TSTP Solution File: LCL155-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL155-1 : 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 12:50:01 EDT 2022
% Result : Unsatisfiable 0.18s 0.54s
% Output : CNFRefutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 97
% Syntax : Number of clauses : 357 ( 183 unt; 0 nHn; 193 RR)
% Number of literals : 613 ( 612 equ; 258 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 410 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(wajsberg_1,axiom,
implies(truth,X) = X ).
cnf(wajsberg_2,axiom,
implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ).
cnf(wajsberg_3,axiom,
implies(implies(X,Y),Y) = implies(implies(Y,X),X) ).
cnf(wajsberg_4,axiom,
implies(implies(not(X),not(Y)),implies(Y,X)) = truth ).
cnf(or_definition,axiom,
or(X,Y) = implies(not(X),Y) ).
cnf(or_associativity,axiom,
or(or(X,Y),Z) = or(X,or(Y,Z)) ).
cnf(or_commutativity,axiom,
or(X,Y) = or(Y,X) ).
cnf(and_definition,axiom,
and(X,Y) = not(or(not(X),not(Y))) ).
cnf(xor_definition,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,x) != falsehood ).
cnf(refute_0_0,plain,
or(not(X_57),Y) = implies(not(not(X_57)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(not(X_57)))]]) ).
cnf(refute_0_1,plain,
implies(implies(X,falsehood),falsehood) = implies(implies(falsehood,X),X),
inference(subst,[],[wajsberg_3:[bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_6,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_5]) ).
cnf(refute_0_7,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_6:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_8,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_9,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(implies(not(X),not(Y)),implies(Y,X))
| implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) ),[1,0],$fot(or(X,not(Y)))]]) ).
cnf(refute_0_10,plain,
( implies(not(X),not(Y)) != or(X,not(Y))
| implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) ),[0],$fot(implies(or(X,not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_13,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_13]) ).
cnf(refute_0_15,plain,
implies(or(falsehood,not(Y)),implies(Y,falsehood)) = truth,
inference(subst,[],[refute_0_14:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_16,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_17,plain,
implies(or(X_5,not(truth)),implies(truth,X_5)) = truth,
inference(subst,[],[refute_0_14:[bind(X,$fot(X_5)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_18,plain,
implies(truth,X_5) = X_5,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_19,plain,
( implies(or(X_5,not(truth)),implies(truth,X_5)) != truth
| implies(truth,X_5) != X_5
| implies(or(X_5,not(truth)),X_5) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_5,not(truth)),implies(truth,X_5)),truth) ),[0,1],$fot(X_5)]]) ).
cnf(refute_0_20,plain,
( implies(or(X_5,not(truth)),implies(truth,X_5)) != truth
| implies(or(X_5,not(truth)),X_5) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_5),X_5) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
implies(or(X_5,not(truth)),X_5) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_5,not(truth)),implies(truth,X_5)),truth) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X_5,not(truth)) = or(X_5,not(truth)),
introduced(tautology,[refl,[$fot(or(X_5,not(truth)))]]) ).
cnf(refute_0_23,plain,
( not(truth) != falsehood
| or(X_5,not(truth)) != or(X_5,not(truth))
| or(X_5,not(truth)) = or(X_5,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_5,not(truth)),or(X_5,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_24,plain,
( not(truth) != falsehood
| or(X_5,not(truth)) = or(X_5,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_5,not(truth)),or(X_5,not(truth))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
or(X_5,not(truth)) = or(X_5,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_24]) ).
cnf(refute_0_26,plain,
implies(or(X_5,not(truth)),X_5) = implies(or(X_5,not(truth)),X_5),
introduced(tautology,[refl,[$fot(implies(or(X_5,not(truth)),X_5))]]) ).
cnf(refute_0_27,plain,
( implies(or(X_5,not(truth)),X_5) != implies(or(X_5,not(truth)),X_5)
| or(X_5,not(truth)) != or(X_5,falsehood)
| implies(or(X_5,not(truth)),X_5) = implies(or(X_5,falsehood),X_5) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_5,not(truth)),X_5),implies(or(X_5,not(truth)),X_5)) ),[1,0],$fot(or(X_5,falsehood))]]) ).
cnf(refute_0_28,plain,
( or(X_5,not(truth)) != or(X_5,falsehood)
| implies(or(X_5,not(truth)),X_5) = implies(or(X_5,falsehood),X_5) ),
inference(resolve,[$cnf( $equal(implies(or(X_5,not(truth)),X_5),implies(or(X_5,not(truth)),X_5)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
implies(or(X_5,not(truth)),X_5) = implies(or(X_5,falsehood),X_5),
inference(resolve,[$cnf( $equal(or(X_5,not(truth)),or(X_5,falsehood)) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( implies(or(X_5,not(truth)),X_5) != implies(or(X_5,falsehood),X_5)
| implies(or(X_5,not(truth)),X_5) != truth
| implies(or(X_5,falsehood),X_5) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_5,not(truth)),X_5),truth) ),[0],$fot(implies(or(X_5,falsehood),X_5))]]) ).
cnf(refute_0_31,plain,
( implies(or(X_5,not(truth)),X_5) != truth
| implies(or(X_5,falsehood),X_5) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_5,not(truth)),X_5),implies(or(X_5,falsehood),X_5)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(or(X_5,falsehood),X_5) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_5,not(truth)),X_5),truth) )],[refute_0_21,refute_0_31]) ).
cnf(refute_0_33,plain,
or(X_5,falsehood) = or(falsehood,X_5),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_5)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_34,plain,
( implies(or(X_5,falsehood),X_5) != truth
| or(X_5,falsehood) != or(falsehood,X_5)
| implies(or(falsehood,X_5),X_5) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_5,falsehood),X_5),truth) ),[0,0],$fot(or(falsehood,X_5))]]) ).
cnf(refute_0_35,plain,
( implies(or(X_5,falsehood),X_5) != truth
| implies(or(falsehood,X_5),X_5) = truth ),
inference(resolve,[$cnf( $equal(or(X_5,falsehood),or(falsehood,X_5)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(or(falsehood,X_5),X_5) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_5,falsehood),X_5),truth) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
implies(or(falsehood,not(falsehood)),not(falsehood)) = truth,
inference(subst,[],[refute_0_36:[bind(X_5,$fot(not(falsehood)))]]) ).
cnf(refute_0_38,plain,
implies(or(truth,falsehood),truth) = truth,
inference(subst,[],[refute_0_32:[bind(X_5,$fot(truth))]]) ).
cnf(refute_0_39,plain,
or(truth,X_12) = implies(not(truth),X_12),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_40,plain,
( not(truth) != falsehood
| or(truth,X_12) != implies(not(truth),X_12)
| or(truth,X_12) = implies(falsehood,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_12),implies(not(truth),X_12)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_41,plain,
( or(truth,X_12) != implies(not(truth),X_12)
| or(truth,X_12) = implies(falsehood,X_12) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_40]) ).
cnf(refute_0_42,plain,
or(truth,X_12) = implies(falsehood,X_12),
inference(resolve,[$cnf( $equal(or(truth,X_12),implies(not(truth),X_12)) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
or(truth,falsehood) = implies(falsehood,falsehood),
inference(subst,[],[refute_0_42:[bind(X_12,$fot(falsehood))]]) ).
cnf(refute_0_44,plain,
( implies(or(truth,falsehood),truth) != truth
| or(truth,falsehood) != implies(falsehood,falsehood)
| implies(implies(falsehood,falsehood),truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) ),[0,0],$fot(implies(falsehood,falsehood))]]) ).
cnf(refute_0_45,plain,
( implies(or(truth,falsehood),truth) != truth
| implies(implies(falsehood,falsehood),truth) = truth ),
inference(resolve,[$cnf( $equal(or(truth,falsehood),implies(falsehood,falsehood)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
implies(implies(falsehood,falsehood),truth) = truth,
inference(resolve,[$cnf( $equal(implies(or(truth,falsehood),truth),truth) )],[refute_0_38,refute_0_45]) ).
cnf(refute_0_47,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_48,plain,
implies(implies(truth,X_27),X_27) = implies(implies(X_27,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_49,plain,
implies(truth,X_27) = X_27,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_50,plain,
( implies(implies(truth,X_27),X_27) != implies(implies(X_27,truth),truth)
| implies(truth,X_27) != X_27
| implies(X_27,X_27) = implies(implies(X_27,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_27),X_27),implies(implies(X_27,truth),truth)) ),[0,0],$fot(X_27)]]) ).
cnf(refute_0_51,plain,
( implies(implies(truth,X_27),X_27) != implies(implies(X_27,truth),truth)
| implies(X_27,X_27) = implies(implies(X_27,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_27),X_27) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
implies(X_27,X_27) = implies(implies(X_27,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_27),X_27),implies(implies(X_27,truth),truth)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(not(X),not(X)) = implies(implies(not(X),truth),truth),
inference(subst,[],[refute_0_52:[bind(X_27,$fot(not(X)))]]) ).
cnf(refute_0_54,plain,
( implies(not(X),not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_55,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
or(X,not(X)) = implies(implies(not(X),truth),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_47,refute_0_55]) ).
cnf(refute_0_57,plain,
or(truth,X_12) = or(X_12,truth),
inference(subst,[],[or_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_58,plain,
( or(truth,X_12) != implies(falsehood,X_12)
| or(truth,X_12) != or(X_12,truth)
| or(X_12,truth) = implies(falsehood,X_12) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_12),implies(falsehood,X_12)) ),[0],$fot(or(X_12,truth))]]) ).
cnf(refute_0_59,plain,
( or(truth,X_12) != implies(falsehood,X_12)
| or(X_12,truth) = implies(falsehood,X_12) ),
inference(resolve,[$cnf( $equal(or(truth,X_12),or(X_12,truth)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
or(X_12,truth) = implies(falsehood,X_12),
inference(resolve,[$cnf( $equal(or(truth,X_12),implies(falsehood,X_12)) )],[refute_0_42,refute_0_59]) ).
cnf(refute_0_61,plain,
or(X,truth) = implies(falsehood,X),
inference(subst,[],[refute_0_60:[bind(X_12,$fot(X))]]) ).
cnf(refute_0_62,plain,
implies(not(X),truth) = or(X,truth),
inference(subst,[],[refute_0_6:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_63,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_64,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_63]) ).
cnf(refute_0_65,plain,
( implies(not(X),truth) != or(X,truth)
| or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(not(X),truth))),bind(Y0,$fot(or(X,truth))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_66,plain,
( or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(not(X),truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_61,refute_0_66]) ).
cnf(refute_0_68,plain,
implies(implies(not(X),truth),truth) = implies(implies(not(X),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_69,plain,
( implies(implies(not(X),truth),truth) != implies(implies(not(X),truth),truth)
| implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) ),[1,0],$fot(implies(falsehood,X))]]) ).
cnf(refute_0_70,plain,
( implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(implies(not(X),truth),implies(falsehood,X)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
( implies(implies(not(X),truth),truth) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) ),[1],$fot(implies(implies(falsehood,X),truth))]]) ).
cnf(refute_0_73,plain,
( or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(falsehood,X),truth)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
or(X,not(X)) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_56,refute_0_73]) ).
cnf(refute_0_75,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| implies(implies(falsehood,X),truth) = or(X,not(X)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(or(X,not(X)))),bind(Y0,$fot(implies(implies(falsehood,X),truth)))]]) ).
cnf(refute_0_76,plain,
implies(implies(falsehood,X),truth) = or(X,not(X)),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
implies(implies(falsehood,falsehood),truth) = or(falsehood,not(falsehood)),
inference(subst,[],[refute_0_76:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_78,plain,
( implies(implies(falsehood,falsehood),truth) != or(falsehood,not(falsehood))
| implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) ),[0],$fot(or(falsehood,not(falsehood)))]]) ).
cnf(refute_0_79,plain,
( implies(implies(falsehood,falsehood),truth) != truth
| or(falsehood,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),or(falsehood,not(falsehood))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
or(falsehood,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(falsehood,falsehood),truth),truth) )],[refute_0_46,refute_0_79]) ).
cnf(refute_0_81,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| or(falsehood,not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_82,plain,
( implies(or(falsehood,not(falsehood)),not(falsehood)) != truth
| implies(truth,not(falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(truth,not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(falsehood)),not(falsehood)),truth) )],[refute_0_37,refute_0_82]) ).
cnf(refute_0_84,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_85,plain,
( implies(truth,not(falsehood)) != not(falsehood)
| implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,not(falsehood)),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_86,plain,
( implies(truth,not(falsehood)) != truth
| not(falsehood) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),truth) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_89,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_16,refute_0_89]) ).
cnf(refute_0_91,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_92,plain,
( implies(truth,Y) != Y
| or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) ),[1],$fot(Y)]]) ).
cnf(refute_0_93,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
or(falsehood,not(Y)) = not(Y),
inference(subst,[],[refute_0_94:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_96,plain,
( implies(or(falsehood,not(Y)),implies(Y,falsehood)) != truth
| or(falsehood,not(Y)) != not(Y)
| implies(not(Y),implies(Y,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,not(Y)),implies(Y,falsehood)),truth) ),[0,0],$fot(not(Y))]]) ).
cnf(refute_0_97,plain,
( implies(or(falsehood,not(Y)),implies(Y,falsehood)) != truth
| implies(not(Y),implies(Y,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,not(Y)),not(Y)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
implies(not(Y),implies(Y,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,not(Y)),implies(Y,falsehood)),truth) )],[refute_0_15,refute_0_97]) ).
cnf(refute_0_99,plain,
implies(not(Y),implies(Y,falsehood)) = or(Y,implies(Y,falsehood)),
inference(subst,[],[refute_0_6:[bind(X,$fot(Y)),bind(Y,$fot(implies(Y,falsehood)))]]) ).
cnf(refute_0_100,plain,
( implies(not(Y),implies(Y,falsehood)) != or(Y,implies(Y,falsehood))
| implies(not(Y),implies(Y,falsehood)) != truth
| or(Y,implies(Y,falsehood)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),truth) ),[0],$fot(or(Y,implies(Y,falsehood)))]]) ).
cnf(refute_0_101,plain,
( implies(not(Y),implies(Y,falsehood)) != truth
| or(Y,implies(Y,falsehood)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),or(Y,implies(Y,falsehood))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
or(Y,implies(Y,falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(not(Y),implies(Y,falsehood)),truth) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)) = truth,
inference(subst,[],[refute_0_102:[bind(Y,$fot(or(X_49,X_50)))]]) ).
cnf(refute_0_104,plain,
or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)) = or(X_49,or(X_50,implies(or(X_49,X_50),falsehood))),
inference(subst,[],[or_associativity:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(implies(or(X_49,X_50),falsehood)))]]) ).
cnf(refute_0_105,plain,
( or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)) != or(X_49,or(X_50,implies(or(X_49,X_50),falsehood)))
| or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)) != truth
| or(X_49,or(X_50,implies(or(X_49,X_50),falsehood))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)),truth) ),[0],$fot(or(X_49,or(X_50,implies(or(X_49,X_50),falsehood))))]]) ).
cnf(refute_0_106,plain,
( or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)) != truth
| or(X_49,or(X_50,implies(or(X_49,X_50),falsehood))) = truth ),
inference(resolve,[$cnf( $equal(or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)),or(X_49,or(X_50,implies(or(X_49,X_50),falsehood)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
or(X_49,or(X_50,implies(or(X_49,X_50),falsehood))) = truth,
inference(resolve,[$cnf( $equal(or(or(X_49,X_50),implies(or(X_49,X_50),falsehood)),truth) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
or(X_52,or(truth,implies(or(X_52,truth),falsehood))) = truth,
inference(subst,[],[refute_0_107:[bind(X_49,$fot(X_52)),bind(X_50,$fot(truth))]]) ).
cnf(refute_0_109,plain,
or(X_52,truth) = implies(falsehood,X_52),
inference(subst,[],[refute_0_60:[bind(X_12,$fot(X_52))]]) ).
cnf(refute_0_110,plain,
( or(X_52,or(truth,implies(or(X_52,truth),falsehood))) != truth
| or(X_52,truth) != implies(falsehood,X_52)
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X_52,or(truth,implies(or(X_52,truth),falsehood))),truth) ),[0,1,1,0],$fot(implies(falsehood,X_52))]]) ).
cnf(refute_0_111,plain,
( or(X_52,or(truth,implies(or(X_52,truth),falsehood))) != truth
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = truth ),
inference(resolve,[$cnf( $equal(or(X_52,truth),implies(falsehood,X_52)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = truth,
inference(resolve,[$cnf( $equal(or(X_52,or(truth,implies(or(X_52,truth),falsehood))),truth) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
implies(implies(implies(falsehood,X_42),truth),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(implies(falsehood,X_42))),bind(Y,$fot(truth))]]) ).
cnf(refute_0_114,plain,
or(falsehood,X_5) = X_5,
inference(subst,[],[refute_0_94:[bind(Y,$fot(X_5))]]) ).
cnf(refute_0_115,plain,
implies(or(falsehood,X_5),X_5) = implies(or(falsehood,X_5),X_5),
introduced(tautology,[refl,[$fot(implies(or(falsehood,X_5),X_5))]]) ).
cnf(refute_0_116,plain,
( implies(or(falsehood,X_5),X_5) != implies(or(falsehood,X_5),X_5)
| or(falsehood,X_5) != X_5
| implies(or(falsehood,X_5),X_5) = implies(X_5,X_5) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_5),X_5),implies(or(falsehood,X_5),X_5)) ),[1,0],$fot(X_5)]]) ).
cnf(refute_0_117,plain,
( or(falsehood,X_5) != X_5
| implies(or(falsehood,X_5),X_5) = implies(X_5,X_5) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_5),X_5),implies(or(falsehood,X_5),X_5)) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(or(falsehood,X_5),X_5) = implies(X_5,X_5),
inference(resolve,[$cnf( $equal(or(falsehood,X_5),X_5) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
( implies(or(falsehood,X_5),X_5) != implies(X_5,X_5)
| implies(or(falsehood,X_5),X_5) != truth
| implies(X_5,X_5) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,X_5),X_5),truth) ),[0],$fot(implies(X_5,X_5))]]) ).
cnf(refute_0_120,plain,
( implies(or(falsehood,X_5),X_5) != truth
| implies(X_5,X_5) = truth ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_5),X_5),implies(X_5,X_5)) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
implies(X_5,X_5) = truth,
inference(resolve,[$cnf( $equal(implies(or(falsehood,X_5),X_5),truth) )],[refute_0_36,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(not(X),not(X)) = truth,
inference(subst,[],[refute_0_121:[bind(X_5,$fot(not(X)))]]) ).
cnf(refute_0_123,plain,
( implies(not(X),not(X)) != truth
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(truth)]]) ).
cnf(refute_0_124,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),truth) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_47,refute_0_124]) ).
cnf(refute_0_126,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != truth
| truth = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) ),[0],$fot(truth)]]) ).
cnf(refute_0_127,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| truth = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(or(X,not(X)),truth) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
truth = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_74,refute_0_127]) ).
cnf(refute_0_129,plain,
truth = implies(implies(falsehood,X_42),truth),
inference(subst,[],[refute_0_128:[bind(X,$fot(X_42))]]) ).
cnf(refute_0_130,plain,
( truth != implies(implies(falsehood,X_42),truth)
| implies(implies(falsehood,X_42),truth) = truth ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(implies(falsehood,X_42),truth)))]]) ).
cnf(refute_0_131,plain,
implies(implies(falsehood,X_42),truth) = truth,
inference(resolve,[$cnf( $equal(truth,implies(implies(falsehood,X_42),truth)) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( implies(implies(falsehood,X_42),truth) != truth
| implies(implies(implies(falsehood,X_42),truth),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(implies(falsehood,X_42),truth),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),truth) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_133,plain,
( implies(implies(implies(falsehood,X_42),truth),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != truth
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_42),truth),truth) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = truth,
inference(resolve,[$cnf( $equal(implies(implies(implies(falsehood,X_42),truth),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),truth) )],[refute_0_113,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(truth,Z) = Z,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Z))]]) ).
cnf(refute_0_136,plain,
implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) = implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)),
introduced(tautology,[refl,[$fot(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)))]]) ).
cnf(refute_0_137,plain,
( implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) != implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))
| implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) = implies(Z,implies(implies(falsehood,X_42),Z)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) ),[1,0],$fot(Z)]]) ).
cnf(refute_0_138,plain,
( implies(truth,Z) != Z
| implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) = implies(Z,implies(implies(falsehood,X_42),Z)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) = implies(Z,implies(implies(falsehood,X_42),Z)),
inference(resolve,[$cnf( $equal(implies(truth,Z),Z) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))))]]) ).
cnf(refute_0_141,plain,
( implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) != implies(Z,implies(implies(falsehood,X_42),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = implies(Z,implies(implies(falsehood,X_42),Z)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))))),bind(Y0,$fot(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)))),bind(Z0,$fot(implies(Z,implies(implies(falsehood,X_42),Z))))]]) ).
cnf(refute_0_142,plain,
( implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)) != implies(Z,implies(implies(falsehood,X_42),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = implies(Z,implies(implies(falsehood,X_42),Z)) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) = implies(Z,implies(implies(falsehood,X_42),Z)),
inference(resolve,[$cnf( $equal(implies(implies(truth,Z),implies(implies(falsehood,X_42),Z)),implies(Z,implies(implies(falsehood,X_42),Z))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != implies(Z,implies(implies(falsehood,X_42),Z))
| implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != truth
| implies(Z,implies(implies(falsehood,X_42),Z)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),truth) ),[0],$fot(implies(Z,implies(implies(falsehood,X_42),Z)))]]) ).
cnf(refute_0_145,plain,
( implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))) != truth
| implies(Z,implies(implies(falsehood,X_42),Z)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),implies(Z,implies(implies(falsehood,X_42),Z))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
implies(Z,implies(implies(falsehood,X_42),Z)) = truth,
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,Z),implies(implies(falsehood,X_42),Z))),truth) )],[refute_0_134,refute_0_145]) ).
cnf(refute_0_147,plain,
implies(falsehood,implies(implies(falsehood,X_52),falsehood)) = truth,
inference(subst,[],[refute_0_146:[bind(Z,$fot(falsehood)),bind(X_42,$fot(X_52))]]) ).
cnf(refute_0_148,plain,
or(truth,implies(implies(falsehood,X_52),falsehood)) = implies(falsehood,implies(implies(falsehood,X_52),falsehood)),
inference(subst,[],[refute_0_42:[bind(X_12,$fot(implies(implies(falsehood,X_52),falsehood)))]]) ).
cnf(refute_0_149,plain,
( implies(falsehood,implies(implies(falsehood,X_52),falsehood)) != truth
| or(truth,implies(implies(falsehood,X_52),falsehood)) != implies(falsehood,implies(implies(falsehood,X_52),falsehood))
| or(truth,implies(implies(falsehood,X_52),falsehood)) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(or(truth,implies(implies(falsehood,X_52),falsehood)))),bind(Y0,$fot(implies(falsehood,implies(implies(falsehood,X_52),falsehood)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_150,plain,
( implies(falsehood,implies(implies(falsehood,X_52),falsehood)) != truth
| or(truth,implies(implies(falsehood,X_52),falsehood)) = truth ),
inference(resolve,[$cnf( $equal(or(truth,implies(implies(falsehood,X_52),falsehood)),implies(falsehood,implies(implies(falsehood,X_52),falsehood))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
or(truth,implies(implies(falsehood,X_52),falsehood)) = truth,
inference(resolve,[$cnf( $equal(implies(falsehood,implies(implies(falsehood,X_52),falsehood)),truth) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),
introduced(tautology,[refl,[$fot(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))))]]) ).
cnf(refute_0_153,plain,
( or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) != or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood)))
| or(truth,implies(implies(falsehood,X_52),falsehood)) != truth
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = or(X_52,truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood)))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_154,plain,
( or(truth,implies(implies(falsehood,X_52),falsehood)) != truth
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = or(X_52,truth) ),
inference(resolve,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood)))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = or(X_52,truth),
inference(resolve,[$cnf( $equal(or(truth,implies(implies(falsehood,X_52),falsehood)),truth) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) != or(X_52,truth)
| or(X_52,truth) != implies(falsehood,X_52)
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = implies(falsehood,X_52) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))))),bind(Y0,$fot(or(X_52,truth))),bind(Z0,$fot(implies(falsehood,X_52)))]]) ).
cnf(refute_0_157,plain,
( or(X_52,truth) != implies(falsehood,X_52)
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = implies(falsehood,X_52) ),
inference(resolve,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),or(X_52,truth)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) = implies(falsehood,X_52),
inference(resolve,[$cnf( $equal(or(X_52,truth),implies(falsehood,X_52)) )],[refute_0_109,refute_0_157]) ).
cnf(refute_0_159,plain,
( or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) != implies(falsehood,X_52)
| or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) != truth
| implies(falsehood,X_52) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),truth) ),[0],$fot(implies(falsehood,X_52))]]) ).
cnf(refute_0_160,plain,
( or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))) != truth
| implies(falsehood,X_52) = truth ),
inference(resolve,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),implies(falsehood,X_52)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
implies(falsehood,X_52) = truth,
inference(resolve,[$cnf( $equal(or(X_52,or(truth,implies(implies(falsehood,X_52),falsehood))),truth) )],[refute_0_112,refute_0_160]) ).
cnf(refute_0_162,plain,
implies(falsehood,X) = truth,
inference(subst,[],[refute_0_161:[bind(X_52,$fot(X))]]) ).
cnf(refute_0_163,plain,
( implies(falsehood,X) != truth
| implies(implies(X,falsehood),falsehood) != implies(implies(falsehood,X),X)
| implies(implies(X,falsehood),falsehood) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(implies(falsehood,X),X)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_164,plain,
( implies(implies(X,falsehood),falsehood) != implies(implies(falsehood,X),X)
| implies(implies(X,falsehood),falsehood) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(falsehood,X),truth) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
implies(implies(X,falsehood),falsehood) = implies(truth,X),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(implies(falsehood,X),X)) )],[refute_0_1,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(implies(not(X),X_27),X_27) = implies(implies(X_27,not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(X_27))]]) ).
cnf(refute_0_167,plain,
or(X,X_27) = implies(not(X),X_27),
inference(subst,[],[or_definition:[bind(Y,$fot(X_27))]]) ).
cnf(refute_0_168,plain,
( or(X,X_27) != implies(not(X),X_27)
| implies(not(X),X_27) = or(X,X_27) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(or(X,X_27))),bind(Y0,$fot(implies(not(X),X_27)))]]) ).
cnf(refute_0_169,plain,
implies(not(X),X_27) = or(X,X_27),
inference(resolve,[$cnf( $equal(or(X,X_27),implies(not(X),X_27)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
( implies(implies(not(X),X_27),X_27) != implies(implies(X_27,not(X)),not(X))
| implies(not(X),X_27) != or(X,X_27)
| implies(or(X,X_27),X_27) = implies(implies(X_27,not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_27),X_27),implies(implies(X_27,not(X)),not(X))) ),[0,0],$fot(or(X,X_27))]]) ).
cnf(refute_0_171,plain,
( implies(implies(not(X),X_27),X_27) != implies(implies(X_27,not(X)),not(X))
| implies(or(X,X_27),X_27) = implies(implies(X_27,not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_27),or(X,X_27)) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
implies(or(X,X_27),X_27) = implies(implies(X_27,not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_27),X_27),implies(implies(X_27,not(X)),not(X))) )],[refute_0_166,refute_0_171]) ).
cnf(refute_0_173,plain,
implies(or(X,falsehood),falsehood) = implies(implies(falsehood,not(X)),not(X)),
inference(subst,[],[refute_0_172:[bind(X_27,$fot(falsehood))]]) ).
cnf(refute_0_174,plain,
implies(falsehood,not(X)) = truth,
inference(subst,[],[refute_0_161:[bind(X_52,$fot(not(X)))]]) ).
cnf(refute_0_175,plain,
( implies(falsehood,not(X)) != truth
| implies(or(X,falsehood),falsehood) != implies(implies(falsehood,not(X)),not(X))
| implies(or(X,falsehood),falsehood) = implies(truth,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(implies(falsehood,not(X)),not(X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_176,plain,
( implies(or(X,falsehood),falsehood) != implies(implies(falsehood,not(X)),not(X))
| implies(or(X,falsehood),falsehood) = implies(truth,not(X)) ),
inference(resolve,[$cnf( $equal(implies(falsehood,not(X)),truth) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
implies(or(X,falsehood),falsehood) = implies(truth,not(X)),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(implies(falsehood,not(X)),not(X))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
or(or(falsehood,falsehood),X_12) = implies(not(or(falsehood,falsehood)),X_12),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,falsehood))),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_179,plain,
and(X_1,truth) = not(or(not(X_1),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_1)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_180,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| not(truth) != falsehood
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_181,plain,
( and(X_1,truth) != not(or(not(X_1),not(truth)))
| and(X_1,truth) = not(or(not(X_1),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_180]) ).
cnf(refute_0_182,plain,
and(X_1,truth) = not(or(not(X_1),falsehood)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),not(truth)))) )],[refute_0_179,refute_0_181]) ).
cnf(refute_0_183,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_184,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_183]) ).
cnf(refute_0_185,plain,
or(not(X_1),falsehood) = or(falsehood,not(X_1)),
inference(subst,[],[refute_0_184:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_186,plain,
not(or(not(X_1),falsehood)) = not(or(not(X_1),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_187,plain,
( not(or(not(X_1),falsehood)) != not(or(not(X_1),falsehood))
| or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) ),[1,0],$fot(or(falsehood,not(X_1)))]]) ).
cnf(refute_0_188,plain,
( or(not(X_1),falsehood) != or(falsehood,not(X_1))
| not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(not(X_1),falsehood))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
not(or(not(X_1),falsehood)) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(or(not(X_1),falsehood),or(falsehood,not(X_1))) )],[refute_0_185,refute_0_188]) ).
cnf(refute_0_190,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| not(or(not(X_1),falsehood)) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) ),[0],$fot(not(or(not(X_1),falsehood)))]]) ).
cnf(refute_0_191,plain,
( and(X_1,truth) != not(or(not(X_1),falsehood))
| and(X_1,truth) = not(or(falsehood,not(X_1))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_1),falsehood)),not(or(falsehood,not(X_1)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
and(X_1,truth) = not(or(falsehood,not(X_1))),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(not(X_1),falsehood))) )],[refute_0_182,refute_0_191]) ).
cnf(refute_0_193,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_192:[bind(X_1,$fot(truth))]]) ).
cnf(refute_0_194,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| not(truth) != falsehood
| and(truth,truth) = not(or(falsehood,falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_195,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_194]) ).
cnf(refute_0_196,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_193,refute_0_195]) ).
cnf(refute_0_197,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_198,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
( not(or(falsehood,falsehood)) != and(truth,truth)
| or(or(falsehood,falsehood),X_12) != implies(not(or(falsehood,falsehood)),X_12)
| or(or(falsehood,falsehood),X_12) = implies(and(truth,truth),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_12),implies(not(or(falsehood,falsehood)),X_12)) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_200,plain,
( or(or(falsehood,falsehood),X_12) != implies(not(or(falsehood,falsehood)),X_12)
| or(or(falsehood,falsehood),X_12) = implies(and(truth,truth),X_12) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
or(or(falsehood,falsehood),X_12) = implies(and(truth,truth),X_12),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_12),implies(not(or(falsehood,falsehood)),X_12)) )],[refute_0_178,refute_0_200]) ).
cnf(refute_0_202,plain,
or(or(falsehood,falsehood),X_12) = or(falsehood,or(falsehood,X_12)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood)),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_203,plain,
( or(or(falsehood,falsehood),X_12) != implies(and(truth,truth),X_12)
| or(or(falsehood,falsehood),X_12) != or(falsehood,or(falsehood,X_12))
| or(falsehood,or(falsehood,X_12)) = implies(and(truth,truth),X_12) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),X_12),implies(and(truth,truth),X_12)) ),[0],$fot(or(falsehood,or(falsehood,X_12)))]]) ).
cnf(refute_0_204,plain,
( or(or(falsehood,falsehood),X_12) != implies(and(truth,truth),X_12)
| or(falsehood,or(falsehood,X_12)) = implies(and(truth,truth),X_12) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_12),or(falsehood,or(falsehood,X_12))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
or(falsehood,or(falsehood,X_12)) = implies(and(truth,truth),X_12),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),X_12),implies(and(truth,truth),X_12)) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
or(falsehood,or(falsehood,X_24)) = implies(and(truth,truth),X_24),
inference(subst,[],[refute_0_205:[bind(X_12,$fot(X_24))]]) ).
cnf(refute_0_207,plain,
or(X_24,falsehood) = or(falsehood,X_24),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_24)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_208,plain,
( or(X_24,falsehood) != or(falsehood,X_24)
| or(falsehood,X_24) = or(X_24,falsehood) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(or(X_24,falsehood))),bind(Y0,$fot(or(falsehood,X_24)))]]) ).
cnf(refute_0_209,plain,
or(falsehood,X_24) = or(X_24,falsehood),
inference(resolve,[$cnf( $equal(or(X_24,falsehood),or(falsehood,X_24)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
( or(falsehood,X_24) != or(X_24,falsehood)
| or(falsehood,or(falsehood,X_24)) != implies(and(truth,truth),X_24)
| or(falsehood,or(X_24,falsehood)) = implies(and(truth,truth),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,X_24)),implies(and(truth,truth),X_24)) ),[0,1],$fot(or(X_24,falsehood))]]) ).
cnf(refute_0_211,plain,
( or(falsehood,or(falsehood,X_24)) != implies(and(truth,truth),X_24)
| or(falsehood,or(X_24,falsehood)) = implies(and(truth,truth),X_24) ),
inference(resolve,[$cnf( $equal(or(falsehood,X_24),or(X_24,falsehood)) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
or(falsehood,or(X_24,falsehood)) = implies(and(truth,truth),X_24),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_24)),implies(and(truth,truth),X_24)) )],[refute_0_206,refute_0_211]) ).
cnf(refute_0_213,plain,
or(falsehood,or(X_24,falsehood)) = or(X_24,falsehood),
inference(subst,[],[refute_0_94:[bind(Y,$fot(or(X_24,falsehood)))]]) ).
cnf(refute_0_214,plain,
( or(falsehood,or(X_24,falsehood)) != implies(and(truth,truth),X_24)
| or(falsehood,or(X_24,falsehood)) != or(X_24,falsehood)
| or(X_24,falsehood) = implies(and(truth,truth),X_24) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_24,falsehood)),implies(and(truth,truth),X_24)) ),[0],$fot(or(X_24,falsehood))]]) ).
cnf(refute_0_215,plain,
( or(falsehood,or(X_24,falsehood)) != implies(and(truth,truth),X_24)
| or(X_24,falsehood) = implies(and(truth,truth),X_24) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_24,falsehood)),or(X_24,falsehood)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
implies(truth,X_24) = X_24,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_217,plain,
not(not(truth)) = not(not(truth)),
introduced(tautology,[refl,[$fot(not(not(truth)))]]) ).
cnf(refute_0_218,plain,
( not(not(truth)) != not(not(truth))
| not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(not(truth)),not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_219,plain,
( not(truth) != falsehood
| not(not(truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(not(truth))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
not(not(truth)) = not(falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_219]) ).
cnf(refute_0_221,plain,
( not(falsehood) != truth
| not(not(truth)) != not(falsehood)
| not(not(truth)) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(not(not(truth)))),bind(Y0,$fot(not(falsehood))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_222,plain,
( not(falsehood) != truth
| not(not(truth)) = truth ),
inference(resolve,[$cnf( $equal(not(not(truth)),not(falsehood)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
not(not(truth)) = truth,
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_87,refute_0_222]) ).
cnf(refute_0_224,plain,
or(falsehood,not(X_1)) = not(X_1),
inference(subst,[],[refute_0_94:[bind(Y,$fot(not(X_1)))]]) ).
cnf(refute_0_225,plain,
not(or(falsehood,not(X_1))) = not(or(falsehood,not(X_1))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_226,plain,
( not(or(falsehood,not(X_1))) != not(or(falsehood,not(X_1)))
| or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) ),[1,0],$fot(not(X_1))]]) ).
cnf(refute_0_227,plain,
( or(falsehood,not(X_1)) != not(X_1)
| not(or(falsehood,not(X_1))) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(or(falsehood,not(X_1)))) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
not(or(falsehood,not(X_1))) = not(not(X_1)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_1)),not(X_1)) )],[refute_0_224,refute_0_227]) ).
cnf(refute_0_229,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| not(or(falsehood,not(X_1))) != not(not(X_1))
| and(X_1,truth) = not(not(X_1)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_1,truth),not(not(X_1))) ),[0],$fot(not(or(falsehood,not(X_1))))]]) ).
cnf(refute_0_230,plain,
( and(X_1,truth) != not(or(falsehood,not(X_1)))
| and(X_1,truth) = not(not(X_1)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_1))),not(not(X_1))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
and(X_1,truth) = not(not(X_1)),
inference(resolve,[$cnf( $equal(and(X_1,truth),not(or(falsehood,not(X_1)))) )],[refute_0_192,refute_0_230]) ).
cnf(refute_0_232,plain,
and(truth,truth) = not(not(truth)),
inference(subst,[],[refute_0_231:[bind(X_1,$fot(truth))]]) ).
cnf(refute_0_233,plain,
( and(truth,truth) != not(not(truth))
| not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(not(truth)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_234,plain,
( not(not(truth)) != truth
| and(truth,truth) = truth ),
inference(resolve,[$cnf( $equal(and(truth,truth),not(not(truth))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
and(truth,truth) = truth,
inference(resolve,[$cnf( $equal(not(not(truth)),truth) )],[refute_0_223,refute_0_234]) ).
cnf(refute_0_236,plain,
implies(and(truth,truth),X_24) = implies(and(truth,truth),X_24),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),X_24))]]) ).
cnf(refute_0_237,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_24) != implies(and(truth,truth),X_24)
| implies(and(truth,truth),X_24) = implies(truth,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),X_24),implies(and(truth,truth),X_24)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_238,plain,
( and(truth,truth) != truth
| implies(and(truth,truth),X_24) = implies(truth,X_24) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_24),implies(and(truth,truth),X_24)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
implies(and(truth,truth),X_24) = implies(truth,X_24),
inference(resolve,[$cnf( $equal(and(truth,truth),truth) )],[refute_0_235,refute_0_238]) ).
cnf(refute_0_240,plain,
( implies(and(truth,truth),X_24) != implies(truth,X_24)
| implies(truth,X_24) != X_24
| implies(and(truth,truth),X_24) = X_24 ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(and(truth,truth),X_24))),bind(Y0,$fot(implies(truth,X_24))),bind(Z0,$fot(X_24))]]) ).
cnf(refute_0_241,plain,
( implies(truth,X_24) != X_24
| implies(and(truth,truth),X_24) = X_24 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_24),implies(truth,X_24)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
implies(and(truth,truth),X_24) = X_24,
inference(resolve,[$cnf( $equal(implies(truth,X_24),X_24) )],[refute_0_216,refute_0_241]) ).
cnf(refute_0_243,plain,
( implies(and(truth,truth),X_24) != X_24
| or(X_24,falsehood) != implies(and(truth,truth),X_24)
| or(X_24,falsehood) = X_24 ),
introduced(tautology,[equality,[$cnf( $equal(or(X_24,falsehood),implies(and(truth,truth),X_24)) ),[1],$fot(X_24)]]) ).
cnf(refute_0_244,plain,
( or(X_24,falsehood) != implies(and(truth,truth),X_24)
| or(X_24,falsehood) = X_24 ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_24),X_24) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
( or(falsehood,or(X_24,falsehood)) != implies(and(truth,truth),X_24)
| or(X_24,falsehood) = X_24 ),
inference(resolve,[$cnf( $equal(or(X_24,falsehood),implies(and(truth,truth),X_24)) )],[refute_0_215,refute_0_244]) ).
cnf(refute_0_246,plain,
or(X_24,falsehood) = X_24,
inference(resolve,[$cnf( $equal(or(falsehood,or(X_24,falsehood)),implies(and(truth,truth),X_24)) )],[refute_0_212,refute_0_245]) ).
cnf(refute_0_247,plain,
or(X,falsehood) = X,
inference(subst,[],[refute_0_246:[bind(X_24,$fot(X))]]) ).
cnf(refute_0_248,plain,
implies(or(X,falsehood),falsehood) = implies(or(X,falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(or(X,falsehood),falsehood))]]) ).
cnf(refute_0_249,plain,
( implies(or(X,falsehood),falsehood) != implies(or(X,falsehood),falsehood)
| or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_250,plain,
( or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
implies(or(X,falsehood),falsehood) = implies(X,falsehood),
inference(resolve,[$cnf( $equal(or(X,falsehood),X) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
( implies(or(X,falsehood),falsehood) != implies(X,falsehood)
| implies(or(X,falsehood),falsehood) != implies(truth,not(X))
| implies(X,falsehood) = implies(truth,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(truth,not(X))) ),[0],$fot(implies(X,falsehood))]]) ).
cnf(refute_0_253,plain,
( implies(or(X,falsehood),falsehood) != implies(truth,not(X))
| implies(X,falsehood) = implies(truth,not(X)) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(X,falsehood)) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(truth,not(X)) = not(X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_255,plain,
( implies(X,falsehood) != implies(truth,not(X))
| implies(truth,not(X)) != not(X)
| implies(X,falsehood) = not(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,falsehood),not(X)) ),[0],$fot(implies(truth,not(X)))]]) ).
cnf(refute_0_256,plain,
( implies(X,falsehood) != implies(truth,not(X))
| implies(X,falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(truth,not(X)),not(X)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( implies(or(X,falsehood),falsehood) != implies(truth,not(X))
| implies(X,falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(X,falsehood),implies(truth,not(X))) )],[refute_0_253,refute_0_256]) ).
cnf(refute_0_258,plain,
implies(X,falsehood) = not(X),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(truth,not(X))) )],[refute_0_177,refute_0_257]) ).
cnf(refute_0_259,plain,
not(implies(X,falsehood)) = not(implies(X,falsehood)),
introduced(tautology,[refl,[$fot(not(implies(X,falsehood)))]]) ).
cnf(refute_0_260,plain,
( implies(X,falsehood) != not(X)
| not(implies(X,falsehood)) != not(implies(X,falsehood))
| not(implies(X,falsehood)) = not(not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X,falsehood)),not(implies(X,falsehood))) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_261,plain,
( implies(X,falsehood) != not(X)
| not(implies(X,falsehood)) = not(not(X)) ),
inference(resolve,[$cnf( $equal(not(implies(X,falsehood)),not(implies(X,falsehood))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
not(implies(X,falsehood)) = not(not(X)),
inference(resolve,[$cnf( $equal(implies(X,falsehood),not(X)) )],[refute_0_258,refute_0_261]) ).
cnf(refute_0_263,plain,
implies(implies(X,falsehood),falsehood) = not(implies(X,falsehood)),
inference(subst,[],[refute_0_258:[bind(X,$fot(implies(X,falsehood)))]]) ).
cnf(refute_0_264,plain,
( implies(implies(X,falsehood),falsehood) != not(implies(X,falsehood))
| not(implies(X,falsehood)) != not(not(X))
| implies(implies(X,falsehood),falsehood) = not(not(X)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(implies(X,falsehood),falsehood))),bind(Y0,$fot(not(implies(X,falsehood)))),bind(Z0,$fot(not(not(X))))]]) ).
cnf(refute_0_265,plain,
( not(implies(X,falsehood)) != not(not(X))
| implies(implies(X,falsehood),falsehood) = not(not(X)) ),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),not(implies(X,falsehood))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
implies(implies(X,falsehood),falsehood) = not(not(X)),
inference(resolve,[$cnf( $equal(not(implies(X,falsehood)),not(not(X))) )],[refute_0_262,refute_0_265]) ).
cnf(refute_0_267,plain,
( implies(implies(X,falsehood),falsehood) != implies(truth,X)
| implies(implies(X,falsehood),falsehood) != not(not(X))
| not(not(X)) = implies(truth,X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(truth,X)) ),[0],$fot(not(not(X)))]]) ).
cnf(refute_0_268,plain,
( implies(implies(X,falsehood),falsehood) != implies(truth,X)
| not(not(X)) = implies(truth,X) ),
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),not(not(X))) )],[refute_0_266,refute_0_267]) ).
cnf(refute_0_269,plain,
( implies(truth,X) != X
| not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(not(not(X)),implies(truth,X)) ),[1],$fot(X)]]) ).
cnf(refute_0_270,plain,
( not(not(X)) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(implies(truth,X),X) )],[wajsberg_1,refute_0_269]) ).
cnf(refute_0_271,plain,
( implies(implies(X,falsehood),falsehood) != implies(truth,X)
| not(not(X)) = X ),
inference(resolve,[$cnf( $equal(not(not(X)),implies(truth,X)) )],[refute_0_268,refute_0_270]) ).
cnf(refute_0_272,plain,
not(not(X)) = X,
inference(resolve,[$cnf( $equal(implies(implies(X,falsehood),falsehood),implies(truth,X)) )],[refute_0_165,refute_0_271]) ).
cnf(refute_0_273,plain,
not(not(X_57)) = X_57,
inference(subst,[],[refute_0_272:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_274,plain,
( not(not(X_57)) != X_57
| or(not(X_57),Y) != implies(not(not(X_57)),Y)
| or(not(X_57),Y) = implies(X_57,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_57),Y),implies(not(not(X_57)),Y)) ),[1,0],$fot(X_57)]]) ).
cnf(refute_0_275,plain,
( or(not(X_57),Y) != implies(not(not(X_57)),Y)
| or(not(X_57),Y) = implies(X_57,Y) ),
inference(resolve,[$cnf( $equal(not(not(X_57)),X_57) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
or(not(X_57),Y) = implies(X_57,Y),
inference(resolve,[$cnf( $equal(or(not(X_57),Y),implies(not(not(X_57)),Y)) )],[refute_0_0,refute_0_275]) ).
cnf(refute_0_277,plain,
or(not(implies(X,Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(subst,[],[refute_0_276:[bind(Y,$fot(and(not(X),Y))),bind(X_57,$fot(implies(X,Y)))]]) ).
cnf(refute_0_278,plain,
and(X,not(X_57)) = not(or(not(X),not(not(X_57)))),
inference(subst,[],[and_definition:[bind(Y,$fot(not(X_57)))]]) ).
cnf(refute_0_279,plain,
( and(X,not(X_57)) != not(or(not(X),not(not(X_57))))
| not(not(X_57)) != X_57
| and(X,not(X_57)) = not(or(not(X),X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_57)),not(or(not(X),not(not(X_57))))) ),[1,0,1],$fot(X_57)]]) ).
cnf(refute_0_280,plain,
( and(X,not(X_57)) != not(or(not(X),not(not(X_57))))
| and(X,not(X_57)) = not(or(not(X),X_57)) ),
inference(resolve,[$cnf( $equal(not(not(X_57)),X_57) )],[refute_0_273,refute_0_279]) ).
cnf(refute_0_281,plain,
and(X,not(X_57)) = not(or(not(X),X_57)),
inference(resolve,[$cnf( $equal(and(X,not(X_57)),not(or(not(X),not(not(X_57))))) )],[refute_0_278,refute_0_280]) ).
cnf(refute_0_282,plain,
or(not(X),X_57) = implies(X,X_57),
inference(subst,[],[refute_0_276:[bind(Y,$fot(X_57)),bind(X_57,$fot(X))]]) ).
cnf(refute_0_283,plain,
not(or(not(X),X_57)) = not(or(not(X),X_57)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_57)))]]) ).
cnf(refute_0_284,plain,
( not(or(not(X),X_57)) != not(or(not(X),X_57))
| or(not(X),X_57) != implies(X,X_57)
| not(or(not(X),X_57)) = not(implies(X,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_57)),not(or(not(X),X_57))) ),[1,0],$fot(implies(X,X_57))]]) ).
cnf(refute_0_285,plain,
( or(not(X),X_57) != implies(X,X_57)
| not(or(not(X),X_57)) = not(implies(X,X_57)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_57)),not(or(not(X),X_57))) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
not(or(not(X),X_57)) = not(implies(X,X_57)),
inference(resolve,[$cnf( $equal(or(not(X),X_57),implies(X,X_57)) )],[refute_0_282,refute_0_285]) ).
cnf(refute_0_287,plain,
( and(X,not(X_57)) != not(or(not(X),X_57))
| not(or(not(X),X_57)) != not(implies(X,X_57))
| and(X,not(X_57)) = not(implies(X,X_57)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_57)),not(implies(X,X_57))) ),[0],$fot(not(or(not(X),X_57)))]]) ).
cnf(refute_0_288,plain,
( and(X,not(X_57)) != not(or(not(X),X_57))
| and(X,not(X_57)) = not(implies(X,X_57)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_57)),not(implies(X,X_57))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
and(X,not(X_57)) = not(implies(X,X_57)),
inference(resolve,[$cnf( $equal(and(X,not(X_57)),not(or(not(X),X_57))) )],[refute_0_281,refute_0_288]) ).
cnf(refute_0_290,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(subst,[],[refute_0_289:[bind(X_57,$fot(Y))]]) ).
cnf(refute_0_291,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(and(X,not(Y)),and(not(X),Y)),
introduced(tautology,[refl,[$fot(or(and(X,not(Y)),and(not(X),Y)))]]) ).
cnf(refute_0_292,plain,
( and(X,not(Y)) != not(implies(X,Y))
| or(and(X,not(Y)),and(not(X),Y)) != or(and(X,not(Y)),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(and(X,not(Y)),and(not(X),Y))) ),[1,0],$fot(not(implies(X,Y)))]]) ).
cnf(refute_0_293,plain,
( and(X,not(Y)) != not(implies(X,Y))
| or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(and(X,not(Y)),and(not(X),Y))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)),
inference(resolve,[$cnf( $equal(and(X,not(Y)),not(implies(X,Y))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
( or(and(X,not(Y)),and(not(X),Y)) != or(not(implies(X,Y)),and(not(X),Y))
| or(not(implies(X,Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(or(and(X,not(Y)),and(not(X),Y)))),bind(Y0,$fot(or(not(implies(X,Y)),and(not(X),Y)))),bind(Z0,$fot(implies(implies(X,Y),and(not(X),Y))))]]) ).
cnf(refute_0_296,plain,
( or(not(implies(X,Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),or(not(implies(X,Y)),and(not(X),Y))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(or(not(implies(X,Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_277,refute_0_296]) ).
cnf(refute_0_298,plain,
( or(and(X,not(Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = implies(implies(X,Y),and(not(X),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) ),[1],$fot(implies(implies(X,Y),and(not(X),Y)))]]) ).
cnf(refute_0_299,plain,
( xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = implies(implies(X,Y),and(not(X),Y)) ),
inference(resolve,[$cnf( $equal(or(and(X,not(Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
xor(X,Y) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) )],[xor_definition,refute_0_299]) ).
cnf(refute_0_301,plain,
xor(X_81,X_81) = implies(implies(X_81,X_81),and(not(X_81),X_81)),
inference(subst,[],[refute_0_300:[bind(X,$fot(X_81)),bind(Y,$fot(X_81))]]) ).
cnf(refute_0_302,plain,
implies(X_81,X_81) = truth,
inference(subst,[],[refute_0_121:[bind(X_5,$fot(X_81))]]) ).
cnf(refute_0_303,plain,
( implies(X_81,X_81) != truth
| xor(X_81,X_81) != implies(implies(X_81,X_81),and(not(X_81),X_81))
| xor(X_81,X_81) = implies(truth,and(not(X_81),X_81)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_81,X_81),implies(implies(X_81,X_81),and(not(X_81),X_81))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_304,plain,
( xor(X_81,X_81) != implies(implies(X_81,X_81),and(not(X_81),X_81))
| xor(X_81,X_81) = implies(truth,and(not(X_81),X_81)) ),
inference(resolve,[$cnf( $equal(implies(X_81,X_81),truth) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
xor(X_81,X_81) = implies(truth,and(not(X_81),X_81)),
inference(resolve,[$cnf( $equal(xor(X_81,X_81),implies(implies(X_81,X_81),and(not(X_81),X_81))) )],[refute_0_301,refute_0_304]) ).
cnf(refute_0_306,plain,
not(implies(X_81,X_81)) = not(implies(X_81,X_81)),
introduced(tautology,[refl,[$fot(not(implies(X_81,X_81)))]]) ).
cnf(refute_0_307,plain,
( implies(X_81,X_81) != truth
| not(implies(X_81,X_81)) != not(implies(X_81,X_81))
| not(implies(X_81,X_81)) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_81,X_81)),not(implies(X_81,X_81))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_308,plain,
( implies(X_81,X_81) != truth
| not(implies(X_81,X_81)) = not(truth) ),
inference(resolve,[$cnf( $equal(not(implies(X_81,X_81)),not(implies(X_81,X_81))) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
not(implies(X_81,X_81)) = not(truth),
inference(resolve,[$cnf( $equal(implies(X_81,X_81),truth) )],[refute_0_302,refute_0_308]) ).
cnf(refute_0_310,plain,
( not(implies(X_81,X_81)) != not(truth)
| not(truth) != falsehood
| not(implies(X_81,X_81)) = falsehood ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(not(implies(X_81,X_81)))),bind(Y0,$fot(not(truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_311,plain,
( not(truth) != falsehood
| not(implies(X_81,X_81)) = falsehood ),
inference(resolve,[$cnf( $equal(not(implies(X_81,X_81)),not(truth)) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
not(implies(X_81,X_81)) = falsehood,
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_311]) ).
cnf(refute_0_313,plain,
and(X_81,not(X_81)) = not(implies(X_81,X_81)),
inference(subst,[],[refute_0_289:[bind(X,$fot(X_81)),bind(X_57,$fot(X_81))]]) ).
cnf(refute_0_314,plain,
or(not(X),not(Y)) = or(not(Y),not(X)),
inference(subst,[],[or_commutativity:[bind(X,$fot(not(X))),bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_315,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| or(not(X),not(Y)) != or(not(Y),not(X))
| and(X,Y) = not(or(not(Y),not(X))) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) ),[1,0],$fot(or(not(Y),not(X)))]]) ).
cnf(refute_0_316,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| and(X,Y) = not(or(not(Y),not(X))) ),
inference(resolve,[$cnf( $equal(or(not(X),not(Y)),or(not(Y),not(X))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
and(X,Y) = not(or(not(Y),not(X))),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_316]) ).
cnf(refute_0_318,plain,
( and(X,Y) != not(or(not(X),not(Y)))
| not(or(not(X),not(Y))) = and(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(not(or(not(X),not(Y)))))]]) ).
cnf(refute_0_319,plain,
not(or(not(X),not(Y))) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(X),not(Y)))) )],[and_definition,refute_0_318]) ).
cnf(refute_0_320,plain,
not(or(not(Y),not(X))) = and(Y,X),
inference(subst,[],[refute_0_319:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).
cnf(refute_0_321,plain,
( and(X,Y) != not(or(not(Y),not(X)))
| not(or(not(Y),not(X))) != and(Y,X)
| and(X,Y) = and(Y,X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,Y),and(Y,X)) ),[0],$fot(not(or(not(Y),not(X))))]]) ).
cnf(refute_0_322,plain,
( and(X,Y) != not(or(not(Y),not(X)))
| and(X,Y) = and(Y,X) ),
inference(resolve,[$cnf( $equal(not(or(not(Y),not(X))),and(Y,X)) )],[refute_0_320,refute_0_321]) ).
cnf(refute_0_323,plain,
and(X,Y) = and(Y,X),
inference(resolve,[$cnf( $equal(and(X,Y),not(or(not(Y),not(X)))) )],[refute_0_317,refute_0_322]) ).
cnf(refute_0_324,plain,
( and(X,Y) != and(Y,X)
| and(Y,X) = and(X,Y) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(and(Y,X)))]]) ).
cnf(refute_0_325,plain,
and(Y,X) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),and(Y,X)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
and(not(X_81),X_81) = and(X_81,not(X_81)),
inference(subst,[],[refute_0_325:[bind(X,$fot(X_81)),bind(Y,$fot(not(X_81)))]]) ).
cnf(refute_0_327,plain,
( and(X_81,not(X_81)) != not(implies(X_81,X_81))
| and(not(X_81),X_81) != and(X_81,not(X_81))
| and(not(X_81),X_81) = not(implies(X_81,X_81)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(and(not(X_81),X_81))),bind(Y0,$fot(and(X_81,not(X_81)))),bind(Z0,$fot(not(implies(X_81,X_81))))]]) ).
cnf(refute_0_328,plain,
( and(X_81,not(X_81)) != not(implies(X_81,X_81))
| and(not(X_81),X_81) = not(implies(X_81,X_81)) ),
inference(resolve,[$cnf( $equal(and(not(X_81),X_81),and(X_81,not(X_81))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
and(not(X_81),X_81) = not(implies(X_81,X_81)),
inference(resolve,[$cnf( $equal(and(X_81,not(X_81)),not(implies(X_81,X_81))) )],[refute_0_313,refute_0_328]) ).
cnf(refute_0_330,plain,
implies(truth,and(not(X_81),X_81)) = and(not(X_81),X_81),
inference(subst,[],[wajsberg_1:[bind(X,$fot(and(not(X_81),X_81)))]]) ).
cnf(refute_0_331,plain,
( and(not(X_81),X_81) != not(implies(X_81,X_81))
| implies(truth,and(not(X_81),X_81)) != and(not(X_81),X_81)
| implies(truth,and(not(X_81),X_81)) = not(implies(X_81,X_81)) ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,and(not(X_81),X_81)))),bind(Y0,$fot(and(not(X_81),X_81))),bind(Z0,$fot(not(implies(X_81,X_81))))]]) ).
cnf(refute_0_332,plain,
( and(not(X_81),X_81) != not(implies(X_81,X_81))
| implies(truth,and(not(X_81),X_81)) = not(implies(X_81,X_81)) ),
inference(resolve,[$cnf( $equal(implies(truth,and(not(X_81),X_81)),and(not(X_81),X_81)) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
implies(truth,and(not(X_81),X_81)) = not(implies(X_81,X_81)),
inference(resolve,[$cnf( $equal(and(not(X_81),X_81),not(implies(X_81,X_81))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
( implies(truth,and(not(X_81),X_81)) != not(implies(X_81,X_81))
| not(implies(X_81,X_81)) != falsehood
| implies(truth,and(not(X_81),X_81)) = falsehood ),
inference(subst,[],[refute_0_64:[bind(X0,$fot(implies(truth,and(not(X_81),X_81)))),bind(Y0,$fot(not(implies(X_81,X_81)))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_335,plain,
( not(implies(X_81,X_81)) != falsehood
| implies(truth,and(not(X_81),X_81)) = falsehood ),
inference(resolve,[$cnf( $equal(implies(truth,and(not(X_81),X_81)),not(implies(X_81,X_81))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
implies(truth,and(not(X_81),X_81)) = falsehood,
inference(resolve,[$cnf( $equal(not(implies(X_81,X_81)),falsehood) )],[refute_0_312,refute_0_335]) ).
cnf(refute_0_337,plain,
( implies(truth,and(not(X_81),X_81)) != falsehood
| xor(X_81,X_81) != implies(truth,and(not(X_81),X_81))
| xor(X_81,X_81) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_81,X_81),implies(truth,and(not(X_81),X_81))) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_338,plain,
( xor(X_81,X_81) != implies(truth,and(not(X_81),X_81))
| xor(X_81,X_81) = falsehood ),
inference(resolve,[$cnf( $equal(implies(truth,and(not(X_81),X_81)),falsehood) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
xor(X_81,X_81) = falsehood,
inference(resolve,[$cnf( $equal(xor(X_81,X_81),implies(truth,and(not(X_81),X_81))) )],[refute_0_305,refute_0_338]) ).
cnf(refute_0_340,plain,
xor(x,x) = falsehood,
inference(subst,[],[refute_0_339:[bind(X_81,$fot(x))]]) ).
cnf(refute_0_341,plain,
( falsehood != falsehood
| xor(x,x) != falsehood
| xor(x,x) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(xor(x,x),falsehood) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_342,plain,
( falsehood != falsehood
| xor(x,x) = falsehood ),
inference(resolve,[$cnf( $equal(xor(x,x),falsehood) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
falsehood != falsehood,
inference(resolve,[$cnf( $equal(xor(x,x),falsehood) )],[refute_0_342,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_344,plain,
falsehood = falsehood,
introduced(tautology,[refl,[$fot(falsehood)]]) ).
cnf(refute_0_345,plain,
$false,
inference(resolve,[$cnf( $equal(falsehood,falsehood) )],[refute_0_344,refute_0_343]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL155-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 23:14:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54
% 0.18/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.39/0.57
%------------------------------------------------------------------------------