plain,
( implies(big_V(truth,not(X_26)),big_V(X_26,truth)) != big_V(X_26,truth)
| implies(big_V(truth,not(X_26)),big_V(X_26,truth)) != truth
| big_V(X_26,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),truth) ),[0],$fot(big_V(X_26,truth))]]) ).
cnf(refute_0_353,plain,
( implies(big_V(truth,not(X_26)),big_V(X_26,truth)) != truth
| big_V(X_26,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),big_V(X_26,truth)) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
big_V(X_26,truth) = truth,
inference(resolve,[$cnf( $equal(implies(big_V(truth,not(X_26)),big_V(X_26,truth)),truth) )],[refute_0_342,refute_0_353]) ).
cnf(refute_0_355,plain,
big_V(X_50,truth) = truth,
inference(subst,[],[refute_0_354:[bind(X_26,$fot(X_50))]]) ).
cnf(refute_0_356,plain,
( big_V(X_50,truth) != truth
| implies(X_50,big_V(X_50,truth)) != truth
| implies(X_50,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_50,big_V(X_50,truth)),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_357,plain,
( implies(X_50,big_V(X_50,truth)) != truth
| implies(X_50,truth) = truth ),
inference(resolve,[$cnf( $equal(big_V(X_50,truth),truth) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
implies(X_50,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_50,big_V(X_50,truth)),truth) )],[refute_0_335,refute_0_357]) ).
cnf(refute_0_359,plain,
implies(X_47,truth) = truth,
inference(subst,[],[refute_0_358:[bind(X_50,$fot(X_47))]]) ).
cnf(refute_0_360,plain,
implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),
introduced(tautology,[refl,[$fot(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))))]]) ).
cnf(refute_0_361,plain,
( implies(X_47,truth) != truth
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) != implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49)))
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(truth,implies(X_49,implies(X_47,X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_362,plain,
( implies(X_47,truth) != truth
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(truth,implies(X_49,implies(X_47,X_49))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49)))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(truth,implies(X_49,implies(X_47,X_49))),
inference(resolve,[$cnf( $equal(implies(X_47,truth),truth) )],[refute_0_359,refute_0_362]) ).
cnf(refute_0_364,plain,
( implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) != implies(truth,implies(X_49,implies(X_47,X_49)))
| implies(truth,implies(X_49,implies(X_47,X_49))) != implies(X_49,implies(X_47,X_49))
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(X_49,implies(X_47,X_49)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))))),bind(Y0,$fot(implies(truth,implies(X_49,implies(X_47,X_49))))),bind(Z0,$fot(implies(X_49,implies(X_47,X_49))))]]) ).
cnf(refute_0_365,plain,
( implies(truth,implies(X_49,implies(X_47,X_49))) != implies(X_49,implies(X_47,X_49))
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(X_49,implies(X_47,X_49)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),implies(truth,implies(X_49,implies(X_47,X_49)))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) = implies(X_49,implies(X_47,X_49)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_49,implies(X_47,X_49))),implies(X_49,implies(X_47,X_49))) )],[refute_0_314,refute_0_365]) ).
cnf(refute_0_367,plain,
( implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) != implies(X_49,implies(X_47,X_49))
| implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) != truth
| implies(X_49,implies(X_47,X_49)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),truth) ),[0],$fot(implies(X_49,implies(X_47,X_49)))]]) ).
cnf(refute_0_368,plain,
( implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))) != truth
| implies(X_49,implies(X_47,X_49)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),implies(X_49,implies(X_47,X_49))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
implies(X_49,implies(X_47,X_49)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_47,truth),implies(X_49,implies(X_47,X_49))),truth) )],[refute_0_313,refute_0_368]) ).
cnf(refute_0_370,plain,
implies(X,implies(X_55,X)) = truth,
inference(subst,[],[refute_0_369:[bind(X_47,$fot(X_55)),bind(X_49,$fot(X))]]) ).
cnf(refute_0_371,plain,
( big_V(X,implies(X_55,X)) != implies(implies(X,implies(X_55,X)),implies(X_55,X))
| implies(X,implies(X_55,X)) != truth
| big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(implies(X,implies(X_55,X)),implies(X_55,X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_372,plain,
( big_V(X,implies(X_55,X)) != implies(implies(X,implies(X_55,X)),implies(X_55,X))
| big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_55,X)),truth) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
big_V(X,implies(X_55,X)) = implies(truth,implies(X_55,X)),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(implies(X,implies(X_55,X)),implies(X_55,X))) )],[refute_0_308,refute_0_372]) ).
cnf(refute_0_374,plain,
implies(truth,implies(X_55,X)) = implies(X_55,X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_55,X)))]]) ).
cnf(refute_0_375,plain,
( big_V(X,implies(X_55,X)) != implies(truth,implies(X_55,X))
| implies(truth,implies(X_55,X)) != implies(X_55,X)
| big_V(X,implies(X_55,X)) = implies(X_55,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,implies(X_55,X)),implies(X_55,X)) ),[0],$fot(implies(truth,implies(X_55,X)))]]) ).
cnf(refute_0_376,plain,
( big_V(X,implies(X_55,X)) != implies(truth,implies(X_55,X))
| big_V(X,implies(X_55,X)) = implies(X_55,X) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_55,X)),implies(X_55,X)) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
big_V(X,implies(X_55,X)) = implies(X_55,X),
inference(resolve,[$cnf( $equal(big_V(X,implies(X_55,X)),implies(truth,implies(X_55,X))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
big_V(Y,implies(X_1,Y)) = implies(X_1,Y),
inference(subst,[],[refute_0_377:[bind(X,$fot(Y)),bind(X_55,$fot(X_1))]]) ).
cnf(refute_0_379,plain,
( big_V(Y,implies(X_1,Y)) != implies(X_1,Y)
| big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| implies(X_1,Y) = implies(big_V(X_1,Y),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) ),[0],$fot(implies(X_1,Y))]]) ).
cnf(refute_0_380,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| implies(X_1,Y) = implies(big_V(X_1,Y),Y) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(X_1,Y)) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
implies(X_1,Y) = implies(big_V(X_1,Y),Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) )],[refute_0_307,refute_0_380]) ).
cnf(refute_0_382,plain,
( implies(X_1,Y) != implies(big_V(X_1,Y),Y)
| implies(big_V(X_1,Y),Y) = implies(X_1,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_1,Y))),bind(Y0,$fot(implies(big_V(X_1,Y),Y)))]]) ).
cnf(refute_0_383,plain,
implies(big_V(X_1,Y),Y) = implies(X_1,Y),
inference(resolve,[$cnf( $equal(implies(X_1,Y),implies(big_V(X_1,Y),Y)) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
implies(big_V(X_59,X_61),X_61) = implies(X_59,X_61),
inference(subst,[],[refute_0_383:[bind(Y,$fot(X_61)),bind(X_1,$fot(X_59))]]) ).
cnf(refute_0_385,plain,
( implies(big_V(X_59,X_61),X_61) != big_hat(implies(X_59,X_61),truth)
| implies(big_V(X_59,X_61),X_61) != implies(X_59,X_61)
| implies(X_59,X_61) = big_hat(implies(X_59,X_61),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,X_61),X_61),big_hat(implies(X_59,X_61),truth)) ),[0],$fot(implies(X_59,X_61))]]) ).
cnf(refute_0_386,plain,
( implies(big_V(X_59,X_61),X_61) != big_hat(implies(X_59,X_61),truth)
| implies(X_59,X_61) = big_hat(implies(X_59,X_61),truth) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_61),X_61),implies(X_59,X_61)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
( big_hat(X,Y) != big_hat(Y,X)
| big_hat(Y,X) = big_hat(X,Y) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X,Y))),bind(Y0,$fot(big_hat(Y,X)))]]) ).
cnf(refute_0_388,plain,
big_hat(Y,X) = big_hat(X,Y),
inference(resolve,[$cnf( $equal(big_hat(X,Y),big_hat(Y,X)) )],[refute_0_180,refute_0_387]) ).
cnf(refute_0_389,plain,
big_hat(implies(X_59,X_61),truth) = big_hat(truth,implies(X_59,X_61)),
inference(subst,[],[refute_0_388:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_59,X_61)))]]) ).
cnf(refute_0_390,plain,
( big_hat(implies(X_59,X_61),truth) != big_hat(truth,implies(X_59,X_61))
| implies(X_59,X_61) != big_hat(implies(X_59,X_61),truth)
| implies(X_59,X_61) = big_hat(truth,implies(X_59,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_59,X_61),big_hat(implies(X_59,X_61),truth)) ),[1],$fot(big_hat(truth,implies(X_59,X_61)))]]) ).
cnf(refute_0_391,plain,
( implies(X_59,X_61) != big_hat(implies(X_59,X_61),truth)
| implies(X_59,X_61) = big_hat(truth,implies(X_59,X_61)) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,X_61),truth),big_hat(truth,implies(X_59,X_61))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
( implies(big_V(X_59,X_61),X_61) != big_hat(implies(X_59,X_61),truth)
| implies(X_59,X_61) = big_hat(truth,implies(X_59,X_61)) ),
inference(resolve,[$cnf( $equal(implies(X_59,X_61),big_hat(implies(X_59,X_61),truth)) )],[refute_0_386,refute_0_391]) ).
cnf(refute_0_393,plain,
implies(X_59,X_61) = big_hat(truth,implies(X_59,X_61)),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_61),X_61),big_hat(implies(X_59,X_61),truth)) )],[refute_0_296,refute_0_392]) ).
cnf(refute_0_394,plain,
implies(truth,X_63) = big_hat(truth,implies(truth,X_63)),
inference(subst,[],[refute_0_393:[bind(X_59,$fot(truth)),bind(X_61,$fot(X_63))]]) ).
cnf(refute_0_395,plain,
implies(truth,X_63) = X_63,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_63))]]) ).
cnf(refute_0_396,plain,
( implies(truth,X_63) != X_63
| implies(truth,X_63) != big_hat(truth,implies(truth,X_63))
| implies(truth,X_63) = big_hat(truth,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,X_63),big_hat(truth,implies(truth,X_63))) ),[1,1],$fot(X_63)]]) ).
cnf(refute_0_397,plain,
( implies(truth,X_63) != big_hat(truth,implies(truth,X_63))
| implies(truth,X_63) = big_hat(truth,X_63) ),
inference(resolve,[$cnf( $equal(implies(truth,X_63),X_63) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
implies(truth,X_63) = big_hat(truth,X_63),
inference(resolve,[$cnf( $equal(implies(truth,X_63),big_hat(truth,implies(truth,X_63))) )],[refute_0_394,refute_0_397]) ).
cnf(refute_0_399,plain,
( implies(truth,X_63) != X_63
| implies(truth,X_63) != big_hat(truth,X_63)
| X_63 = big_hat(truth,X_63) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,X_63),big_hat(truth,X_63)) ),[0],$fot(X_63)]]) ).
cnf(refute_0_400,plain,
( implies(truth,X_63) != big_hat(truth,X_63)
| X_63 = big_hat(truth,X_63) ),
inference(resolve,[$cnf( $equal(implies(truth,X_63),X_63) )],[refute_0_395,refute_0_399]) ).
cnf(refute_0_401,plain,
X_63 = big_hat(truth,X_63),
inference(resolve,[$cnf( $equal(implies(truth,X_63),big_hat(truth,X_63)) )],[refute_0_398,refute_0_400]) ).
cnf(refute_0_402,plain,
( X_63 != big_hat(truth,X_63)
| big_hat(truth,X_63) = X_63 ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X_63)),bind(Y0,$fot(big_hat(truth,X_63)))]]) ).
cnf(refute_0_403,plain,
big_hat(truth,X_63) = X_63,
inference(resolve,[$cnf( $equal(X_63,big_hat(truth,X_63)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
big_hat(truth,implies(X_79,X_80)) = implies(X_79,X_80),
inference(subst,[],[refute_0_403:[bind(X_63,$fot(implies(X_79,X_80)))]]) ).
cnf(refute_0_405,plain,
( big_hat(truth,implies(X_79,X_80)) != implies(X_79,X_80)
| implies(X_79,big_hat(X_79,X_80)) != big_hat(truth,implies(X_79,X_80))
| implies(X_79,big_hat(X_79,X_80)) = implies(X_79,X_80) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_79,big_hat(X_79,X_80)),big_hat(truth,implies(X_79,X_80))) ),[1],$fot(implies(X_79,X_80))]]) ).
cnf(refute_0_406,plain,
( implies(X_79,big_hat(X_79,X_80)) != big_hat(truth,implies(X_79,X_80))
| implies(X_79,big_hat(X_79,X_80)) = implies(X_79,X_80) ),
inference(resolve,[$cnf( $equal(big_hat(truth,implies(X_79,X_80)),implies(X_79,X_80)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
implies(X_79,big_hat(X_79,X_80)) = implies(X_79,X_80),
inference(resolve,[$cnf( $equal(implies(X_79,big_hat(X_79,X_80)),big_hat(truth,implies(X_79,X_80))) )],[refute_0_289,refute_0_406]) ).
cnf(refute_0_408,plain,
implies(X,big_hat(X,X_84)) = implies(X,X_84),
inference(subst,[],[refute_0_407:[bind(X_79,$fot(X)),bind(X_80,$fot(X_84))]]) ).
cnf(refute_0_409,plain,
( big_V(X,big_hat(X,X_84)) != implies(implies(X,big_hat(X,X_84)),big_hat(X,X_84))
| implies(X,big_hat(X,X_84)) != implies(X,X_84)
| big_V(X,big_hat(X,X_84)) = implies(implies(X,X_84),big_hat(X,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_hat(X,X_84)),implies(implies(X,big_hat(X,X_84)),big_hat(X,X_84))) ),[1,0],$fot(implies(X,X_84))]]) ).
cnf(refute_0_410,plain,
( big_V(X,big_hat(X,X_84)) != implies(implies(X,big_hat(X,X_84)),big_hat(X,X_84))
| big_V(X,big_hat(X,X_84)) = implies(implies(X,X_84),big_hat(X,X_84)) ),
inference(resolve,[$cnf( $equal(implies(X,big_hat(X,X_84)),implies(X,X_84)) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
big_V(X,big_hat(X,X_84)) = implies(implies(X,X_84),big_hat(X,X_84)),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X,X_84)),implies(implies(X,big_hat(X,X_84)),big_hat(X,X_84))) )],[refute_0_0,refute_0_410]) ).
cnf(refute_0_412,plain,
big_V(X,not(not(X))) = implies(implies(X,not(not(X))),not(not(X))),
inference(subst,[],[big_V_definition:[bind(Y,$fot(not(not(X))))]]) ).
cnf(refute_0_413,plain,
implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_414,plain,
implies(not(not(not(Y))),not(Y)) = truth,
inference(subst,[],[refute_0_258:[bind(X_22,$fot(not(Y)))]]) ).
cnf(refute_0_415,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(not(not(not(Y))),not(Y)) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_416,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(Y)),truth) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
implies(truth,implies(Y,not(not(Y)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) )],[refute_0_413,refute_0_416]) ).
cnf(refute_0_418,plain,
implies(truth,implies(Y,not(not(Y)))) = implies(Y,not(not(Y))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(not(Y)))))]]) ).
cnf(refute_0_419,plain,
( implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
| implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) ),[0],$fot(implies(Y,not(not(Y))))]]) ).
cnf(refute_0_420,plain,
( implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
implies(Y,not(not(Y))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) )],[refute_0_417,refute_0_420]) ).
cnf(refute_0_422,plain,
implies(X,not(not(X))) = truth,
inference(subst,[],[refute_0_421:[bind(Y,$fot(X))]]) ).
cnf(refute_0_423,plain,
( big_V(X,not(not(X))) != implies(implies(X,not(not(X))),not(not(X)))
| implies(X,not(not(X))) != truth
| big_V(X,not(not(X))) = implies(truth,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_424,plain,
( big_V(X,not(not(X))) != implies(implies(X,not(not(X))),not(not(X)))
| big_V(X,not(not(X))) = implies(truth,not(not(X))) ),
inference(resolve,[$cnf( $equal(implies(X,not(not(X))),truth) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
big_V(X,not(not(X))) = implies(truth,not(not(X))),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(implies(X,not(not(X))),not(not(X)))) )],[refute_0_412,refute_0_424]) ).
cnf(refute_0_426,plain,
implies(not(Y),not(truth)) = not(not(Y)),
inference(subst,[],[refute_0_250:[bind(X_33,$fot(Y))]]) ).
cnf(refute_0_427,plain,
big_V(Y,implies(not(Y),not(truth))) = big_V(Y,implies(not(Y),not(truth))),
introduced(tautology,[refl,[$fot(big_V(Y,implies(not(Y),not(truth))))]]) ).
cnf(refute_0_428,plain,
( big_V(Y,implies(not(Y),not(truth))) != big_V(Y,implies(not(Y),not(truth)))
| implies(not(Y),not(truth)) != not(not(Y))
| big_V(Y,implies(not(Y),not(truth))) = big_V(Y,not(not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),big_V(Y,implies(not(Y),not(truth)))) ),[1,1],$fot(not(not(Y)))]]) ).
cnf(refute_0_429,plain,
( implies(not(Y),not(truth)) != not(not(Y))
| big_V(Y,implies(not(Y),not(truth))) = big_V(Y,not(not(Y))) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),big_V(Y,implies(not(Y),not(truth)))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
big_V(Y,implies(not(Y),not(truth))) = big_V(Y,not(not(Y))),
inference(resolve,[$cnf( $equal(implies(not(Y),not(truth)),not(not(Y))) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
( big_V(Y,implies(not(Y),not(truth))) != Y
| big_V(Y,implies(not(Y),not(truth))) != big_V(Y,not(not(Y)))
| big_V(Y,not(not(Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),Y) ),[0],$fot(big_V(Y,not(not(Y))))]]) ).
cnf(refute_0_432,plain,
( big_V(Y,implies(not(Y),not(truth))) != Y
| big_V(Y,not(not(Y))) = Y ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),big_V(Y,not(not(Y)))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
big_V(Y,not(not(Y))) = Y,
inference(resolve,[$cnf( $equal(big_V(Y,implies(not(Y),not(truth))),Y) )],[refute_0_56,refute_0_432]) ).
cnf(refute_0_434,plain,
big_V(X,not(not(X))) = X,
inference(subst,[],[refute_0_433:[bind(Y,$fot(X))]]) ).
cnf(refute_0_435,plain,
( big_V(X,not(not(X))) != X
| big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = implies(truth,not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,not(not(X))),implies(truth,not(not(X)))) ),[0],$fot(X)]]) ).
cnf(refute_0_436,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = implies(truth,not(not(X))) ),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),X) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
implies(truth,not(not(X))) = not(not(X)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X))))]]) ).
cnf(refute_0_438,plain,
( X != implies(truth,not(not(X)))
| implies(truth,not(not(X))) != not(not(X))
| X = not(not(X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,not(not(X))) ),[0],$fot(implies(truth,not(not(X))))]]) ).
cnf(refute_0_439,plain,
( X != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X))),not(not(X))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
( big_V(X,not(not(X))) != implies(truth,not(not(X)))
| X = not(not(X)) ),
inference(resolve,[$cnf( $equal(X,implies(truth,not(not(X)))) )],[refute_0_436,refute_0_439]) ).
cnf(refute_0_441,plain,
X = not(not(X)),
inference(resolve,[$cnf( $equal(big_V(X,not(not(X))),implies(truth,not(not(X)))) )],[refute_0_425,refute_0_440]) ).
cnf(refute_0_442,plain,
big_V(X_72,big_hat(X_72,X_73)) = not(not(big_V(X_72,big_hat(X_72,X_73)))),
inference(subst,[],[refute_0_441:[bind(X,$fot(big_V(X_72,big_hat(X_72,X_73))))]]) ).
cnf(refute_0_443,plain,
implies(big_V(X_59,truth),X_61) = big_hat(implies(X_59,X_61),implies(truth,X_61)),
inference(subst,[],[lemma_6:[bind(X,$fot(X_59)),bind(Y,$fot(truth)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_444,plain,
implies(truth,X_61) = X_61,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_445,plain,
( implies(big_V(X_59,truth),X_61) != big_hat(implies(X_59,X_61),implies(truth,X_61))
| implies(truth,X_61) != X_61
| implies(big_V(X_59,truth),X_61) = big_hat(implies(X_59,X_61),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,truth),X_61),big_hat(implies(X_59,X_61),implies(truth,X_61))) ),[1,1],$fot(X_61)]]) ).
cnf(refute_0_446,plain,
( implies(big_V(X_59,truth),X_61) != big_hat(implies(X_59,X_61),implies(truth,X_61))
| implies(big_V(X_59,truth),X_61) = big_hat(implies(X_59,X_61),X_61) ),
inference(resolve,[$cnf( $equal(implies(truth,X_61),X_61) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
implies(big_V(X_59,truth),X_61) = big_hat(implies(X_59,X_61),X_61),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,truth),X_61),big_hat(implies(X_59,X_61),implies(truth,X_61))) )],[refute_0_443,refute_0_446]) ).
cnf(refute_0_448,plain,
big_V(X_59,truth) = truth,
inference(subst,[],[refute_0_354:[bind(X_26,$fot(X_59))]]) ).
cnf(refute_0_449,plain,
implies(big_V(X_59,truth),X_61) = implies(big_V(X_59,truth),X_61),
introduced(tautology,[refl,[$fot(implies(big_V(X_59,truth),X_61))]]) ).
cnf(refute_0_450,plain,
( big_V(X_59,truth) != truth
| implies(big_V(X_59,truth),X_61) != implies(big_V(X_59,truth),X_61)
| implies(big_V(X_59,truth),X_61) = implies(truth,X_61) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,truth),X_61),implies(big_V(X_59,truth),X_61)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_451,plain,
( big_V(X_59,truth) != truth
| implies(big_V(X_59,truth),X_61) = implies(truth,X_61) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,truth),X_61),implies(big_V(X_59,truth),X_61)) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
implies(big_V(X_59,truth),X_61) = implies(truth,X_61),
inference(resolve,[$cnf( $equal(big_V(X_59,truth),truth) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( implies(big_V(X_59,truth),X_61) != implies(truth,X_61)
| implies(truth,X_61) != X_61
| implies(big_V(X_59,truth),X_61) = X_61 ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(X_59,truth),X_61))),bind(Y0,$fot(implies(truth,X_61))),bind(Z0,$fot(X_61))]]) ).
cnf(refute_0_454,plain,
( implies(truth,X_61) != X_61
| implies(big_V(X_59,truth),X_61) = X_61 ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,truth),X_61),implies(truth,X_61)) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
implies(big_V(X_59,truth),X_61) = X_61,
inference(resolve,[$cnf( $equal(implies(truth,X_61),X_61) )],[refute_0_444,refute_0_454]) ).
cnf(refute_0_456,plain,
( implies(big_V(X_59,truth),X_61) != X_61
| implies(big_V(X_59,truth),X_61) != big_hat(implies(X_59,X_61),X_61)
| X_61 = big_hat(implies(X_59,X_61),X_61) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,truth),X_61),big_hat(implies(X_59,X_61),X_61)) ),[0],$fot(X_61)]]) ).
cnf(refute_0_457,plain,
( implies(big_V(X_59,truth),X_61) != big_hat(implies(X_59,X_61),X_61)
| X_61 = big_hat(implies(X_59,X_61),X_61) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,truth),X_61),X_61) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
big_hat(implies(X_59,X_61),X_61) = big_hat(X_61,implies(X_59,X_61)),
inference(subst,[],[refute_0_388:[bind(X,$fot(X_61)),bind(Y,$fot(implies(X_59,X_61)))]]) ).
cnf(refute_0_459,plain,
( X_61 != big_hat(implies(X_59,X_61),X_61)
| big_hat(implies(X_59,X_61),X_61) != big_hat(X_61,implies(X_59,X_61))
| X_61 = big_hat(X_61,implies(X_59,X_61)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_61,big_hat(X_61,implies(X_59,X_61))) ),[0],$fot(big_hat(implies(X_59,X_61),X_61))]]) ).
cnf(refute_0_460,plain,
( X_61 != big_hat(implies(X_59,X_61),X_61)
| X_61 = big_hat(X_61,implies(X_59,X_61)) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,X_61),X_61),big_hat(X_61,implies(X_59,X_61))) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
( implies(big_V(X_59,truth),X_61) != big_hat(implies(X_59,X_61),X_61)
| X_61 = big_hat(X_61,implies(X_59,X_61)) ),
inference(resolve,[$cnf( $equal(X_61,big_hat(implies(X_59,X_61),X_61)) )],[refute_0_457,refute_0_460]) ).
cnf(refute_0_462,plain,
X_61 = big_hat(X_61,implies(X_59,X_61)),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,truth),X_61),big_hat(implies(X_59,X_61),X_61)) )],[refute_0_447,refute_0_461]) ).
cnf(refute_0_463,plain,
X_67 = big_hat(X_67,implies(implies(X,X_67),X_67)),
inference(subst,[],[refute_0_462:[bind(X_59,$fot(implies(X,X_67))),bind(X_61,$fot(X_67))]]) ).
cnf(refute_0_464,plain,
big_V(X,X_67) = implies(implies(X,X_67),X_67),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_67))]]) ).
cnf(refute_0_465,plain,
( big_V(X,X_67) != implies(implies(X,X_67),X_67)
| implies(implies(X,X_67),X_67) = big_V(X,X_67) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_67))),bind(Y0,$fot(implies(implies(X,X_67),X_67)))]]) ).
cnf(refute_0_466,plain,
implies(implies(X,X_67),X_67) = big_V(X,X_67),
inference(resolve,[$cnf( $equal(big_V(X,X_67),implies(implies(X,X_67),X_67)) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
( X_67 != big_hat(X_67,implies(implies(X,X_67),X_67))
| implies(implies(X,X_67),X_67) != big_V(X,X_67)
| X_67 = big_hat(X_67,big_V(X,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(X_67,big_hat(X_67,implies(implies(X,X_67),X_67))) ),[1,1],$fot(big_V(X,X_67))]]) ).
cnf(refute_0_468,plain,
( X_67 != big_hat(X_67,implies(implies(X,X_67),X_67))
| X_67 = big_hat(X_67,big_V(X,X_67)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_67),X_67),big_V(X,X_67)) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
X_67 = big_hat(X_67,big_V(X,X_67)),
inference(resolve,[$cnf( $equal(X_67,big_hat(X_67,implies(implies(X,X_67),X_67))) )],[refute_0_463,refute_0_468]) ).
cnf(refute_0_470,plain,
X_69 = big_hat(X_69,big_V(X_68,X_69)),
inference(subst,[],[refute_0_469:[bind(X,$fot(X_68)),bind(X_67,$fot(X_69))]]) ).
cnf(refute_0_471,plain,
big_V(X_69,X_68) = big_V(X_68,X_69),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_69)),bind(Y,$fot(X_68))]]) ).
cnf(refute_0_472,plain,
( big_V(X_69,X_68) != big_V(X_68,X_69)
| big_V(X_68,X_69) = big_V(X_69,X_68) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X_69,X_68))),bind(Y0,$fot(big_V(X_68,X_69)))]]) ).
cnf(refute_0_473,plain,
big_V(X_68,X_69) = big_V(X_69,X_68),
inference(resolve,[$cnf( $equal(big_V(X_69,X_68),big_V(X_68,X_69)) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
( X_69 != big_hat(X_69,big_V(X_68,X_69))
| big_V(X_68,X_69) != big_V(X_69,X_68)
| X_69 = big_hat(X_69,big_V(X_69,X_68)) ),
introduced(tautology,[equality,[$cnf( $equal(X_69,big_hat(X_69,big_V(X_68,X_69))) ),[1,1],$fot(big_V(X_69,X_68))]]) ).
cnf(refute_0_475,plain,
( X_69 != big_hat(X_69,big_V(X_68,X_69))
| X_69 = big_hat(X_69,big_V(X_69,X_68)) ),
inference(resolve,[$cnf( $equal(big_V(X_68,X_69),big_V(X_69,X_68)) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
X_69 = big_hat(X_69,big_V(X_69,X_68)),
inference(resolve,[$cnf( $equal(X_69,big_hat(X_69,big_V(X_68,X_69))) )],[refute_0_470,refute_0_475]) ).
cnf(refute_0_477,plain,
not(X) = big_hat(not(X),big_V(not(X),not(Y))),
inference(subst,[],[refute_0_476:[bind(X_68,$fot(not(Y))),bind(X_69,$fot(not(X)))]]) ).
cnf(refute_0_478,plain,
( big_V(not(X),not(Y)) != not(big_hat(X,Y))
| not(X) != big_hat(not(X),big_V(not(X),not(Y)))
| not(X) = big_hat(not(X),not(big_hat(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(X),big_hat(not(X),big_V(not(X),not(Y)))) ),[1,1],$fot(not(big_hat(X,Y)))]]) ).
cnf(refute_0_479,plain,
( not(X) != big_hat(not(X),big_V(not(X),not(Y)))
| not(X) = big_hat(not(X),not(big_hat(X,Y))) ),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) )],[refute_0_59,refute_0_478]) ).
cnf(refute_0_480,plain,
not(X) = big_hat(not(X),not(big_hat(X,Y))),
inference(resolve,[$cnf( $equal(not(X),big_hat(not(X),big_V(not(X),not(Y)))) )],[refute_0_477,refute_0_479]) ).
cnf(refute_0_481,plain,
( not(big_V(X,Y)) != big_hat(not(X),not(Y))
| big_hat(not(X),not(Y)) = not(big_V(X,Y)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_V(X,Y)))),bind(Y0,$fot(big_hat(not(X),not(Y))))]]) ).
cnf(refute_0_482,plain,
big_hat(not(X),not(Y)) = not(big_V(X,Y)),
inference(resolve,[$cnf( $equal(not(big_V(X,Y)),big_hat(not(X),not(Y))) )],[lemma_4,refute_0_481]) ).
cnf(refute_0_483,plain,
big_hat(not(X),not(big_hat(X,Y))) = not(big_V(X,big_hat(X,Y))),
inference(subst,[],[refute_0_482:[bind(Y,$fot(big_hat(X,Y)))]]) ).
cnf(refute_0_484,plain,
( big_hat(not(X),not(big_hat(X,Y))) != not(big_V(X,big_hat(X,Y)))
| not(X) != big_hat(not(X),not(big_hat(X,Y)))
| not(X) = not(big_V(X,big_hat(X,Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(X),big_hat(not(X),not(big_hat(X,Y)))) ),[1],$fot(not(big_V(X,big_hat(X,Y))))]]) ).
cnf(refute_0_485,plain,
( not(X) != big_hat(not(X),not(big_hat(X,Y)))
| not(X) = not(big_V(X,big_hat(X,Y))) ),
inference(resolve,[$cnf( $equal(big_hat(not(X),not(big_hat(X,Y))),not(big_V(X,big_hat(X,Y)))) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
not(X) = not(big_V(X,big_hat(X,Y))),
inference(resolve,[$cnf( $equal(not(X),big_hat(not(X),not(big_hat(X,Y)))) )],[refute_0_480,refute_0_485]) ).
cnf(refute_0_487,plain,
not(X_72) = not(big_V(X_72,big_hat(X_72,X_73))),
inference(subst,[],[refute_0_486:[bind(X,$fot(X_72)),bind(Y,$fot(X_73))]]) ).
cnf(refute_0_488,plain,
( not(X_72) != not(big_V(X_72,big_hat(X_72,X_73)))
| not(big_V(X_72,big_hat(X_72,X_73))) = not(X_72) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_72))),bind(Y0,$fot(not(big_V(X_72,big_hat(X_72,X_73)))))]]) ).
cnf(refute_0_489,plain,
not(big_V(X_72,big_hat(X_72,X_73))) = not(X_72),
inference(resolve,[$cnf( $equal(not(X_72),not(big_V(X_72,big_hat(X_72,X_73)))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
( big_V(X_72,big_hat(X_72,X_73)) != not(not(big_V(X_72,big_hat(X_72,X_73))))
| not(big_V(X_72,big_hat(X_72,X_73))) != not(X_72)
| big_V(X_72,big_hat(X_72,X_73)) = not(not(X_72)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_72,big_hat(X_72,X_73)),not(not(big_V(X_72,big_hat(X_72,X_73))))) ),[1,0],$fot(not(X_72))]]) ).
cnf(refute_0_491,plain,
( big_V(X_72,big_hat(X_72,X_73)) != not(not(big_V(X_72,big_hat(X_72,X_73))))
| big_V(X_72,big_hat(X_72,X_73)) = not(not(X_72)) ),
inference(resolve,[$cnf( $equal(not(big_V(X_72,big_hat(X_72,X_73))),not(X_72)) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
big_V(X_72,big_hat(X_72,X_73)) = not(not(X_72)),
inference(resolve,[$cnf( $equal(big_V(X_72,big_hat(X_72,X_73)),not(not(big_V(X_72,big_hat(X_72,X_73))))) )],[refute_0_442,refute_0_491]) ).
cnf(refute_0_493,plain,
( X != not(not(X))
| not(not(X)) = X ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X)),bind(Y0,$fot(not(not(X))))]]) ).
cnf(refute_0_494,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(X,not(not(X))) )],[refute_0_441,refute_0_493]) ).
cnf(refute_0_495,plain,
not(not(X_72)) = X_72,
inference(subst,[],[refute_0_494:[bind(X,$fot(X_72))]]) ).
cnf(refute_0_496,plain,
( big_V(X_72,big_hat(X_72,X_73)) != not(not(X_72))
| not(not(X_72)) != X_72
| big_V(X_72,big_hat(X_72,X_73)) = X_72 ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X_72,big_hat(X_72,X_73)),X_72) ),[0],$fot(not(not(X_72)))]]) ).
cnf(refute_0_497,plain,
( big_V(X_72,big_hat(X_72,X_73)) != not(not(X_72))
| big_V(X_72,big_hat(X_72,X_73)) = X_72 ),
inference(resolve,[$cnf( $equal(not(not(X_72)),X_72) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
big_V(X_72,big_hat(X_72,X_73)) = X_72,
inference(resolve,[$cnf( $equal(big_V(X_72,big_hat(X_72,X_73)),not(not(X_72))) )],[refute_0_492,refute_0_497]) ).
cnf(refute_0_499,plain,
big_V(X,big_hat(X,X_84)) = X,
inference(subst,[],[refute_0_498:[bind(X_72,$fot(X)),bind(X_73,$fot(X_84))]]) ).
cnf(refute_0_500,plain,
( big_V(X,big_hat(X,X_84)) != X
| big_V(X,big_hat(X,X_84)) != implies(implies(X,X_84),big_hat(X,X_84))
| X = implies(implies(X,X_84),big_hat(X,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_hat(X,X_84)),implies(implies(X,X_84),big_hat(X,X_84))) ),[0],$fot(X)]]) ).
cnf(refute_0_501,plain,
( big_V(X,big_hat(X,X_84)) != implies(implies(X,X_84),big_hat(X,X_84))
| X = implies(implies(X,X_84),big_hat(X,X_84)) ),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X,X_84)),X) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
X = implies(implies(X,X_84),big_hat(X,X_84)),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X,X_84)),implies(implies(X,X_84),big_hat(X,X_84))) )],[refute_0_411,refute_0_501]) ).
cnf(refute_0_503,plain,
X = implies(implies(X,implies(X_455,implies(X_453,X))),big_hat(X,implies(X_455,implies(X_453,X)))),
inference(subst,[],[refute_0_502:[bind(X_84,$fot(implies(X_455,implies(X_453,X))))]]) ).
cnf(refute_0_504,plain,
implies(X_78,big_hat(implies(X_47,X_78),X_80)) = big_hat(implies(X_78,implies(X_47,X_78)),implies(X_78,X_80)),
inference(subst,[],[lemma_7:[bind(X,$fot(X_78)),bind(Y,$fot(implies(X_47,X_78))),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_505,plain,
implies(X_78,implies(X_47,X_78)) = truth,
inference(subst,[],[refute_0_369:[bind(X_49,$fot(X_78))]]) ).
cnf(refute_0_506,plain,
( implies(X_78,big_hat(implies(X_47,X_78),X_80)) != big_hat(implies(X_78,implies(X_47,X_78)),implies(X_78,X_80))
| implies(X_78,implies(X_47,X_78)) != truth
| implies(X_78,big_hat(implies(X_47,X_78),X_80)) = big_hat(truth,implies(X_78,X_80)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_78,big_hat(implies(X_47,X_78),X_80)),big_hat(implies(X_78,implies(X_47,X_78)),implies(X_78,X_80))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_507,plain,
( implies(X_78,big_hat(implies(X_47,X_78),X_80)) != big_hat(implies(X_78,implies(X_47,X_78)),implies(X_78,X_80))
| implies(X_78,big_hat(implies(X_47,X_78),X_80)) = big_hat(truth,implies(X_78,X_80)) ),
inference(resolve,[$cnf( $equal(implies(X_78,implies(X_47,X_78)),truth) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
implies(X_78,big_hat(implies(X_47,X_78),X_80)) = big_hat(truth,implies(X_78,X_80)),
inference(resolve,[$cnf( $equal(implies(X_78,big_hat(implies(X_47,X_78),X_80)),big_hat(implies(X_78,implies(X_47,X_78)),implies(X_78,X_80))) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
big_hat(truth,implies(X_78,X_80)) = implies(X_78,X_80),
inference(subst,[],[refute_0_403:[bind(X_63,$fot(implies(X_78,X_80)))]]) ).
cnf(refute_0_510,plain,
( big_hat(truth,implies(X_78,X_80)) != implies(X_78,X_80)
| implies(X_78,big_hat(implies(X_47,X_78),X_80)) != big_hat(truth,implies(X_78,X_80))
| implies(X_78,big_hat(implies(X_47,X_78),X_80)) = implies(X_78,X_80) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_78,big_hat(implies(X_47,X_78),X_80)),big_hat(truth,implies(X_78,X_80))) ),[1],$fot(implies(X_78,X_80))]]) ).
cnf(refute_0_511,plain,
( implies(X_78,big_hat(implies(X_47,X_78),X_80)) != big_hat(truth,implies(X_78,X_80))
| implies(X_78,big_hat(implies(X_47,X_78),X_80)) = implies(X_78,X_80) ),
inference(resolve,[$cnf( $equal(big_hat(truth,implies(X_78,X_80)),implies(X_78,X_80)) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
implies(X_78,big_hat(implies(X_47,X_78),X_80)) = implies(X_78,X_80),
inference(resolve,[$cnf( $equal(implies(X_78,big_hat(implies(X_47,X_78),X_80)),big_hat(truth,implies(X_78,X_80))) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
implies(X_114,big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))) = implies(X_114,implies(X_59,implies(X_113,X_114))),
inference(subst,[],[refute_0_512:[bind(X_47,$fot(X_113)),bind(X_78,$fot(X_114)),bind(X_80,$fot(implies(X_59,implies(X_113,X_114))))]]) ).
cnf(refute_0_514,plain,
implies(X_113,X_114) = big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114))),
inference(subst,[],[refute_0_462:[bind(X_61,$fot(implies(X_113,X_114)))]]) ).
cnf(refute_0_515,plain,
( implies(X_113,X_114) != big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))
| big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114))) = implies(X_113,X_114) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_113,X_114))),bind(Y0,$fot(big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))))]]) ).
cnf(refute_0_516,plain,
big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114))) = implies(X_113,X_114),
inference(resolve,[$cnf( $equal(implies(X_113,X_114),big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))) )],[refute_0_514,refute_0_515]) ).
cnf(refute_0_517,plain,
( big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114))) != implies(X_113,X_114)
| implies(X_114,big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))) != implies(X_114,implies(X_59,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) = implies(X_114,implies(X_59,implies(X_113,X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_114,big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))),implies(X_114,implies(X_59,implies(X_113,X_114)))) ),[0,1],$fot(implies(X_113,X_114))]]) ).
cnf(refute_0_518,plain,
( implies(X_114,big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))) != implies(X_114,implies(X_59,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) = implies(X_114,implies(X_59,implies(X_113,X_114))) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114))),implies(X_113,X_114)) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
implies(X_114,implies(X_113,X_114)) = implies(X_114,implies(X_59,implies(X_113,X_114))),
inference(resolve,[$cnf( $equal(implies(X_114,big_hat(implies(X_113,X_114),implies(X_59,implies(X_113,X_114)))),implies(X_114,implies(X_59,implies(X_113,X_114)))) )],[refute_0_513,refute_0_518]) ).
cnf(refute_0_520,plain,
implies(X_114,implies(X_113,X_114)) = truth,
inference(subst,[],[refute_0_369:[bind(X_47,$fot(X_113)),bind(X_49,$fot(X_114))]]) ).
cnf(refute_0_521,plain,
( implies(X_114,implies(X_113,X_114)) != implies(X_114,implies(X_59,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) != truth
| truth = implies(X_114,implies(X_59,implies(X_113,X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),implies(X_114,implies(X_59,implies(X_113,X_114)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_522,plain,
( implies(X_114,implies(X_113,X_114)) != implies(X_114,implies(X_59,implies(X_113,X_114)))
| truth = implies(X_114,implies(X_59,implies(X_113,X_114))) ),
inference(resolve,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),truth) )],[refute_0_520,refute_0_521]) ).
cnf(refute_0_523,plain,
truth = implies(X_114,implies(X_59,implies(X_113,X_114))),
inference(resolve,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),implies(X_114,implies(X_59,implies(X_113,X_114)))) )],[refute_0_519,refute_0_522]) ).
cnf(refute_0_524,plain,
truth = implies(X,implies(X_455,implies(X_453,X))),
inference(subst,[],[refute_0_523:[bind(X_113,$fot(X_453)),bind(X_114,$fot(X)),bind(X_59,$fot(X_455))]]) ).
cnf(refute_0_525,plain,
( truth != implies(X,implies(X_455,implies(X_453,X)))
| implies(X,implies(X_455,implies(X_453,X))) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X,implies(X_455,implies(X_453,X)))))]]) ).
cnf(refute_0_526,plain,
implies(X,implies(X_455,implies(X_453,X))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X,implies(X_455,implies(X_453,X)))) )],[refute_0_524,refute_0_525]) ).
cnf(refute_0_527,plain,
( X != implies(implies(X,implies(X_455,implies(X_453,X))),big_hat(X,implies(X_455,implies(X_453,X))))
| implies(X,implies(X_455,implies(X_453,X))) != truth
| X = implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(X,implies(implies(X,implies(X_455,implies(X_453,X))),big_hat(X,implies(X_455,implies(X_453,X))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_528,plain,
( X != implies(implies(X,implies(X_455,implies(X_453,X))),big_hat(X,implies(X_455,implies(X_453,X))))
| X = implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_455,implies(X_453,X))),truth) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
X = implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))),
inference(resolve,[$cnf( $equal(X,implies(implies(X,implies(X_455,implies(X_453,X))),big_hat(X,implies(X_455,implies(X_453,X))))) )],[refute_0_503,refute_0_528]) ).
cnf(refute_0_530,plain,
implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))) = big_hat(X,implies(X_455,implies(X_453,X))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_hat(X,implies(X_455,implies(X_453,X)))))]]) ).
cnf(refute_0_531,plain,
( X != implies(truth,big_hat(X,implies(X_455,implies(X_453,X))))
| implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))) != big_hat(X,implies(X_455,implies(X_453,X)))
| X = big_hat(X,implies(X_455,implies(X_453,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,big_hat(X,implies(X_455,implies(X_453,X)))) ),[0],$fot(implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))))]]) ).
cnf(refute_0_532,plain,
( X != implies(truth,big_hat(X,implies(X_455,implies(X_453,X))))
| X = big_hat(X,implies(X_455,implies(X_453,X))) ),
inference(resolve,[$cnf( $equal(implies(truth,big_hat(X,implies(X_455,implies(X_453,X)))),big_hat(X,implies(X_455,implies(X_453,X)))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
X = big_hat(X,implies(X_455,implies(X_453,X))),
inference(resolve,[$cnf( $equal(X,implies(truth,big_hat(X,implies(X_455,implies(X_453,X))))) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
X_600 = big_hat(X_600,implies(X_602,implies(big_V(implies(X,X_600),X_60),X_600))),
inference(subst,[],[refute_0_533:[bind(X,$fot(X_600)),bind(X_453,$fot(big_V(implies(X,X_600),X_60))),bind(X_455,$fot(X_602))]]) ).
cnf(refute_0_535,plain,
implies(big_V(implies(X,X_61),X_60),X_61) = big_hat(implies(implies(X,X_61),X_61),implies(X_60,X_61)),
inference(subst,[],[lemma_6:[bind(X,$fot(implies(X,X_61))),bind(Y,$fot(X_60)),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_536,plain,
big_V(X,X_61) = implies(implies(X,X_61),X_61),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_61))]]) ).
cnf(refute_0_537,plain,
( big_V(X,X_61) != implies(implies(X,X_61),X_61)
| implies(implies(X,X_61),X_61) = big_V(X,X_61) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_61))),bind(Y0,$fot(implies(implies(X,X_61),X_61)))]]) ).
cnf(refute_0_538,plain,
implies(implies(X,X_61),X_61) = big_V(X,X_61),
inference(resolve,[$cnf( $equal(big_V(X,X_61),implies(implies(X,X_61),X_61)) )],[refute_0_536,refute_0_537]) ).
cnf(refute_0_539,plain,
( implies(big_V(implies(X,X_61),X_60),X_61) != big_hat(implies(implies(X,X_61),X_61),implies(X_60,X_61))
| implies(implies(X,X_61),X_61) != big_V(X,X_61)
| implies(big_V(implies(X,X_61),X_60),X_61) = big_hat(big_V(X,X_61),implies(X_60,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(implies(X,X_61),X_60),X_61),big_hat(implies(implies(X,X_61),X_61),implies(X_60,X_61))) ),[1,0],$fot(big_V(X,X_61))]]) ).
cnf(refute_0_540,plain,
( implies(big_V(implies(X,X_61),X_60),X_61) != big_hat(implies(implies(X,X_61),X_61),implies(X_60,X_61))
| implies(big_V(implies(X,X_61),X_60),X_61) = big_hat(big_V(X,X_61),implies(X_60,X_61)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_61),X_61),big_V(X,X_61)) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
implies(big_V(implies(X,X_61),X_60),X_61) = big_hat(big_V(X,X_61),implies(X_60,X_61)),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X,X_61),X_60),X_61),big_hat(implies(implies(X,X_61),X_61),implies(X_60,X_61))) )],[refute_0_535,refute_0_540]) ).
cnf(refute_0_542,plain,
implies(big_V(implies(X,X_600),X_60),X_600) = big_hat(big_V(X,X_600),implies(X_60,X_600)),
inference(subst,[],[refute_0_541:[bind(X_61,$fot(X_600))]]) ).
cnf(refute_0_543,plain,
( X_600 != big_hat(X_600,implies(X_602,implies(big_V(implies(X,X_600),X_60),X_600)))
| implies(big_V(implies(X,X_600),X_60),X_600) != big_hat(big_V(X,X_600),implies(X_60,X_600))
| X_600 = big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_600,big_hat(X_600,implies(X_602,implies(big_V(implies(X,X_600),X_60),X_600)))) ),[1,1,1],$fot(big_hat(big_V(X,X_600),implies(X_60,X_600)))]]) ).
cnf(refute_0_544,plain,
( X_600 != big_hat(X_600,implies(X_602,implies(big_V(implies(X,X_600),X_60),X_600)))
| X_600 = big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))) ),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X,X_600),X_60),X_600),big_hat(big_V(X,X_600),implies(X_60,X_600))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
X_600 = big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))),
inference(resolve,[$cnf( $equal(X_600,big_hat(X_600,implies(X_602,implies(big_V(implies(X,X_600),X_60),X_600)))) )],[refute_0_534,refute_0_544]) ).
cnf(refute_0_546,plain,
not(big_hat(not(X_44),Y)) = big_V(not(not(X_44)),not(Y)),
inference(subst,[],[lemma_5:[bind(X,$fot(not(X_44)))]]) ).
cnf(refute_0_547,plain,
X_44 = not(not(X_44)),
inference(subst,[],[refute_0_441:[bind(X,$fot(X_44))]]) ).
cnf(refute_0_548,plain,
( X_44 != not(not(X_44))
| not(not(X_44)) = X_44 ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X_44)),bind(Y0,$fot(not(not(X_44))))]]) ).
cnf(refute_0_549,plain,
not(not(X_44)) = X_44,
inference(resolve,[$cnf( $equal(X_44,not(not(X_44))) )],[refute_0_547,refute_0_548]) ).
cnf(refute_0_550,plain,
( not(big_hat(not(X_44),Y)) != big_V(not(not(X_44)),not(Y))
| not(not(X_44)) != X_44
| not(big_hat(not(X_44),Y)) = big_V(X_44,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(not(X_44),Y)),big_V(not(not(X_44)),not(Y))) ),[1,0],$fot(X_44)]]) ).
cnf(refute_0_551,plain,
( not(big_hat(not(X_44),Y)) != big_V(not(not(X_44)),not(Y))
| not(big_hat(not(X_44),Y)) = big_V(X_44,not(Y)) ),
inference(resolve,[$cnf( $equal(not(not(X_44)),X_44) )],[refute_0_549,refute_0_550]) ).
cnf(refute_0_552,plain,
not(big_hat(not(X_44),Y)) = big_V(X_44,not(Y)),
inference(resolve,[$cnf( $equal(not(big_hat(not(X_44),Y)),big_V(not(not(X_44)),not(Y))) )],[refute_0_546,refute_0_551]) ).
cnf(refute_0_553,plain,
not(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))) = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))),
inference(subst,[],[refute_0_552:[bind(Y,$fot(big_V(X_561,implies(X_562,not(X_44)))))]]) ).
cnf(refute_0_554,plain,
X = implies(implies(X,big_V(X_213,implies(X_214,X))),big_hat(X,big_V(X_213,implies(X_214,X)))),
inference(subst,[],[refute_0_502:[bind(X_84,$fot(big_V(X_213,implies(X_214,X))))]]) ).
cnf(refute_0_555,plain,
implies(X_114,big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))) = implies(X_114,big_V(X,implies(X_113,X_114))),
inference(subst,[],[refute_0_512:[bind(X_47,$fot(X_113)),bind(X_78,$fot(X_114)),bind(X_80,$fot(big_V(X,implies(X_113,X_114))))]]) ).
cnf(refute_0_556,plain,
implies(X_113,X_114) = big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114))),
inference(subst,[],[refute_0_469:[bind(X_67,$fot(implies(X_113,X_114)))]]) ).
cnf(refute_0_557,plain,
( implies(X_113,X_114) != big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))
| big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114))) = implies(X_113,X_114) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_113,X_114))),bind(Y0,$fot(big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))))]]) ).
cnf(refute_0_558,plain,
big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114))) = implies(X_113,X_114),
inference(resolve,[$cnf( $equal(implies(X_113,X_114),big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
( big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114))) != implies(X_113,X_114)
| implies(X_114,big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))) != implies(X_114,big_V(X,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) = implies(X_114,big_V(X,implies(X_113,X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_114,big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))),implies(X_114,big_V(X,implies(X_113,X_114)))) ),[0,1],$fot(implies(X_113,X_114))]]) ).
cnf(refute_0_560,plain,
( implies(X_114,big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))) != implies(X_114,big_V(X,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) = implies(X_114,big_V(X,implies(X_113,X_114))) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114))),implies(X_113,X_114)) )],[refute_0_558,refute_0_559]) ).
cnf(refute_0_561,plain,
implies(X_114,implies(X_113,X_114)) = implies(X_114,big_V(X,implies(X_113,X_114))),
inference(resolve,[$cnf( $equal(implies(X_114,big_hat(implies(X_113,X_114),big_V(X,implies(X_113,X_114)))),implies(X_114,big_V(X,implies(X_113,X_114)))) )],[refute_0_555,refute_0_560]) ).
cnf(refute_0_562,plain,
( implies(X_114,implies(X_113,X_114)) != implies(X_114,big_V(X,implies(X_113,X_114)))
| implies(X_114,implies(X_113,X_114)) != truth
| truth = implies(X_114,big_V(X,implies(X_113,X_114))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),implies(X_114,big_V(X,implies(X_113,X_114)))) ),[0],$fot(truth)]]) ).
cnf(refute_0_563,plain,
( implies(X_114,implies(X_113,X_114)) != implies(X_114,big_V(X,implies(X_113,X_114)))
| truth = implies(X_114,big_V(X,implies(X_113,X_114))) ),
inference(resolve,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),truth) )],[refute_0_520,refute_0_562]) ).
cnf(refute_0_564,plain,
truth = implies(X_114,big_V(X,implies(X_113,X_114))),
inference(resolve,[$cnf( $equal(implies(X_114,implies(X_113,X_114)),implies(X_114,big_V(X,implies(X_113,X_114)))) )],[refute_0_561,refute_0_563]) ).
cnf(refute_0_565,plain,
truth = implies(X,big_V(X_213,implies(X_214,X))),
inference(subst,[],[refute_0_564:[bind(X,$fot(X_213)),bind(X_113,$fot(X_214)),bind(X_114,$fot(X))]]) ).
cnf(refute_0_566,plain,
( truth != implies(X,big_V(X_213,implies(X_214,X)))
| implies(X,big_V(X_213,implies(X_214,X))) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X,big_V(X_213,implies(X_214,X)))))]]) ).
cnf(refute_0_567,plain,
implies(X,big_V(X_213,implies(X_214,X))) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X,big_V(X_213,implies(X_214,X)))) )],[refute_0_565,refute_0_566]) ).
cnf(refute_0_568,plain,
( X != implies(implies(X,big_V(X_213,implies(X_214,X))),big_hat(X,big_V(X_213,implies(X_214,X))))
| implies(X,big_V(X_213,implies(X_214,X))) != truth
| X = implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))) ),
introduced(tautology,[equality,[$cnf( $equal(X,implies(implies(X,big_V(X_213,implies(X_214,X))),big_hat(X,big_V(X_213,implies(X_214,X))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_569,plain,
( X != implies(implies(X,big_V(X_213,implies(X_214,X))),big_hat(X,big_V(X_213,implies(X_214,X))))
| X = implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))) ),
inference(resolve,[$cnf( $equal(implies(X,big_V(X_213,implies(X_214,X))),truth) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
X = implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))),
inference(resolve,[$cnf( $equal(X,implies(implies(X,big_V(X_213,implies(X_214,X))),big_hat(X,big_V(X_213,implies(X_214,X))))) )],[refute_0_554,refute_0_569]) ).
cnf(refute_0_571,plain,
implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))) = big_hat(X,big_V(X_213,implies(X_214,X))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_hat(X,big_V(X_213,implies(X_214,X)))))]]) ).
cnf(refute_0_572,plain,
( X != implies(truth,big_hat(X,big_V(X_213,implies(X_214,X))))
| implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))) != big_hat(X,big_V(X_213,implies(X_214,X)))
| X = big_hat(X,big_V(X_213,implies(X_214,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,big_hat(X,big_V(X_213,implies(X_214,X)))) ),[0],$fot(implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))))]]) ).
cnf(refute_0_573,plain,
( X != implies(truth,big_hat(X,big_V(X_213,implies(X_214,X))))
| X = big_hat(X,big_V(X_213,implies(X_214,X))) ),
inference(resolve,[$cnf( $equal(implies(truth,big_hat(X,big_V(X_213,implies(X_214,X)))),big_hat(X,big_V(X_213,implies(X_214,X)))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
X = big_hat(X,big_V(X_213,implies(X_214,X))),
inference(resolve,[$cnf( $equal(X,implies(truth,big_hat(X,big_V(X_213,implies(X_214,X))))) )],[refute_0_570,refute_0_573]) ).
cnf(refute_0_575,plain,
not(X_44) = big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44)))),
inference(subst,[],[refute_0_574:[bind(X,$fot(not(X_44))),bind(X_213,$fot(X_561)),bind(X_214,$fot(X_562))]]) ).
cnf(refute_0_576,plain,
( not(X_44) != big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))
| big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44)))) = not(X_44) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(X_44))),bind(Y0,$fot(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))))]]) ).
cnf(refute_0_577,plain,
big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44)))) = not(X_44),
inference(resolve,[$cnf( $equal(not(X_44),big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
( big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44)))) != not(X_44)
| not(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))) != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| not(not(X_44)) = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))),big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))) ),[0,0],$fot(not(X_44))]]) ).
cnf(refute_0_579,plain,
( not(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))) != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| not(not(X_44)) = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) ),
inference(resolve,[$cnf( $equal(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44)))),not(X_44)) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
not(not(X_44)) = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))),
inference(resolve,[$cnf( $equal(not(big_hat(not(X_44),big_V(X_561,implies(X_562,not(X_44))))),big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))) )],[refute_0_553,refute_0_579]) ).
cnf(refute_0_581,plain,
( not(not(X_44)) != X_44
| not(not(X_44)) != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| X_44 = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(X_44)),big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))) ),[0],$fot(X_44)]]) ).
cnf(refute_0_582,plain,
( not(not(X_44)) != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| X_44 = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) ),
inference(resolve,[$cnf( $equal(not(not(X_44)),X_44) )],[refute_0_549,refute_0_581]) ).
cnf(refute_0_583,plain,
X_44 = big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))),
inference(resolve,[$cnf( $equal(not(not(X_44)),big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))) )],[refute_0_580,refute_0_582]) ).
cnf(refute_0_584,plain,
X_61 = big_hat(X_61,implies(big_V(implies(X_245,X_61),X_246),X_61)),
inference(subst,[],[refute_0_462:[bind(X_59,$fot(big_V(implies(X_245,X_61),X_246)))]]) ).
cnf(refute_0_585,plain,
implies(big_V(implies(X_245,X_61),X_246),X_61) = big_hat(big_V(X_245,X_61),implies(X_246,X_61)),
inference(subst,[],[refute_0_541:[bind(X,$fot(X_245)),bind(X_60,$fot(X_246))]]) ).
cnf(refute_0_586,plain,
( X_61 != big_hat(X_61,implies(big_V(implies(X_245,X_61),X_246),X_61))
| implies(big_V(implies(X_245,X_61),X_246),X_61) != big_hat(big_V(X_245,X_61),implies(X_246,X_61))
| X_61 = big_hat(X_61,big_hat(big_V(X_245,X_61),implies(X_246,X_61))) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,big_hat(X_61,implies(big_V(implies(X_245,X_61),X_246),X_61))) ),[1,1],$fot(big_hat(big_V(X_245,X_61),implies(X_246,X_61)))]]) ).
cnf(refute_0_587,plain,
( X_61 != big_hat(X_61,implies(big_V(implies(X_245,X_61),X_246),X_61))
| X_61 = big_hat(X_61,big_hat(big_V(X_245,X_61),implies(X_246,X_61))) ),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X_245,X_61),X_246),X_61),big_hat(big_V(X_245,X_61),implies(X_246,X_61))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
X_61 = big_hat(X_61,big_hat(big_V(X_245,X_61),implies(X_246,X_61))),
inference(resolve,[$cnf( $equal(X_61,big_hat(X_61,implies(big_V(implies(X_245,X_61),X_246),X_61))) )],[refute_0_584,refute_0_587]) ).
cnf(refute_0_589,plain,
X_556 = big_hat(X_556,big_hat(big_V(X_554,X_556),implies(big_V(implies(X,X_556),X_60),X_556))),
inference(subst,[],[refute_0_588:[bind(X_245,$fot(X_554)),bind(X_246,$fot(big_V(implies(X,X_556),X_60))),bind(X_61,$fot(X_556))]]) ).
cnf(refute_0_590,plain,
implies(big_V(implies(X,X_556),X_60),X_556) = big_hat(big_V(X,X_556),implies(X_60,X_556)),
inference(subst,[],[refute_0_541:[bind(X_61,$fot(X_556))]]) ).
cnf(refute_0_591,plain,
( X_556 != big_hat(X_556,big_hat(big_V(X_554,X_556),implies(big_V(implies(X,X_556),X_60),X_556)))
| implies(big_V(implies(X,X_556),X_60),X_556) != big_hat(big_V(X,X_556),implies(X_60,X_556))
| X_556 = big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_556,big_hat(X_556,big_hat(big_V(X_554,X_556),implies(big_V(implies(X,X_556),X_60),X_556)))) ),[1,1,1],$fot(big_hat(big_V(X,X_556),implies(X_60,X_556)))]]) ).
cnf(refute_0_592,plain,
( X_556 != big_hat(X_556,big_hat(big_V(X_554,X_556),implies(big_V(implies(X,X_556),X_60),X_556)))
| X_556 = big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))) ),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X,X_556),X_60),X_556),big_hat(big_V(X,X_556),implies(X_60,X_556))) )],[refute_0_590,refute_0_591]) ).
cnf(refute_0_593,plain,
X_556 = big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))),
inference(resolve,[$cnf( $equal(X_556,big_hat(X_556,big_hat(big_V(X_554,X_556),implies(big_V(implies(X,X_556),X_60),X_556)))) )],[refute_0_589,refute_0_592]) ).
cnf(refute_0_594,plain,
X_61 = big_hat(X_61,implies(not(X_92),X_61)),
inference(subst,[],[refute_0_462:[bind(X_59,$fot(not(X_92)))]]) ).
cnf(refute_0_595,plain,
big_V(X_1,Y) = big_V(Y,X_1),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_1))]]) ).
cnf(refute_0_596,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| big_V(X_1,Y) != big_V(Y,X_1)
| big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) ),[1,0],$fot(big_V(Y,X_1))]]) ).
cnf(refute_0_597,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(X_1,Y),Y)
| big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y) ),
inference(resolve,[$cnf( $equal(big_V(X_1,Y),big_V(Y,X_1)) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
big_V(Y,implies(X_1,Y)) = implies(big_V(Y,X_1),Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(X_1,Y),Y)) )],[refute_0_307,refute_0_597]) ).
cnf(refute_0_599,plain,
big_V(not(X),implies(not(Y),not(X))) = implies(big_V(not(X),not(Y)),not(X)),
inference(subst,[],[refute_0_598:[bind(Y,$fot(not(X))),bind(X_1,$fot(not(Y)))]]) ).
cnf(refute_0_600,plain,
( big_V(not(X),implies(not(Y),not(X))) != implies(big_V(not(X),not(Y)),not(X))
| big_V(not(X),not(Y)) != not(big_hat(X,Y))
| big_V(not(X),implies(not(Y),not(X))) = implies(not(big_hat(X,Y)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X),implies(not(Y),not(X))),implies(big_V(not(X),not(Y)),not(X))) ),[1,0],$fot(not(big_hat(X,Y)))]]) ).
cnf(refute_0_601,plain,
( big_V(not(X),implies(not(Y),not(X))) != implies(big_V(not(X),not(Y)),not(X))
| big_V(not(X),implies(not(Y),not(X))) = implies(not(big_hat(X,Y)),not(X)) ),
inference(resolve,[$cnf( $equal(big_V(not(X),not(Y)),not(big_hat(X,Y))) )],[refute_0_59,refute_0_600]) ).
cnf(refute_0_602,plain,
big_V(not(X),implies(not(Y),not(X))) = implies(not(big_hat(X,Y)),not(X)),
inference(resolve,[$cnf( $equal(big_V(not(X),implies(not(Y),not(X))),implies(big_V(not(X),not(Y)),not(X))) )],[refute_0_599,refute_0_601]) ).
cnf(refute_0_603,plain,
big_V(not(X_11),implies(not(X_10),not(X_11))) = implies(big_V(not(X_10),not(X_11)),not(X_11)),
inference(subst,[],[refute_0_307:[bind(Y,$fot(not(X_11))),bind(X_1,$fot(not(X_10)))]]) ).
cnf(refute_0_604,plain,
not(big_hat(X_10,X_11)) = big_V(not(X_10),not(X_11)),
inference(subst,[],[lemma_5:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_605,plain,
( not(big_hat(X_10,X_11)) != big_V(not(X_10),not(X_11))
| big_V(not(X_10),not(X_11)) = not(big_hat(X_10,X_11)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(not(big_hat(X_10,X_11)))),bind(Y0,$fot(big_V(not(X_10),not(X_11))))]]) ).
cnf(refute_0_606,plain,
big_V(not(X_10),not(X_11)) = not(big_hat(X_10,X_11)),
inference(resolve,[$cnf( $equal(not(big_hat(X_10,X_11)),big_V(not(X_10),not(X_11))) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
( big_V(not(X_10),not(X_11)) != not(big_hat(X_10,X_11))
| big_V(not(X_11),implies(not(X_10),not(X_11))) != implies(big_V(not(X_10),not(X_11)),not(X_11))
| big_V(not(X_11),implies(not(X_10),not(X_11))) = implies(not(big_hat(X_10,X_11)),not(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_11),implies(not(X_10),not(X_11))),implies(big_V(not(X_10),not(X_11)),not(X_11))) ),[1,0],$fot(not(big_hat(X_10,X_11)))]]) ).
cnf(refute_0_608,plain,
( big_V(not(X_11),implies(not(X_10),not(X_11))) != implies(big_V(not(X_10),not(X_11)),not(X_11))
| big_V(not(X_11),implies(not(X_10),not(X_11))) = implies(not(big_hat(X_10,X_11)),not(X_11)) ),
inference(resolve,[$cnf( $equal(big_V(not(X_10),not(X_11)),not(big_hat(X_10,X_11))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
big_V(not(X_11),implies(not(X_10),not(X_11))) = implies(not(big_hat(X_10,X_11)),not(X_11)),
inference(resolve,[$cnf( $equal(big_V(not(X_11),implies(not(X_10),not(X_11))),implies(big_V(not(X_10),not(X_11)),not(X_11))) )],[refute_0_603,refute_0_608]) ).
cnf(refute_0_610,plain,
big_V(not(X),implies(not(Y),not(X))) = implies(not(big_hat(Y,X)),not(X)),
inference(subst,[],[refute_0_609:[bind(X_10,$fot(Y)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_611,plain,
( big_V(not(X),implies(not(Y),not(X))) != implies(not(big_hat(X,Y)),not(X))
| big_V(not(X),implies(not(Y),not(X))) != implies(not(big_hat(Y,X)),not(X))
| implies(not(big_hat(Y,X)),not(X)) = implies(not(big_hat(X,Y)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X),implies(not(Y),not(X))),implies(not(big_hat(X,Y)),not(X))) ),[0],$fot(implies(not(big_hat(Y,X)),not(X)))]]) ).
cnf(refute_0_612,plain,
( big_V(not(X),implies(not(Y),not(X))) != implies(not(big_hat(X,Y)),not(X))
| implies(not(big_hat(Y,X)),not(X)) = implies(not(big_hat(X,Y)),not(X)) ),
inference(resolve,[$cnf( $equal(big_V(not(X),implies(not(Y),not(X))),implies(not(big_hat(Y,X)),not(X))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
implies(not(big_hat(Y,X)),not(X)) = implies(not(big_hat(X,Y)),not(X)),
inference(resolve,[$cnf( $equal(big_V(not(X),implies(not(Y),not(X))),implies(not(big_hat(X,Y)),not(X))) )],[refute_0_602,refute_0_612]) ).
cnf(refute_0_614,plain,
big_V(not(X_11),implies(not(X_10),not(X_11))) = implies(not(X_10),not(X_11)),
inference(subst,[],[refute_0_377:[bind(X,$fot(not(X_11))),bind(X_55,$fot(not(X_10)))]]) ).
cnf(refute_0_615,plain,
( big_V(not(X_11),implies(not(X_10),not(X_11))) != implies(not(X_10),not(X_11))
| big_V(not(X_11),implies(not(X_10),not(X_11))) != implies(not(big_hat(X_10,X_11)),not(X_11))
| implies(not(X_10),not(X_11)) = implies(not(big_hat(X_10,X_11)),not(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(X_11),implies(not(X_10),not(X_11))),implies(not(big_hat(X_10,X_11)),not(X_11))) ),[0],$fot(implies(not(X_10),not(X_11)))]]) ).
cnf(refute_0_616,plain,
( big_V(not(X_11),implies(not(X_10),not(X_11))) != implies(not(big_hat(X_10,X_11)),not(X_11))
| implies(not(X_10),not(X_11)) = implies(not(big_hat(X_10,X_11)),not(X_11)) ),
inference(resolve,[$cnf( $equal(big_V(not(X_11),implies(not(X_10),not(X_11))),implies(not(X_10),not(X_11))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
implies(not(X_10),not(X_11)) = implies(not(big_hat(X_10,X_11)),not(X_11)),
inference(resolve,[$cnf( $equal(big_V(not(X_11),implies(not(X_10),not(X_11))),implies(not(big_hat(X_10,X_11)),not(X_11))) )],[refute_0_609,refute_0_616]) ).
cnf(refute_0_618,plain,
( implies(not(X_10),not(X_11)) != implies(not(big_hat(X_10,X_11)),not(X_11))
| implies(not(big_hat(X_10,X_11)),not(X_11)) = implies(not(X_10),not(X_11)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(not(X_10),not(X_11)))),bind(Y0,$fot(implies(not(big_hat(X_10,X_11)),not(X_11))))]]) ).
cnf(refute_0_619,plain,
implies(not(big_hat(X_10,X_11)),not(X_11)) = implies(not(X_10),not(X_11)),
inference(resolve,[$cnf( $equal(implies(not(X_10),not(X_11)),implies(not(big_hat(X_10,X_11)),not(X_11))) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
implies(not(big_hat(Y,X)),not(X)) = implies(not(Y),not(X)),
inference(subst,[],[refute_0_619:[bind(X_10,$fot(Y)),bind(X_11,$fot(X))]]) ).
cnf(refute_0_621,plain,
( implies(not(big_hat(Y,X)),not(X)) != implies(not(Y),not(X))
| implies(not(big_hat(Y,X)),not(X)) != implies(not(big_hat(X,Y)),not(X))
| implies(not(Y),not(X)) = implies(not(big_hat(X,Y)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(big_hat(Y,X)),not(X)),implies(not(big_hat(X,Y)),not(X))) ),[0],$fot(implies(not(Y),not(X)))]]) ).
cnf(refute_0_622,plain,
( implies(not(big_hat(Y,X)),not(X)) != implies(not(big_hat(X,Y)),not(X))
| implies(not(Y),not(X)) = implies(not(big_hat(X,Y)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(Y,X)),not(X)),implies(not(Y),not(X))) )],[refute_0_620,refute_0_621]) ).
cnf(refute_0_623,plain,
implies(not(Y),not(X)) = implies(not(big_hat(X,Y)),not(X)),
inference(resolve,[$cnf( $equal(implies(not(big_hat(Y,X)),not(X)),implies(not(big_hat(X,Y)),not(X))) )],[refute_0_613,refute_0_622]) ).
cnf(refute_0_624,plain,
implies(not(X_88),not(not(X))) = implies(not(big_hat(not(X),X_88)),not(not(X))),
inference(subst,[],[refute_0_623:[bind(X,$fot(not(X))),bind(Y,$fot(X_88))]]) ).
cnf(refute_0_625,plain,
( implies(not(X_88),not(not(X))) != implies(not(big_hat(not(X),X_88)),not(not(X)))
| not(not(X)) != X
| implies(not(X_88),X) = implies(not(big_hat(not(X),X_88)),not(not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_88),not(not(X))),implies(not(big_hat(not(X),X_88)),not(not(X)))) ),[0,1],$fot(X)]]) ).
cnf(refute_0_626,plain,
( implies(not(X_88),not(not(X))) != implies(not(big_hat(not(X),X_88)),not(not(X)))
| implies(not(X_88),X) = implies(not(big_hat(not(X),X_88)),not(not(X))) ),
inference(resolve,[$cnf( $equal(not(not(X)),X) )],[refute_0_494,refute_0_625]) ).
cnf(refute_0_627,plain,
implies(not(X_88),X) = implies(not(big_hat(not(X),X_88)),not(not(X))),
inference(resolve,[$cnf( $equal(implies(not(X_88),not(not(X))),implies(not(big_hat(not(X),X_88)),not(not(X)))) )],[refute_0_624,refute_0_626]) ).
cnf(refute_0_628,plain,
implies(not(X),big_hat(not(X),X_88)) = implies(not(X),X_88),
inference(subst,[],[refute_0_407:[bind(X_79,$fot(not(X))),bind(X_80,$fot(X_88))]]) ).
cnf(refute_0_629,plain,
big_V(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(not(big_hat(X_87,X_88)),not(X_87)),
inference(subst,[],[refute_0_107:[bind(X_22,$fot(not(X_87))),bind(X_23,$fot(not(big_hat(X_87,X_88))))]]) ).
cnf(refute_0_630,plain,
implies(not(X_88),not(X_87)) = implies(not(big_hat(X_87,X_88)),not(X_87)),
inference(subst,[],[refute_0_623:[bind(X,$fot(X_87)),bind(Y,$fot(X_88))]]) ).
cnf(refute_0_631,plain,
( implies(not(X_88),not(X_87)) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(not(big_hat(X_87,X_88)),not(X_87)) = implies(not(X_88),not(X_87)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(not(X_88),not(X_87)))),bind(Y0,$fot(implies(not(big_hat(X_87,X_88)),not(X_87))))]]) ).
cnf(refute_0_632,plain,
implies(not(big_hat(X_87,X_88)),not(X_87)) = implies(not(X_88),not(X_87)),
inference(resolve,[$cnf( $equal(implies(not(X_88),not(X_87)),implies(not(big_hat(X_87,X_88)),not(X_87))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
( big_V(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(not(big_hat(X_87,X_88)),not(X_87)) != implies(not(X_88),not(X_87))
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(not(big_hat(X_87,X_88)),not(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),implies(not(big_hat(X_87,X_88)),not(X_87))) ),[0,0],$fot(implies(not(X_88),not(X_87)))]]) ).
cnf(refute_0_634,plain,
( big_V(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(not(big_hat(X_87,X_88)),not(X_87))
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(not(big_hat(X_87,X_88)),not(X_87)) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(X_88),not(X_87))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(not(big_hat(X_87,X_88)),not(X_87)),
inference(resolve,[$cnf( $equal(big_V(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),implies(not(big_hat(X_87,X_88)),not(X_87))) )],[refute_0_629,refute_0_634]) ).
cnf(refute_0_636,plain,
big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))) = implies(X_87,X_88),
inference(subst,[],[refute_0_107:[bind(X_22,$fot(X_88)),bind(X_23,$fot(X_87))]]) ).
cnf(refute_0_637,plain,
big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) = big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))),
inference(subst,[],[refute_0_48:[bind(X,$fot(implies(X_87,X_88))),bind(Y,$fot(implies(not(X_88),not(X_87))))]]) ).
cnf(refute_0_638,plain,
( big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) != big_V(implies(X_87,X_88),implies(not(X_88),not(X_87)))
| big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) = implies(X_87,X_88) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)))),bind(Y0,$fot(big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))))),bind(Z0,$fot(implies(X_87,X_88)))]]) ).
cnf(refute_0_639,plain,
( big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) = implies(X_87,X_88) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)),big_V(implies(X_87,X_88),implies(not(X_88),not(X_87)))) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) = implies(X_87,X_88),
inference(resolve,[$cnf( $equal(big_V(implies(X_87,X_88),implies(not(X_88),not(X_87))),implies(X_87,X_88)) )],[refute_0_636,refute_0_639]) ).
cnf(refute_0_641,plain,
implies(X_87,big_hat(X_87,X_88)) = implies(X_87,X_88),
inference(subst,[],[refute_0_407:[bind(X_79,$fot(X_87)),bind(X_80,$fot(X_88))]]) ).
cnf(refute_0_642,plain,
not(not(big_hat(X_87,X_88))) = big_hat(X_87,X_88),
inference(subst,[],[refute_0_494:[bind(X,$fot(big_hat(X_87,X_88)))]]) ).
cnf(refute_0_643,plain,
implies(X_87,not(not(big_hat(X_87,X_88)))) = implies(X_87,not(not(big_hat(X_87,X_88)))),
introduced(tautology,[refl,[$fot(implies(X_87,not(not(big_hat(X_87,X_88)))))]]) ).
cnf(refute_0_644,plain,
( implies(X_87,not(not(big_hat(X_87,X_88)))) != implies(X_87,not(not(big_hat(X_87,X_88))))
| not(not(big_hat(X_87,X_88))) != big_hat(X_87,X_88)
| implies(X_87,not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_87,not(not(big_hat(X_87,X_88)))),implies(X_87,not(not(big_hat(X_87,X_88))))) ),[1,1],$fot(big_hat(X_87,X_88))]]) ).
cnf(refute_0_645,plain,
( not(not(big_hat(X_87,X_88))) != big_hat(X_87,X_88)
| implies(X_87,not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(implies(X_87,not(not(big_hat(X_87,X_88)))),implies(X_87,not(not(big_hat(X_87,X_88))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
implies(X_87,not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)),
inference(resolve,[$cnf( $equal(not(not(big_hat(X_87,X_88))),big_hat(X_87,X_88)) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
not(not(X_87)) = X_87,
inference(subst,[],[refute_0_494:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_648,plain,
implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),
introduced(tautology,[refl,[$fot(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))]]) ).
cnf(refute_0_649,plain,
( implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) != implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))
| not(not(X_87)) != X_87
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,not(not(big_hat(X_87,X_88)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) ),[1,0],$fot(X_87)]]) ).
cnf(refute_0_650,plain,
( not(not(X_87)) != X_87
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,not(not(big_hat(X_87,X_88)))) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) )],[refute_0_648,refute_0_649]) ).
cnf(refute_0_651,plain,
implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,not(not(big_hat(X_87,X_88)))),
inference(resolve,[$cnf( $equal(not(not(X_87)),X_87) )],[refute_0_647,refute_0_650]) ).
cnf(refute_0_652,plain,
( implies(X_87,not(not(big_hat(X_87,X_88)))) != implies(X_87,big_hat(X_87,X_88))
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) != implies(X_87,not(not(big_hat(X_87,X_88))))
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))),bind(Y0,$fot(implies(X_87,not(not(big_hat(X_87,X_88)))))),bind(Z0,$fot(implies(X_87,big_hat(X_87,X_88))))]]) ).
cnf(refute_0_653,plain,
( implies(X_87,not(not(big_hat(X_87,X_88)))) != implies(X_87,big_hat(X_87,X_88))
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),implies(X_87,not(not(big_hat(X_87,X_88))))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,big_hat(X_87,X_88)),
inference(resolve,[$cnf( $equal(implies(X_87,not(not(big_hat(X_87,X_88)))),implies(X_87,big_hat(X_87,X_88))) )],[refute_0_646,refute_0_653]) ).
cnf(refute_0_655,plain,
( implies(X_87,big_hat(X_87,X_88)) != implies(X_87,X_88)
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) != implies(X_87,big_hat(X_87,X_88))
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,X_88) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))),bind(Y0,$fot(implies(X_87,big_hat(X_87,X_88)))),bind(Z0,$fot(implies(X_87,X_88)))]]) ).
cnf(refute_0_656,plain,
( implies(X_87,big_hat(X_87,X_88)) != implies(X_87,X_88)
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,X_88) ),
inference(resolve,[$cnf( $equal(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),implies(X_87,big_hat(X_87,X_88))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) = implies(X_87,X_88),
inference(resolve,[$cnf( $equal(implies(X_87,big_hat(X_87,X_88)),implies(X_87,X_88)) )],[refute_0_641,refute_0_656]) ).
cnf(refute_0_658,plain,
big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),
introduced(tautology,[refl,[$fot(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))))]]) ).
cnf(refute_0_659,plain,
( big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))
| implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))) ),[1,1],$fot(implies(X_87,X_88))]]) ).
cnf(refute_0_660,plain,
( implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))))) )],[refute_0_658,refute_0_659]) ).
cnf(refute_0_661,plain,
big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)),
inference(resolve,[$cnf( $equal(implies(not(not(X_87)),not(not(big_hat(X_87,X_88)))),implies(X_87,X_88)) )],[refute_0_657,refute_0_660]) ).
cnf(refute_0_662,plain,
( big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88))
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(X_87,X_88) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))))),bind(Y0,$fot(big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)))),bind(Z0,$fot(implies(X_87,X_88)))]]) ).
cnf(refute_0_663,plain,
( big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(X_87,X_88) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) = implies(X_87,X_88),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(X_87,X_88)),implies(X_87,X_88)) )],[refute_0_640,refute_0_663]) ).
cnf(refute_0_665,plain,
( big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(X_87,X_88)
| big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(X_87,X_88) = implies(not(big_hat(X_87,X_88)),not(X_87)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),implies(not(big_hat(X_87,X_88)),not(X_87))) ),[0],$fot(implies(X_87,X_88))]]) ).
cnf(refute_0_666,plain,
( big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(X_87,X_88) = implies(not(big_hat(X_87,X_88)),not(X_87)) ),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),implies(X_87,X_88)) )],[refute_0_664,refute_0_665]) ).
cnf(refute_0_667,plain,
( implies(X_87,X_88) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(not(big_hat(X_87,X_88)),not(X_87)) != implies(not(X_88),not(X_87))
| implies(X_87,X_88) = implies(not(X_88),not(X_87)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_87,X_88),implies(not(X_88),not(X_87))) ),[0],$fot(implies(not(big_hat(X_87,X_88)),not(X_87)))]]) ).
cnf(refute_0_668,plain,
( implies(X_87,X_88) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(X_87,X_88) = implies(not(X_88),not(X_87)) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(X_87,X_88)),not(X_87)),implies(not(X_88),not(X_87))) )],[refute_0_632,refute_0_667]) ).
cnf(refute_0_669,plain,
( big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))) != implies(not(big_hat(X_87,X_88)),not(X_87))
| implies(X_87,X_88) = implies(not(X_88),not(X_87)) ),
inference(resolve,[$cnf( $equal(implies(X_87,X_88),implies(not(big_hat(X_87,X_88)),not(X_87))) )],[refute_0_666,refute_0_668]) ).
cnf(refute_0_670,plain,
implies(X_87,X_88) = implies(not(X_88),not(X_87)),
inference(resolve,[$cnf( $equal(big_V(implies(not(X_88),not(X_87)),implies(not(not(X_87)),not(not(big_hat(X_87,X_88))))),implies(not(big_hat(X_87,X_88)),not(X_87))) )],[refute_0_635,refute_0_669]) ).
cnf(refute_0_671,plain,
( implies(X_87,X_88) != implies(not(X_88),not(X_87))
| implies(not(X_88),not(X_87)) = implies(X_87,X_88) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_87,X_88))),bind(Y0,$fot(implies(not(X_88),not(X_87))))]]) ).
cnf(refute_0_672,plain,
implies(not(X_88),not(X_87)) = implies(X_87,X_88),
inference(resolve,[$cnf( $equal(implies(X_87,X_88),implies(not(X_88),not(X_87))) )],[refute_0_670,refute_0_671]) ).
cnf(refute_0_673,plain,
implies(not(big_hat(not(X),X_88)),not(not(X))) = implies(not(X),big_hat(not(X),X_88)),
inference(subst,[],[refute_0_672:[bind(X_87,$fot(not(X))),bind(X_88,$fot(big_hat(not(X),X_88)))]]) ).
cnf(refute_0_674,plain,
( implies(not(X),big_hat(not(X),X_88)) != implies(not(X),X_88)
| implies(not(big_hat(not(X),X_88)),not(not(X))) != implies(not(X),big_hat(not(X),X_88))
| implies(not(big_hat(not(X),X_88)),not(not(X))) = implies(not(X),X_88) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(not(big_hat(not(X),X_88)),not(not(X))))),bind(Y0,$fot(implies(not(X),big_hat(not(X),X_88)))),bind(Z0,$fot(implies(not(X),X_88)))]]) ).
cnf(refute_0_675,plain,
( implies(not(X),big_hat(not(X),X_88)) != implies(not(X),X_88)
| implies(not(big_hat(not(X),X_88)),not(not(X))) = implies(not(X),X_88) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(not(X),X_88)),not(not(X))),implies(not(X),big_hat(not(X),X_88))) )],[refute_0_673,refute_0_674]) ).
cnf(refute_0_676,plain,
implies(not(big_hat(not(X),X_88)),not(not(X))) = implies(not(X),X_88),
inference(resolve,[$cnf( $equal(implies(not(X),big_hat(not(X),X_88)),implies(not(X),X_88)) )],[refute_0_628,refute_0_675]) ).
cnf(refute_0_677,plain,
( implies(not(X_88),X) != implies(not(big_hat(not(X),X_88)),not(not(X)))
| implies(not(big_hat(not(X),X_88)),not(not(X))) != implies(not(X),X_88)
| implies(not(X_88),X) = implies(not(X),X_88) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(X_88),X),implies(not(X),X_88)) ),[0],$fot(implies(not(big_hat(not(X),X_88)),not(not(X))))]]) ).
cnf(refute_0_678,plain,
( implies(not(X_88),X) != implies(not(big_hat(not(X),X_88)),not(not(X)))
| implies(not(X_88),X) = implies(not(X),X_88) ),
inference(resolve,[$cnf( $equal(implies(not(big_hat(not(X),X_88)),not(not(X))),implies(not(X),X_88)) )],[refute_0_676,refute_0_677]) ).
cnf(refute_0_679,plain,
implies(not(X_88),X) = implies(not(X),X_88),
inference(resolve,[$cnf( $equal(implies(not(X_88),X),implies(not(big_hat(not(X),X_88)),not(not(X)))) )],[refute_0_627,refute_0_678]) ).
cnf(refute_0_680,plain,
implies(not(X_92),X_61) = implies(not(X_61),X_92),
inference(subst,[],[refute_0_679:[bind(X,$fot(X_61)),bind(X_88,$fot(X_92))]]) ).
cnf(refute_0_681,plain,
( X_61 != big_hat(X_61,implies(not(X_92),X_61))
| implies(not(X_92),X_61) != implies(not(X_61),X_92)
| X_61 = big_hat(X_61,implies(not(X_61),X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,big_hat(X_61,implies(not(X_92),X_61))) ),[1,1],$fot(implies(not(X_61),X_92))]]) ).
cnf(refute_0_682,plain,
( X_61 != big_hat(X_61,implies(not(X_92),X_61))
| X_61 = big_hat(X_61,implies(not(X_61),X_92)) ),
inference(resolve,[$cnf( $equal(implies(not(X_92),X_61),implies(not(X_61),X_92)) )],[refute_0_680,refute_0_681]) ).
cnf(refute_0_683,plain,
X_61 = big_hat(X_61,implies(not(X_61),X_92)),
inference(resolve,[$cnf( $equal(X_61,big_hat(X_61,implies(not(X_92),X_61))) )],[refute_0_594,refute_0_682]) ).
cnf(refute_0_684,plain,
X_61 = big_hat(X_61,implies(not(X_61),implies(X_541,X_539))),
inference(subst,[],[refute_0_683:[bind(X_92,$fot(implies(X_541,X_539)))]]) ).
cnf(refute_0_685,plain,
implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(implies(X_59,implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))),
inference(subst,[],[lemma_6:[bind(X,$fot(X_59)),bind(Y,$fot(implies(not(X),not(Y)))),bind(Z,$fot(implies(Y,X)))]]) ).
cnf(refute_0_686,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(implies(X_59,implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X)))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(implies(X_59,implies(Y,X)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(implies(X_59,implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_687,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(implies(X_59,implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X)))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(implies(X_59,implies(Y,X)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_686]) ).
cnf(refute_0_688,plain,
implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(implies(X_59,implies(Y,X)),truth),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(implies(X_59,implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X)))) )],[refute_0_685,refute_0_687]) ).
cnf(refute_0_689,plain,
big_hat(implies(X_59,implies(Y,X)),truth) = big_hat(truth,implies(X_59,implies(Y,X))),
inference(subst,[],[refute_0_388:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_59,implies(Y,X))))]]) ).
cnf(refute_0_690,plain,
( big_hat(implies(X_59,implies(Y,X)),truth) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(implies(X_59,implies(Y,X)),truth)
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(truth,implies(X_59,implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(implies(X_59,implies(Y,X)),truth)) ),[1],$fot(big_hat(truth,implies(X_59,implies(Y,X))))]]) ).
cnf(refute_0_691,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(implies(X_59,implies(Y,X)),truth)
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(truth,implies(X_59,implies(Y,X))) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,implies(Y,X)),truth),big_hat(truth,implies(X_59,implies(Y,X)))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = big_hat(truth,implies(X_59,implies(Y,X))),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(implies(X_59,implies(Y,X)),truth)) )],[refute_0_688,refute_0_691]) ).
cnf(refute_0_693,plain,
implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = big_hat(implies(X_78,X_79),implies(X_78,big_V(X_78,X_49))),
inference(subst,[],[lemma_7:[bind(X,$fot(X_78)),bind(Y,$fot(X_79)),bind(Z,$fot(big_V(X_78,X_49)))]]) ).
cnf(refute_0_694,plain,
implies(X_78,big_V(X_78,X_49)) = truth,
inference(subst,[],[refute_0_334:[bind(X_48,$fot(X_78))]]) ).
cnf(refute_0_695,plain,
( implies(X_78,big_V(X_78,X_49)) != truth
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) != big_hat(implies(X_78,X_79),implies(X_78,big_V(X_78,X_49)))
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = big_hat(implies(X_78,X_79),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_78,big_hat(X_79,big_V(X_78,X_49))),big_hat(implies(X_78,X_79),implies(X_78,big_V(X_78,X_49)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_696,plain,
( implies(X_78,big_hat(X_79,big_V(X_78,X_49))) != big_hat(implies(X_78,X_79),implies(X_78,big_V(X_78,X_49)))
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = big_hat(implies(X_78,X_79),truth) ),
inference(resolve,[$cnf( $equal(implies(X_78,big_V(X_78,X_49)),truth) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = big_hat(implies(X_78,X_79),truth),
inference(resolve,[$cnf( $equal(implies(X_78,big_hat(X_79,big_V(X_78,X_49))),big_hat(implies(X_78,X_79),implies(X_78,big_V(X_78,X_49)))) )],[refute_0_693,refute_0_696]) ).
cnf(refute_0_698,plain,
big_hat(X,truth) = big_hat(truth,X),
inference(subst,[],[refute_0_180:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_699,plain,
X = big_hat(truth,X),
inference(subst,[],[refute_0_401:[bind(X_63,$fot(X))]]) ).
cnf(refute_0_700,plain,
( X != big_hat(truth,X)
| big_hat(truth,X) = X ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X)),bind(Y0,$fot(big_hat(truth,X)))]]) ).
cnf(refute_0_701,plain,
big_hat(truth,X) = X,
inference(resolve,[$cnf( $equal(X,big_hat(truth,X)) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
( big_hat(X,truth) != big_hat(truth,X)
| big_hat(truth,X) != X
| big_hat(X,truth) = X ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(X,truth),X) ),[0],$fot(big_hat(truth,X))]]) ).
cnf(refute_0_703,plain,
( big_hat(X,truth) != big_hat(truth,X)
| big_hat(X,truth) = X ),
inference(resolve,[$cnf( $equal(big_hat(truth,X),X) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
big_hat(X,truth) = X,
inference(resolve,[$cnf( $equal(big_hat(X,truth),big_hat(truth,X)) )],[refute_0_698,refute_0_703]) ).
cnf(refute_0_705,plain,
big_hat(implies(X_78,X_79),truth) = implies(X_78,X_79),
inference(subst,[],[refute_0_704:[bind(X,$fot(implies(X_78,X_79)))]]) ).
cnf(refute_0_706,plain,
( big_hat(implies(X_78,X_79),truth) != implies(X_78,X_79)
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) != big_hat(implies(X_78,X_79),truth)
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = implies(X_78,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_78,big_hat(X_79,big_V(X_78,X_49))),big_hat(implies(X_78,X_79),truth)) ),[1],$fot(implies(X_78,X_79))]]) ).
cnf(refute_0_707,plain,
( implies(X_78,big_hat(X_79,big_V(X_78,X_49))) != big_hat(implies(X_78,X_79),truth)
| implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = implies(X_78,X_79) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_78,X_79),truth),implies(X_78,X_79)) )],[refute_0_705,refute_0_706]) ).
cnf(refute_0_708,plain,
implies(X_78,big_hat(X_79,big_V(X_78,X_49))) = implies(X_78,X_79),
inference(resolve,[$cnf( $equal(implies(X_78,big_hat(X_79,big_V(X_78,X_49))),big_hat(implies(X_78,X_79),truth)) )],[refute_0_697,refute_0_707]) ).
cnf(refute_0_709,plain,
implies(Y,big_hat(implies(X_59,X),big_V(Y,X))) = implies(Y,implies(X_59,X)),
inference(subst,[],[refute_0_708:[bind(X_49,$fot(X)),bind(X_78,$fot(Y)),bind(X_79,$fot(implies(X_59,X)))]]) ).
cnf(refute_0_710,plain,
not(not(Y)) = Y,
inference(subst,[],[refute_0_494:[bind(X,$fot(Y))]]) ).
cnf(refute_0_711,plain,
big_V(not(not(Y)),X) = big_V(not(not(Y)),X),
introduced(tautology,[refl,[$fot(big_V(not(not(Y)),X))]]) ).
cnf(refute_0_712,plain,
( big_V(not(not(Y)),X) != big_V(not(not(Y)),X)
| not(not(Y)) != Y
| big_V(not(not(Y)),X) = big_V(Y,X) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(not(not(Y)),X),big_V(not(not(Y)),X)) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_713,plain,
( not(not(Y)) != Y
| big_V(not(not(Y)),X) = big_V(Y,X) ),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),X),big_V(not(not(Y)),X)) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
big_V(not(not(Y)),X) = big_V(Y,X),
inference(resolve,[$cnf( $equal(not(not(Y)),Y) )],[refute_0_710,refute_0_713]) ).
cnf(refute_0_715,plain,
big_hat(implies(X_59,X),big_V(not(not(Y)),X)) = big_hat(implies(X_59,X),big_V(not(not(Y)),X)),
introduced(tautology,[refl,[$fot(big_hat(implies(X_59,X),big_V(not(not(Y)),X)))]]) ).
cnf(refute_0_716,plain,
( big_V(not(not(Y)),X) != big_V(Y,X)
| big_hat(implies(X_59,X),big_V(not(not(Y)),X)) != big_hat(implies(X_59,X),big_V(not(not(Y)),X))
| big_hat(implies(X_59,X),big_V(not(not(Y)),X)) = big_hat(implies(X_59,X),big_V(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(implies(X_59,X),big_V(not(not(Y)),X)),big_hat(implies(X_59,X),big_V(not(not(Y)),X))) ),[1,1],$fot(big_V(Y,X))]]) ).
cnf(refute_0_717,plain,
( big_V(not(not(Y)),X) != big_V(Y,X)
| big_hat(implies(X_59,X),big_V(not(not(Y)),X)) = big_hat(implies(X_59,X),big_V(Y,X)) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,X),big_V(not(not(Y)),X)),big_hat(implies(X_59,X),big_V(not(not(Y)),X))) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
big_hat(implies(X_59,X),big_V(not(not(Y)),X)) = big_hat(implies(X_59,X),big_V(Y,X)),
inference(resolve,[$cnf( $equal(big_V(not(not(Y)),X),big_V(Y,X)) )],[refute_0_714,refute_0_717]) ).
cnf(refute_0_719,plain,
implies(big_V(X_59,implies(X,X_61)),X_61) = big_hat(implies(X_59,X_61),implies(implies(X,X_61),X_61)),
inference(subst,[],[lemma_6:[bind(X,$fot(X_59)),bind(Y,$fot(implies(X,X_61))),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_720,plain,
( implies(big_V(X_59,implies(X,X_61)),X_61) != big_hat(implies(X_59,X_61),implies(implies(X,X_61),X_61))
| implies(implies(X,X_61),X_61) != big_V(X,X_61)
| implies(big_V(X_59,implies(X,X_61)),X_61) = big_hat(implies(X_59,X_61),big_V(X,X_61)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,implies(X,X_61)),X_61),big_hat(implies(X_59,X_61),implies(implies(X,X_61),X_61))) ),[1,1],$fot(big_V(X,X_61))]]) ).
cnf(refute_0_721,plain,
( implies(big_V(X_59,implies(X,X_61)),X_61) != big_hat(implies(X_59,X_61),implies(implies(X,X_61),X_61))
| implies(big_V(X_59,implies(X,X_61)),X_61) = big_hat(implies(X_59,X_61),big_V(X,X_61)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_61),X_61),big_V(X,X_61)) )],[refute_0_538,refute_0_720]) ).
cnf(refute_0_722,plain,
implies(big_V(X_59,implies(X,X_61)),X_61) = big_hat(implies(X_59,X_61),big_V(X,X_61)),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(X,X_61)),X_61),big_hat(implies(X_59,X_61),implies(implies(X,X_61),X_61))) )],[refute_0_719,refute_0_721]) ).
cnf(refute_0_723,plain,
implies(big_V(X_514,implies(not(X),X_515)),X_515) = big_hat(implies(X_514,X_515),big_V(not(X),X_515)),
inference(subst,[],[refute_0_722:[bind(X,$fot(not(X))),bind(X_59,$fot(X_514)),bind(X_61,$fot(X_515))]]) ).
cnf(refute_0_724,plain,
implies(not(X_515),X) = implies(not(X),X_515),
inference(subst,[],[refute_0_679:[bind(X_88,$fot(X_515))]]) ).
cnf(refute_0_725,plain,
( implies(not(X_515),X) != implies(not(X),X_515)
| implies(not(X),X_515) = implies(not(X_515),X) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(not(X_515),X))),bind(Y0,$fot(implies(not(X),X_515)))]]) ).
cnf(refute_0_726,plain,
implies(not(X),X_515) = implies(not(X_515),X),
inference(resolve,[$cnf( $equal(implies(not(X_515),X),implies(not(X),X_515)) )],[refute_0_724,refute_0_725]) ).
cnf(refute_0_727,plain,
( implies(big_V(X_514,implies(not(X),X_515)),X_515) != big_hat(implies(X_514,X_515),big_V(not(X),X_515))
| implies(not(X),X_515) != implies(not(X_515),X)
| implies(big_V(X_514,implies(not(X_515),X)),X_515) = big_hat(implies(X_514,X_515),big_V(not(X),X_515)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_514,implies(not(X),X_515)),X_515),big_hat(implies(X_514,X_515),big_V(not(X),X_515))) ),[0,0,1],$fot(implies(not(X_515),X))]]) ).
cnf(refute_0_728,plain,
( implies(big_V(X_514,implies(not(X),X_515)),X_515) != big_hat(implies(X_514,X_515),big_V(not(X),X_515))
| implies(big_V(X_514,implies(not(X_515),X)),X_515) = big_hat(implies(X_514,X_515),big_V(not(X),X_515)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_515),implies(not(X_515),X)) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
implies(big_V(X_514,implies(not(X_515),X)),X_515) = big_hat(implies(X_514,X_515),big_V(not(X),X_515)),
inference(resolve,[$cnf( $equal(implies(big_V(X_514,implies(not(X),X_515)),X_515),big_hat(implies(X_514,X_515),big_V(not(X),X_515))) )],[refute_0_723,refute_0_728]) ).
cnf(refute_0_730,plain,
implies(big_V(X_59,implies(not(X),not(Y))),X) = big_hat(implies(X_59,X),big_V(not(not(Y)),X)),
inference(subst,[],[refute_0_729:[bind(X,$fot(not(Y))),bind(X_514,$fot(X_59)),bind(X_515,$fot(X))]]) ).
cnf(refute_0_731,plain,
( big_hat(implies(X_59,X),big_V(not(not(Y)),X)) != big_hat(implies(X_59,X),big_V(Y,X))
| implies(big_V(X_59,implies(not(X),not(Y))),X) != big_hat(implies(X_59,X),big_V(not(not(Y)),X))
| implies(big_V(X_59,implies(not(X),not(Y))),X) = big_hat(implies(X_59,X),big_V(Y,X)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(X_59,implies(not(X),not(Y))),X))),bind(Y0,$fot(big_hat(implies(X_59,X),big_V(not(not(Y)),X)))),bind(Z0,$fot(big_hat(implies(X_59,X),big_V(Y,X))))]]) ).
cnf(refute_0_732,plain,
( big_hat(implies(X_59,X),big_V(not(not(Y)),X)) != big_hat(implies(X_59,X),big_V(Y,X))
| implies(big_V(X_59,implies(not(X),not(Y))),X) = big_hat(implies(X_59,X),big_V(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),X),big_hat(implies(X_59,X),big_V(not(not(Y)),X))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
implies(big_V(X_59,implies(not(X),not(Y))),X) = big_hat(implies(X_59,X),big_V(Y,X)),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,X),big_V(not(not(Y)),X)),big_hat(implies(X_59,X),big_V(Y,X))) )],[refute_0_718,refute_0_732]) ).
cnf(refute_0_734,plain,
implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),
introduced(tautology,[refl,[$fot(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)))]]) ).
cnf(refute_0_735,plain,
( implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) != implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X))
| implies(big_V(X_59,implies(not(X),not(Y))),X) != big_hat(implies(X_59,X),big_V(Y,X))
| implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,big_hat(implies(X_59,X),big_V(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X))) ),[1,1],$fot(big_hat(implies(X_59,X),big_V(Y,X)))]]) ).
cnf(refute_0_736,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),X) != big_hat(implies(X_59,X),big_V(Y,X))
| implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,big_hat(implies(X_59,X),big_V(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,big_hat(implies(X_59,X),big_V(Y,X))),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),X),big_hat(implies(X_59,X),big_V(Y,X))) )],[refute_0_733,refute_0_736]) ).
cnf(refute_0_738,plain,
( implies(Y,big_hat(implies(X_59,X),big_V(Y,X))) != implies(Y,implies(X_59,X))
| implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) != implies(Y,big_hat(implies(X_59,X),big_V(Y,X)))
| implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,implies(X_59,X)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)))),bind(Y0,$fot(implies(Y,big_hat(implies(X_59,X),big_V(Y,X))))),bind(Z0,$fot(implies(Y,implies(X_59,X))))]]) ).
cnf(refute_0_739,plain,
( implies(Y,big_hat(implies(X_59,X),big_V(Y,X))) != implies(Y,implies(X_59,X))
| implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,implies(X_59,X)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),implies(Y,big_hat(implies(X_59,X),big_V(Y,X)))) )],[refute_0_737,refute_0_738]) ).
cnf(refute_0_740,plain,
implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) = implies(Y,implies(X_59,X)),
inference(resolve,[$cnf( $equal(implies(Y,big_hat(implies(X_59,X),big_V(Y,X))),implies(Y,implies(X_59,X))) )],[refute_0_709,refute_0_739]) ).
cnf(refute_0_741,plain,
implies(big_V(X_517,X_518),implies(X_516,X_518)) = implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)),
inference(subst,[],[refute_0_381:[bind(Y,$fot(implies(X_516,X_518))),bind(X_1,$fot(big_V(X_517,X_518)))]]) ).
cnf(refute_0_742,plain,
implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(implies(X_59,implies(X_47,X_60)),implies(X_60,implies(X_47,X_60))),
inference(subst,[],[lemma_6:[bind(X,$fot(X_59)),bind(Y,$fot(X_60)),bind(Z,$fot(implies(X_47,X_60)))]]) ).
cnf(refute_0_743,plain,
implies(X_60,implies(X_47,X_60)) = truth,
inference(subst,[],[refute_0_369:[bind(X_49,$fot(X_60))]]) ).
cnf(refute_0_744,plain,
( implies(X_60,implies(X_47,X_60)) != truth
| implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(implies(X_59,implies(X_47,X_60)),implies(X_60,implies(X_47,X_60)))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(implies(X_59,implies(X_47,X_60)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(implies(X_59,implies(X_47,X_60)),implies(X_60,implies(X_47,X_60)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_745,plain,
( implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(implies(X_59,implies(X_47,X_60)),implies(X_60,implies(X_47,X_60)))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(implies(X_59,implies(X_47,X_60)),truth) ),
inference(resolve,[$cnf( $equal(implies(X_60,implies(X_47,X_60)),truth) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(implies(X_59,implies(X_47,X_60)),truth),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(implies(X_59,implies(X_47,X_60)),implies(X_60,implies(X_47,X_60)))) )],[refute_0_742,refute_0_745]) ).
cnf(refute_0_747,plain,
big_hat(implies(X_59,implies(X_47,X_60)),truth) = big_hat(truth,implies(X_59,implies(X_47,X_60))),
inference(subst,[],[refute_0_388:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_59,implies(X_47,X_60))))]]) ).
cnf(refute_0_748,plain,
( big_hat(implies(X_59,implies(X_47,X_60)),truth) != big_hat(truth,implies(X_59,implies(X_47,X_60)))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(implies(X_59,implies(X_47,X_60)),truth)
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(truth,implies(X_59,implies(X_47,X_60))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(implies(X_59,implies(X_47,X_60)),truth)) ),[1],$fot(big_hat(truth,implies(X_59,implies(X_47,X_60))))]]) ).
cnf(refute_0_749,plain,
( implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(implies(X_59,implies(X_47,X_60)),truth)
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(truth,implies(X_59,implies(X_47,X_60))) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_59,implies(X_47,X_60)),truth),big_hat(truth,implies(X_59,implies(X_47,X_60)))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
implies(big_V(X_59,X_60),implies(X_47,X_60)) = big_hat(truth,implies(X_59,implies(X_47,X_60))),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(implies(X_59,implies(X_47,X_60)),truth)) )],[refute_0_746,refute_0_749]) ).
cnf(refute_0_751,plain,
( implies(X_59,X_61) != big_hat(truth,implies(X_59,X_61))
| big_hat(truth,implies(X_59,X_61)) = implies(X_59,X_61) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_59,X_61))),bind(Y0,$fot(big_hat(truth,implies(X_59,X_61))))]]) ).
cnf(refute_0_752,plain,
big_hat(truth,implies(X_59,X_61)) = implies(X_59,X_61),
inference(resolve,[$cnf( $equal(implies(X_59,X_61),big_hat(truth,implies(X_59,X_61))) )],[refute_0_393,refute_0_751]) ).
cnf(refute_0_753,plain,
big_hat(truth,implies(X_59,implies(X_47,X_60))) = implies(X_59,implies(X_47,X_60)),
inference(subst,[],[refute_0_752:[bind(X_61,$fot(implies(X_47,X_60)))]]) ).
cnf(refute_0_754,plain,
( big_hat(truth,implies(X_59,implies(X_47,X_60))) != implies(X_59,implies(X_47,X_60))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(truth,implies(X_59,implies(X_47,X_60)))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = implies(X_59,implies(X_47,X_60)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(truth,implies(X_59,implies(X_47,X_60)))) ),[1],$fot(implies(X_59,implies(X_47,X_60)))]]) ).
cnf(refute_0_755,plain,
( implies(big_V(X_59,X_60),implies(X_47,X_60)) != big_hat(truth,implies(X_59,implies(X_47,X_60)))
| implies(big_V(X_59,X_60),implies(X_47,X_60)) = implies(X_59,implies(X_47,X_60)) ),
inference(resolve,[$cnf( $equal(big_hat(truth,implies(X_59,implies(X_47,X_60))),implies(X_59,implies(X_47,X_60))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
implies(big_V(X_59,X_60),implies(X_47,X_60)) = implies(X_59,implies(X_47,X_60)),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,X_60),implies(X_47,X_60)),big_hat(truth,implies(X_59,implies(X_47,X_60)))) )],[refute_0_750,refute_0_755]) ).
cnf(refute_0_757,plain,
implies(big_V(X_517,X_518),implies(X_516,X_518)) = implies(X_517,implies(X_516,X_518)),
inference(subst,[],[refute_0_756:[bind(X_47,$fot(X_516)),bind(X_59,$fot(X_517)),bind(X_60,$fot(X_518))]]) ).
cnf(refute_0_758,plain,
( implies(big_V(X_517,X_518),implies(X_516,X_518)) != implies(X_517,implies(X_516,X_518))
| implies(big_V(X_517,X_518),implies(X_516,X_518)) != implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))
| implies(X_517,implies(X_516,X_518)) = implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_517,X_518),implies(X_516,X_518)),implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))) ),[0],$fot(implies(X_517,implies(X_516,X_518)))]]) ).
cnf(refute_0_759,plain,
( implies(big_V(X_517,X_518),implies(X_516,X_518)) != implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))
| implies(X_517,implies(X_516,X_518)) = implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_517,implies(X_516,X_518))) )],[refute_0_757,refute_0_758]) ).
cnf(refute_0_760,plain,
implies(X_517,implies(X_516,X_518)) = implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)),
inference(resolve,[$cnf( $equal(implies(big_V(X_517,X_518),implies(X_516,X_518)),implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))) )],[refute_0_741,refute_0_759]) ).
cnf(refute_0_761,plain,
implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))) = implies(X_516,implies(X_517,X_518)),
inference(subst,[],[refute_0_708:[bind(X_49,$fot(X_518)),bind(X_78,$fot(X_516)),bind(X_79,$fot(implies(X_517,X_518)))]]) ).
cnf(refute_0_762,plain,
implies(big_V(X_517,implies(X_516,X_518)),X_518) = big_hat(implies(X_517,X_518),big_V(X_516,X_518)),
inference(subst,[],[refute_0_722:[bind(X,$fot(X_516)),bind(X_59,$fot(X_517)),bind(X_61,$fot(X_518))]]) ).
cnf(refute_0_763,plain,
implies(big_V(implies(implies(X,X_247),X_247),X_246),X_247) = big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)),
inference(subst,[],[refute_0_541:[bind(X,$fot(implies(X,X_247))),bind(X_60,$fot(X_246)),bind(X_61,$fot(X_247))]]) ).
cnf(refute_0_764,plain,
big_V(X,X_247) = implies(implies(X,X_247),X_247),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_247))]]) ).
cnf(refute_0_765,plain,
( big_V(X,X_247) != implies(implies(X,X_247),X_247)
| implies(implies(X,X_247),X_247) = big_V(X,X_247) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_247))),bind(Y0,$fot(implies(implies(X,X_247),X_247)))]]) ).
cnf(refute_0_766,plain,
implies(implies(X,X_247),X_247) = big_V(X,X_247),
inference(resolve,[$cnf( $equal(big_V(X,X_247),implies(implies(X,X_247),X_247)) )],[refute_0_764,refute_0_765]) ).
cnf(refute_0_767,plain,
( implies(big_V(implies(implies(X,X_247),X_247),X_246),X_247) != big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))
| implies(implies(X,X_247),X_247) != big_V(X,X_247)
| implies(big_V(big_V(X,X_247),X_246),X_247) = big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(implies(implies(X,X_247),X_247),X_246),X_247),big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))) ),[0,0,0],$fot(big_V(X,X_247))]]) ).
cnf(refute_0_768,plain,
( implies(big_V(implies(implies(X,X_247),X_247),X_246),X_247) != big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))
| implies(big_V(big_V(X,X_247),X_246),X_247) = big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_247),X_247),big_V(X,X_247)) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
implies(big_V(big_V(X,X_247),X_246),X_247) = big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)),
inference(resolve,[$cnf( $equal(implies(big_V(implies(implies(X,X_247),X_247),X_246),X_247),big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))) )],[refute_0_763,refute_0_768]) ).
cnf(refute_0_770,plain,
( implies(big_V(X,Y),Z) != big_hat(implies(X,Z),implies(Y,Z))
| big_hat(implies(X,Z),implies(Y,Z)) = implies(big_V(X,Y),Z) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(big_V(X,Y),Z))),bind(Y0,$fot(big_hat(implies(X,Z),implies(Y,Z))))]]) ).
cnf(refute_0_771,plain,
big_hat(implies(X,Z),implies(Y,Z)) = implies(big_V(X,Y),Z),
inference(resolve,[$cnf( $equal(implies(big_V(X,Y),Z),big_hat(implies(X,Z),implies(Y,Z))) )],[lemma_6,refute_0_770]) ).
cnf(refute_0_772,plain,
big_hat(implies(X,X_247),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247),
inference(subst,[],[refute_0_771:[bind(Y,$fot(X_246)),bind(Z,$fot(X_247))]]) ).
cnf(refute_0_773,plain,
big_V(X_247,implies(X,X_247)) = implies(X,X_247),
inference(subst,[],[refute_0_377:[bind(X,$fot(X_247)),bind(X_55,$fot(X))]]) ).
cnf(refute_0_774,plain,
big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),
introduced(tautology,[refl,[$fot(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)))]]) ).
cnf(refute_0_775,plain,
( big_V(X_247,implies(X,X_247)) != implies(X,X_247)
| big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) != big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247))
| big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = big_hat(implies(X,X_247),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247))) ),[1,0],$fot(implies(X,X_247))]]) ).
cnf(refute_0_776,plain,
( big_V(X_247,implies(X,X_247)) != implies(X,X_247)
| big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = big_hat(implies(X,X_247),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247))) )],[refute_0_774,refute_0_775]) ).
cnf(refute_0_777,plain,
big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = big_hat(implies(X,X_247),implies(X_246,X_247)),
inference(resolve,[$cnf( $equal(big_V(X_247,implies(X,X_247)),implies(X,X_247)) )],[refute_0_773,refute_0_776]) ).
cnf(refute_0_778,plain,
( big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) != big_hat(implies(X,X_247),implies(X_246,X_247))
| big_hat(implies(X,X_247),implies(X_246,X_247)) != implies(big_V(X,X_246),X_247)
| big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)))),bind(Y0,$fot(big_hat(implies(X,X_247),implies(X_246,X_247)))),bind(Z0,$fot(implies(big_V(X,X_246),X_247)))]]) ).
cnf(refute_0_779,plain,
( big_hat(implies(X,X_247),implies(X_246,X_247)) != implies(big_V(X,X_246),X_247)
| big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),big_hat(implies(X,X_247),implies(X_246,X_247))) )],[refute_0_777,refute_0_778]) ).
cnf(refute_0_780,plain,
big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247),
inference(resolve,[$cnf( $equal(big_hat(implies(X,X_247),implies(X_246,X_247)),implies(big_V(X,X_246),X_247)) )],[refute_0_772,refute_0_779]) ).
cnf(refute_0_781,plain,
implies(big_V(implies(big_V(X_247,X_1),X_247),X_246),X_247) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),
inference(subst,[],[refute_0_541:[bind(X,$fot(big_V(X_247,X_1))),bind(X_60,$fot(X_246)),bind(X_61,$fot(X_247))]]) ).
cnf(refute_0_782,plain,
( big_V(Y,implies(X_1,Y)) != implies(X_1,Y)
| big_V(Y,implies(X_1,Y)) != implies(big_V(Y,X_1),Y)
| implies(X_1,Y) = implies(big_V(Y,X_1),Y) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(Y,X_1),Y)) ),[0],$fot(implies(X_1,Y))]]) ).
cnf(refute_0_783,plain,
( big_V(Y,implies(X_1,Y)) != implies(big_V(Y,X_1),Y)
| implies(X_1,Y) = implies(big_V(Y,X_1),Y) ),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(X_1,Y)) )],[refute_0_378,refute_0_782]) ).
cnf(refute_0_784,plain,
implies(X_1,Y) = implies(big_V(Y,X_1),Y),
inference(resolve,[$cnf( $equal(big_V(Y,implies(X_1,Y)),implies(big_V(Y,X_1),Y)) )],[refute_0_598,refute_0_783]) ).
cnf(refute_0_785,plain,
implies(X_1,X_247) = implies(big_V(X_247,X_1),X_247),
inference(subst,[],[refute_0_784:[bind(Y,$fot(X_247))]]) ).
cnf(refute_0_786,plain,
( implies(X_1,X_247) != implies(big_V(X_247,X_1),X_247)
| implies(big_V(X_247,X_1),X_247) = implies(X_1,X_247) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_1,X_247))),bind(Y0,$fot(implies(big_V(X_247,X_1),X_247)))]]) ).
cnf(refute_0_787,plain,
implies(big_V(X_247,X_1),X_247) = implies(X_1,X_247),
inference(resolve,[$cnf( $equal(implies(X_1,X_247),implies(big_V(X_247,X_1),X_247)) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
( implies(big_V(X_247,X_1),X_247) != implies(X_1,X_247)
| implies(big_V(implies(big_V(X_247,X_1),X_247),X_246),X_247) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| implies(big_V(implies(X_1,X_247),X_246),X_247) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(implies(big_V(X_247,X_1),X_247),X_246),X_247),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) ),[0,0,0],$fot(implies(X_1,X_247))]]) ).
cnf(refute_0_789,plain,
( implies(big_V(implies(big_V(X_247,X_1),X_247),X_246),X_247) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| implies(big_V(implies(X_1,X_247),X_246),X_247) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_247,X_1),X_247),implies(X_1,X_247)) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
implies(big_V(implies(X_1,X_247),X_246),X_247) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),
inference(resolve,[$cnf( $equal(implies(big_V(implies(big_V(X_247,X_1),X_247),X_246),X_247),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) )],[refute_0_781,refute_0_789]) ).
cnf(refute_0_791,plain,
implies(big_V(implies(X_1,X_247),X_246),X_247) = big_hat(big_V(X_1,X_247),implies(X_246,X_247)),
inference(subst,[],[refute_0_541:[bind(X,$fot(X_1)),bind(X_60,$fot(X_246)),bind(X_61,$fot(X_247))]]) ).
cnf(refute_0_792,plain,
( implies(big_V(implies(X_1,X_247),X_246),X_247) != big_hat(big_V(X_1,X_247),implies(X_246,X_247))
| implies(big_V(implies(X_1,X_247),X_246),X_247) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(implies(X_1,X_247),X_246),X_247),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) ),[0],$fot(big_hat(big_V(X_1,X_247),implies(X_246,X_247)))]]) ).
cnf(refute_0_793,plain,
( implies(big_V(implies(X_1,X_247),X_246),X_247) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X_1,X_247),X_246),X_247),big_hat(big_V(X_1,X_247),implies(X_246,X_247))) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
big_V(X,big_V(X,X_51)) = implies(implies(X,big_V(X,X_51)),big_V(X,X_51)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(big_V(X,X_51)))]]) ).
cnf(refute_0_795,plain,
implies(X,big_V(X,X_51)) = truth,
inference(subst,[],[refute_0_334:[bind(X_48,$fot(X)),bind(X_49,$fot(X_51))]]) ).
cnf(refute_0_796,plain,
( big_V(X,big_V(X,X_51)) != implies(implies(X,big_V(X,X_51)),big_V(X,X_51))
| implies(X,big_V(X,X_51)) != truth
| big_V(X,big_V(X,X_51)) = implies(truth,big_V(X,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_V(X,X_51)),implies(implies(X,big_V(X,X_51)),big_V(X,X_51))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_797,plain,
( big_V(X,big_V(X,X_51)) != implies(implies(X,big_V(X,X_51)),big_V(X,X_51))
| big_V(X,big_V(X,X_51)) = implies(truth,big_V(X,X_51)) ),
inference(resolve,[$cnf( $equal(implies(X,big_V(X,X_51)),truth) )],[refute_0_795,refute_0_796]) ).
cnf(refute_0_798,plain,
big_V(X,big_V(X,X_51)) = implies(truth,big_V(X,X_51)),
inference(resolve,[$cnf( $equal(big_V(X,big_V(X,X_51)),implies(implies(X,big_V(X,X_51)),big_V(X,X_51))) )],[refute_0_794,refute_0_797]) ).
cnf(refute_0_799,plain,
implies(truth,big_V(X,X_51)) = big_V(X,X_51),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_V(X,X_51)))]]) ).
cnf(refute_0_800,plain,
( big_V(X,big_V(X,X_51)) != implies(truth,big_V(X,X_51))
| implies(truth,big_V(X,X_51)) != big_V(X,X_51)
| big_V(X,big_V(X,X_51)) = big_V(X,X_51) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_V(X,big_V(X,X_51)),big_V(X,X_51)) ),[0],$fot(implies(truth,big_V(X,X_51)))]]) ).
cnf(refute_0_801,plain,
( big_V(X,big_V(X,X_51)) != implies(truth,big_V(X,X_51))
| big_V(X,big_V(X,X_51)) = big_V(X,X_51) ),
inference(resolve,[$cnf( $equal(implies(truth,big_V(X,X_51)),big_V(X,X_51)) )],[refute_0_799,refute_0_800]) ).
cnf(refute_0_802,plain,
big_V(X,big_V(X,X_51)) = big_V(X,X_51),
inference(resolve,[$cnf( $equal(big_V(X,big_V(X,X_51)),implies(truth,big_V(X,X_51))) )],[refute_0_798,refute_0_801]) ).
cnf(refute_0_803,plain,
big_V(X_247,big_V(X_247,X_1)) = big_V(X_247,X_1),
inference(subst,[],[refute_0_802:[bind(X,$fot(X_247)),bind(X_51,$fot(X_1))]]) ).
cnf(refute_0_804,plain,
big_V(big_V(X_247,X_1),X_247) = big_V(X_247,big_V(X_247,X_1)),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_247)),bind(Y,$fot(big_V(X_247,X_1)))]]) ).
cnf(refute_0_805,plain,
( big_V(X_247,big_V(X_247,X_1)) != big_V(X_247,X_1)
| big_V(big_V(X_247,X_1),X_247) != big_V(X_247,big_V(X_247,X_1))
| big_V(big_V(X_247,X_1),X_247) = big_V(X_247,X_1) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_V(big_V(X_247,X_1),X_247))),bind(Y0,$fot(big_V(X_247,big_V(X_247,X_1)))),bind(Z0,$fot(big_V(X_247,X_1)))]]) ).
cnf(refute_0_806,plain,
( big_V(X_247,big_V(X_247,X_1)) != big_V(X_247,X_1)
| big_V(big_V(X_247,X_1),X_247) = big_V(X_247,X_1) ),
inference(resolve,[$cnf( $equal(big_V(big_V(X_247,X_1),X_247),big_V(X_247,big_V(X_247,X_1))) )],[refute_0_804,refute_0_805]) ).
cnf(refute_0_807,plain,
big_V(big_V(X_247,X_1),X_247) = big_V(X_247,X_1),
inference(resolve,[$cnf( $equal(big_V(X_247,big_V(X_247,X_1)),big_V(X_247,X_1)) )],[refute_0_803,refute_0_806]) ).
cnf(refute_0_808,plain,
big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) = big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),
introduced(tautology,[refl,[$fot(big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)))]]) ).
cnf(refute_0_809,plain,
( big_V(big_V(X_247,X_1),X_247) != big_V(X_247,X_1)
| big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( $equal(big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) ),[1,0],$fot(big_V(X_247,X_1))]]) ).
cnf(refute_0_810,plain,
( big_V(big_V(X_247,X_1),X_247) != big_V(X_247,X_1)
| big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)),
inference(resolve,[$cnf( $equal(big_V(big_V(X_247,X_1),X_247),big_V(X_247,X_1)) )],[refute_0_807,refute_0_810]) ).
cnf(refute_0_812,plain,
( big_hat(big_V(X_1,X_247),implies(X_246,X_247)) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)) != big_hat(big_V(X_247,X_1),implies(X_246,X_247))
| big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(big_hat(big_V(X_1,X_247),implies(X_246,X_247)),big_hat(big_V(X_247,X_1),implies(X_246,X_247))) ),[0],$fot(big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)))]]) ).
cnf(refute_0_813,plain,
( big_hat(big_V(X_1,X_247),implies(X_246,X_247)) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247)),big_hat(big_V(X_247,X_1),implies(X_246,X_247))) )],[refute_0_811,refute_0_812]) ).
cnf(refute_0_814,plain,
( implies(big_V(implies(X_1,X_247),X_246),X_247) != big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))
| big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(X_1,X_247),implies(X_246,X_247)),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) )],[refute_0_793,refute_0_813]) ).
cnf(refute_0_815,plain,
big_hat(big_V(X_1,X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,X_1),implies(X_246,X_247)),
inference(resolve,[$cnf( $equal(implies(big_V(implies(X_1,X_247),X_246),X_247),big_hat(big_V(big_V(X_247,X_1),X_247),implies(X_246,X_247))) )],[refute_0_790,refute_0_814]) ).
cnf(refute_0_816,plain,
big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) = big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),
inference(subst,[],[refute_0_815:[bind(X_1,$fot(implies(X,X_247)))]]) ).
cnf(refute_0_817,plain,
( big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) != implies(big_V(X,X_246),X_247)
| big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) != big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247))
| big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)))),bind(Y0,$fot(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)))),bind(Z0,$fot(implies(big_V(X,X_246),X_247)))]]) ).
cnf(refute_0_818,plain,
( big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)) != implies(big_V(X,X_246),X_247)
| big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)),big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247))) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) = implies(big_V(X,X_246),X_247),
inference(resolve,[$cnf( $equal(big_hat(big_V(X_247,implies(X,X_247)),implies(X_246,X_247)),implies(big_V(X,X_246),X_247)) )],[refute_0_780,refute_0_818]) ).
cnf(refute_0_820,plain,
( big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)) != implies(big_V(X,X_246),X_247)
| implies(big_V(big_V(X,X_247),X_246),X_247) != big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))
| implies(big_V(big_V(X,X_247),X_246),X_247) = implies(big_V(X,X_246),X_247) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(big_V(X,X_247),X_246),X_247),big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))) ),[1],$fot(implies(big_V(X,X_246),X_247))]]) ).
cnf(refute_0_821,plain,
( implies(big_V(big_V(X,X_247),X_246),X_247) != big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))
| implies(big_V(big_V(X,X_247),X_246),X_247) = implies(big_V(X,X_246),X_247) ),
inference(resolve,[$cnf( $equal(big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247)),implies(big_V(X,X_246),X_247)) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
implies(big_V(big_V(X,X_247),X_246),X_247) = implies(big_V(X,X_246),X_247),
inference(resolve,[$cnf( $equal(implies(big_V(big_V(X,X_247),X_246),X_247),big_hat(big_V(implies(X,X_247),X_247),implies(X_246,X_247))) )],[refute_0_769,refute_0_821]) ).
cnf(refute_0_823,plain,
implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) = implies(big_V(X_517,implies(X_516,X_518)),X_518),
inference(subst,[],[refute_0_822:[bind(X,$fot(X_517)),bind(X_246,$fot(implies(X_516,X_518))),bind(X_247,$fot(X_518))]]) ).
cnf(refute_0_824,plain,
( implies(big_V(X_517,implies(X_516,X_518)),X_518) != big_hat(implies(X_517,X_518),big_V(X_516,X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) != implies(big_V(X_517,implies(X_516,X_518)),X_518)
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) = big_hat(implies(X_517,X_518),big_V(X_516,X_518)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))),bind(Y0,$fot(implies(big_V(X_517,implies(X_516,X_518)),X_518))),bind(Z0,$fot(big_hat(implies(X_517,X_518),big_V(X_516,X_518))))]]) ).
cnf(refute_0_825,plain,
( implies(big_V(X_517,implies(X_516,X_518)),X_518) != big_hat(implies(X_517,X_518),big_V(X_516,X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) = big_hat(implies(X_517,X_518),big_V(X_516,X_518)) ),
inference(resolve,[$cnf( $equal(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518),implies(big_V(X_517,implies(X_516,X_518)),X_518)) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) = big_hat(implies(X_517,X_518),big_V(X_516,X_518)),
inference(resolve,[$cnf( $equal(implies(big_V(X_517,implies(X_516,X_518)),X_518),big_hat(implies(X_517,X_518),big_V(X_516,X_518))) )],[refute_0_762,refute_0_825]) ).
cnf(refute_0_827,plain,
implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),
introduced(tautology,[refl,[$fot(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)))]]) ).
cnf(refute_0_828,plain,
( implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) != implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) != big_hat(implies(X_517,X_518),big_V(X_516,X_518))
| implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))) ),[1,1],$fot(big_hat(implies(X_517,X_518),big_V(X_516,X_518)))]]) ).
cnf(refute_0_829,plain,
( implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518) != big_hat(implies(X_517,X_518),big_V(X_516,X_518))
| implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))) ),
inference(resolve,[$cnf( $equal(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))),
inference(resolve,[$cnf( $equal(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518),big_hat(implies(X_517,X_518),big_V(X_516,X_518))) )],[refute_0_826,refute_0_829]) ).
cnf(refute_0_831,plain,
( implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))) != implies(X_516,implies(X_517,X_518))
| implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) != implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518)))
| implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,implies(X_517,X_518)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)))),bind(Y0,$fot(implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))))),bind(Z0,$fot(implies(X_516,implies(X_517,X_518))))]]) ).
cnf(refute_0_832,plain,
( implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))) != implies(X_516,implies(X_517,X_518))
| implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,implies(X_517,X_518)) ),
inference(resolve,[$cnf( $equal(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518)))) )],[refute_0_830,refute_0_831]) ).
cnf(refute_0_833,plain,
implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) = implies(X_516,implies(X_517,X_518)),
inference(resolve,[$cnf( $equal(implies(X_516,big_hat(implies(X_517,X_518),big_V(X_516,X_518))),implies(X_516,implies(X_517,X_518))) )],[refute_0_761,refute_0_832]) ).
cnf(refute_0_834,plain,
big_V(X,big_hat(X_81,X)) = implies(implies(X,big_hat(X_81,X)),big_hat(X_81,X)),
inference(subst,[],[big_V_definition:[bind(Y,$fot(big_hat(X_81,X)))]]) ).
cnf(refute_0_835,plain,
implies(X_80,big_hat(X_79,X_80)) = big_hat(implies(X_80,X_79),implies(X_80,X_80)),
inference(subst,[],[lemma_7:[bind(X,$fot(X_80)),bind(Y,$fot(X_79)),bind(Z,$fot(X_80))]]) ).
cnf(refute_0_836,plain,
truth = implies(X_80,X_80),
inference(subst,[],[refute_0_283:[bind(X_2,$fot(X_80))]]) ).
cnf(refute_0_837,plain,
( truth != implies(X_80,X_80)
| implies(X_80,X_80) = truth ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_80,X_80)))]]) ).
cnf(refute_0_838,plain,
implies(X_80,X_80) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_80,X_80)) )],[refute_0_836,refute_0_837]) ).
cnf(refute_0_839,plain,
( implies(X_80,X_80) != truth
| implies(X_80,big_hat(X_79,X_80)) != big_hat(implies(X_80,X_79),implies(X_80,X_80))
| implies(X_80,big_hat(X_79,X_80)) = big_hat(implies(X_80,X_79),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_80,big_hat(X_79,X_80)),big_hat(implies(X_80,X_79),implies(X_80,X_80))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_840,plain,
( implies(X_80,big_hat(X_79,X_80)) != big_hat(implies(X_80,X_79),implies(X_80,X_80))
| implies(X_80,big_hat(X_79,X_80)) = big_hat(implies(X_80,X_79),truth) ),
inference(resolve,[$cnf( $equal(implies(X_80,X_80),truth) )],[refute_0_838,refute_0_839]) ).
cnf(refute_0_841,plain,
implies(X_80,big_hat(X_79,X_80)) = big_hat(implies(X_80,X_79),truth),
inference(resolve,[$cnf( $equal(implies(X_80,big_hat(X_79,X_80)),big_hat(implies(X_80,X_79),implies(X_80,X_80))) )],[refute_0_835,refute_0_840]) ).
cnf(refute_0_842,plain,
big_hat(implies(X_80,X_79),truth) = implies(X_80,X_79),
inference(subst,[],[refute_0_704:[bind(X,$fot(implies(X_80,X_79)))]]) ).
cnf(refute_0_843,plain,
( big_hat(implies(X_80,X_79),truth) != implies(X_80,X_79)
| implies(X_80,big_hat(X_79,X_80)) != big_hat(implies(X_80,X_79),truth)
| implies(X_80,big_hat(X_79,X_80)) = implies(X_80,X_79) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_80,big_hat(X_79,X_80)),big_hat(implies(X_80,X_79),truth)) ),[1],$fot(implies(X_80,X_79))]]) ).
cnf(refute_0_844,plain,
( implies(X_80,big_hat(X_79,X_80)) != big_hat(implies(X_80,X_79),truth)
| implies(X_80,big_hat(X_79,X_80)) = implies(X_80,X_79) ),
inference(resolve,[$cnf( $equal(big_hat(implies(X_80,X_79),truth),implies(X_80,X_79)) )],[refute_0_842,refute_0_843]) ).
cnf(refute_0_845,plain,
implies(X_80,big_hat(X_79,X_80)) = implies(X_80,X_79),
inference(resolve,[$cnf( $equal(implies(X_80,big_hat(X_79,X_80)),big_hat(implies(X_80,X_79),truth)) )],[refute_0_841,refute_0_844]) ).
cnf(refute_0_846,plain,
implies(X,big_hat(X_81,X)) = implies(X,X_81),
inference(subst,[],[refute_0_845:[bind(X_79,$fot(X_81)),bind(X_80,$fot(X))]]) ).
cnf(refute_0_847,plain,
( big_V(X,big_hat(X_81,X)) != implies(implies(X,big_hat(X_81,X)),big_hat(X_81,X))
| implies(X,big_hat(X_81,X)) != implies(X,X_81)
| big_V(X,big_hat(X_81,X)) = implies(implies(X,X_81),big_hat(X_81,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_hat(X_81,X)),implies(implies(X,big_hat(X_81,X)),big_hat(X_81,X))) ),[1,0],$fot(implies(X,X_81))]]) ).
cnf(refute_0_848,plain,
( big_V(X,big_hat(X_81,X)) != implies(implies(X,big_hat(X_81,X)),big_hat(X_81,X))
| big_V(X,big_hat(X_81,X)) = implies(implies(X,X_81),big_hat(X_81,X)) ),
inference(resolve,[$cnf( $equal(implies(X,big_hat(X_81,X)),implies(X,X_81)) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
big_V(X,big_hat(X_81,X)) = implies(implies(X,X_81),big_hat(X_81,X)),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X_81,X)),implies(implies(X,big_hat(X_81,X)),big_hat(X_81,X))) )],[refute_0_834,refute_0_848]) ).
cnf(refute_0_850,plain,
big_V(X_74,big_hat(X_74,X_75)) = X_74,
inference(subst,[],[refute_0_498:[bind(X_72,$fot(X_74)),bind(X_73,$fot(X_75))]]) ).
cnf(refute_0_851,plain,
big_hat(X_75,X_74) = big_hat(X_74,X_75),
inference(subst,[],[refute_0_180:[bind(X,$fot(X_75)),bind(Y,$fot(X_74))]]) ).
cnf(refute_0_852,plain,
( big_hat(X_75,X_74) != big_hat(X_74,X_75)
| big_hat(X_74,X_75) = big_hat(X_75,X_74) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_hat(X_75,X_74))),bind(Y0,$fot(big_hat(X_74,X_75)))]]) ).
cnf(refute_0_853,plain,
big_hat(X_74,X_75) = big_hat(X_75,X_74),
inference(resolve,[$cnf( $equal(big_hat(X_75,X_74),big_hat(X_74,X_75)) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
( big_V(X_74,big_hat(X_74,X_75)) != X_74
| big_hat(X_74,X_75) != big_hat(X_75,X_74)
| big_V(X_74,big_hat(X_75,X_74)) = X_74 ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X_74,big_hat(X_74,X_75)),X_74) ),[0,1],$fot(big_hat(X_75,X_74))]]) ).
cnf(refute_0_855,plain,
( big_V(X_74,big_hat(X_74,X_75)) != X_74
| big_V(X_74,big_hat(X_75,X_74)) = X_74 ),
inference(resolve,[$cnf( $equal(big_hat(X_74,X_75),big_hat(X_75,X_74)) )],[refute_0_853,refute_0_854]) ).
cnf(refute_0_856,plain,
big_V(X_74,big_hat(X_75,X_74)) = X_74,
inference(resolve,[$cnf( $equal(big_V(X_74,big_hat(X_74,X_75)),X_74) )],[refute_0_850,refute_0_855]) ).
cnf(refute_0_857,plain,
big_V(X,big_hat(X_81,X)) = X,
inference(subst,[],[refute_0_856:[bind(X_74,$fot(X)),bind(X_75,$fot(X_81))]]) ).
cnf(refute_0_858,plain,
( big_V(X,big_hat(X_81,X)) != X
| big_V(X,big_hat(X_81,X)) != implies(implies(X,X_81),big_hat(X_81,X))
| X = implies(implies(X,X_81),big_hat(X_81,X)) ),
introduced(tautology,[equality,[$cnf( $equal(big_V(X,big_hat(X_81,X)),implies(implies(X,X_81),big_hat(X_81,X))) ),[0],$fot(X)]]) ).
cnf(refute_0_859,plain,
( big_V(X,big_hat(X_81,X)) != implies(implies(X,X_81),big_hat(X_81,X))
| X = implies(implies(X,X_81),big_hat(X_81,X)) ),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X_81,X)),X) )],[refute_0_857,refute_0_858]) ).
cnf(refute_0_860,plain,
X = implies(implies(X,X_81),big_hat(X_81,X)),
inference(resolve,[$cnf( $equal(big_V(X,big_hat(X_81,X)),implies(implies(X,X_81),big_hat(X_81,X))) )],[refute_0_849,refute_0_859]) ).
cnf(refute_0_861,plain,
implies(X_318,implies(X_317,X_319)) = implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))),
inference(subst,[],[refute_0_860:[bind(X,$fot(implies(X_318,implies(X_317,X_319)))),bind(X_81,$fot(implies(X_317,implies(X_318,X_319))))]]) ).
cnf(refute_0_862,plain,
implies(implies(X_47,implies(X,X_49)),implies(implies(implies(X,X_49),X_49),implies(X_47,X_49))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_47)),bind(Y,$fot(implies(X,X_49))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_863,plain,
big_V(X,X_49) = implies(implies(X,X_49),X_49),
inference(subst,[],[big_V_definition:[bind(Y,$fot(X_49))]]) ).
cnf(refute_0_864,plain,
( big_V(X,X_49) != implies(implies(X,X_49),X_49)
| implies(implies(X,X_49),X_49) = big_V(X,X_49) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(big_V(X,X_49))),bind(Y0,$fot(implies(implies(X,X_49),X_49)))]]) ).
cnf(refute_0_865,plain,
implies(implies(X,X_49),X_49) = big_V(X,X_49),
inference(resolve,[$cnf( $equal(big_V(X,X_49),implies(implies(X,X_49),X_49)) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
( implies(implies(X,X_49),X_49) != big_V(X,X_49)
| implies(implies(X_47,implies(X,X_49)),implies(implies(implies(X,X_49),X_49),implies(X_47,X_49))) != truth
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(implies(implies(X,X_49),X_49),implies(X_47,X_49))),truth) ),[0,1,0],$fot(big_V(X,X_49))]]) ).
cnf(refute_0_867,plain,
( implies(implies(X_47,implies(X,X_49)),implies(implies(implies(X,X_49),X_49),implies(X_47,X_49))) != truth
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,X_49),X_49),big_V(X,X_49)) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(implies(implies(X,X_49),X_49),implies(X_47,X_49))),truth) )],[refute_0_862,refute_0_867]) ).
cnf(refute_0_869,plain,
implies(big_V(X,X_49),implies(X_47,X_49)) = implies(X,implies(X_47,X_49)),
inference(subst,[],[refute_0_756:[bind(X_59,$fot(X)),bind(X_60,$fot(X_49))]]) ).
cnf(refute_0_870,plain,
implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),
introduced(tautology,[refl,[$fot(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))))]]) ).
cnf(refute_0_871,plain,
( implies(big_V(X,X_49),implies(X_47,X_49)) != implies(X,implies(X_47,X_49))
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) != implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49)))
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49)))) ),[1,1],$fot(implies(X,implies(X_47,X_49)))]]) ).
cnf(refute_0_872,plain,
( implies(big_V(X,X_49),implies(X_47,X_49)) != implies(X,implies(X_47,X_49))
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49)))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) = implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))),
inference(resolve,[$cnf( $equal(implies(big_V(X,X_49),implies(X_47,X_49)),implies(X,implies(X_47,X_49))) )],[refute_0_869,refute_0_872]) ).
cnf(refute_0_874,plain,
( implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) != implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49)))
| implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) != truth
| implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),truth) ),[0],$fot(implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))))]]) ).
cnf(refute_0_875,plain,
( implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))) != truth
| implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49)))) )],[refute_0_873,refute_0_874]) ).
cnf(refute_0_876,plain,
implies(implies(X_47,implies(X,X_49)),implies(X,implies(X_47,X_49))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_47,implies(X,X_49)),implies(big_V(X,X_49),implies(X_47,X_49))),truth) )],[refute_0_868,refute_0_875]) ).
cnf(refute_0_877,plain,
implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) = truth,
inference(subst,[],[refute_0_876:[bind(X,$fot(X_317)),bind(X_47,$fot(X_318)),bind(X_49,$fot(X_319))]]) ).
cnf(refute_0_878,plain,
( implies(X_318,implies(X_317,X_319)) != implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))
| implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) != truth
| implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_879,plain,
( implies(X_318,implies(X_317,X_319)) != implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))
| implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),truth) )],[refute_0_877,refute_0_878]) ).
cnf(refute_0_880,plain,
implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))) )],[refute_0_861,refute_0_879]) ).
cnf(refute_0_881,plain,
implies(X_318,implies(X_317,X_319)) = implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))),
inference(subst,[],[refute_0_502:[bind(X,$fot(implies(X_318,implies(X_317,X_319)))),bind(X_84,$fot(implies(X_317,implies(X_318,X_319))))]]) ).
cnf(refute_0_882,plain,
( implies(X_318,implies(X_317,X_319)) != implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))
| implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) != truth
| implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_883,plain,
( implies(X_318,implies(X_317,X_319)) != implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))
| implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),truth) )],[refute_0_877,refute_0_882]) ).
cnf(refute_0_884,plain,
implies(X_318,implies(X_317,X_319)) = implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(implies(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))) )],[refute_0_881,refute_0_883]) ).
cnf(refute_0_885,plain,
implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) = big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))))]]) ).
cnf(refute_0_886,plain,
( implies(X_318,implies(X_317,X_319)) != implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))
| implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) != big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))
| implies(X_318,implies(X_317,X_319)) = big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_318,implies(X_317,X_319)),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) ),[0],$fot(implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))))]]) ).
cnf(refute_0_887,plain,
( implies(X_318,implies(X_317,X_319)) != implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))
| implies(X_318,implies(X_317,X_319)) = big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) ),
inference(resolve,[$cnf( $equal(implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
implies(X_318,implies(X_317,X_319)) = big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(truth,big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))))) )],[refute_0_884,refute_0_887]) ).
cnf(refute_0_889,plain,
( implies(X_318,implies(X_317,X_319)) != big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))
| big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) = implies(X_318,implies(X_317,X_319)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_318,implies(X_317,X_319)))),bind(Y0,$fot(big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))))]]) ).
cnf(refute_0_890,plain,
big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) = implies(X_318,implies(X_317,X_319)),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),big_hat(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319)))) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))) = implies(X_317,implies(X_318,X_319)),
inference(subst,[],[refute_0_890:[bind(X_317,$fot(X_318)),bind(X_318,$fot(X_317))]]) ).
cnf(refute_0_892,plain,
implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) = big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))))]]) ).
cnf(refute_0_893,plain,
( big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))) != implies(X_317,implies(X_318,X_319))
| implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) != big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))
| implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) = implies(X_317,implies(X_318,X_319)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))))),bind(Y0,$fot(big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))),bind(Z0,$fot(implies(X_317,implies(X_318,X_319))))]]) ).
cnf(refute_0_894,plain,
( big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))) != implies(X_317,implies(X_318,X_319))
| implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) = implies(X_317,implies(X_318,X_319)) ),
inference(resolve,[$cnf( $equal(implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))),big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) )],[refute_0_892,refute_0_893]) ).
cnf(refute_0_895,plain,
implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) = implies(X_317,implies(X_318,X_319)),
inference(resolve,[$cnf( $equal(big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))),implies(X_317,implies(X_318,X_319))) )],[refute_0_891,refute_0_894]) ).
cnf(refute_0_896,plain,
( implies(X_318,implies(X_317,X_319)) != implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))
| implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))) != implies(X_317,implies(X_318,X_319))
| implies(X_318,implies(X_317,X_319)) = implies(X_317,implies(X_318,X_319)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) ),[0],$fot(implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))))]]) ).
cnf(refute_0_897,plain,
( implies(X_318,implies(X_317,X_319)) != implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))
| implies(X_318,implies(X_317,X_319)) = implies(X_317,implies(X_318,X_319)) ),
inference(resolve,[$cnf( $equal(implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319)))),implies(X_317,implies(X_318,X_319))) )],[refute_0_895,refute_0_896]) ).
cnf(refute_0_898,plain,
implies(X_318,implies(X_317,X_319)) = implies(X_317,implies(X_318,X_319)),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(truth,big_hat(implies(X_317,implies(X_318,X_319)),implies(X_318,implies(X_317,X_319))))) )],[refute_0_880,refute_0_897]) ).
cnf(refute_0_899,plain,
( implies(X_318,implies(X_317,X_319)) != implies(X_317,implies(X_318,X_319))
| implies(X_317,implies(X_318,X_319)) = implies(X_318,implies(X_317,X_319)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_318,implies(X_317,X_319)))),bind(Y0,$fot(implies(X_317,implies(X_318,X_319))))]]) ).
cnf(refute_0_900,plain,
implies(X_317,implies(X_318,X_319)) = implies(X_318,implies(X_317,X_319)),
inference(resolve,[$cnf( $equal(implies(X_318,implies(X_317,X_319)),implies(X_317,implies(X_318,X_319))) )],[refute_0_898,refute_0_899]) ).
cnf(refute_0_901,plain,
implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) = implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),
inference(subst,[],[refute_0_900:[bind(X_317,$fot(big_V(big_V(X_517,X_518),implies(X_516,X_518)))),bind(X_318,$fot(X_516)),bind(X_319,$fot(X_518))]]) ).
cnf(refute_0_902,plain,
( implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) != implies(X_516,implies(X_517,X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) != implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)))),bind(Y0,$fot(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)))),bind(Z0,$fot(implies(X_516,implies(X_517,X_518))))]]) ).
cnf(refute_0_903,plain,
( implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)) != implies(X_516,implies(X_517,X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)) ),
inference(resolve,[$cnf( $equal(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)),implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518))) )],[refute_0_901,refute_0_902]) ).
cnf(refute_0_904,plain,
implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)),
inference(resolve,[$cnf( $equal(implies(X_516,implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),X_518)),implies(X_516,implies(X_517,X_518))) )],[refute_0_833,refute_0_903]) ).
cnf(refute_0_905,plain,
( implies(X_517,implies(X_516,X_518)) != implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))
| implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)) != implies(X_516,implies(X_517,X_518))
| implies(X_517,implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_517,implies(X_516,X_518)),implies(X_516,implies(X_517,X_518))) ),[0],$fot(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)))]]) ).
cnf(refute_0_906,plain,
( implies(X_517,implies(X_516,X_518)) != implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))
| implies(X_517,implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)) ),
inference(resolve,[$cnf( $equal(implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518)),implies(X_516,implies(X_517,X_518))) )],[refute_0_904,refute_0_905]) ).
cnf(refute_0_907,plain,
implies(X_517,implies(X_516,X_518)) = implies(X_516,implies(X_517,X_518)),
inference(resolve,[$cnf( $equal(implies(X_517,implies(X_516,X_518)),implies(big_V(big_V(X_517,X_518),implies(X_516,X_518)),implies(X_516,X_518))) )],[refute_0_760,refute_0_906]) ).
cnf(refute_0_908,plain,
( implies(X_517,implies(X_516,X_518)) != implies(X_516,implies(X_517,X_518))
| implies(X_516,implies(X_517,X_518)) = implies(X_517,implies(X_516,X_518)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(X_517,implies(X_516,X_518)))),bind(Y0,$fot(implies(X_516,implies(X_517,X_518))))]]) ).
cnf(refute_0_909,plain,
implies(X_516,implies(X_517,X_518)) = implies(X_517,implies(X_516,X_518)),
inference(resolve,[$cnf( $equal(implies(X_517,implies(X_516,X_518)),implies(X_516,implies(X_517,X_518))) )],[refute_0_907,refute_0_908]) ).
cnf(refute_0_910,plain,
implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),
inference(subst,[],[refute_0_909:[bind(X_516,$fot(big_V(X_59,implies(not(X),not(Y))))),bind(X_517,$fot(Y)),bind(X_518,$fot(X))]]) ).
cnf(refute_0_911,plain,
( implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) != implies(Y,implies(X_59,X))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = implies(Y,implies(X_59,X)) ),
inference(subst,[],[refute_0_173:[bind(X0,$fot(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)))),bind(Y0,$fot(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)))),bind(Z0,$fot(implies(Y,implies(X_59,X))))]]) ).
cnf(refute_0_912,plain,
( implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)) != implies(Y,implies(X_59,X))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = implies(Y,implies(X_59,X)) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) = implies(Y,implies(X_59,X)),
inference(resolve,[$cnf( $equal(implies(Y,implies(big_V(X_59,implies(not(X),not(Y))),X)),implies(Y,implies(X_59,X))) )],[refute_0_740,refute_0_912]) ).
cnf(refute_0_914,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != implies(Y,implies(X_59,X))
| implies(Y,implies(X_59,X)) = big_hat(truth,implies(X_59,implies(Y,X))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(truth,implies(X_59,implies(Y,X)))) ),[0],$fot(implies(Y,implies(X_59,X)))]]) ).
cnf(refute_0_915,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(Y,implies(X_59,X)) = big_hat(truth,implies(X_59,implies(Y,X))) ),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),implies(Y,implies(X_59,X))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
big_hat(truth,implies(X_59,implies(Y,X))) = implies(X_59,implies(Y,X)),
inference(subst,[],[refute_0_403:[bind(X_63,$fot(implies(X_59,implies(Y,X))))]]) ).
cnf(refute_0_917,plain,
( big_hat(truth,implies(X_59,implies(Y,X))) != implies(X_59,implies(Y,X))
| implies(Y,implies(X_59,X)) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(Y,implies(X_59,X)) = implies(X_59,implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Y,implies(X_59,X)),big_hat(truth,implies(X_59,implies(Y,X)))) ),[1],$fot(implies(X_59,implies(Y,X)))]]) ).
cnf(refute_0_918,plain,
( implies(Y,implies(X_59,X)) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(Y,implies(X_59,X)) = implies(X_59,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(big_hat(truth,implies(X_59,implies(Y,X))),implies(X_59,implies(Y,X))) )],[refute_0_916,refute_0_917]) ).
cnf(refute_0_919,plain,
( implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)) != big_hat(truth,implies(X_59,implies(Y,X)))
| implies(Y,implies(X_59,X)) = implies(X_59,implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(Y,implies(X_59,X)),big_hat(truth,implies(X_59,implies(Y,X)))) )],[refute_0_915,refute_0_918]) ).
cnf(refute_0_920,plain,
implies(Y,implies(X_59,X)) = implies(X_59,implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(big_V(X_59,implies(not(X),not(Y))),implies(Y,X)),big_hat(truth,implies(X_59,implies(Y,X)))) )],[refute_0_692,refute_0_919]) ).
cnf(refute_0_921,plain,
implies(not(X_61),implies(X_541,X_539)) = implies(X_541,implies(not(X_61),X_539)),
inference(subst,[],[refute_0_920:[bind(X,$fot(X_539)),bind(Y,$fot(not(X_61))),bind(X_59,$fot(X_541))]]) ).
cnf(refute_0_922,plain,
( X_61 != big_hat(X_61,implies(not(X_61),implies(X_541,X_539)))
| implies(not(X_61),implies(X_541,X_539)) != implies(X_541,implies(not(X_61),X_539))
| X_61 = big_hat(X_61,implies(X_541,implies(not(X_61),X_539))) ),
introduced(tautology,[equality,[$cnf( $equal(X_61,big_hat(X_61,implies(not(X_61),implies(X_541,X_539)))) ),[1,1],$fot(implies(X_541,implies(not(X_61),X_539)))]]) ).
cnf(refute_0_923,plain,
( X_61 != big_hat(X_61,implies(not(X_61),implies(X_541,X_539)))
| X_61 = big_hat(X_61,implies(X_541,implies(not(X_61),X_539))) ),
inference(resolve,[$cnf( $equal(implies(not(X_61),implies(X_541,X_539)),implies(X_541,implies(not(X_61),X_539))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
X_61 = big_hat(X_61,implies(X_541,implies(not(X_61),X_539))),
inference(resolve,[$cnf( $equal(X_61,big_hat(X_61,implies(not(X_61),implies(X_541,X_539)))) )],[refute_0_684,refute_0_923]) ).
cnf(refute_0_925,plain,
X_544 = big_hat(X_544,implies(X_543,implies(not(X_544),implies(Y,X)))),
inference(subst,[],[refute_0_924:[bind(X_539,$fot(implies(Y,X))),bind(X_541,$fot(X_543)),bind(X_61,$fot(X_544))]]) ).
cnf(refute_0_926,plain,
implies(Y,implies(not(X_544),X)) = implies(not(X_544),implies(Y,X)),
inference(subst,[],[refute_0_920:[bind(X_59,$fot(not(X_544)))]]) ).
cnf(refute_0_927,plain,
( implies(Y,implies(not(X_544),X)) != implies(not(X_544),implies(Y,X))
| implies(not(X_544),implies(Y,X)) = implies(Y,implies(not(X_544),X)) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(implies(Y,implies(not(X_544),X)))),bind(Y0,$fot(implies(not(X_544),implies(Y,X))))]]) ).
cnf(refute_0_928,plain,
implies(not(X_544),implies(Y,X)) = implies(Y,implies(not(X_544),X)),
inference(resolve,[$cnf( $equal(implies(Y,implies(not(X_544),X)),implies(not(X_544),implies(Y,X))) )],[refute_0_926,refute_0_927]) ).
cnf(refute_0_929,plain,
( X_544 != big_hat(X_544,implies(X_543,implies(not(X_544),implies(Y,X))))
| implies(not(X_544),implies(Y,X)) != implies(Y,implies(not(X_544),X))
| X_544 = big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_544,big_hat(X_544,implies(X_543,implies(not(X_544),implies(Y,X))))) ),[1,1,1],$fot(implies(Y,implies(not(X_544),X)))]]) ).
cnf(refute_0_930,plain,
( X_544 != big_hat(X_544,implies(X_543,implies(not(X_544),implies(Y,X))))
| X_544 = big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))) ),
inference(resolve,[$cnf( $equal(implies(not(X_544),implies(Y,X)),implies(Y,implies(not(X_544),X))) )],[refute_0_928,refute_0_929]) ).
cnf(refute_0_931,plain,
X_544 = big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))),
inference(resolve,[$cnf( $equal(X_544,big_hat(X_544,implies(X_543,implies(not(X_544),implies(Y,X))))) )],[refute_0_925,refute_0_930]) ).
cnf(refute_0_932,plain,
X = implies(implies(X,implies(X_541,X_539)),big_hat(implies(X_541,X_539),X)),
inference(subst,[],[refute_0_860:[bind(X_81,$fot(implies(X_541,X_539)))]]) ).
cnf(refute_0_933,plain,
implies(X,implies(X_541,X_539)) = implies(X_541,implies(X,X_539)),
inference(subst,[],[refute_0_920:[bind(X,$fot(X_539)),bind(Y,$fot(X)),bind(X_59,$fot(X_541))]]) ).
cnf(refute_0_934,plain,
( X != implies(implies(X,implies(X_541,X_539)),big_hat(implies(X_541,X_539),X))
| implies(X,implies(X_541,X_539)) != implies(X_541,implies(X,X_539))
| X = implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)) ),
introduced(tautology,[equality,[$cnf( $equal(X,implies(implies(X,implies(X_541,X_539)),big_hat(implies(X_541,X_539),X))) ),[1,0],$fot(implies(X_541,implies(X,X_539)))]]) ).
cnf(refute_0_935,plain,
( X != implies(implies(X,implies(X_541,X_539)),big_hat(implies(X_541,X_539),X))
| X = implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)) ),
inference(resolve,[$cnf( $equal(implies(X,implies(X_541,X_539)),implies(X_541,implies(X,X_539))) )],[refute_0_933,refute_0_934]) ).
cnf(refute_0_936,plain,
X = implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)),
inference(resolve,[$cnf( $equal(X,implies(implies(X,implies(X_541,X_539)),big_hat(implies(X_541,X_539),X))) )],[refute_0_932,refute_0_935]) ).
cnf(refute_0_937,plain,
( ~ ordered(truth,implies(X_627,X_628))
| implies(truth,implies(X_627,X_628)) = truth ),
inference(subst,[],[partial_order_definition1:[bind(X,$fot(truth)),bind(Y,$fot(implies(X_627,X_628)))]]) ).
cnf(refute_0_938,plain,
( implies(not(truth),X_123) != truth
| ordered(not(truth),X_123) ),
inference(subst,[],[partial_order_definition2:[bind(X,$fot(not(truth))),bind(Y,$fot(X_123))]]) ).
cnf(refute_0_939,plain,
implies(not(X_92),truth) = truth,
inference(subst,[],[refute_0_358:[bind(X_50,$fot(not(X_92)))]]) ).
cnf(refute_0_940,plain,
implies(not(X_92),truth) = implies(not(truth),X_92),
inference(subst,[],[refute_0_679:[bind(X,$fot(truth)),bind(X_88,$fot(X_92))]]) ).
cnf(refute_0_941,plain,
( implies(not(X_92),truth) != implies(not(truth),X_92)
| implies(not(X_92),truth) != truth
| implies(not(truth),X_92) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(X_92),truth),truth) ),[0],$fot(implies(not(truth),X_92))]]) ).
cnf(refute_0_942,plain,
( implies(not(X_92),truth) != truth
| implies(not(truth),X_92) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_92),truth),implies(not(truth),X_92)) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
implies(not(truth),X_92) = truth,
inference(resolve,[$cnf( $equal(implies(not(X_92),truth),truth) )],[refute_0_939,refute_0_942]) ).
cnf(refute_0_944,plain,
implies(not(truth),X_123) = truth,
inference(subst,[],[refute_0_943:[bind(X_92,$fot(X_123))]]) ).
cnf(refute_0_945,plain,
( implies(not(truth),X_123) != truth
| truth != truth
| implies(not(truth),X_123) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(truth),X_123),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_946,plain,
( truth != truth
| implies(not(truth),X_123) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),X_123),truth) )],[refute_0_944,refute_0_945]) ).
cnf(refute_0_947,plain,
( truth != truth
| ordered(not(truth),X_123) ),
inference(resolve,[$cnf( $equal(implies(not(truth),X_123),truth) )],[refute_0_946,refute_0_938]) ).
cnf(refute_0_948,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_949,plain,
ordered(not(truth),X_123),
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_948,refute_0_947]) ).
cnf(refute_0_950,plain,
ordered(not(truth),X_625),
inference(subst,[],[refute_0_949:[bind(X_123,$fot(X_625))]]) ).
cnf(refute_0_951,plain,
( ~ ordered(not(truth),X_625)
| ordered(implies(not(truth),X_626),implies(X_625,X_626)) ),
inference(subst,[],[lemma_1:[bind(X,$fot(not(truth))),bind(Y,$fot(X_625)),bind(Z,$fot(X_626))]]) ).
cnf(refute_0_952,plain,
ordered(implies(not(truth),X_626),implies(X_625,X_626)),
inference(resolve,[$cnf( ordered(not(truth),X_625) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
implies(not(truth),X_626) = truth,
inference(subst,[],[refute_0_943:[bind(X_92,$fot(X_626))]]) ).
cnf(refute_0_954,plain,
( implies(not(truth),X_626) != truth
| ~ ordered(implies(not(truth),X_626),implies(X_625,X_626))
| ordered(truth,implies(X_625,X_626)) ),
introduced(tautology,[equality,[$cnf( ordered(implies(not(truth),X_626),implies(X_625,X_626)) ),[0],$fot(truth)]]) ).
cnf(refute_0_955,plain,
( ~ ordered(implies(not(truth),X_626),implies(X_625,X_626))
| ordered(truth,implies(X_625,X_626)) ),
inference(resolve,[$cnf( $equal(implies(not(truth),X_626),truth) )],[refute_0_953,refute_0_954]) ).
cnf(refute_0_956,plain,
ordered(truth,implies(X_625,X_626)),
inference(resolve,[$cnf( ordered(implies(not(truth),X_626),implies(X_625,X_626)) )],[refute_0_952,refute_0_955]) ).
cnf(refute_0_957,plain,
ordered(truth,implies(X_627,X_628)),
inference(subst,[],[refute_0_956:[bind(X_625,$fot(X_627)),bind(X_626,$fot(X_628))]]) ).
cnf(refute_0_958,plain,
implies(truth,implies(X_627,X_628)) = truth,
inference(resolve,[$cnf( ordered(truth,implies(X_627,X_628)) )],[refute_0_957,refute_0_937]) ).
cnf(refute_0_959,plain,
implies(truth,implies(X_627,X_628)) = implies(X_627,X_628),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_627,X_628)))]]) ).
cnf(refute_0_960,plain,
( implies(truth,implies(X_627,X_628)) != implies(X_627,X_628)
| implies(truth,implies(X_627,X_628)) != truth
| implies(X_627,X_628) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(X_627,X_628)),truth) ),[0],$fot(implies(X_627,X_628))]]) ).
cnf(refute_0_961,plain,
( implies(truth,implies(X_627,X_628)) != truth
| implies(X_627,X_628) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_627,X_628)),implies(X_627,X_628)) )],[refute_0_959,refute_0_960]) ).
cnf(refute_0_962,plain,
implies(X_627,X_628) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(X_627,X_628)),truth) )],[refute_0_958,refute_0_961]) ).
cnf(refute_0_963,plain,
implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)) = truth,
inference(subst,[],[refute_0_962:[bind(X_627,$fot(implies(X_541,implies(X,X_539)))),bind(X_628,$fot(big_hat(implies(X_541,X_539),X)))]]) ).
cnf(refute_0_964,plain,
( X != implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X))
| implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)) != truth
| X = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(X,truth) ),[0],$fot(implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)))]]) ).
cnf(refute_0_965,plain,
( X != implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X))
| X = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X)),truth) )],[refute_0_963,refute_0_964]) ).
cnf(refute_0_966,plain,
X = truth,
inference(resolve,[$cnf( $equal(X,implies(implies(X_541,implies(X,X_539)),big_hat(implies(X_541,X_539),X))) )],[refute_0_936,refute_0_965]) ).
cnf(refute_0_967,plain,
big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))) = truth,
inference(subst,[],[refute_0_966:[bind(X,$fot(big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X))))))]]) ).
cnf(refute_0_968,plain,
( X_544 != big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X))))
| big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))) != truth
| X_544 = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_544,truth) ),[0],$fot(big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))))]]) ).
cnf(refute_0_969,plain,
( X_544 != big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X))))
| X_544 = truth ),
inference(resolve,[$cnf( $equal(big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X)))),truth) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
X_544 = truth,
inference(resolve,[$cnf( $equal(X_544,big_hat(X_544,implies(X_543,implies(Y,implies(not(X_544),X))))) )],[refute_0_931,refute_0_969]) ).
cnf(refute_0_971,plain,
big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))) = truth,
inference(subst,[],[refute_0_970:[bind(X_544,$fot(big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556))))))]]) ).
cnf(refute_0_972,plain,
( X_556 != big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556))))
| big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))) != truth
| X_556 = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_556,truth) ),[0],$fot(big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))))]]) ).
cnf(refute_0_973,plain,
( X_556 != big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556))))
| X_556 = truth ),
inference(resolve,[$cnf( $equal(big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556)))),truth) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
X_556 = truth,
inference(resolve,[$cnf( $equal(X_556,big_hat(X_556,big_hat(big_V(X_554,X_556),big_hat(big_V(X,X_556),implies(X_60,X_556))))) )],[refute_0_593,refute_0_973]) ).
cnf(refute_0_975,plain,
big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) = truth,
inference(subst,[],[refute_0_974:[bind(X_556,$fot(big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))))]]) ).
cnf(refute_0_976,plain,
( X_44 != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))) != truth
| X_44 = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_44,truth) ),[0],$fot(big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))))]]) ).
cnf(refute_0_977,plain,
( X_44 != big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))
| X_44 = truth ),
inference(resolve,[$cnf( $equal(big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44))))),truth) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
X_44 = truth,
inference(resolve,[$cnf( $equal(X_44,big_V(X_44,not(big_V(X_561,implies(X_562,not(X_44)))))) )],[refute_0_583,refute_0_977]) ).
cnf(refute_0_979,plain,
big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))) = truth,
inference(subst,[],[refute_0_978:[bind(X_44,$fot(big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600))))))]]) ).
cnf(refute_0_980,plain,
( X_600 != big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600))))
| big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))) != truth
| X_600 = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_600,truth) ),[0],$fot(big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))))]]) ).
cnf(refute_0_981,plain,
( X_600 != big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600))))
| X_600 = truth ),
inference(resolve,[$cnf( $equal(big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600)))),truth) )],[refute_0_979,refute_0_980]) ).
cnf(refute_0_982,plain,
X_600 = truth,
inference(resolve,[$cnf( $equal(X_600,big_hat(X_600,implies(X_602,big_hat(big_V(X,X_600),implies(X_60,X_600))))) )],[refute_0_545,refute_0_981]) ).
cnf(refute_0_983,plain,
big_V(implies(x,y),implies(y,x)) = truth,
inference(subst,[],[refute_0_982:[bind(X_600,$fot(big_V(implies(x,y),implies(y,x))))]]) ).
cnf(refute_0_984,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_985,plain,
( truth != truth
| big_V(implies(x,y),implies(y,x)) = truth ),
inference(resolve,[$cnf( $equal(big_V(implies(x,y),implies(y,x)),truth) )],[refute_0_983,refute_0_984]) ).
cnf(refute_0_986,plain,
truth != truth,
inference(resolve,[$cnf( $equal(big_V(implies(x,y),implies(y,x)),truth) )],[refute_0_985,prove_mv_4]) ).
cnf(refute_0_987,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_948,refute_0_986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL109-5 : TPTP v8.1.0. Released v1.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 2 10:08:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.04/9.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.04/9.24
% 9.04/9.24 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.15/9.33
%------------------------------------------------------------------------------