TSTP Solution File: LCL135-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL135-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 12:49:50 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 62
% Syntax : Number of clauses : 220 ( 111 unt; 0 nHn; 128 RR)
% Number of literals : 382 ( 381 equ; 164 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 228 ( 10 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_wajsberg_lemma,negated_conjecture,
implies(x,implies(y,x)) != truth ).
cnf(refute_0_0,plain,
implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(truth)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_1,plain,
implies(truth,X_14) = X_14,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
( implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) != truth
| implies(truth,X_14) != X_14
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))),truth) ),[0,1,0],$fot(X_14)]]) ).
cnf(refute_0_3,plain,
( implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(implies(truth,X_14),implies(X_12,X_14))),truth) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
implies(truth,implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_6,plain,
implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(X_6),truth),truth))),bind(Y,$fot(X_13)),bind(Z,$fot(implies(X_6,X_6)))]]) ).
cnf(refute_0_7,plain,
implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_8,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_9,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_10,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_11,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( $equal(implies(truth,X_2),X_2) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
implies(not(X_6),not(X_6)) = implies(implies(not(X_6),truth),truth),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(not(X_6)))]]) ).
cnf(refute_0_14,plain,
( implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(not(X_6),not(X_6)) != implies(implies(not(X_6),truth),truth)
| implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) ),[0,0],$fot(implies(implies(not(X_6),truth),truth))]]) ).
cnf(refute_0_15,plain,
( implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_6),not(X_6)),implies(implies(not(X_6),truth),truth)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) )],[refute_0_7,refute_0_15]) ).
cnf(refute_0_17,plain,
( implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)))) != truth
| implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)) != truth
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_18,plain,
( implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)))) != truth
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)),truth) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),implies(implies(implies(not(X_6),truth),truth),implies(X_6,X_6)))),truth) )],[refute_0_6,refute_0_18]) ).
cnf(refute_0_20,plain,
implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(implies(X_3,truth),truth),truth),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(implies(X_3,truth)))]]) ).
cnf(refute_0_21,plain,
implies(X_3,X_3) = implies(implies(X_3,truth),truth),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(X_3))]]) ).
cnf(refute_0_22,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( implies(X_3,X_3) != implies(implies(X_3,truth),truth)
| implies(implies(X_3,truth),truth) = implies(X_3,X_3) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(implies(X_3,X_3))),bind(Y0,$fot(implies(implies(X_3,truth),truth)))]]) ).
cnf(refute_0_26,plain,
implies(implies(X_3,truth),truth) = implies(X_3,X_3),
inference(resolve,[$cnf( $equal(implies(X_3,X_3),implies(implies(X_3,truth),truth)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
( implies(implies(X_3,truth),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(X_3,truth),truth) != implies(X_3,X_3)
| implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(X_3,X_3),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_3,truth),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) ),[1,0],$fot(implies(X_3,X_3))]]) ).
cnf(refute_0_28,plain,
( implies(implies(X_3,truth),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(X_3,X_3),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_3,truth),truth),implies(X_3,X_3)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(X_3,X_3),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_3,truth),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
implies(implies(implies(X_2,truth),truth),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),
inference(subst,[],[refute_0_29:[bind(X_3,$fot(implies(X_2,truth)))]]) ).
cnf(refute_0_31,plain,
( implies(X_2,X_2) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,truth),truth) = implies(X_2,X_2) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(implies(X_2,X_2))),bind(Y0,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_32,plain,
implies(implies(X_2,truth),truth) = implies(X_2,X_2),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),implies(implies(X_2,truth),truth)) )],[refute_0_12,refute_0_31]) ).
cnf(refute_0_33,plain,
( implies(implies(X_2,truth),truth) != implies(X_2,X_2)
| implies(implies(implies(X_2,truth),truth),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_2,truth),truth),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)) ),[0,0],$fot(implies(X_2,X_2))]]) ).
cnf(refute_0_34,plain,
( implies(implies(implies(X_2,truth),truth),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,truth),truth),implies(X_2,X_2)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,truth),truth),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(implies(X_2,truth),implies(X_2,truth)) = implies(implies(X_2,X_2),truth),
inference(subst,[],[refute_0_29:[bind(X_3,$fot(X_2))]]) ).
cnf(refute_0_37,plain,
implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) = implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_2,truth),implies(X_2,truth)),truth))]]) ).
cnf(refute_0_38,plain,
( implies(implies(X_2,truth),implies(X_2,truth)) != implies(implies(X_2,X_2),truth)
| implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) != implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)
| implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) = implies(implies(implies(X_2,X_2),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)) ),[1,0],$fot(implies(implies(X_2,X_2),truth))]]) ).
cnf(refute_0_39,plain,
( implies(implies(X_2,truth),implies(X_2,truth)) != implies(implies(X_2,X_2),truth)
| implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) = implies(implies(implies(X_2,X_2),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) = implies(implies(implies(X_2,X_2),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_2,truth),implies(X_2,truth)),implies(implies(X_2,X_2),truth)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)
| implies(implies(implies(X_2,truth),implies(X_2,truth)),truth) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,X_2),truth),truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,X_2),truth),truth)) ),[0],$fot(implies(implies(implies(X_2,truth),implies(X_2,truth)),truth))]]) ).
cnf(refute_0_42,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,X_2),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,truth),implies(X_2,truth)),truth),implies(implies(implies(X_2,X_2),truth),truth)) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(implies(X_2,X_2),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,truth),implies(X_2,truth)),truth)) )],[refute_0_35,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(truth,implies(implies(X_2,truth),truth)) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_45,plain,
implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(not(not(truth)),not(not(truth))))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_46,plain,
implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) = truth,
inference(subst,[],[refute_0_16:[bind(X_6,$fot(not(truth)))]]) ).
cnf(refute_0_47,plain,
implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(implies(not(truth),truth))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_48,plain,
implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) = truth,
inference(subst,[],[refute_0_16:[bind(X_6,$fot(truth))]]) ).
cnf(refute_0_49,plain,
( implies(implies(implies(not(truth),truth),truth),implies(truth,truth)) != truth
| implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_50,plain,
( implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))) != truth
| implies(implies(truth,implies(not(truth),truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(truth),truth),truth),implies(truth,truth)),truth) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),implies(implies(implies(not(truth),truth),truth),implies(truth,truth))),truth) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(implies(not(truth),truth),truth) = implies(not(truth),not(truth)),
inference(subst,[],[refute_0_32:[bind(X_2,$fot(not(truth)))]]) ).
cnf(refute_0_53,plain,
implies(truth,implies(not(truth),truth)) = implies(not(truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(not(truth),truth)))]]) ).
cnf(refute_0_54,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(truth,implies(not(truth),truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(truth,implies(not(truth),truth)),truth))]]) ).
cnf(refute_0_55,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(truth,implies(not(truth),truth)),truth)
| implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) ),[1,0],$fot(implies(not(truth),truth))]]) ).
cnf(refute_0_56,plain,
( implies(truth,implies(not(truth),truth)) != implies(not(truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(truth,implies(not(truth),truth)),truth)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(implies(not(truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(not(truth),truth)),implies(not(truth),truth)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_59,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_24,refute_0_58]) ).
cnf(refute_0_60,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != implies(implies(not(truth),truth),truth)
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(truth,implies(not(truth),truth)),truth))),bind(Y0,$fot(implies(implies(not(truth),truth),truth))),bind(Z0,$fot(implies(not(truth),not(truth))))]]) ).
cnf(refute_0_61,plain,
( implies(implies(not(truth),truth),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(implies(not(truth),truth),truth)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
implies(implies(truth,implies(not(truth),truth)),truth) = implies(not(truth),not(truth)),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),truth),truth),implies(not(truth),not(truth))) )],[refute_0_52,refute_0_61]) ).
cnf(refute_0_63,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != implies(not(truth),not(truth))
| implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) ),[0],$fot(implies(not(truth),not(truth)))]]) ).
cnf(refute_0_64,plain,
( implies(implies(truth,implies(not(truth),truth)),truth) != truth
| implies(not(truth),not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),implies(not(truth),not(truth))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
implies(not(truth),not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(not(truth),truth)),truth),truth) )],[refute_0_51,refute_0_64]) ).
cnf(refute_0_66,plain,
( implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) != truth
| implies(not(truth),not(truth)) != truth
| implies(implies(implies(not(not(truth)),truth),truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_67,plain,
( implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))) != truth
| implies(implies(implies(not(not(truth)),truth),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(truth)),truth) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(implies(implies(not(not(truth)),truth),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),implies(not(truth),not(truth))),truth) )],[refute_0_46,refute_0_67]) ).
cnf(refute_0_69,plain,
implies(implies(X_4,truth),implies(X_4,truth)) = implies(implies(implies(X_4,truth),truth),truth),
inference(subst,[],[refute_0_12:[bind(X_2,$fot(implies(X_4,truth)))]]) ).
cnf(refute_0_70,plain,
implies(implies(X_4,truth),implies(X_4,truth)) = implies(implies(X_4,X_4),truth),
inference(subst,[],[refute_0_29:[bind(X_3,$fot(X_4))]]) ).
cnf(refute_0_71,plain,
( implies(implies(X_4,truth),implies(X_4,truth)) != implies(implies(X_4,X_4),truth)
| implies(implies(X_4,truth),implies(X_4,truth)) != implies(implies(implies(X_4,truth),truth),truth)
| implies(implies(X_4,X_4),truth) = implies(implies(implies(X_4,truth),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_4,truth),implies(X_4,truth)),implies(implies(implies(X_4,truth),truth),truth)) ),[0],$fot(implies(implies(X_4,X_4),truth))]]) ).
cnf(refute_0_72,plain,
( implies(implies(X_4,truth),implies(X_4,truth)) != implies(implies(implies(X_4,truth),truth),truth)
| implies(implies(X_4,X_4),truth) = implies(implies(implies(X_4,truth),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_4,truth),implies(X_4,truth)),implies(implies(X_4,X_4),truth)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
implies(implies(X_4,X_4),truth) = implies(implies(implies(X_4,truth),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_4,truth),implies(X_4,truth)),implies(implies(implies(X_4,truth),truth),truth)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( implies(implies(X_4,X_4),truth) != implies(implies(implies(X_4,truth),truth),truth)
| implies(implies(implies(X_4,truth),truth),truth) = implies(implies(X_4,X_4),truth) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(implies(implies(X_4,X_4),truth))),bind(Y0,$fot(implies(implies(implies(X_4,truth),truth),truth)))]]) ).
cnf(refute_0_75,plain,
implies(implies(implies(X_4,truth),truth),truth) = implies(implies(X_4,X_4),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_4,X_4),truth),implies(implies(implies(X_4,truth),truth),truth)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
implies(implies(implies(not(not(truth)),truth),truth),truth) = implies(implies(not(not(truth)),not(not(truth))),truth),
inference(subst,[],[refute_0_75:[bind(X_4,$fot(not(not(truth))))]]) ).
cnf(refute_0_77,plain,
( implies(implies(implies(not(not(truth)),truth),truth),truth) != implies(implies(not(not(truth)),not(not(truth))),truth)
| implies(implies(implies(not(not(truth)),truth),truth),truth) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(truth))),truth))]]) ).
cnf(refute_0_78,plain,
( implies(implies(implies(not(not(truth)),truth),truth),truth) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),implies(implies(not(not(truth)),not(not(truth))),truth)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(implies(not(not(truth)),not(not(truth))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),truth),truth),truth),truth) )],[refute_0_68,refute_0_78]) ).
cnf(refute_0_80,plain,
( implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(implies(not(not(truth)),not(not(truth))),truth) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_81,plain,
( implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),truth),truth) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(truth))),truth),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) )],[refute_0_45,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(truth,Z) = Z,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_84,plain,
implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),
introduced(tautology,[refl,[$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_85,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) ),[1,0],$fot(Z)]]) ).
cnf(refute_0_86,plain,
( implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))))]]) ).
cnf(refute_0_89,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))))),bind(Y0,$fot(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)))),bind(Z0,$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))))]]) ).
cnf(refute_0_90,plain,
( implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) ),[0],$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_93,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))) != truth
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(not(not(truth)),not(not(truth))),Z))),truth) )],[refute_0_82,refute_0_93]) ).
cnf(refute_0_95,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(implies(not(not(truth)),truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(not(not(truth))))]]) ).
cnf(refute_0_96,plain,
implies(implies(X_12,not(not(X_12))),implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(not(not(X_12)))),bind(Z,$fot(not(X_12)))]]) ).
cnf(refute_0_97,plain,
implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(X_12))),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_98,plain,
( implies(implies(X_12,not(not(X_12))),implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12)))) != truth
| implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12))) != truth
| implies(implies(X_12,not(not(X_12))),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,not(not(X_12))),implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_99,plain,
( implies(implies(X_12,not(not(X_12))),implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12)))) != truth
| implies(implies(X_12,not(not(X_12))),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12))),truth) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(implies(X_12,not(not(X_12))),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,not(not(X_12))),implies(implies(not(not(X_12)),not(X_12)),implies(X_12,not(X_12)))),truth) )],[refute_0_96,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(implies(truth,not(not(truth))),truth) = truth,
inference(subst,[],[refute_0_100:[bind(X_12,$fot(truth))]]) ).
cnf(refute_0_102,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_103,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(not(truth)),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) ),[0,0],$fot(not(not(truth)))]]) ).
cnf(refute_0_104,plain,
( implies(implies(truth,not(not(truth))),truth) != truth
| implies(not(not(truth)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
implies(not(not(truth)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),truth),truth) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(not(not(truth)),truth) != truth
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_107,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),truth),truth) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(truth,truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) )],[refute_0_95,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(implies(not(not(truth)),truth),truth) = implies(not(not(truth)),not(not(truth))),
inference(subst,[],[refute_0_32:[bind(X_2,$fot(not(not(truth))))]]) ).
cnf(refute_0_110,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) != implies(implies(not(not(truth)),truth),truth)
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(truth,not(not(truth))),not(not(truth))))),bind(Y0,$fot(implies(implies(not(not(truth)),truth),truth))),bind(Z0,$fot(implies(not(not(truth)),not(not(truth)))))]]) ).
cnf(refute_0_111,plain,
( implies(implies(not(not(truth)),truth),truth) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(implies(not(not(truth)),truth),truth)) )],[refute_0_95,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(implies(truth,not(not(truth))),not(not(truth))) = implies(not(not(truth)),not(not(truth))),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),truth),truth),implies(not(not(truth)),not(not(truth)))) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(not(not(truth)),not(not(truth)))
| implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(truth,truth)) ),[0],$fot(implies(not(not(truth)),not(not(truth))))]]) ).
cnf(refute_0_114,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(not(not(truth)),not(not(truth)))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(truth,truth) = truth,
inference(subst,[],[wajsberg_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_116,plain,
( implies(not(not(truth)),not(not(truth))) != implies(truth,truth)
| implies(truth,truth) != truth
| implies(not(not(truth)),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(not(truth)),not(not(truth))),truth) ),[0],$fot(implies(truth,truth))]]) ).
cnf(refute_0_117,plain,
( implies(not(not(truth)),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(implies(truth,not(not(truth))),not(not(truth))) != implies(truth,truth)
| implies(not(not(truth)),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),implies(truth,truth)) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(not(not(truth)),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,not(not(truth))),not(not(truth))),implies(truth,truth)) )],[refute_0_108,refute_0_118]) ).
cnf(refute_0_120,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = implies(implies(not(not(truth)),not(not(truth))),Z),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(truth))),Z))]]) ).
cnf(refute_0_121,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != implies(implies(not(not(truth)),not(not(truth))),Z)
| implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(implies(not(not(truth)),not(not(truth))),Z)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_122,plain,
( implies(not(not(truth)),not(not(truth))) != truth
| implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(implies(not(not(truth)),not(not(truth))),Z)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = implies(truth,Z),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(truth))),truth) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != implies(truth,Z)
| implies(truth,Z) != Z
| implies(implies(not(not(truth)),not(not(truth))),Z) = Z ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(not(not(truth)),not(not(truth))),Z))),bind(Y0,$fot(implies(truth,Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_125,plain,
( implies(truth,Z) != Z
| implies(implies(not(not(truth)),not(not(truth))),Z) = Z ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),implies(truth,Z)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(implies(not(not(truth)),not(not(truth))),Z) = Z,
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_83,refute_0_125]) ).
cnf(refute_0_127,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),
introduced(tautology,[refl,[$fot(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)))]]) ).
cnf(refute_0_128,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))
| implies(implies(not(not(truth)),not(not(truth))),Z) != Z
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_129,plain,
( implies(implies(not(not(truth)),not(not(truth))),Z) != Z
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z) ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) = implies(Z,Z),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(truth))),Z),Z) )],[refute_0_126,refute_0_129]) ).
cnf(refute_0_131,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != implies(Z,Z)
| implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != truth
| implies(Z,Z) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),truth) ),[0],$fot(implies(Z,Z))]]) ).
cnf(refute_0_132,plain,
( implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)) != truth
| implies(Z,Z) = truth ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),implies(Z,Z)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
implies(Z,Z) = truth,
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(not(not(truth)),not(not(truth))),Z)),truth) )],[refute_0_94,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(X_2,X_2) = truth,
inference(subst,[],[refute_0_133:[bind(Z,$fot(X_2))]]) ).
cnf(refute_0_135,plain,
implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_136,plain,
( implies(X_2,X_2) != truth
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(X_2,X_2),implies(implies(X_2,truth),truth))
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(truth,implies(implies(X_2,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(X_2,X_2),implies(implies(X_2,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_137,plain,
( implies(X_2,X_2) != truth
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(truth,implies(implies(X_2,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(X_2,X_2),implies(implies(X_2,truth),truth))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(truth,implies(implies(X_2,truth),truth)),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),truth) )],[refute_0_134,refute_0_137]) ).
cnf(refute_0_139,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(truth,implies(implies(X_2,truth),truth))
| implies(truth,implies(implies(X_2,truth),truth)) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(X_2,truth),truth) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)))),bind(Y0,$fot(implies(truth,implies(implies(X_2,truth),truth)))),bind(Z0,$fot(implies(implies(X_2,truth),truth)))]]) ).
cnf(refute_0_140,plain,
( implies(truth,implies(implies(X_2,truth),truth)) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(X_2,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(truth,implies(implies(X_2,truth),truth))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_2,truth),truth)),implies(implies(X_2,truth),truth)) )],[refute_0_44,refute_0_140]) ).
cnf(refute_0_142,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(X_2,truth),truth)
| implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(X_2,truth),truth) = implies(implies(implies(X_2,X_2),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,X_2),truth),truth)) ),[0],$fot(implies(implies(X_2,truth),truth))]]) ).
cnf(refute_0_143,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(X_2,truth),truth) = implies(implies(implies(X_2,X_2),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(X_2,truth),truth)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
implies(implies(X_2,X_2),truth) = implies(implies(X_2,X_2),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_2,X_2),truth))]]) ).
cnf(refute_0_145,plain,
( implies(X_2,X_2) != truth
| implies(implies(X_2,X_2),truth) != implies(implies(X_2,X_2),truth)
| implies(implies(X_2,X_2),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_2,X_2),truth),implies(implies(X_2,X_2),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_146,plain,
( implies(X_2,X_2) != truth
| implies(implies(X_2,X_2),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),truth),implies(implies(X_2,X_2),truth)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(implies(X_2,X_2),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(implies(X_2,X_2),truth) )],[refute_0_134,refute_0_146]) ).
cnf(refute_0_148,plain,
( implies(implies(X_2,X_2),truth) != implies(truth,truth)
| implies(truth,truth) != truth
| implies(implies(X_2,X_2),truth) = truth ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(X_2,X_2),truth))),bind(Y0,$fot(implies(truth,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_149,plain,
( implies(truth,truth) != truth
| implies(implies(X_2,X_2),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),truth),implies(truth,truth)) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(implies(X_2,X_2),truth) = truth,
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_115,refute_0_149]) ).
cnf(refute_0_151,plain,
implies(implies(implies(X_2,X_2),truth),truth) = implies(implies(implies(X_2,X_2),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_2,X_2),truth),truth))]]) ).
cnf(refute_0_152,plain,
( implies(implies(X_2,X_2),truth) != truth
| implies(implies(implies(X_2,X_2),truth),truth) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(implies(X_2,X_2),truth),truth) = implies(truth,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_2,X_2),truth),truth),implies(implies(implies(X_2,X_2),truth),truth)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_153,plain,
( implies(implies(X_2,X_2),truth) != truth
| implies(implies(implies(X_2,X_2),truth),truth) = implies(truth,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,X_2),truth),truth),implies(implies(implies(X_2,X_2),truth),truth)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
implies(implies(implies(X_2,X_2),truth),truth) = implies(truth,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),truth),truth) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
( implies(implies(implies(X_2,X_2),truth),truth) != implies(truth,truth)
| implies(truth,truth) != truth
| implies(implies(implies(X_2,X_2),truth),truth) = truth ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(implies(X_2,X_2),truth),truth))),bind(Y0,$fot(implies(truth,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_156,plain,
( implies(truth,truth) != truth
| implies(implies(implies(X_2,X_2),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,X_2),truth),truth),implies(truth,truth)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
implies(implies(implies(X_2,X_2),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(truth,truth),truth) )],[refute_0_115,refute_0_156]) ).
cnf(refute_0_158,plain,
( implies(implies(X_2,truth),truth) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(implies(X_2,X_2),truth),truth) != truth
| implies(implies(X_2,truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(X_2,truth),truth),truth) ),[0],$fot(implies(implies(implies(X_2,X_2),truth),truth))]]) ).
cnf(refute_0_159,plain,
( implies(implies(X_2,truth),truth) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(X_2,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_2,X_2),truth),truth),truth) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)) != implies(implies(implies(X_2,X_2),truth),truth)
| implies(implies(X_2,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_2,truth),truth),implies(implies(implies(X_2,X_2),truth),truth)) )],[refute_0_143,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(implies(X_2,truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_2,X_2),implies(implies(X_2,truth),truth)),implies(implies(implies(X_2,X_2),truth),truth)) )],[refute_0_43,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(implies(X_13,truth),truth) = truth,
inference(subst,[],[refute_0_161:[bind(X_2,$fot(X_13))]]) ).
cnf(refute_0_163,plain,
implies(X_6,X_6) = truth,
inference(subst,[],[refute_0_133:[bind(Z,$fot(X_6))]]) ).
cnf(refute_0_164,plain,
implies(X_13,implies(X_6,X_6)) = implies(X_13,implies(X_6,X_6)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(X_6,X_6)))]]) ).
cnf(refute_0_165,plain,
( implies(X_13,implies(X_6,X_6)) != implies(X_13,implies(X_6,X_6))
| implies(X_6,X_6) != truth
| implies(X_13,implies(X_6,X_6)) = implies(X_13,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(X_6,X_6)),implies(X_13,implies(X_6,X_6))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_166,plain,
( implies(X_6,X_6) != truth
| implies(X_13,implies(X_6,X_6)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(X_6,X_6)),implies(X_13,implies(X_6,X_6))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
implies(X_13,implies(X_6,X_6)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(X_6,X_6),truth) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
implies(implies(X_13,implies(X_6,X_6)),truth) = implies(implies(X_13,implies(X_6,X_6)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_13,implies(X_6,X_6)),truth))]]) ).
cnf(refute_0_169,plain,
( implies(X_13,implies(X_6,X_6)) != implies(X_13,truth)
| implies(implies(X_13,implies(X_6,X_6)),truth) != implies(implies(X_13,implies(X_6,X_6)),truth)
| implies(implies(X_13,implies(X_6,X_6)),truth) = implies(implies(X_13,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(X_6,X_6)),truth),implies(implies(X_13,implies(X_6,X_6)),truth)) ),[1,0],$fot(implies(X_13,truth))]]) ).
cnf(refute_0_170,plain,
( implies(X_13,implies(X_6,X_6)) != implies(X_13,truth)
| implies(implies(X_13,implies(X_6,X_6)),truth) = implies(implies(X_13,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_6,X_6)),truth),implies(implies(X_13,implies(X_6,X_6)),truth)) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(X_13,implies(X_6,X_6)),truth) = implies(implies(X_13,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_13,implies(X_6,X_6)),implies(X_13,truth)) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
( implies(implies(X_13,implies(X_6,X_6)),truth) != implies(implies(X_13,truth),truth)
| implies(implies(X_13,truth),truth) != truth
| implies(implies(X_13,implies(X_6,X_6)),truth) = truth ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(X_13,implies(X_6,X_6)),truth))),bind(Y0,$fot(implies(implies(X_13,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_173,plain,
( implies(implies(X_13,truth),truth) != truth
| implies(implies(X_13,implies(X_6,X_6)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_6,X_6)),truth),implies(implies(X_13,truth),truth)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(implies(X_13,implies(X_6,X_6)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,truth),truth),truth) )],[refute_0_162,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)))]]) ).
cnf(refute_0_176,plain,
( implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth))
| implies(implies(X_13,implies(X_6,X_6)),truth) != truth
| implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)),implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_177,plain,
( implies(implies(X_13,implies(X_6,X_6)),truth) != truth
| implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)),implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_6,X_6)),truth),truth) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(truth,X_13) = X_13,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_180,plain,
implies(implies(not(X_6),truth),truth) = truth,
inference(subst,[],[refute_0_161:[bind(X_2,$fot(not(X_6)))]]) ).
cnf(refute_0_181,plain,
implies(implies(implies(not(X_6),truth),truth),X_13) = implies(implies(implies(not(X_6),truth),truth),X_13),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_6),truth),truth),X_13))]]) ).
cnf(refute_0_182,plain,
( implies(implies(implies(not(X_6),truth),truth),X_13) != implies(implies(implies(not(X_6),truth),truth),X_13)
| implies(implies(not(X_6),truth),truth) != truth
| implies(implies(implies(not(X_6),truth),truth),X_13) = implies(truth,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(implies(not(X_6),truth),truth),X_13)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_183,plain,
( implies(implies(not(X_6),truth),truth) != truth
| implies(implies(implies(not(X_6),truth),truth),X_13) = implies(truth,X_13) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(implies(not(X_6),truth),truth),X_13)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
implies(implies(implies(not(X_6),truth),truth),X_13) = implies(truth,X_13),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),truth),truth),truth) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
( implies(implies(implies(not(X_6),truth),truth),X_13) != implies(truth,X_13)
| implies(truth,X_13) != X_13
| implies(implies(implies(not(X_6),truth),truth),X_13) = X_13 ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(implies(not(X_6),truth),truth),X_13))),bind(Y0,$fot(implies(truth,X_13))),bind(Z0,$fot(X_13))]]) ).
cnf(refute_0_186,plain,
( implies(truth,X_13) != X_13
| implies(implies(implies(not(X_6),truth),truth),X_13) = X_13 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_6),truth),truth),X_13),implies(truth,X_13)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(implies(implies(not(X_6),truth),truth),X_13) = X_13,
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_179,refute_0_186]) ).
cnf(refute_0_188,plain,
implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)))]]) ).
cnf(refute_0_189,plain,
( implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth))
| implies(implies(implies(not(X_6),truth),truth),X_13) != X_13
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_190,plain,
( implies(implies(implies(not(X_6),truth),truth),X_13) != X_13
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth))) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_6),truth),truth),X_13),X_13) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
( implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth))
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)))),bind(Y0,$fot(implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)))),bind(Z0,$fot(implies(X_13,truth)))]]) ).
cnf(refute_0_193,plain,
( implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_6,X_6)),truth)),implies(X_13,truth)) )],[refute_0_178,refute_0_193]) ).
cnf(refute_0_195,plain,
( implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) != truth
| implies(X_13,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),truth) ),[0],$fot(implies(X_13,truth))]]) ).
cnf(refute_0_196,plain,
( implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)) != truth
| implies(X_13,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),implies(X_13,truth)) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(X_13,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_6),truth),truth),X_13),implies(implies(X_13,implies(X_6,X_6)),truth)),truth) )],[refute_0_19,refute_0_196]) ).
cnf(refute_0_198,plain,
implies(X_12,truth) = truth,
inference(subst,[],[refute_0_197:[bind(X_13,$fot(X_12))]]) ).
cnf(refute_0_199,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),
introduced(tautology,[refl,[$fot(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_200,plain,
( implies(X_12,truth) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_201,plain,
( implies(X_12,truth) != truth
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14)))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(implies(X_12,truth),truth) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(truth,implies(X_14,implies(X_12,X_14)))
| implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))))),bind(Y0,$fot(implies(truth,implies(X_14,implies(X_12,X_14))))),bind(Z0,$fot(implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_204,plain,
( implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(truth,implies(X_14,implies(X_12,X_14)))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_14,implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_5,refute_0_204]) ).
cnf(refute_0_206,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),truth) ),[0],$fot(implies(X_14,implies(X_12,X_14)))]]) ).
cnf(refute_0_207,plain,
( implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
implies(X_14,implies(X_12,X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,truth),implies(X_14,implies(X_12,X_14))),truth) )],[refute_0_4,refute_0_207]) ).
cnf(refute_0_209,plain,
implies(x,implies(y,x)) = truth,
inference(subst,[],[refute_0_208:[bind(X_12,$fot(y)),bind(X_14,$fot(x))]]) ).
cnf(refute_0_210,plain,
( implies(x,implies(y,x)) != truth
| truth != truth
| implies(x,implies(y,x)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(x,implies(y,x)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_211,plain,
( truth != truth
| implies(x,implies(y,x)) = truth ),
inference(resolve,[$cnf( $equal(implies(x,implies(y,x)),truth) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(x,implies(y,x)),truth) )],[refute_0_211,prove_wajsberg_lemma]) ).
cnf(refute_0_213,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_214,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_213,refute_0_212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL135-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 01:02:40 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41
% 0.19/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------