%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:41:54 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.54s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 66
% Syntax : Number of clauses : 233 ( 122 unt; 0 nHn; 120 RR)
% Number of literals : 399 ( 398 equ; 168 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 288 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(prove_mv_24,negated_conjecture,
implies(not(not(x)),x) != truth ).
cnf(refute_0_0,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(implies(not(X_18),not(truth)))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_1,plain,
implies(implies(not(X_4),not(truth)),implies(truth,X_4)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_4)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_2,plain,
implies(truth,X_4) = X_4,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_4))]]) ).
cnf(refute_0_3,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(truth,X_4) != X_4
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_4,plain,
( implies(implies(not(X_4),not(truth)),implies(truth,X_4)) != truth
| implies(implies(not(X_4),not(truth)),X_4) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_4),X_4) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(implies(not(X_4),not(truth)),X_4) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_4),not(truth)),implies(truth,X_4)),truth) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(implies(not(X_18),not(truth)),X_18) = truth,
inference(subst,[],[refute_0_5:[bind(X_4,$fot(X_18))]]) ).
cnf(refute_0_7,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) != truth
| implies(implies(not(X_18),not(truth)),X_18) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_8,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_18),not(truth)),X_18),truth) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(implies(implies(not(X_18),not(truth)),X_18),implies(X_16,X_18))),truth) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(truth,implies(X_16,X_18)) = implies(X_16,X_18),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_16,X_18)))]]) ).
cnf(refute_0_11,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))))]]) ).
cnf(refute_0_12,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))
| implies(truth,implies(X_16,X_18)) != implies(X_16,X_18)
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))) ),[1,1],$fot(implies(X_16,X_18))]]) ).
cnf(refute_0_13,plain,
( implies(truth,implies(X_16,X_18)) != implies(X_16,X_18)
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) = implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_16,X_18)),implies(X_16,X_18)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18))
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),truth) ),[0],$fot(implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)))]]) ).
cnf(refute_0_16,plain,
( implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
implies(implies(X_16,implies(not(X_18),not(truth))),implies(X_16,X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(not(X_18),not(truth))),implies(truth,implies(X_16,X_18))),truth) )],[refute_0_9,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),implies(implies(not(not(truth)),not(not(X_30))),X_30)) = truth,
inference(subst,[],[refute_0_17:[bind(X_16,$fot(implies(not(not(truth)),not(not(X_30))))),bind(X_18,$fot(X_30))]]) ).
cnf(refute_0_19,plain,
implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_30)))]]) ).
cnf(refute_0_20,plain,
( implies(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),implies(implies(not(not(truth)),not(not(X_30))),X_30)) != truth
| implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),implies(implies(not(not(truth)),not(not(X_30))),X_30)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_21,plain,
( implies(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),implies(implies(not(not(truth)),not(not(X_30))),X_30)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),truth) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_30))),implies(not(X_30),not(truth))),implies(implies(not(not(truth)),not(not(X_30))),X_30)),truth) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) = implies(implies(not(not(truth)),not(not(X_30))),X_30),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_30))),X_30)))]]) ).
cnf(refute_0_24,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) != implies(implies(not(not(truth)),not(not(X_30))),X_30)
| implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) != truth
| implies(implies(not(not(truth)),not(not(X_30))),X_30) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_30))),X_30))]]) ).
cnf(refute_0_25,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)) != truth
| implies(implies(not(not(truth)),not(not(X_30))),X_30) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)),implies(implies(not(not(truth)),not(not(X_30))),X_30)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(implies(not(not(truth)),not(not(X_30))),X_30) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_30))),X_30)),truth) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(truth,not(not(X_30))) = not(not(X_30)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_30))))]]) ).
cnf(refute_0_28,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(not(not(truth)),not(truth)))),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_29,plain,
implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) = truth,
inference(subst,[],[refute_0_17:[bind(X_16,$fot(not(not(truth)))),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_30,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))
| implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) ),[0],$fot(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))))]]) ).
cnf(refute_0_31,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth))),truth) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),implies(not(not(truth)),not(truth))),implies(not(not(truth)),not(truth)))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_34,plain,
implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(X_17),not(truth)))),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_35,plain,
implies(implies(not(X_17),not(truth)),X_17) = truth,
inference(subst,[],[refute_0_5:[bind(X_4,$fot(X_17))]]) ).
cnf(refute_0_36,plain,
( implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(not(X_17),not(truth)),X_17) != truth
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_37,plain,
( implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_17),not(truth)),X_17),truth) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_17),not(truth)),X_17),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) = implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))))]]) ).
cnf(refute_0_40,plain,
( implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))
| implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) ),[0],$fot(implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)))]]) ).
cnf(refute_0_41,plain,
( implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) != truth
| implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_17,X_18),implies(implies(not(X_17),not(truth)),X_18))),truth) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(not(truth),X_18),implies(implies(not(not(truth)),not(truth)),X_18)) = truth,
inference(subst,[],[refute_0_42:[bind(X_17,$fot(not(truth)))]]) ).
cnf(refute_0_44,plain,
implies(implies(not(truth),implies(not(X_18),not(truth))),implies(not(truth),X_18)) = truth,
inference(subst,[],[refute_0_17:[bind(X_16,$fot(not(truth)))]]) ).
cnf(refute_0_45,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_16)),bind(Y,$fot(implies(implies(X_18,truth),truth))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_46,plain,
implies(implies(X,X),X) = implies(implies(X,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(X))]]) ).
cnf(refute_0_47,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_48,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_49,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(truth,X_2) != X_2
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) ),[0,0],$fot(X_2)]]) ).
cnf(refute_0_50,plain,
( implies(implies(truth,X_2),X_2) != implies(implies(X_2,truth),truth)
| implies(X_2,X_2) = implies(implies(X_2,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_2),X_2) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_53,plain,
( implies(X,X) != implies(implies(X,truth),truth)
| implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) ),[1,0],$fot(implies(implies(X,truth),truth))]]) ).
cnf(refute_0_54,plain,
( implies(implies(X,X),X) != implies(implies(X,X),X)
| implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X) ),
inference(resolve,[$cnf( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X),
inference(resolve,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) )],[refute_0_46,refute_0_54]) ).
cnf(refute_0_56,plain,
implies(implies(X_18,X_18),X_18) = implies(implies(implies(X_18,truth),truth),X_18),
inference(subst,[],[refute_0_55:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_57,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_58,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_59,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( implies(implies(X_18,X_18),X_18) != implies(implies(implies(X_18,truth),truth),X_18)
| implies(implies(implies(X_18,truth),truth),X_18) = implies(implies(X_18,X_18),X_18) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(X_18,X_18),X_18))),bind(Y0,$fot(implies(implies(implies(X_18,truth),truth),X_18)))]]) ).
cnf(refute_0_61,plain,
implies(implies(implies(X_18,truth),truth),X_18) = implies(implies(X_18,X_18),X_18),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(implies(X_18,truth),truth),X_18)) )],[refute_0_56,refute_0_60]) ).
cnf(refute_0_62,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) != truth
| implies(implies(implies(X_18,truth),truth),X_18) != implies(implies(X_18,X_18),X_18)
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))),truth) ),[0,1,0],$fot(implies(implies(X_18,X_18),X_18))]]) ).
cnf(refute_0_63,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,truth),truth),X_18),implies(implies(X_18,X_18),X_18)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(implies(X_18,truth),truth),X_18),implies(X_16,X_18))),truth) )],[refute_0_45,refute_0_63]) ).
cnf(refute_0_65,plain,
implies(truth,implies(X_18,implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_66,plain,
implies(truth,X_18) = X_18,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_18))]]) ).
cnf(refute_0_67,plain,
implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),
inference(subst,[],[refute_0_55:[bind(X,$fot(implies(implies(truth,X_26),X_26)))]]) ).
cnf(refute_0_68,plain,
implies(implies(implies(implies(Y,X_18),X_18),Y),implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(Y,X_18),X_18))),bind(Z,$fot(implies(Y,X_18)))]]) ).
cnf(refute_0_69,plain,
implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,X_18))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_70,plain,
( implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18))) != truth
| implies(implies(implies(implies(Y,X_18),X_18),Y),implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18)))) != truth
| implies(implies(implies(implies(Y,X_18),X_18),Y),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_18),X_18),Y),implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_71,plain,
( implies(implies(implies(implies(Y,X_18),X_18),Y),implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18)))) != truth
| implies(implies(implies(implies(Y,X_18),X_18),Y),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18))),truth) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
implies(implies(implies(implies(Y,X_18),X_18),Y),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_18),X_18),Y),implies(implies(Y,implies(Y,X_18)),implies(implies(implies(Y,X_18),X_18),implies(Y,X_18)))),truth) )],[refute_0_68,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(implies(implies(implies(truth,X_26),X_26),truth),truth) = truth,
inference(subst,[],[refute_0_72:[bind(Y,$fot(truth)),bind(X_18,$fot(X_26))]]) ).
cnf(refute_0_74,plain,
( implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))
| implies(implies(implies(implies(truth,X_26),X_26),truth),truth) != truth
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_75,plain,
( implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),truth) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))) )],[refute_0_67,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(truth,implies(X_26,X_26)) = implies(X_26,X_26),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_26,X_26)))]]) ).
cnf(refute_0_78,plain,
implies(truth,X_26) = X_26,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_79,plain,
implies(implies(truth,X_26),X_26) = implies(implies(truth,X_26),X_26),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_26),X_26))]]) ).
cnf(refute_0_80,plain,
( implies(implies(truth,X_26),X_26) != implies(implies(truth,X_26),X_26)
| implies(truth,X_26) != X_26
| implies(implies(truth,X_26),X_26) = implies(X_26,X_26) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)) ),[1,0],$fot(X_26)]]) ).
cnf(refute_0_81,plain,
( implies(truth,X_26) != X_26
| implies(implies(truth,X_26),X_26) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(implies(truth,X_26),X_26) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(truth,X_26),X_26) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(truth,implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)),
introduced(tautology,[refl,[$fot(implies(truth,implies(implies(truth,X_26),X_26)))]]) ).
cnf(refute_0_84,plain,
( implies(implies(truth,X_26),X_26) != implies(X_26,X_26)
| implies(truth,implies(implies(truth,X_26),X_26)) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(truth,implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),X_26)),implies(truth,implies(implies(truth,X_26),X_26))) ),[1,1],$fot(implies(X_26,X_26))]]) ).
cnf(refute_0_85,plain,
( implies(implies(truth,X_26),X_26) != implies(X_26,X_26)
| implies(truth,implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),X_26)),implies(truth,implies(implies(truth,X_26),X_26))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
implies(truth,implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_26),X_26),implies(X_26,X_26)) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)))]]) ).
cnf(refute_0_88,plain,
( implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) != implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))
| implies(implies(implies(implies(truth,X_26),X_26),truth),truth) != truth
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_89,plain,
( implies(implies(implies(implies(truth,X_26),X_26),truth),truth) != truth
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(implies(truth,X_26),X_26)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),truth) )],[refute_0_73,refute_0_89]) ).
cnf(refute_0_91,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_92,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_59,refute_0_91]) ).
cnf(refute_0_93,plain,
( implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(truth,implies(implies(truth,X_26),X_26)) != implies(truth,implies(X_26,X_26))
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)))),bind(Y0,$fot(implies(truth,implies(implies(truth,X_26),X_26)))),bind(Z0,$fot(implies(truth,implies(X_26,X_26))))]]) ).
cnf(refute_0_94,plain,
( implies(truth,implies(implies(truth,X_26),X_26)) != implies(truth,implies(X_26,X_26))
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),implies(truth,implies(implies(truth,X_26),X_26))) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(truth,implies(X_26,X_26)),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),X_26)),implies(truth,implies(X_26,X_26))) )],[refute_0_86,refute_0_94]) ).
cnf(refute_0_96,plain,
( implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) != implies(truth,implies(X_26,X_26))
| implies(truth,implies(X_26,X_26)) != implies(X_26,X_26)
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)))),bind(Y0,$fot(implies(truth,implies(X_26,X_26)))),bind(Z0,$fot(implies(X_26,X_26)))]]) ).
cnf(refute_0_97,plain,
( implies(truth,implies(X_26,X_26)) != implies(X_26,X_26)
| implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),implies(truth,implies(X_26,X_26))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_26,X_26)),implies(X_26,X_26)) )],[refute_0_77,refute_0_97]) ).
cnf(refute_0_99,plain,
( implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) != implies(X_26,X_26)
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)))),bind(Y0,$fot(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)))),bind(Z0,$fot(implies(X_26,X_26)))]]) ).
cnf(refute_0_100,plain,
( implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)) != implies(X_26,X_26)
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26))) )],[refute_0_67,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(truth,X_26),X_26),truth),truth),implies(implies(truth,X_26),X_26)),implies(X_26,X_26)) )],[refute_0_98,refute_0_100]) ).
cnf(refute_0_102,plain,
( implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(X_26,X_26)
| implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(X_26,X_26) = implies(truth,implies(implies(truth,X_26),X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(truth,implies(implies(truth,X_26),X_26))) ),[0],$fot(implies(X_26,X_26))]]) ).
cnf(refute_0_103,plain,
( implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(X_26,X_26) = implies(truth,implies(implies(truth,X_26),X_26)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(X_26,X_26)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_105,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) != truth
| implies(truth,X_18) != X_18
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))),truth) ),[0,1,1],$fot(X_18)]]) ).
cnf(refute_0_106,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))) != truth
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_66,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),implies(truth,X_18))),truth) )],[refute_0_104,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_109,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)))]]) ).
cnf(refute_0_110,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))
| implies(truth,X_17) != X_17
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))) ),[1,0],$fot(X_17)]]) ).
cnf(refute_0_111,plain,
( implies(truth,X_17) != X_17
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) = implies(X_17,implies(implies(X_17,X_18),X_18)),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != implies(X_17,implies(implies(X_17,X_18),X_18))
| implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != truth
| implies(X_17,implies(implies(X_17,X_18),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),truth) ),[0],$fot(implies(X_17,implies(implies(X_17,X_18),X_18)))]]) ).
cnf(refute_0_114,plain,
( implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)) != truth
| implies(X_17,implies(implies(X_17,X_18),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),implies(X_17,implies(implies(X_17,X_18),X_18))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(X_17,implies(implies(X_17,X_18),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),implies(implies(X_17,X_18),X_18)),truth) )],[refute_0_107,refute_0_114]) ).
cnf(refute_0_116,plain,
implies(truth,implies(implies(truth,X_26),X_26)) = truth,
inference(subst,[],[refute_0_115:[bind(X_17,$fot(truth)),bind(X_18,$fot(X_26))]]) ).
cnf(refute_0_117,plain,
( implies(X_26,X_26) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(truth,implies(implies(truth,X_26),X_26)) != truth
| implies(X_26,X_26) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_26,X_26),truth) ),[0],$fot(implies(truth,implies(implies(truth,X_26),X_26)))]]) ).
cnf(refute_0_118,plain,
( implies(X_26,X_26) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(X_26,X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_26),X_26)),truth) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)) != implies(truth,implies(implies(truth,X_26),X_26))
| implies(X_26,X_26) = truth ),
inference(resolve,[$cnf( $equal(implies(X_26,X_26),implies(truth,implies(implies(truth,X_26),X_26))) )],[refute_0_103,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(X_26,X_26) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_26),X_26),implies(implies(truth,X_26),X_26)),implies(implies(truth,X_26),X_26)),implies(truth,implies(implies(truth,X_26),X_26))) )],[refute_0_76,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(X_18,X_18) = truth,
inference(subst,[],[refute_0_120:[bind(X_26,$fot(X_18))]]) ).
cnf(refute_0_122,plain,
implies(implies(X_18,X_18),X_18) = implies(implies(X_18,X_18),X_18),
introduced(tautology,[refl,[$fot(implies(implies(X_18,X_18),X_18))]]) ).
cnf(refute_0_123,plain,
( implies(X_18,X_18) != truth
| implies(implies(X_18,X_18),X_18) != implies(implies(X_18,X_18),X_18)
| implies(implies(X_18,X_18),X_18) = implies(truth,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(X_18,X_18),X_18)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_124,plain,
( implies(X_18,X_18) != truth
| implies(implies(X_18,X_18),X_18) = implies(truth,X_18) ),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(implies(X_18,X_18),X_18)) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(implies(X_18,X_18),X_18) = implies(truth,X_18),
inference(resolve,[$cnf( $equal(implies(X_18,X_18),truth) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
( implies(implies(X_18,X_18),X_18) != implies(truth,X_18)
| implies(truth,X_18) != X_18
| implies(implies(X_18,X_18),X_18) = X_18 ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(X_18,X_18),X_18))),bind(Y0,$fot(implies(truth,X_18))),bind(Z0,$fot(X_18))]]) ).
cnf(refute_0_127,plain,
( implies(truth,X_18) != X_18
| implies(implies(X_18,X_18),X_18) = X_18 ),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),implies(truth,X_18)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(implies(X_18,X_18),X_18) = X_18,
inference(resolve,[$cnf( $equal(implies(truth,X_18),X_18) )],[refute_0_66,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))]]) ).
cnf(refute_0_130,plain,
( implies(implies(X_18,X_18),X_18) != X_18
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) ),[1,0],$fot(X_18)]]) ).
cnf(refute_0_131,plain,
( implies(implies(X_18,X_18),X_18) != X_18
| implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) = implies(X_18,implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(implies(X_18,X_18),X_18),X_18) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_134,plain,
( implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(X_18,implies(X_16,X_18))
| implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))
| implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) ),[1,1],$fot(implies(X_18,implies(X_16,X_18)))]]) ).
cnf(refute_0_135,plain,
( implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)) != implies(X_18,implies(X_16,X_18))
| implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)),implies(X_18,implies(X_16,X_18))) )],[refute_0_132,refute_0_135]) ).
cnf(refute_0_137,plain,
implies(implies(implies(implies(X_25,truth),truth),X_25),truth) = truth,
inference(subst,[],[refute_0_72:[bind(Y,$fot(X_25)),bind(X_18,$fot(truth))]]) ).
cnf(refute_0_138,plain,
implies(X_25,X_25) = implies(implies(X_25,truth),truth),
inference(subst,[],[refute_0_51:[bind(X_2,$fot(X_25))]]) ).
cnf(refute_0_139,plain,
( implies(X_25,X_25) != implies(implies(X_25,truth),truth)
| implies(implies(X_25,truth),truth) = implies(X_25,X_25) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(X_25,X_25))),bind(Y0,$fot(implies(implies(X_25,truth),truth)))]]) ).
cnf(refute_0_140,plain,
implies(implies(X_25,truth),truth) = implies(X_25,X_25),
inference(resolve,[$cnf( $equal(implies(X_25,X_25),implies(implies(X_25,truth),truth)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( implies(implies(X_25,truth),truth) != implies(X_25,X_25)
| implies(implies(implies(implies(X_25,truth),truth),X_25),truth) != truth
| implies(implies(implies(X_25,X_25),X_25),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_25,truth),truth),X_25),truth),truth) ),[0,0,0],$fot(implies(X_25,X_25))]]) ).
cnf(refute_0_142,plain,
( implies(implies(implies(implies(X_25,truth),truth),X_25),truth) != truth
| implies(implies(implies(X_25,X_25),X_25),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,truth),truth),implies(X_25,X_25)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(implies(X_25,X_25),X_25),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_25,truth),truth),X_25),truth),truth) )],[refute_0_137,refute_0_142]) ).
cnf(refute_0_144,plain,
implies(truth,X_25) = X_25,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_25))]]) ).
cnf(refute_0_145,plain,
implies(X_25,X_25) = truth,
inference(subst,[],[refute_0_120:[bind(X_26,$fot(X_25))]]) ).
cnf(refute_0_146,plain,
implies(implies(X_25,X_25),X_25) = implies(implies(X_25,X_25),X_25),
introduced(tautology,[refl,[$fot(implies(implies(X_25,X_25),X_25))]]) ).
cnf(refute_0_147,plain,
( implies(X_25,X_25) != truth
| implies(implies(X_25,X_25),X_25) != implies(implies(X_25,X_25),X_25)
| implies(implies(X_25,X_25),X_25) = implies(truth,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_25,X_25),X_25),implies(implies(X_25,X_25),X_25)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_148,plain,
( implies(X_25,X_25) != truth
| implies(implies(X_25,X_25),X_25) = implies(truth,X_25) ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,X_25),X_25),implies(implies(X_25,X_25),X_25)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(implies(X_25,X_25),X_25) = implies(truth,X_25),
inference(resolve,[$cnf( $equal(implies(X_25,X_25),truth) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( implies(implies(X_25,X_25),X_25) != implies(truth,X_25)
| implies(truth,X_25) != X_25
| implies(implies(X_25,X_25),X_25) = X_25 ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(X_25,X_25),X_25))),bind(Y0,$fot(implies(truth,X_25))),bind(Z0,$fot(X_25))]]) ).
cnf(refute_0_151,plain,
( implies(truth,X_25) != X_25
| implies(implies(X_25,X_25),X_25) = X_25 ),
inference(resolve,[$cnf( $equal(implies(implies(X_25,X_25),X_25),implies(truth,X_25)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
implies(implies(X_25,X_25),X_25) = X_25,
inference(resolve,[$cnf( $equal(implies(truth,X_25),X_25) )],[refute_0_144,refute_0_151]) ).
cnf(refute_0_153,plain,
implies(implies(implies(X_25,X_25),X_25),truth) = implies(implies(implies(X_25,X_25),X_25),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_25,X_25),X_25),truth))]]) ).
cnf(refute_0_154,plain,
( implies(implies(X_25,X_25),X_25) != X_25
| implies(implies(implies(X_25,X_25),X_25),truth) != implies(implies(implies(X_25,X_25),X_25),truth)
| implies(implies(implies(X_25,X_25),X_25),truth) = implies(X_25,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_25,X_25),X_25),truth),implies(implies(implies(X_25,X_25),X_25),truth)) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_155,plain,
( implies(implies(X_25,X_25),X_25) != X_25
| implies(implies(implies(X_25,X_25),X_25),truth) = implies(X_25,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_25,X_25),X_25),truth),implies(implies(implies(X_25,X_25),X_25),truth)) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
implies(implies(implies(X_25,X_25),X_25),truth) = implies(X_25,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_25,X_25),X_25),X_25) )],[refute_0_152,refute_0_155]) ).
cnf(refute_0_157,plain,
( implies(implies(implies(X_25,X_25),X_25),truth) != implies(X_25,truth)
| implies(implies(implies(X_25,X_25),X_25),truth) != truth
| implies(X_25,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_25,X_25),X_25),truth),truth) ),[0],$fot(implies(X_25,truth))]]) ).
cnf(refute_0_158,plain,
( implies(implies(implies(X_25,X_25),X_25),truth) != truth
| implies(X_25,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_25,X_25),X_25),truth),implies(X_25,truth)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
implies(X_25,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_25,X_25),X_25),truth),truth) )],[refute_0_143,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(X_16,truth) = truth,
inference(subst,[],[refute_0_159:[bind(X_25,$fot(X_16))]]) ).
cnf(refute_0_161,plain,
implies(implies(X_18,truth),truth) = truth,
inference(subst,[],[refute_0_159:[bind(X_25,$fot(implies(X_18,truth)))]]) ).
cnf(refute_0_162,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,implies(implies(X_18,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_16,implies(implies(X_18,truth),truth)))]]) ).
cnf(refute_0_163,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != implies(X_16,implies(implies(X_18,truth),truth))
| implies(implies(X_18,truth),truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,implies(implies(X_18,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_164,plain,
( implies(implies(X_18,truth),truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth) ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,implies(implies(X_18,truth),truth))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = implies(X_16,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_18,truth),truth),truth) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != implies(X_16,truth)
| implies(X_16,truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = truth ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(X_16,implies(implies(X_18,truth),truth)))),bind(Y0,$fot(implies(X_16,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_167,plain,
( implies(X_16,truth) != truth
| implies(X_16,implies(implies(X_18,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),implies(X_16,truth)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(X_16,implies(implies(X_18,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(X_16,truth),truth) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),
introduced(tautology,[refl,[$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))]]) ).
cnf(refute_0_170,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_171,plain,
( implies(X_16,implies(implies(X_18,truth),truth)) != truth
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(X_16,implies(implies(X_18,truth),truth)),truth) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))
| implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(truth,implies(X_18,implies(X_16,X_18)))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))),bind(Y0,$fot(implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))),bind(Z0,$fot(implies(truth,implies(X_18,implies(X_16,X_18)))))]]) ).
cnf(refute_0_174,plain,
( implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(truth,implies(X_18,implies(X_16,X_18)))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(truth,implies(X_18,implies(X_16,X_18))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(truth,implies(X_18,implies(X_16,X_18)))) )],[refute_0_136,refute_0_174]) ).
cnf(refute_0_176,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(truth,implies(X_18,implies(X_16,X_18)))
| implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))))),bind(Y0,$fot(implies(truth,implies(X_18,implies(X_16,X_18))))),bind(Z0,$fot(implies(X_18,implies(X_16,X_18))))]]) ).
cnf(refute_0_177,plain,
( implies(truth,implies(X_18,implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(truth,implies(X_18,implies(X_16,X_18)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) = implies(X_18,implies(X_16,X_18)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_18,implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_65,refute_0_177]) ).
cnf(refute_0_179,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != implies(X_18,implies(X_16,X_18))
| implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),truth) ),[0],$fot(implies(X_18,implies(X_16,X_18)))]]) ).
cnf(refute_0_180,plain,
( implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))) != truth
| implies(X_18,implies(X_16,X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),implies(X_18,implies(X_16,X_18))) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
implies(X_18,implies(X_16,X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_16,implies(implies(X_18,truth),truth)),implies(implies(implies(X_18,X_18),X_18),implies(X_16,X_18))),truth) )],[refute_0_64,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(not(truth),implies(not(X_18),not(truth))) = truth,
inference(subst,[],[refute_0_181:[bind(X_16,$fot(not(X_18))),bind(X_18,$fot(not(truth)))]]) ).
cnf(refute_0_183,plain,
( implies(implies(not(truth),implies(not(X_18),not(truth))),implies(not(truth),X_18)) != truth
| implies(not(truth),implies(not(X_18),not(truth))) != truth
| implies(truth,implies(not(truth),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(X_18),not(truth))),implies(not(truth),X_18)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_184,plain,
( implies(implies(not(truth),implies(not(X_18),not(truth))),implies(not(truth),X_18)) != truth
| implies(truth,implies(not(truth),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(X_18),not(truth))),truth) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(truth,implies(not(truth),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(X_18),not(truth))),implies(not(truth),X_18)),truth) )],[refute_0_44,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(truth,implies(not(truth),X_18)) = implies(not(truth),X_18),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),X_18)))]]) ).
cnf(refute_0_187,plain,
( implies(truth,implies(not(truth),X_18)) != implies(not(truth),X_18)
| implies(truth,implies(not(truth),X_18)) != truth
| implies(not(truth),X_18) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(not(truth),X_18)),truth) ),[0],$fot(implies(not(truth),X_18))]]) ).
cnf(refute_0_188,plain,
( implies(truth,implies(not(truth),X_18)) != truth
| implies(not(truth),X_18) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_18)),implies(not(truth),X_18)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
implies(not(truth),X_18) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),X_18)),truth) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( implies(implies(not(truth),X_18),implies(implies(not(not(truth)),not(truth)),X_18)) != truth
| implies(not(truth),X_18) != truth
| implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),X_18),implies(implies(not(not(truth)),not(truth)),X_18)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_191,plain,
( implies(implies(not(truth),X_18),implies(implies(not(not(truth)),not(truth)),X_18)) != truth
| implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),X_18),truth) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),X_18),implies(implies(not(not(truth)),not(truth)),X_18)),truth) )],[refute_0_43,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) = implies(implies(not(not(truth)),not(truth)),X_18),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(truth)),X_18)))]]) ).
cnf(refute_0_194,plain,
( implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) != implies(implies(not(not(truth)),not(truth)),X_18)
| implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) != truth
| implies(implies(not(not(truth)),not(truth)),X_18) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(truth)),X_18))]]) ).
cnf(refute_0_195,plain,
( implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)) != truth
| implies(implies(not(not(truth)),not(truth)),X_18) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)),implies(implies(not(not(truth)),not(truth)),X_18)) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
implies(implies(not(not(truth)),not(truth)),X_18) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(truth)),X_18)),truth) )],[refute_0_192,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(implies(not(not(truth)),not(truth)),not(not(truth))) = truth,
inference(subst,[],[refute_0_196:[bind(X_18,$fot(not(not(truth))))]]) ).
cnf(refute_0_198,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))]]) ).
cnf(refute_0_199,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))
| implies(implies(not(not(truth)),not(truth)),not(not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_200,plain,
( implies(implies(not(not(truth)),not(truth)),not(not(truth))) != truth
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth)))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(not(truth))),truth) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_203,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_33,refute_0_203]) ).
cnf(refute_0_205,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_206,plain,
( implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(truth)),not(not(truth))),not(not(truth))),truth) )],[refute_0_32,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(not(not(truth)),not(not(X_30))) = implies(not(not(truth)),not(not(X_30))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_30))))]]) ).
cnf(refute_0_209,plain,
( implies(not(not(truth)),not(not(X_30))) != implies(not(not(truth)),not(not(X_30)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_30))) = implies(truth,not(not(X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_30))),implies(not(not(truth)),not(not(X_30)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_210,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_30))) = implies(truth,not(not(X_30))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_30))),implies(not(not(truth)),not(not(X_30)))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(not(not(truth)),not(not(X_30))) = implies(truth,not(not(X_30))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_207,refute_0_210]) ).
cnf(refute_0_212,plain,
( implies(not(not(truth)),not(not(X_30))) != implies(truth,not(not(X_30)))
| implies(truth,not(not(X_30))) != not(not(X_30))
| implies(not(not(truth)),not(not(X_30))) = not(not(X_30)) ),
inference(subst,[],[refute_0_92:[bind(X0,$fot(implies(not(not(truth)),not(not(X_30))))),bind(Y0,$fot(implies(truth,not(not(X_30))))),bind(Z0,$fot(not(not(X_30))))]]) ).
cnf(refute_0_213,plain,
( implies(truth,not(not(X_30))) != not(not(X_30))
| implies(not(not(truth)),not(not(X_30))) = not(not(X_30)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_30))),implies(truth,not(not(X_30)))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(not(not(truth)),not(not(X_30))) = not(not(X_30)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_30))),not(not(X_30))) )],[refute_0_27,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(implies(not(not(truth)),not(not(X_30))),X_30) = implies(implies(not(not(truth)),not(not(X_30))),X_30),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_30))),X_30))]]) ).
cnf(refute_0_216,plain,
( implies(implies(not(not(truth)),not(not(X_30))),X_30) != implies(implies(not(not(truth)),not(not(X_30))),X_30)
| implies(not(not(truth)),not(not(X_30))) != not(not(X_30))
| implies(implies(not(not(truth)),not(not(X_30))),X_30) = implies(not(not(X_30)),X_30) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),X_30),implies(implies(not(not(truth)),not(not(X_30))),X_30)) ),[1,0],$fot(not(not(X_30)))]]) ).
cnf(refute_0_217,plain,
( implies(not(not(truth)),not(not(X_30))) != not(not(X_30))
| implies(implies(not(not(truth)),not(not(X_30))),X_30) = implies(not(not(X_30)),X_30) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),X_30),implies(implies(not(not(truth)),not(not(X_30))),X_30)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
implies(implies(not(not(truth)),not(not(X_30))),X_30) = implies(not(not(X_30)),X_30),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_30))),not(not(X_30))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
( implies(implies(not(not(truth)),not(not(X_30))),X_30) != implies(not(not(X_30)),X_30)
| implies(implies(not(not(truth)),not(not(X_30))),X_30) != truth
| implies(not(not(X_30)),X_30) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),X_30),truth) ),[0],$fot(implies(not(not(X_30)),X_30))]]) ).
cnf(refute_0_220,plain,
( implies(implies(not(not(truth)),not(not(X_30))),X_30) != truth
| implies(not(not(X_30)),X_30) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),X_30),implies(not(not(X_30)),X_30)) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
implies(not(not(X_30)),X_30) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_30))),X_30),truth) )],[refute_0_26,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(not(not(x)),x) = truth,
inference(subst,[],[refute_0_221:[bind(X_30,$fot(x))]]) ).
cnf(refute_0_223,plain,
( implies(not(not(x)),x) != truth
| truth != truth
| implies(not(not(x)),x) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(x)),x),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_224,plain,
( truth != truth
| implies(not(not(x)),x) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(x)),x),truth) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(not(not(x)),x),truth) )],[refute_0_224,prove_mv_24]) ).
cnf(refute_0_226,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_227,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_226,refute_0_225]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL110-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : metis --show proof --show saturation %s
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 4 14:40:13 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.28/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.28/0.54
% 0.28/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.28/0.58
%------------------------------------------------------------------------------