TSTP Solution File: LCL112-2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL112-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:49:39 EDT 2022
% Result : Unsatisfiable 0.47s 0.63s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 75
% Number of leaves : 102
% Syntax : Number of clauses : 383 ( 198 unt; 0 nHn; 190 RR)
% Number of literals : 657 ( 656 equ; 276 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 555 ( 15 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_29,negated_conjecture,
implies(x,not(not(x))) != truth ).
cnf(refute_0_0,plain,
implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(not(Y))))]]) ).
cnf(refute_0_1,plain,
implies(implies(X_12,implies(not(X_14),not(truth))),implies(implies(implies(not(X_14),not(truth)),X_14),implies(X_12,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(implies(not(X_14),not(truth)))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_2,plain,
implies(implies(not(X_6),not(truth)),implies(truth,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_3,plain,
implies(truth,X_6) = X_6,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_4,plain,
( implies(implies(not(X_6),not(truth)),implies(truth,X_6)) != truth
| implies(truth,X_6) != X_6
| implies(implies(not(X_6),not(truth)),X_6) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(truth)),implies(truth,X_6)),truth) ),[0,1],$fot(X_6)]]) ).
cnf(refute_0_5,plain,
( implies(implies(not(X_6),not(truth)),implies(truth,X_6)) != truth
| implies(implies(not(X_6),not(truth)),X_6) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_6),X_6) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
implies(implies(not(X_6),not(truth)),X_6) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(truth)),implies(truth,X_6)),truth) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(implies(not(X_14),not(truth)),X_14) = truth,
inference(subst,[],[refute_0_6:[bind(X_6,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
( implies(implies(X_12,implies(not(X_14),not(truth))),implies(implies(implies(not(X_14),not(truth)),X_14),implies(X_12,X_14))) != truth
| implies(implies(not(X_14),not(truth)),X_14) != truth
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(implies(implies(not(X_14),not(truth)),X_14),implies(X_12,X_14))),truth) ),[0,1,0],$fot(truth)]]) ).
cnf(refute_0_9,plain,
( implies(implies(X_12,implies(not(X_14),not(truth))),implies(implies(implies(not(X_14),not(truth)),X_14),implies(X_12,X_14))) != truth
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_14),not(truth)),X_14),truth) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(implies(implies(not(X_14),not(truth)),X_14),implies(X_12,X_14))),truth) )],[refute_0_1,refute_0_9]) ).
cnf(refute_0_11,plain,
implies(truth,implies(X_12,X_14)) = implies(X_12,X_14),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_12,X_14)))]]) ).
cnf(refute_0_12,plain,
implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),
introduced(tautology,[refl,[$fot(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))))]]) ).
cnf(refute_0_13,plain,
( implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) != implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14)))
| implies(truth,implies(X_12,X_14)) != implies(X_12,X_14)
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14)))) ),[1,1],$fot(implies(X_12,X_14))]]) ).
cnf(refute_0_14,plain,
( implies(truth,implies(X_12,X_14)) != implies(X_12,X_14)
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) = implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_12,X_14)),implies(X_12,X_14)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) != implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14))
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) != truth
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),truth) ),[0],$fot(implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)))]]) ).
cnf(refute_0_17,plain,
( implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))) != truth
| implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
implies(implies(X_12,implies(not(X_14),not(truth))),implies(X_12,X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(not(X_14),not(truth))),implies(truth,implies(X_12,X_14))),truth) )],[refute_0_10,refute_0_17]) ).
cnf(refute_0_19,plain,
implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth,
inference(subst,[],[refute_0_18:[bind(X_12,$fot(implies(not(not(truth)),not(not(X_25))))),bind(X_14,$fot(X_25))]]) ).
cnf(refute_0_20,plain,
implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(not(truth))),bind(Y,$fot(not(X_25)))]]) ).
cnf(refute_0_21,plain,
( implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_22,plain,
( implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),truth) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(not(not(truth)),not(not(X_25))),implies(not(X_25),not(truth))),implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) = implies(implies(not(not(truth)),not(not(X_25))),X_25),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25)))]]) ).
cnf(refute_0_25,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != implies(implies(not(not(truth)),not(not(X_25))),X_25)
| implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) ),[0],$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25))]]) ).
cnf(refute_0_26,plain,
( implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)) != truth
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),implies(implies(not(not(truth)),not(not(X_25))),X_25)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(not(not(truth)),not(not(X_25))),X_25)),truth) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(truth,not(not(X_25))) = not(not(X_25)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(X_25))))]]) ).
cnf(refute_0_29,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) = truth,
inference(subst,[],[refute_0_18:[bind(X_12,$fot(not(truth))),bind(X_14,$fot(not(not(truth))))]]) ).
cnf(refute_0_30,plain,
implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(implies(implies(X_37,X_36),X_36),X_37))),bind(Y,$fot(implies(X_36,X_37)))]]) ).
cnf(refute_0_31,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_32,plain,
implies(truth,X_14) = X_14,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_33,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) != truth
| implies(truth,X_14) != X_14
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))),truth) ),[0,1,1],$fot(X_14)]]) ).
cnf(refute_0_34,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))) != truth
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),implies(truth,X_14))),truth) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(truth,X_13) = X_13,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_37,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)))]]) ).
cnf(refute_0_38,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))
| implies(truth,X_13) != X_13
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_39,plain,
( implies(truth,X_13) != X_13
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) = implies(X_13,implies(implies(X_13,X_14),X_14)),
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != implies(X_13,implies(implies(X_13,X_14),X_14))
| implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != truth
| implies(X_13,implies(implies(X_13,X_14),X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),truth) ),[0],$fot(implies(X_13,implies(implies(X_13,X_14),X_14)))]]) ).
cnf(refute_0_42,plain,
( implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)) != truth
| implies(X_13,implies(implies(X_13,X_14),X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),implies(X_13,implies(implies(X_13,X_14),X_14))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
implies(X_13,implies(implies(X_13,X_14),X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_13),implies(implies(X_13,X_14),X_14)),truth) )],[refute_0_35,refute_0_42]) ).
cnf(refute_0_44,plain,
implies(implies(Y,X_27),implies(implies(implies(Y,X_27),X_27),X_27)) = truth,
inference(subst,[],[refute_0_43:[bind(X_13,$fot(implies(Y,X_27))),bind(X_14,$fot(X_27))]]) ).
cnf(refute_0_45,plain,
implies(implies(X_27,Y),Y) = implies(implies(Y,X_27),X_27),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_46,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_47,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_48,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( implies(implies(X_27,Y),Y) != implies(implies(Y,X_27),X_27)
| implies(implies(Y,X_27),X_27) = implies(implies(X_27,Y),Y) ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(implies(implies(X_27,Y),Y))),bind(Y0,$fot(implies(implies(Y,X_27),X_27)))]]) ).
cnf(refute_0_50,plain,
implies(implies(Y,X_27),X_27) = implies(implies(X_27,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X_27,Y),Y),implies(implies(Y,X_27),X_27)) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( implies(implies(Y,X_27),X_27) != implies(implies(X_27,Y),Y)
| implies(implies(Y,X_27),implies(implies(implies(Y,X_27),X_27),X_27)) != truth
| implies(implies(Y,X_27),implies(implies(implies(X_27,Y),Y),X_27)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(Y,X_27),implies(implies(implies(Y,X_27),X_27),X_27)),truth) ),[0,1,0],$fot(implies(implies(X_27,Y),Y))]]) ).
cnf(refute_0_52,plain,
( implies(implies(Y,X_27),implies(implies(implies(Y,X_27),X_27),X_27)) != truth
| implies(implies(Y,X_27),implies(implies(implies(X_27,Y),Y),X_27)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,X_27),X_27),implies(implies(X_27,Y),Y)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(implies(Y,X_27),implies(implies(implies(X_27,Y),Y),X_27)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(Y,X_27),implies(implies(implies(Y,X_27),X_27),X_27)),truth) )],[refute_0_44,refute_0_52]) ).
cnf(refute_0_54,plain,
implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)) = truth,
inference(subst,[],[refute_0_53:[bind(Y,$fot(X_36)),bind(X_27,$fot(X_37))]]) ).
cnf(refute_0_55,plain,
( implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)) != truth
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_56,plain,
( implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),truth) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(implies(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37))) )],[refute_0_30,refute_0_56]) ).
cnf(refute_0_58,plain,
implies(truth,implies(X_36,X_37)) = implies(X_36,X_37),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_36,X_37)))]]) ).
cnf(refute_0_59,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X_1,X),X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(implies(X_1,X)))]]) ).
cnf(refute_0_60,plain,
implies(implies(X_1,X),X) = implies(implies(X,X_1),X_1),
inference(subst,[],[wajsberg_3:[bind(X,$fot(X_1)),bind(Y,$fot(X))]]) ).
cnf(refute_0_61,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X_1,X),X) != implies(implies(X,X_1),X_1)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) ),[1,0],$fot(implies(implies(X,X_1),X_1))]]) ).
cnf(refute_0_62,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X_1,X),X),implies(implies(X,X_1),X_1)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(implies(X,implies(X_1,X)),implies(X_1,X)) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X_1,X),X),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) ),[0],$fot(implies(implies(implies(X_1,X),X),X))]]) ).
cnf(refute_0_65,plain,
( implies(implies(X,implies(X_1,X)),implies(X_1,X)) != implies(implies(implies(X,X_1),X_1),X)
| implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X_1,X),X),X)) )],[refute_0_59,refute_0_64]) ).
cnf(refute_0_66,plain,
implies(implies(implies(X_1,X),X),X) = implies(implies(implies(X,X_1),X_1),X),
inference(resolve,[$cnf( $equal(implies(implies(X,implies(X_1,X)),implies(X_1,X)),implies(implies(implies(X,X_1),X_1),X)) )],[refute_0_63,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),
inference(subst,[],[refute_0_66:[bind(X,$fot(implies(X_21,X_1)))]]) ).
cnf(refute_0_68,plain,
implies(implies(implies(X_21,X_1),X_1),X_1) = implies(implies(implies(X_1,X_21),X_21),X_1),
inference(subst,[],[refute_0_66:[bind(X,$fot(X_1)),bind(X_1,$fot(X_21))]]) ).
cnf(refute_0_69,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(X_21,X_1),X_1),X_1) != implies(implies(implies(X_1,X_21),X_21),X_1)
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) ),[1,0],$fot(implies(implies(implies(X_1,X_21),X_21),X_1))]]) ).
cnf(refute_0_70,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,X_1),X_1),X_1),implies(implies(implies(X_1,X_21),X_21),X_1)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) ),[0],$fot(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)))]]) ).
cnf(refute_0_73,plain,
( implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1))) )],[refute_0_67,refute_0_72]) ).
cnf(refute_0_74,plain,
implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_1,implies(X_21,X_1)),implies(X_21,X_1)),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_71,refute_0_73]) ).
cnf(refute_0_75,plain,
implies(implies(X,implies(implies(X,X_27),X_27)),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(implies(implies(X,X_27),X_27)))]]) ).
cnf(refute_0_76,plain,
implies(X,implies(implies(X,X_27),X_27)) = truth,
inference(subst,[],[refute_0_43:[bind(X_13,$fot(X)),bind(X_14,$fot(X_27))]]) ).
cnf(refute_0_77,plain,
( implies(X,implies(implies(X,X_27),X_27)) != truth
| implies(implies(X,implies(implies(X,X_27),X_27)),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,implies(implies(X,X_27),X_27)),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_78,plain,
( implies(implies(X,implies(implies(X,X_27),X_27)),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) != truth
| implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(X,implies(implies(X,X_27),X_27)),truth) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,implies(implies(X,X_27),X_27)),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))),truth) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) = implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))))]]) ).
cnf(refute_0_81,plain,
( implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) != implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))
| implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))),truth) ),[0],$fot(implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z)))]]) ).
cnf(refute_0_82,plain,
( implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) != truth
| implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))),implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(implies(X,X_27),X_27),Z),implies(X,Z))),truth) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) = truth,
inference(subst,[],[refute_0_83:[bind(X,$fot(X_21)),bind(Z,$fot(X_1)),bind(X_27,$fot(X_1))]]) ).
cnf(refute_0_85,plain,
( implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != truth
| truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) ),[0],$fot(truth)]]) ).
cnf(refute_0_86,plain,
( implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)) != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),truth) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
truth = implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_21,X_1),X_1),X_1),implies(X_21,X_1)),implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_74,refute_0_86]) ).
cnf(refute_0_88,plain,
( truth != implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))
| implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) = truth ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))))]]) ).
cnf(refute_0_89,plain,
implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(implies(implies(X_1,X_21),X_21),X_1),implies(X_21,X_1))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)) = truth,
inference(subst,[],[refute_0_89:[bind(X_1,$fot(X_37)),bind(X_21,$fot(X_36))]]) ).
cnf(refute_0_91,plain,
implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)))]]) ).
cnf(refute_0_92,plain,
( implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)) != truth
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37))
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(X_36,X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_93,plain,
( implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)) != truth
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(X_36,X_37)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(truth,implies(X_36,X_37)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),truth) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_96,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_48,refute_0_95]) ).
cnf(refute_0_97,plain,
( implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(truth,implies(X_36,X_37))
| implies(truth,implies(X_36,X_37)) != implies(X_36,X_37)
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(X_36,X_37) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)))),bind(Y0,$fot(implies(truth,implies(X_36,X_37)))),bind(Z0,$fot(implies(X_36,X_37)))]]) ).
cnf(refute_0_98,plain,
( implies(truth,implies(X_36,X_37)) != implies(X_36,X_37)
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(X_36,X_37) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(truth,implies(X_36,X_37))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) = implies(X_36,X_37),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_36,X_37)),implies(X_36,X_37)) )],[refute_0_58,refute_0_98]) ).
cnf(refute_0_100,plain,
( implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(X_36,X_37)
| implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(X_36,X_37) = implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))) ),[0],$fot(implies(X_36,X_37))]]) ).
cnf(refute_0_101,plain,
( implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(X_36,X_37) = implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(X_36,X_37)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) = implies(implies(implies(X_37,X_36),X_36),X_37),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(implies(X_37,X_36),X_36),X_37)))]]) ).
cnf(refute_0_103,plain,
( implies(X_36,X_37) != implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)) != implies(implies(implies(X_37,X_36),X_36),X_37)
| implies(X_36,X_37) = implies(implies(implies(X_37,X_36),X_36),X_37) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_36,X_37),implies(implies(implies(X_37,X_36),X_36),X_37)) ),[0],$fot(implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)))]]) ).
cnf(refute_0_104,plain,
( implies(X_36,X_37) != implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(X_36,X_37) = implies(implies(implies(X_37,X_36),X_36),X_37) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37)),implies(implies(implies(X_37,X_36),X_36),X_37)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)) != implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))
| implies(X_36,X_37) = implies(implies(implies(X_37,X_36),X_36),X_37) ),
inference(resolve,[$cnf( $equal(implies(X_36,X_37),implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
implies(X_36,X_37) = implies(implies(implies(X_37,X_36),X_36),X_37),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(X_37,X_36),X_36),X_37),implies(X_36,X_37)),implies(X_36,X_37)),implies(truth,implies(implies(implies(X_37,X_36),X_36),X_37))) )],[refute_0_57,refute_0_105]) ).
cnf(refute_0_107,plain,
implies(not(truth),not(not(truth))) = implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth))),
inference(subst,[],[refute_0_106:[bind(X_36,$fot(not(truth))),bind(X_37,$fot(not(not(truth))))]]) ).
cnf(refute_0_108,plain,
implies(implies(not(not(truth)),not(truth)),not(truth)) = truth,
inference(subst,[],[refute_0_6:[bind(X_6,$fot(not(truth)))]]) ).
cnf(refute_0_109,plain,
( implies(implies(not(not(truth)),not(truth)),not(truth)) != truth
| implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_110,plain,
( implies(not(truth),not(not(truth))) != implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))
| implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(truth)),not(truth)),truth) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
implies(not(truth),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(implies(implies(not(not(truth)),not(truth)),not(truth)),not(not(truth)))) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
implies(truth,not(not(truth))) = not(not(truth)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(not(truth))))]]) ).
cnf(refute_0_113,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(not(truth),not(not(truth))),not(not(truth))) ),[0],$fot(implies(truth,not(not(truth))))]]) ).
cnf(refute_0_114,plain,
( implies(not(truth),not(not(truth))) != implies(truth,not(not(truth)))
| implies(not(truth),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
implies(not(truth),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_111,refute_0_114]) ).
cnf(refute_0_116,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(not(truth),not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),truth) ),[0,1],$fot(not(not(truth)))]]) ).
cnf(refute_0_117,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(truth),not(not(truth))),not(not(truth))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),implies(not(truth),not(not(truth)))),truth) )],[refute_0_29,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(implies(X_14,truth),truth),X_14),implies(X_12,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(X_12)),bind(Y,$fot(implies(implies(X_14,truth),truth))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_120,plain,
implies(implies(X,X),X) = implies(implies(X,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(X))]]) ).
cnf(refute_0_121,plain,
implies(implies(truth,X_2),X_2) = implies(implies(X_2,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_122,plain,
implies(truth,X_2) = X_2,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_123,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_124,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( $equal(implies(truth,X_2),X_2) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(X_2,X_2) = implies(implies(X_2,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_2),X_2),implies(implies(X_2,truth),truth)) )],[refute_0_121,refute_0_124]) ).
cnf(refute_0_126,plain,
implies(X,X) = implies(implies(X,truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_127,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_128,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( $equal(implies(X,X),implies(implies(X,truth),truth)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(X,X),X) = implies(implies(implies(X,truth),truth),X),
inference(resolve,[$cnf( $equal(implies(implies(X,X),X),implies(implies(X,X),X)) )],[refute_0_120,refute_0_128]) ).
cnf(refute_0_130,plain,
implies(implies(X_14,X_14),X_14) = implies(implies(implies(X_14,truth),truth),X_14),
inference(subst,[],[refute_0_129:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_131,plain,
( implies(implies(X_14,X_14),X_14) != implies(implies(implies(X_14,truth),truth),X_14)
| implies(implies(implies(X_14,truth),truth),X_14) = implies(implies(X_14,X_14),X_14) ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(implies(implies(X_14,X_14),X_14))),bind(Y0,$fot(implies(implies(implies(X_14,truth),truth),X_14)))]]) ).
cnf(refute_0_132,plain,
implies(implies(implies(X_14,truth),truth),X_14) = implies(implies(X_14,X_14),X_14),
inference(resolve,[$cnf( $equal(implies(implies(X_14,X_14),X_14),implies(implies(implies(X_14,truth),truth),X_14)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(implies(X_14,truth),truth),X_14),implies(X_12,X_14))) != truth
| implies(implies(implies(X_14,truth),truth),X_14) != implies(implies(X_14,X_14),X_14)
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(implies(X_14,truth),truth),X_14),implies(X_12,X_14))),truth) ),[0,1,0],$fot(implies(implies(X_14,X_14),X_14))]]) ).
cnf(refute_0_134,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(implies(X_14,truth),truth),X_14),implies(X_12,X_14))) != truth
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_14,truth),truth),X_14),implies(implies(X_14,X_14),X_14)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(implies(X_14,truth),truth),X_14),implies(X_12,X_14))),truth) )],[refute_0_119,refute_0_134]) ).
cnf(refute_0_136,plain,
implies(truth,implies(X_14,implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_14,implies(X_12,X_14))))]]) ).
cnf(refute_0_137,plain,
implies(implies(implies(implies(X_22,X_22),truth),truth),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(X_22,X_22),truth))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_138,plain,
implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(implies(X_21,truth),truth),truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(implies(implies(X_21,truth),truth)))]]) ).
cnf(refute_0_139,plain,
implies(implies(implies(X_21,truth),truth),truth) = implies(implies(implies(truth,X_21),X_21),truth),
inference(subst,[],[refute_0_66:[bind(X,$fot(truth)),bind(X_1,$fot(X_21))]]) ).
cnf(refute_0_140,plain,
( implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(implies(X_21,truth),truth),truth),truth)
| implies(implies(implies(X_21,truth),truth),truth) != implies(implies(implies(truth,X_21),X_21),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(implies(truth,X_21),X_21),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(implies(X_21,truth),truth),truth),truth)) ),[1,0],$fot(implies(implies(implies(truth,X_21),X_21),truth))]]) ).
cnf(refute_0_141,plain,
( implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(implies(X_21,truth),truth),truth),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(implies(truth,X_21),X_21),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),truth),implies(implies(implies(truth,X_21),X_21),truth)) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(implies(truth,X_21),X_21),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(implies(X_21,truth),truth),truth),truth)) )],[refute_0_138,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(implies(X_3,truth),truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(implies(X_3,truth)))]]) ).
cnf(refute_0_144,plain,
implies(X_3,X_3) = implies(implies(X_3,truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(X_3))]]) ).
cnf(refute_0_145,plain,
( implies(X_3,X_3) != implies(implies(X_3,truth),truth)
| implies(implies(X_3,truth),truth) = implies(X_3,X_3) ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(implies(X_3,X_3))),bind(Y0,$fot(implies(implies(X_3,truth),truth)))]]) ).
cnf(refute_0_146,plain,
implies(implies(X_3,truth),truth) = implies(X_3,X_3),
inference(resolve,[$cnf( $equal(implies(X_3,X_3),implies(implies(X_3,truth),truth)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( implies(implies(X_3,truth),implies(X_3,truth)) != implies(implies(implies(X_3,truth),truth),truth)
| implies(implies(X_3,truth),truth) != implies(X_3,X_3)
| implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(X_3,X_3),truth) ),
introduced(tautology,[equality,[$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_148,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( $equal(implies(implies(X_3,truth),truth),implies(X_3,X_3)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
implies(implies(X_3,truth),implies(X_3,truth)) = implies(implies(X_3,X_3),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_3,truth),implies(X_3,truth)),implies(implies(implies(X_3,truth),truth),truth)) )],[refute_0_143,refute_0_148]) ).
cnf(refute_0_150,plain,
implies(implies(X_21,truth),implies(X_21,truth)) = implies(implies(X_21,X_21),truth),
inference(subst,[],[refute_0_149:[bind(X_3,$fot(X_21))]]) ).
cnf(refute_0_151,plain,
implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) = implies(implies(implies(X_21,truth),implies(X_21,truth)),truth),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_21,truth),implies(X_21,truth)),truth))]]) ).
cnf(refute_0_152,plain,
( implies(implies(X_21,truth),implies(X_21,truth)) != implies(implies(X_21,X_21),truth)
| implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) != implies(implies(implies(X_21,truth),implies(X_21,truth)),truth)
| implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) = implies(implies(implies(X_21,X_21),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_21,truth),implies(X_21,truth)),truth),implies(implies(implies(X_21,truth),implies(X_21,truth)),truth)) ),[1,0],$fot(implies(implies(X_21,X_21),truth))]]) ).
cnf(refute_0_153,plain,
( implies(implies(X_21,truth),implies(X_21,truth)) != implies(implies(X_21,X_21),truth)
| implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) = implies(implies(implies(X_21,X_21),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),implies(X_21,truth)),truth),implies(implies(implies(X_21,truth),implies(X_21,truth)),truth)) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) = implies(implies(implies(X_21,X_21),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(X_21,truth),implies(X_21,truth)),implies(implies(X_21,X_21),truth)) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(X_21,truth),implies(X_21,truth)),truth),
inference(subst,[],[refute_0_149:[bind(X_3,$fot(implies(X_21,truth)))]]) ).
cnf(refute_0_156,plain,
( implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) != implies(implies(implies(X_21,X_21),truth),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(X_21,truth),implies(X_21,truth)),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(X_21,X_21),truth),truth) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)))),bind(Y0,$fot(implies(implies(implies(X_21,truth),implies(X_21,truth)),truth))),bind(Z0,$fot(implies(implies(implies(X_21,X_21),truth),truth)))]]) ).
cnf(refute_0_157,plain,
( implies(implies(implies(X_21,truth),implies(X_21,truth)),truth) != implies(implies(implies(X_21,X_21),truth),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(X_21,X_21),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(X_21,truth),implies(X_21,truth)),truth)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) = implies(implies(implies(X_21,X_21),truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),implies(X_21,truth)),truth),implies(implies(implies(X_21,X_21),truth),truth)) )],[refute_0_154,refute_0_157]) ).
cnf(refute_0_159,plain,
( implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(X_21,X_21),truth),truth)
| implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(implies(truth,X_21),X_21),truth),truth)
| implies(implies(implies(X_21,X_21),truth),truth) = implies(implies(implies(implies(truth,X_21),X_21),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(implies(truth,X_21),X_21),truth),truth)) ),[0],$fot(implies(implies(implies(X_21,X_21),truth),truth))]]) ).
cnf(refute_0_160,plain,
( implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(implies(truth,X_21),X_21),truth),truth)
| implies(implies(implies(X_21,X_21),truth),truth) = implies(implies(implies(implies(truth,X_21),X_21),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(X_21,X_21),truth),truth)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(implies(implies(implies(Y,X_14),X_14),Y),implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(Y,X_14),X_14))),bind(Z,$fot(implies(Y,X_14)))]]) ).
cnf(refute_0_162,plain,
implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,X_14))),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_163,plain,
( implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14))) != truth
| implies(implies(implies(implies(Y,X_14),X_14),Y),implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14)))) != truth
| implies(implies(implies(implies(Y,X_14),X_14),Y),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(Y,X_14),X_14),Y),implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14)))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_164,plain,
( implies(implies(implies(implies(Y,X_14),X_14),Y),implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14)))) != truth
| implies(implies(implies(implies(Y,X_14),X_14),Y),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14))),truth) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(implies(implies(Y,X_14),X_14),Y),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(Y,X_14),X_14),Y),implies(implies(Y,implies(Y,X_14)),implies(implies(implies(Y,X_14),X_14),implies(Y,X_14)))),truth) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(implies(implies(implies(truth,X_21),X_21),truth),truth) = truth,
inference(subst,[],[refute_0_165:[bind(Y,$fot(truth)),bind(X_14,$fot(X_21))]]) ).
cnf(refute_0_167,plain,
( implies(implies(implies(X_21,X_21),truth),truth) != implies(implies(implies(implies(truth,X_21),X_21),truth),truth)
| implies(implies(implies(implies(truth,X_21),X_21),truth),truth) != truth
| implies(implies(implies(X_21,X_21),truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_21,X_21),truth),truth),truth) ),[0],$fot(implies(implies(implies(implies(truth,X_21),X_21),truth),truth))]]) ).
cnf(refute_0_168,plain,
( implies(implies(implies(X_21,X_21),truth),truth) != implies(implies(implies(implies(truth,X_21),X_21),truth),truth)
| implies(implies(implies(X_21,X_21),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(truth,X_21),X_21),truth),truth),truth) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
( implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)) != implies(implies(implies(implies(truth,X_21),X_21),truth),truth)
| implies(implies(implies(X_21,X_21),truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,X_21),truth),truth),implies(implies(implies(implies(truth,X_21),X_21),truth),truth)) )],[refute_0_160,refute_0_168]) ).
cnf(refute_0_170,plain,
implies(implies(implies(X_21,X_21),truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_21,truth),truth),implies(implies(X_21,truth),truth)),implies(implies(implies(implies(truth,X_21),X_21),truth),truth)) )],[refute_0_142,refute_0_169]) ).
cnf(refute_0_171,plain,
implies(implies(implies(X_22,X_22),truth),truth) = truth,
inference(subst,[],[refute_0_170:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_172,plain,
( implies(implies(implies(X_22,X_22),truth),truth) != truth
| implies(implies(implies(implies(X_22,X_22),truth),truth),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_22,X_22),truth),truth),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_173,plain,
( implies(implies(implies(implies(X_22,X_22),truth),truth),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_22,X_22),truth),truth),truth) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_22,X_22),truth),truth),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),truth) )],[refute_0_137,refute_0_173]) ).
cnf(refute_0_175,plain,
implies(truth,Z) = Z,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_176,plain,
implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) = implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)),
introduced(tautology,[refl,[$fot(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)))]]) ).
cnf(refute_0_177,plain,
( implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) != implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))
| implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) ),[1,0],$fot(Z)]]) ).
cnf(refute_0_178,plain,
( implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))))]]) ).
cnf(refute_0_181,plain,
( implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) != implies(Z,implies(implies(implies(X_22,X_22),truth),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))))),bind(Y0,$fot(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)))),bind(Z0,$fot(implies(Z,implies(implies(implies(X_22,X_22),truth),Z))))]]) ).
cnf(refute_0_182,plain,
( implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)) != implies(Z,implies(implies(implies(X_22,X_22),truth),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z)),implies(Z,implies(implies(implies(X_22,X_22),truth),Z))) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != implies(Z,implies(implies(implies(X_22,X_22),truth),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != truth
| implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),truth) ),[0],$fot(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)))]]) ).
cnf(refute_0_185,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))) != truth
| implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),implies(Z,implies(implies(implies(X_22,X_22),truth),Z))) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(implies(X_22,X_22),truth),Z))),truth) )],[refute_0_174,refute_0_185]) ).
cnf(refute_0_187,plain,
implies(implies(X,X),implies(implies(X,X),implies(X,X))) = truth,
inference(subst,[],[wajsberg_2:[bind(Y,$fot(X)),bind(Z,$fot(X))]]) ).
cnf(refute_0_188,plain,
implies(implies(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),implies(X_7,X_7)),implies(X_7,X_7)) = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),
inference(subst,[],[refute_0_66:[bind(X,$fot(implies(X_7,X_7))),bind(X_1,$fot(implies(implies(not(X_7),truth),truth)))]]) ).
cnf(refute_0_189,plain,
implies(implies(not(X_7),not(X_7)),implies(X_7,X_7)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_7)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_190,plain,
implies(not(X_7),not(X_7)) = implies(implies(not(X_7),truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(not(X_7)))]]) ).
cnf(refute_0_191,plain,
( implies(implies(not(X_7),not(X_7)),implies(X_7,X_7)) != truth
| implies(not(X_7),not(X_7)) != implies(implies(not(X_7),truth),truth)
| implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_7),not(X_7)),implies(X_7,X_7)),truth) ),[0,0],$fot(implies(implies(not(X_7),truth),truth))]]) ).
cnf(refute_0_192,plain,
( implies(implies(not(X_7),not(X_7)),implies(X_7,X_7)) != truth
| implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X_7),not(X_7)),implies(implies(not(X_7),truth),truth)) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_7),not(X_7)),implies(X_7,X_7)),truth) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
( implies(implies(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)) != truth
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),implies(X_7,X_7)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) ),[0,0,0],$fot(truth)]]) ).
cnf(refute_0_195,plain,
( implies(implies(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),truth) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),implies(X_7,X_7)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) )],[refute_0_188,refute_0_195]) ).
cnf(refute_0_197,plain,
implies(implies(implies(X_7,X_7),truth),truth) = truth,
inference(subst,[],[refute_0_170:[bind(X_21,$fot(X_7))]]) ).
cnf(refute_0_198,plain,
( implies(implies(X,Y),Y) != implies(implies(Y,X),X)
| implies(implies(Y,X),X) = implies(implies(X,Y),Y) ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(implies(implies(X,Y),Y))),bind(Y0,$fot(implies(implies(Y,X),X)))]]) ).
cnf(refute_0_199,plain,
implies(implies(Y,X),X) = implies(implies(X,Y),Y),
inference(resolve,[$cnf( $equal(implies(implies(X,Y),Y),implies(implies(Y,X),X)) )],[wajsberg_3,refute_0_198]) ).
cnf(refute_0_200,plain,
implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = implies(implies(implies(X_7,X_7),truth),truth),
inference(subst,[],[refute_0_199:[bind(X,$fot(implies(X_7,X_7))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_201,plain,
( implies(implies(implies(X_7,X_7),truth),truth) != truth
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(X_7,X_7),truth),truth)
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = truth ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)))),bind(Y0,$fot(implies(implies(implies(X_7,X_7),truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_202,plain,
( implies(implies(implies(X_7,X_7),truth),truth) != truth
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)),implies(implies(implies(X_7,X_7),truth),truth)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(X_7,X_7),truth),truth),truth) )],[refute_0_197,refute_0_202]) ).
cnf(refute_0_204,plain,
( implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) != truth
| truth = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) ),[0],$fot(truth)]]) ).
cnf(refute_0_205,plain,
( implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| truth = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)),truth) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),implies(X_9,X_9)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(implies(X_9,X_9))),bind(Y,$fot(implies(implies(not(X_9),truth),truth)))]]) ).
cnf(refute_0_207,plain,
implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)) = truth,
inference(subst,[],[refute_0_193:[bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_208,plain,
( implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) != implies(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),implies(X_9,X_9))
| implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)) != truth
| implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(truth,implies(X_9,X_9)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)),implies(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),implies(X_9,X_9))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_209,plain,
( implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) != implies(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),implies(X_9,X_9))
| implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(truth,implies(X_9,X_9)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),truth) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(truth,implies(X_9,X_9)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)),implies(implies(implies(implies(not(X_9),truth),truth),implies(X_9,X_9)),implies(X_9,X_9))) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
implies(truth,implies(X_9,X_9)) = implies(X_9,X_9),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(X_9,X_9)))]]) ).
cnf(refute_0_212,plain,
( implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) != implies(truth,implies(X_9,X_9))
| implies(truth,implies(X_9,X_9)) != implies(X_9,X_9)
| implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(X_9,X_9) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)),implies(X_9,X_9)) ),[0],$fot(implies(truth,implies(X_9,X_9)))]]) ).
cnf(refute_0_213,plain,
( implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) != implies(truth,implies(X_9,X_9))
| implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(X_9,X_9) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_9,X_9)),implies(X_9,X_9)) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)) = implies(X_9,X_9),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_9,X_9),implies(implies(not(X_9),truth),truth)),implies(implies(not(X_9),truth),truth)),implies(truth,implies(X_9,X_9))) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)) = implies(X_7,X_7),
inference(subst,[],[refute_0_214:[bind(X_9,$fot(X_7))]]) ).
cnf(refute_0_216,plain,
implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) = implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)))]]) ).
cnf(refute_0_217,plain,
( implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)) != implies(X_7,X_7)
| implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) = implies(implies(X_7,X_7),implies(X_7,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) ),[1,0],$fot(implies(X_7,X_7))]]) ).
cnf(refute_0_218,plain,
( implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)) != implies(X_7,X_7)
| implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) = implies(implies(X_7,X_7),implies(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) = implies(implies(X_7,X_7),implies(X_7,X_7)),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) )],[refute_0_215,refute_0_218]) ).
cnf(refute_0_220,plain,
( implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)) != implies(implies(X_7,X_7),implies(X_7,X_7))
| truth != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| truth = implies(implies(X_7,X_7),implies(X_7,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) ),[1],$fot(implies(implies(X_7,X_7),implies(X_7,X_7)))]]) ).
cnf(refute_0_221,plain,
( truth != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| truth = implies(implies(X_7,X_7),implies(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7)),implies(implies(X_7,X_7),implies(X_7,X_7))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
( implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)) != implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))
| truth = implies(implies(X_7,X_7),implies(X_7,X_7)) ),
inference(resolve,[$cnf( $equal(truth,implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) )],[refute_0_205,refute_0_221]) ).
cnf(refute_0_223,plain,
truth = implies(implies(X_7,X_7),implies(X_7,X_7)),
inference(resolve,[$cnf( $equal(implies(implies(truth,implies(X_7,X_7)),implies(X_7,X_7)),implies(implies(implies(implies(X_7,X_7),implies(implies(not(X_7),truth),truth)),implies(implies(not(X_7),truth),truth)),implies(X_7,X_7))) )],[refute_0_196,refute_0_222]) ).
cnf(refute_0_224,plain,
truth = implies(implies(X,X),implies(X,X)),
inference(subst,[],[refute_0_223:[bind(X_7,$fot(X))]]) ).
cnf(refute_0_225,plain,
( truth != implies(implies(X,X),implies(X,X))
| implies(implies(X,X),implies(X,X)) = truth ),
inference(subst,[],[refute_0_48:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(X,X),implies(X,X))))]]) ).
cnf(refute_0_226,plain,
implies(implies(X,X),implies(X,X)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(X,X),implies(X,X))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
( implies(implies(X,X),implies(X,X)) != truth
| implies(implies(X,X),implies(implies(X,X),implies(X,X))) != truth
| implies(implies(X,X),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,X),implies(implies(X,X),implies(X,X))),truth) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_228,plain,
( implies(implies(X,X),implies(implies(X,X),implies(X,X))) != truth
| implies(implies(X,X),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X,X),implies(X,X)),truth) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
implies(implies(X,X),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X,X),implies(implies(X,X),implies(X,X))),truth) )],[refute_0_187,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(implies(X_22,X_22),truth) = truth,
inference(subst,[],[refute_0_229:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_231,plain,
implies(implies(implies(X_22,X_22),truth),Z) = implies(implies(implies(X_22,X_22),truth),Z),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_22,X_22),truth),Z))]]) ).
cnf(refute_0_232,plain,
( implies(implies(X_22,X_22),truth) != truth
| implies(implies(implies(X_22,X_22),truth),Z) != implies(implies(implies(X_22,X_22),truth),Z)
| implies(implies(implies(X_22,X_22),truth),Z) = implies(truth,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_22,X_22),truth),Z),implies(implies(implies(X_22,X_22),truth),Z)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_233,plain,
( implies(implies(X_22,X_22),truth) != truth
| implies(implies(implies(X_22,X_22),truth),Z) = implies(truth,Z) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_22,X_22),truth),Z),implies(implies(implies(X_22,X_22),truth),Z)) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
implies(implies(implies(X_22,X_22),truth),Z) = implies(truth,Z),
inference(resolve,[$cnf( $equal(implies(implies(X_22,X_22),truth),truth) )],[refute_0_230,refute_0_233]) ).
cnf(refute_0_235,plain,
( implies(implies(implies(X_22,X_22),truth),Z) != implies(truth,Z)
| implies(truth,Z) != Z
| implies(implies(implies(X_22,X_22),truth),Z) = Z ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(implies(X_22,X_22),truth),Z))),bind(Y0,$fot(implies(truth,Z))),bind(Z0,$fot(Z))]]) ).
cnf(refute_0_236,plain,
( implies(truth,Z) != Z
| implies(implies(implies(X_22,X_22),truth),Z) = Z ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_22,X_22),truth),Z),implies(truth,Z)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
implies(implies(implies(X_22,X_22),truth),Z) = Z,
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_175,refute_0_236]) ).
cnf(refute_0_238,plain,
implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),
introduced(tautology,[refl,[$fot(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)))]]) ).
cnf(refute_0_239,plain,
( implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) != implies(Z,implies(implies(implies(X_22,X_22),truth),Z))
| implies(implies(implies(X_22,X_22),truth),Z) != Z
| implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,Z) ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),implies(Z,implies(implies(implies(X_22,X_22),truth),Z))) ),[1,1],$fot(Z)]]) ).
cnf(refute_0_240,plain,
( implies(implies(implies(X_22,X_22),truth),Z) != Z
| implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,Z) ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),implies(Z,implies(implies(implies(X_22,X_22),truth),Z))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) = implies(Z,Z),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_22,X_22),truth),Z),Z) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) != implies(Z,Z)
| implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) != truth
| implies(Z,Z) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),truth) ),[0],$fot(implies(Z,Z))]]) ).
cnf(refute_0_243,plain,
( implies(Z,implies(implies(implies(X_22,X_22),truth),Z)) != truth
| implies(Z,Z) = truth ),
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),implies(Z,Z)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
implies(Z,Z) = truth,
inference(resolve,[$cnf( $equal(implies(Z,implies(implies(implies(X_22,X_22),truth),Z)),truth) )],[refute_0_186,refute_0_243]) ).
cnf(refute_0_245,plain,
implies(X_14,X_14) = truth,
inference(subst,[],[refute_0_244:[bind(Z,$fot(X_14))]]) ).
cnf(refute_0_246,plain,
implies(implies(X_14,X_14),X_14) = implies(implies(X_14,X_14),X_14),
introduced(tautology,[refl,[$fot(implies(implies(X_14,X_14),X_14))]]) ).
cnf(refute_0_247,plain,
( implies(X_14,X_14) != truth
| implies(implies(X_14,X_14),X_14) != implies(implies(X_14,X_14),X_14)
| implies(implies(X_14,X_14),X_14) = implies(truth,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_14,X_14),X_14),implies(implies(X_14,X_14),X_14)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_248,plain,
( implies(X_14,X_14) != truth
| implies(implies(X_14,X_14),X_14) = implies(truth,X_14) ),
inference(resolve,[$cnf( $equal(implies(implies(X_14,X_14),X_14),implies(implies(X_14,X_14),X_14)) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
implies(implies(X_14,X_14),X_14) = implies(truth,X_14),
inference(resolve,[$cnf( $equal(implies(X_14,X_14),truth) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( implies(implies(X_14,X_14),X_14) != implies(truth,X_14)
| implies(truth,X_14) != X_14
| implies(implies(X_14,X_14),X_14) = X_14 ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(X_14,X_14),X_14))),bind(Y0,$fot(implies(truth,X_14))),bind(Z0,$fot(X_14))]]) ).
cnf(refute_0_251,plain,
( implies(truth,X_14) != X_14
| implies(implies(X_14,X_14),X_14) = X_14 ),
inference(resolve,[$cnf( $equal(implies(implies(X_14,X_14),X_14),implies(truth,X_14)) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
implies(implies(X_14,X_14),X_14) = X_14,
inference(resolve,[$cnf( $equal(implies(truth,X_14),X_14) )],[refute_0_32,refute_0_251]) ).
cnf(refute_0_253,plain,
implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) = implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)),
introduced(tautology,[refl,[$fot(implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))]]) ).
cnf(refute_0_254,plain,
( implies(implies(X_14,X_14),X_14) != X_14
| implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) != implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))
| implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) = implies(X_14,implies(X_12,X_14)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) ),[1,0],$fot(X_14)]]) ).
cnf(refute_0_255,plain,
( implies(implies(X_14,X_14),X_14) != X_14
| implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) = implies(X_14,implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) = implies(X_14,implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(implies(implies(X_14,X_14),X_14),X_14) )],[refute_0_252,refute_0_255]) ).
cnf(refute_0_257,plain,
implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),
introduced(tautology,[refl,[$fot(implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))))]]) ).
cnf(refute_0_258,plain,
( implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) != implies(X_14,implies(X_12,X_14))
| implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))
| implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))) ),[1,1],$fot(implies(X_14,implies(X_12,X_14)))]]) ).
cnf(refute_0_259,plain,
( implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)) != implies(X_14,implies(X_12,X_14))
| implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)),implies(X_14,implies(X_12,X_14))) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(implies(not(X_7),truth),truth))),bind(Y,$fot(X_13)),bind(Z,$fot(implies(X_7,X_7)))]]) ).
cnf(refute_0_262,plain,
( implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)))) != truth
| implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)) != truth
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)))),truth) ),[0,1,1],$fot(truth)]]) ).
cnf(refute_0_263,plain,
( implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)))) != truth
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)),truth) )],[refute_0_193,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),implies(implies(implies(not(X_7),truth),truth),implies(X_7,X_7)))),truth) )],[refute_0_261,refute_0_263]) ).
cnf(refute_0_265,plain,
implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) = truth,
inference(subst,[],[wajsberg_4:[bind(X,$fot(X_6)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_266,plain,
implies(X_6,X_6) = implies(implies(X_6,truth),truth),
inference(subst,[],[refute_0_125:[bind(X_2,$fot(X_6))]]) ).
cnf(refute_0_267,plain,
( implies(X_6,X_6) != implies(implies(X_6,truth),truth)
| implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) ),[0,1],$fot(implies(implies(X_6,truth),truth))]]) ).
cnf(refute_0_268,plain,
( implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)) != truth
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_6,X_6),implies(implies(X_6,truth),truth)) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(X_6,X_6)),truth) )],[refute_0_265,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(truth,implies(implies(X_6,truth),truth)) = implies(implies(X_6,truth),truth),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(X_6,truth),truth)))]]) ).
cnf(refute_0_271,plain,
implies(not(X_6),not(X_6)) = truth,
inference(subst,[],[refute_0_244:[bind(Z,$fot(not(X_6)))]]) ).
cnf(refute_0_272,plain,
implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),
introduced(tautology,[refl,[$fot(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)))]]) ).
cnf(refute_0_273,plain,
( implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) != implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth))
| implies(not(X_6),not(X_6)) != truth
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(truth,implies(implies(X_6,truth),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_274,plain,
( implies(not(X_6),not(X_6)) != truth
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(truth,implies(implies(X_6,truth),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(truth,implies(implies(X_6,truth),truth)),
inference(resolve,[$cnf( $equal(implies(not(X_6),not(X_6)),truth) )],[refute_0_271,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) != implies(truth,implies(implies(X_6,truth),truth))
| implies(truth,implies(implies(X_6,truth),truth)) != implies(implies(X_6,truth),truth)
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(implies(X_6,truth),truth) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)))),bind(Y0,$fot(implies(truth,implies(implies(X_6,truth),truth)))),bind(Z0,$fot(implies(implies(X_6,truth),truth)))]]) ).
cnf(refute_0_277,plain,
( implies(truth,implies(implies(X_6,truth),truth)) != implies(implies(X_6,truth),truth)
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(implies(X_6,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),implies(truth,implies(implies(X_6,truth),truth))) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) = implies(implies(X_6,truth),truth),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(X_6,truth),truth)),implies(implies(X_6,truth),truth)) )],[refute_0_270,refute_0_277]) ).
cnf(refute_0_279,plain,
( implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) != implies(implies(X_6,truth),truth)
| implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) != truth
| implies(implies(X_6,truth),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),truth) ),[0],$fot(implies(implies(X_6,truth),truth))]]) ).
cnf(refute_0_280,plain,
( implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)) != truth
| implies(implies(X_6,truth),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),implies(implies(X_6,truth),truth)) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
implies(implies(X_6,truth),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X_6),not(X_6)),implies(implies(X_6,truth),truth)),truth) )],[refute_0_269,refute_0_280]) ).
cnf(refute_0_282,plain,
implies(implies(X_13,truth),truth) = truth,
inference(subst,[],[refute_0_281:[bind(X_6,$fot(X_13))]]) ).
cnf(refute_0_283,plain,
implies(X_7,X_7) = truth,
inference(subst,[],[refute_0_244:[bind(Z,$fot(X_7))]]) ).
cnf(refute_0_284,plain,
implies(X_13,implies(X_7,X_7)) = implies(X_13,implies(X_7,X_7)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(X_7,X_7)))]]) ).
cnf(refute_0_285,plain,
( implies(X_13,implies(X_7,X_7)) != implies(X_13,implies(X_7,X_7))
| implies(X_7,X_7) != truth
| implies(X_13,implies(X_7,X_7)) = implies(X_13,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(X_7,X_7)),implies(X_13,implies(X_7,X_7))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_286,plain,
( implies(X_7,X_7) != truth
| implies(X_13,implies(X_7,X_7)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(X_7,X_7)),implies(X_13,implies(X_7,X_7))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
implies(X_13,implies(X_7,X_7)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(X_7,X_7),truth) )],[refute_0_283,refute_0_286]) ).
cnf(refute_0_288,plain,
implies(implies(X_13,implies(X_7,X_7)),truth) = implies(implies(X_13,implies(X_7,X_7)),truth),
introduced(tautology,[refl,[$fot(implies(implies(X_13,implies(X_7,X_7)),truth))]]) ).
cnf(refute_0_289,plain,
( implies(X_13,implies(X_7,X_7)) != implies(X_13,truth)
| implies(implies(X_13,implies(X_7,X_7)),truth) != implies(implies(X_13,implies(X_7,X_7)),truth)
| implies(implies(X_13,implies(X_7,X_7)),truth) = implies(implies(X_13,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_13,implies(X_7,X_7)),truth),implies(implies(X_13,implies(X_7,X_7)),truth)) ),[1,0],$fot(implies(X_13,truth))]]) ).
cnf(refute_0_290,plain,
( implies(X_13,implies(X_7,X_7)) != implies(X_13,truth)
| implies(implies(X_13,implies(X_7,X_7)),truth) = implies(implies(X_13,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_7,X_7)),truth),implies(implies(X_13,implies(X_7,X_7)),truth)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
implies(implies(X_13,implies(X_7,X_7)),truth) = implies(implies(X_13,truth),truth),
inference(resolve,[$cnf( $equal(implies(X_13,implies(X_7,X_7)),implies(X_13,truth)) )],[refute_0_287,refute_0_290]) ).
cnf(refute_0_292,plain,
( implies(implies(X_13,implies(X_7,X_7)),truth) != implies(implies(X_13,truth),truth)
| implies(implies(X_13,truth),truth) != truth
| implies(implies(X_13,implies(X_7,X_7)),truth) = truth ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(X_13,implies(X_7,X_7)),truth))),bind(Y0,$fot(implies(implies(X_13,truth),truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_293,plain,
( implies(implies(X_13,truth),truth) != truth
| implies(implies(X_13,implies(X_7,X_7)),truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_7,X_7)),truth),implies(implies(X_13,truth),truth)) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
implies(implies(X_13,implies(X_7,X_7)),truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_13,truth),truth),truth) )],[refute_0_282,refute_0_293]) ).
cnf(refute_0_295,plain,
implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)),
introduced(tautology,[refl,[$fot(implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)))]]) ).
cnf(refute_0_296,plain,
( implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth))
| implies(implies(X_13,implies(X_7,X_7)),truth) != truth
| implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)),implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_297,plain,
( implies(implies(X_13,implies(X_7,X_7)),truth) != truth
| implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)),implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_13,implies(X_7,X_7)),truth),truth) )],[refute_0_294,refute_0_297]) ).
cnf(refute_0_299,plain,
implies(implies(not(X_7),truth),truth) = truth,
inference(subst,[],[refute_0_281:[bind(X_6,$fot(not(X_7)))]]) ).
cnf(refute_0_300,plain,
implies(implies(implies(not(X_7),truth),truth),X_13) = implies(implies(implies(not(X_7),truth),truth),X_13),
introduced(tautology,[refl,[$fot(implies(implies(implies(not(X_7),truth),truth),X_13))]]) ).
cnf(refute_0_301,plain,
( implies(implies(implies(not(X_7),truth),truth),X_13) != implies(implies(implies(not(X_7),truth),truth),X_13)
| implies(implies(not(X_7),truth),truth) != truth
| implies(implies(implies(not(X_7),truth),truth),X_13) = implies(truth,X_13) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(implies(not(X_7),truth),truth),X_13)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_302,plain,
( implies(implies(not(X_7),truth),truth) != truth
| implies(implies(implies(not(X_7),truth),truth),X_13) = implies(truth,X_13) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(implies(not(X_7),truth),truth),X_13)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
implies(implies(implies(not(X_7),truth),truth),X_13) = implies(truth,X_13),
inference(resolve,[$cnf( $equal(implies(implies(not(X_7),truth),truth),truth) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
( implies(implies(implies(not(X_7),truth),truth),X_13) != implies(truth,X_13)
| implies(truth,X_13) != X_13
| implies(implies(implies(not(X_7),truth),truth),X_13) = X_13 ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(implies(not(X_7),truth),truth),X_13))),bind(Y0,$fot(implies(truth,X_13))),bind(Z0,$fot(X_13))]]) ).
cnf(refute_0_305,plain,
( implies(truth,X_13) != X_13
| implies(implies(implies(not(X_7),truth),truth),X_13) = X_13 ),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),X_13),implies(truth,X_13)) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
implies(implies(implies(not(X_7),truth),truth),X_13) = X_13,
inference(resolve,[$cnf( $equal(implies(truth,X_13),X_13) )],[refute_0_36,refute_0_305]) ).
cnf(refute_0_307,plain,
implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),
introduced(tautology,[refl,[$fot(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)))]]) ).
cnf(refute_0_308,plain,
( implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth))
| implies(implies(implies(not(X_7),truth),truth),X_13) != X_13
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth))) ),[1,0],$fot(X_13)]]) ).
cnf(refute_0_309,plain,
( implies(implies(implies(not(X_7),truth),truth),X_13) != X_13
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)),
inference(resolve,[$cnf( $equal(implies(implies(implies(not(X_7),truth),truth),X_13),X_13) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
( implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth))
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)))),bind(Y0,$fot(implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)))),bind(Z0,$fot(implies(X_13,truth)))]]) ).
cnf(refute_0_312,plain,
( implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth) ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) = implies(X_13,truth),
inference(resolve,[$cnf( $equal(implies(X_13,implies(implies(X_13,implies(X_7,X_7)),truth)),implies(X_13,truth)) )],[refute_0_298,refute_0_312]) ).
cnf(refute_0_314,plain,
( implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) != implies(X_13,truth)
| implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) != truth
| implies(X_13,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),truth) ),[0],$fot(implies(X_13,truth))]]) ).
cnf(refute_0_315,plain,
( implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)) != truth
| implies(X_13,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),implies(X_13,truth)) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
implies(X_13,truth) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(implies(not(X_7),truth),truth),X_13),implies(implies(X_13,implies(X_7,X_7)),truth)),truth) )],[refute_0_264,refute_0_315]) ).
cnf(refute_0_317,plain,
implies(X_12,truth) = truth,
inference(subst,[],[refute_0_316:[bind(X_13,$fot(X_12))]]) ).
cnf(refute_0_318,plain,
implies(implies(X_14,truth),truth) = truth,
inference(subst,[],[refute_0_316:[bind(X_13,$fot(implies(X_14,truth)))]]) ).
cnf(refute_0_319,plain,
implies(X_12,implies(implies(X_14,truth),truth)) = implies(X_12,implies(implies(X_14,truth),truth)),
introduced(tautology,[refl,[$fot(implies(X_12,implies(implies(X_14,truth),truth)))]]) ).
cnf(refute_0_320,plain,
( implies(X_12,implies(implies(X_14,truth),truth)) != implies(X_12,implies(implies(X_14,truth),truth))
| implies(implies(X_14,truth),truth) != truth
| implies(X_12,implies(implies(X_14,truth),truth)) = implies(X_12,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_12,implies(implies(X_14,truth),truth)),implies(X_12,implies(implies(X_14,truth),truth))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_321,plain,
( implies(implies(X_14,truth),truth) != truth
| implies(X_12,implies(implies(X_14,truth),truth)) = implies(X_12,truth) ),
inference(resolve,[$cnf( $equal(implies(X_12,implies(implies(X_14,truth),truth)),implies(X_12,implies(implies(X_14,truth),truth))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(X_12,implies(implies(X_14,truth),truth)) = implies(X_12,truth),
inference(resolve,[$cnf( $equal(implies(implies(X_14,truth),truth),truth) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( implies(X_12,implies(implies(X_14,truth),truth)) != implies(X_12,truth)
| implies(X_12,truth) != truth
| implies(X_12,implies(implies(X_14,truth),truth)) = truth ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(X_12,implies(implies(X_14,truth),truth)))),bind(Y0,$fot(implies(X_12,truth))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_324,plain,
( implies(X_12,truth) != truth
| implies(X_12,implies(implies(X_14,truth),truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(X_12,implies(implies(X_14,truth),truth)),implies(X_12,truth)) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
implies(X_12,implies(implies(X_14,truth),truth)) = truth,
inference(resolve,[$cnf( $equal(implies(X_12,truth),truth) )],[refute_0_317,refute_0_324]) ).
cnf(refute_0_326,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),
introduced(tautology,[refl,[$fot(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))))]]) ).
cnf(refute_0_327,plain,
( implies(X_12,implies(implies(X_14,truth),truth)) != truth
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_328,plain,
( implies(X_12,implies(implies(X_14,truth),truth)) != truth
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(implies(X_12,implies(implies(X_14,truth),truth)),truth) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))
| implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(truth,implies(X_14,implies(X_12,X_14)))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))))),bind(Y0,$fot(implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))))),bind(Z0,$fot(implies(truth,implies(X_14,implies(X_12,X_14)))))]]) ).
cnf(refute_0_331,plain,
( implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(truth,implies(X_14,implies(X_12,X_14)))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14)))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(truth,implies(X_14,implies(X_12,X_14))),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(truth,implies(X_14,implies(X_12,X_14)))) )],[refute_0_260,refute_0_331]) ).
cnf(refute_0_333,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(truth,implies(X_14,implies(X_12,X_14)))
| implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),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_334,plain,
( implies(truth,implies(X_14,implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(truth,implies(X_14,implies(X_12,X_14)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) = implies(X_14,implies(X_12,X_14)),
inference(resolve,[$cnf( $equal(implies(truth,implies(X_14,implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_136,refute_0_334]) ).
cnf(refute_0_336,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != implies(X_14,implies(X_12,X_14))
| implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),truth) ),[0],$fot(implies(X_14,implies(X_12,X_14)))]]) ).
cnf(refute_0_337,plain,
( implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))) != truth
| implies(X_14,implies(X_12,X_14)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),implies(X_14,implies(X_12,X_14))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
implies(X_14,implies(X_12,X_14)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(X_12,implies(implies(X_14,truth),truth)),implies(implies(implies(X_14,X_14),X_14),implies(X_12,X_14))),truth) )],[refute_0_135,refute_0_337]) ).
cnf(refute_0_339,plain,
implies(not(truth),implies(not(not(not(truth))),not(truth))) = truth,
inference(subst,[],[refute_0_338:[bind(X_12,$fot(not(not(not(truth))))),bind(X_14,$fot(not(truth)))]]) ).
cnf(refute_0_340,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),
introduced(tautology,[refl,[$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))]]) ).
cnf(refute_0_341,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))
| implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_342,plain,
( implies(not(truth),implies(not(not(not(truth))),not(truth))) != truth
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth)))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = implies(truth,not(not(truth))),
inference(resolve,[$cnf( $equal(implies(not(truth),implies(not(not(not(truth))),not(truth))),truth) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != implies(truth,not(not(truth)))
| implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))))),bind(Y0,$fot(implies(truth,not(not(truth))))),bind(Z0,$fot(not(not(truth))))]]) ).
cnf(refute_0_345,plain,
( implies(truth,not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),implies(truth,not(not(truth)))) )],[refute_0_343,refute_0_344]) ).
cnf(refute_0_346,plain,
implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) = not(not(truth)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(truth))),not(not(truth))) )],[refute_0_112,refute_0_345]) ).
cnf(refute_0_347,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != not(not(truth))
| implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) ),[0],$fot(not(not(truth)))]]) ).
cnf(refute_0_348,plain,
( implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),not(not(truth))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(truth),implies(not(not(not(truth))),not(truth))),not(not(truth))),truth) )],[refute_0_118,refute_0_348]) ).
cnf(refute_0_350,plain,
implies(not(not(truth)),not(not(X_25))) = implies(not(not(truth)),not(not(X_25))),
introduced(tautology,[refl,[$fot(implies(not(not(truth)),not(not(X_25))))]]) ).
cnf(refute_0_351,plain,
( implies(not(not(truth)),not(not(X_25))) != implies(not(not(truth)),not(not(X_25)))
| not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(not(not(truth)),not(not(X_25)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_352,plain,
( not(not(truth)) != truth
| implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(not(not(truth)),not(not(X_25)))) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
implies(not(not(truth)),not(not(X_25))) = implies(truth,not(not(X_25))),
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_349,refute_0_352]) ).
cnf(refute_0_354,plain,
( implies(not(not(truth)),not(not(X_25))) != implies(truth,not(not(X_25)))
| implies(truth,not(not(X_25))) != not(not(X_25))
| implies(not(not(truth)),not(not(X_25))) = not(not(X_25)) ),
inference(subst,[],[refute_0_96:[bind(X0,$fot(implies(not(not(truth)),not(not(X_25))))),bind(Y0,$fot(implies(truth,not(not(X_25))))),bind(Z0,$fot(not(not(X_25))))]]) ).
cnf(refute_0_355,plain,
( implies(truth,not(not(X_25))) != not(not(X_25))
| implies(not(not(truth)),not(not(X_25))) = not(not(X_25)) ),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),implies(truth,not(not(X_25)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
implies(not(not(truth)),not(not(X_25))) = not(not(X_25)),
inference(resolve,[$cnf( $equal(implies(truth,not(not(X_25))),not(not(X_25))) )],[refute_0_28,refute_0_355]) ).
cnf(refute_0_357,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(implies(not(not(truth)),not(not(X_25))),X_25),
introduced(tautology,[refl,[$fot(implies(implies(not(not(truth)),not(not(X_25))),X_25))]]) ).
cnf(refute_0_358,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != implies(implies(not(not(truth)),not(not(X_25))),X_25)
| implies(not(not(truth)),not(not(X_25))) != not(not(X_25))
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(implies(not(not(truth)),not(not(X_25))),X_25)) ),[1,0],$fot(not(not(X_25)))]]) ).
cnf(refute_0_359,plain,
( implies(not(not(truth)),not(not(X_25))) != not(not(X_25))
| implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25) ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(implies(not(not(truth)),not(not(X_25))),X_25)) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(implies(not(not(truth)),not(not(X_25))),X_25) = implies(not(not(X_25)),X_25),
inference(resolve,[$cnf( $equal(implies(not(not(truth)),not(not(X_25))),not(not(X_25))) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != implies(not(not(X_25)),X_25)
| implies(implies(not(not(truth)),not(not(X_25))),X_25) != truth
| implies(not(not(X_25)),X_25) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),truth) ),[0],$fot(implies(not(not(X_25)),X_25))]]) ).
cnf(refute_0_362,plain,
( implies(implies(not(not(truth)),not(not(X_25))),X_25) != truth
| implies(not(not(X_25)),X_25) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),implies(not(not(X_25)),X_25)) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
implies(not(not(X_25)),X_25) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(truth)),not(not(X_25))),X_25),truth) )],[refute_0_27,refute_0_362]) ).
cnf(refute_0_364,plain,
implies(not(not(not(Y))),not(Y)) = truth,
inference(subst,[],[refute_0_363:[bind(X_25,$fot(not(Y)))]]) ).
cnf(refute_0_365,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(not(not(not(Y))),not(Y)) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_366,plain,
( implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))) != truth
| implies(truth,implies(Y,not(not(Y)))) = truth ),
inference(resolve,[$cnf( $equal(implies(not(not(not(Y))),not(Y)),truth) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
implies(truth,implies(Y,not(not(Y)))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(not(not(Y))),not(Y)),implies(Y,not(not(Y)))),truth) )],[refute_0_0,refute_0_366]) ).
cnf(refute_0_368,plain,
implies(truth,implies(Y,not(not(Y)))) = implies(Y,not(not(Y))),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(Y,not(not(Y)))))]]) ).
cnf(refute_0_369,plain,
( implies(truth,implies(Y,not(not(Y)))) != implies(Y,not(not(Y)))
| implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) ),[0],$fot(implies(Y,not(not(Y))))]]) ).
cnf(refute_0_370,plain,
( implies(truth,implies(Y,not(not(Y)))) != truth
| implies(Y,not(not(Y))) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),implies(Y,not(not(Y)))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
implies(Y,not(not(Y))) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(Y,not(not(Y)))),truth) )],[refute_0_367,refute_0_370]) ).
cnf(refute_0_372,plain,
implies(x,not(not(x))) = truth,
inference(subst,[],[refute_0_371:[bind(Y,$fot(x))]]) ).
cnf(refute_0_373,plain,
( implies(x,not(not(x))) != truth
| truth != truth
| implies(x,not(not(x))) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(x,not(not(x))),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_374,plain,
( truth != truth
| implies(x,not(not(x))) = truth ),
inference(resolve,[$cnf( $equal(implies(x,not(not(x))),truth) )],[refute_0_372,refute_0_373]) ).
cnf(refute_0_375,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(x,not(not(x))),truth) )],[refute_0_374,prove_mv_29]) ).
cnf(refute_0_376,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_377,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_376,refute_0_375]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL112-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jul 3 09:22:59 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.47/0.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.63
% 0.47/0.63 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.47/0.69
%------------------------------------------------------------------------------