TSTP Solution File: LCL154-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 0.38s 0.54s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 136
% Syntax : Number of clauses : 482 ( 244 unt; 0 nHn; 285 RR)
% Number of literals : 829 ( 828 equ; 350 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 462 ( 11 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(and_commutativity,axiom,
and(X,Y) = and(Y,X) ).
cnf(xor_definition,axiom,
xor(X,Y) = or(and(X,not(Y)),and(not(X),Y)) ).
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(prove_alternative_wajsberg_axiom,negated_conjecture,
xor(x,falsehood) != x ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( xor(X,Y) != xor(Y,X)
| xor(Y,X) = xor(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).
cnf(refute_0_4,plain,
xor(Y,X) = xor(X,Y),
inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_3]) ).
cnf(refute_0_5,plain,
xor(x,falsehood) = xor(falsehood,x),
inference(subst,[],[refute_0_4:[bind(X,$fot(falsehood)),bind(Y,$fot(x))]]) ).
cnf(refute_0_6,plain,
( xor(falsehood,x) != x
| xor(x,falsehood) != xor(falsehood,x)
| xor(x,falsehood) = x ),
introduced(tautology,[equality,[$cnf( $equal(xor(x,falsehood),xor(falsehood,x)) ),[1],$fot(x)]]) ).
cnf(refute_0_7,plain,
( xor(falsehood,x) != x
| xor(x,falsehood) = x ),
inference(resolve,[$cnf( $equal(xor(x,falsehood),xor(falsehood,x)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
xor(falsehood,x) != x,
inference(resolve,[$cnf( $equal(xor(x,falsehood),x) )],[refute_0_7,prove_alternative_wajsberg_axiom]) ).
cnf(refute_0_9,plain,
or(not(X_41),Y) = implies(not(not(X_41)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(not(X_41)))]]) ).
cnf(refute_0_10,plain,
implies(implies(not(X),X_17),X_17) = implies(implies(X_17,not(X)),not(X)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(X))),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_11,plain,
or(X,X_17) = implies(not(X),X_17),
inference(subst,[],[or_definition:[bind(Y,$fot(X_17))]]) ).
cnf(refute_0_12,plain,
( or(X,X_17) != implies(not(X),X_17)
| implies(not(X),X_17) = or(X,X_17) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,X_17))),bind(Y0,$fot(implies(not(X),X_17)))]]) ).
cnf(refute_0_13,plain,
implies(not(X),X_17) = or(X,X_17),
inference(resolve,[$cnf( $equal(or(X,X_17),implies(not(X),X_17)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( implies(implies(not(X),X_17),X_17) != implies(implies(X_17,not(X)),not(X))
| implies(not(X),X_17) != or(X,X_17)
| implies(or(X,X_17),X_17) = implies(implies(X_17,not(X)),not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(X),X_17),X_17),implies(implies(X_17,not(X)),not(X))) ),[0,0],$fot(or(X,X_17))]]) ).
cnf(refute_0_15,plain,
( implies(implies(not(X),X_17),X_17) != implies(implies(X_17,not(X)),not(X))
| implies(or(X,X_17),X_17) = implies(implies(X_17,not(X)),not(X)) ),
inference(resolve,[$cnf( $equal(implies(not(X),X_17),or(X,X_17)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
implies(or(X,X_17),X_17) = implies(implies(X_17,not(X)),not(X)),
inference(resolve,[$cnf( $equal(implies(implies(not(X),X_17),X_17),implies(implies(X_17,not(X)),not(X))) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
implies(or(truth,X_17),X_17) = implies(implies(X_17,not(truth)),not(truth)),
inference(subst,[],[refute_0_16:[bind(X,$fot(truth))]]) ).
cnf(refute_0_18,plain,
or(truth,X_2) = implies(not(truth),X_2),
inference(subst,[],[or_definition:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_19,plain,
( not(truth) != falsehood
| or(truth,X_2) != implies(not(truth),X_2)
| or(truth,X_2) = implies(falsehood,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_2),implies(not(truth),X_2)) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_20,plain,
( or(truth,X_2) != implies(not(truth),X_2)
| or(truth,X_2) = implies(falsehood,X_2) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_19]) ).
cnf(refute_0_21,plain,
or(truth,X_2) = implies(falsehood,X_2),
inference(resolve,[$cnf( $equal(or(truth,X_2),implies(not(truth),X_2)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
or(X,truth) = implies(not(X),truth),
inference(subst,[],[or_definition:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_23,plain,
implies(implies(truth,X_21),implies(implies(X_21,X_22),implies(truth,X_22))) = truth,
inference(subst,[],[wajsberg_2:[bind(X,$fot(truth)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_24,plain,
implies(truth,X_22) = X_22,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_25,plain,
( implies(implies(truth,X_21),implies(implies(X_21,X_22),implies(truth,X_22))) != truth
| implies(truth,X_22) != X_22
| implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),implies(truth,X_22))),truth) ),[0,1,1],$fot(X_22)]]) ).
cnf(refute_0_26,plain,
( implies(implies(truth,X_21),implies(implies(X_21,X_22),implies(truth,X_22))) != truth
| implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_22),X_22) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),implies(truth,X_22))),truth) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
implies(truth,X_21) = X_21,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_29,plain,
implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)))]]) ).
cnf(refute_0_30,plain,
( implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) != implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22))
| implies(truth,X_21) != X_21
| implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = implies(X_21,implies(implies(X_21,X_22),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22))) ),[1,0],$fot(X_21)]]) ).
cnf(refute_0_31,plain,
( implies(truth,X_21) != X_21
| implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = implies(X_21,implies(implies(X_21,X_22),X_22)) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) = implies(X_21,implies(implies(X_21,X_22),X_22)),
inference(resolve,[$cnf( $equal(implies(truth,X_21),X_21) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) != implies(X_21,implies(implies(X_21,X_22),X_22))
| implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) != truth
| implies(X_21,implies(implies(X_21,X_22),X_22)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),truth) ),[0],$fot(implies(X_21,implies(implies(X_21,X_22),X_22)))]]) ).
cnf(refute_0_34,plain,
( implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)) != truth
| implies(X_21,implies(implies(X_21,X_22),X_22)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),implies(X_21,implies(implies(X_21,X_22),X_22))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
implies(X_21,implies(implies(X_21,X_22),X_22)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(truth,X_21),implies(implies(X_21,X_22),X_22)),truth) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
implies(X_26,implies(implies(X_26,truth),truth)) = truth,
inference(subst,[],[refute_0_35:[bind(X_21,$fot(X_26)),bind(X_22,$fot(truth))]]) ).
cnf(refute_0_37,plain,
implies(implies(truth,X_17),X_17) = implies(implies(X_17,truth),truth),
inference(subst,[],[wajsberg_3:[bind(X,$fot(truth)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_38,plain,
implies(truth,X_17) = X_17,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_39,plain,
( implies(implies(truth,X_17),X_17) != implies(implies(X_17,truth),truth)
| implies(truth,X_17) != X_17
| implies(X_17,X_17) = implies(implies(X_17,truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_17),X_17),implies(implies(X_17,truth),truth)) ),[0,0],$fot(X_17)]]) ).
cnf(refute_0_40,plain,
( implies(implies(truth,X_17),X_17) != implies(implies(X_17,truth),truth)
| implies(X_17,X_17) = implies(implies(X_17,truth),truth) ),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
implies(X_17,X_17) = implies(implies(X_17,truth),truth),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_17),X_17),implies(implies(X_17,truth),truth)) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
implies(X_26,X_26) = implies(implies(X_26,truth),truth),
inference(subst,[],[refute_0_41:[bind(X_17,$fot(X_26))]]) ).
cnf(refute_0_43,plain,
( implies(X_26,X_26) != implies(implies(X_26,truth),truth)
| implies(implies(X_26,truth),truth) = implies(X_26,X_26) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_26,X_26))),bind(Y0,$fot(implies(implies(X_26,truth),truth)))]]) ).
cnf(refute_0_44,plain,
implies(implies(X_26,truth),truth) = implies(X_26,X_26),
inference(resolve,[$cnf( $equal(implies(X_26,X_26),implies(implies(X_26,truth),truth)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( implies(X_26,implies(implies(X_26,truth),truth)) != truth
| implies(implies(X_26,truth),truth) != implies(X_26,X_26)
| implies(X_26,implies(X_26,X_26)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,implies(implies(X_26,truth),truth)),truth) ),[0,1],$fot(implies(X_26,X_26))]]) ).
cnf(refute_0_46,plain,
( implies(X_26,implies(implies(X_26,truth),truth)) != truth
| implies(X_26,implies(X_26,X_26)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(X_26,truth),truth),implies(X_26,X_26)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
implies(X_26,implies(X_26,X_26)) = truth,
inference(resolve,[$cnf( $equal(implies(X_26,implies(implies(X_26,truth),truth)),truth) )],[refute_0_36,refute_0_46]) ).
cnf(refute_0_48,plain,
implies(truth,implies(implies(truth,X_27),X_27)) = implies(implies(truth,X_27),X_27),
inference(subst,[],[wajsberg_1:[bind(X,$fot(implies(implies(truth,X_27),X_27)))]]) ).
cnf(refute_0_49,plain,
implies(truth,implies(implies(truth,X_27),X_27)) = truth,
inference(subst,[],[refute_0_35:[bind(X_21,$fot(truth)),bind(X_22,$fot(X_27))]]) ).
cnf(refute_0_50,plain,
( implies(truth,implies(implies(truth,X_27),X_27)) != implies(implies(truth,X_27),X_27)
| implies(truth,implies(implies(truth,X_27),X_27)) != truth
| truth = implies(implies(truth,X_27),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,implies(implies(truth,X_27),X_27)),implies(implies(truth,X_27),X_27)) ),[0],$fot(truth)]]) ).
cnf(refute_0_51,plain,
( implies(truth,implies(implies(truth,X_27),X_27)) != implies(implies(truth,X_27),X_27)
| truth = implies(implies(truth,X_27),X_27) ),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_27),X_27)),truth) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
truth = implies(implies(truth,X_27),X_27),
inference(resolve,[$cnf( $equal(implies(truth,implies(implies(truth,X_27),X_27)),implies(implies(truth,X_27),X_27)) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
implies(truth,X_27) = X_27,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_27))]]) ).
cnf(refute_0_54,plain,
implies(implies(truth,X_27),X_27) = implies(implies(truth,X_27),X_27),
introduced(tautology,[refl,[$fot(implies(implies(truth,X_27),X_27))]]) ).
cnf(refute_0_55,plain,
( implies(implies(truth,X_27),X_27) != implies(implies(truth,X_27),X_27)
| implies(truth,X_27) != X_27
| implies(implies(truth,X_27),X_27) = implies(X_27,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(truth,X_27),X_27),implies(implies(truth,X_27),X_27)) ),[1,0],$fot(X_27)]]) ).
cnf(refute_0_56,plain,
( implies(truth,X_27) != X_27
| implies(implies(truth,X_27),X_27) = implies(X_27,X_27) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_27),X_27),implies(implies(truth,X_27),X_27)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
implies(implies(truth,X_27),X_27) = implies(X_27,X_27),
inference(resolve,[$cnf( $equal(implies(truth,X_27),X_27) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
( implies(implies(truth,X_27),X_27) != implies(X_27,X_27)
| truth != implies(implies(truth,X_27),X_27)
| truth = implies(X_27,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(truth,implies(implies(truth,X_27),X_27)) ),[1],$fot(implies(X_27,X_27))]]) ).
cnf(refute_0_59,plain,
( truth != implies(implies(truth,X_27),X_27)
| truth = implies(X_27,X_27) ),
inference(resolve,[$cnf( $equal(implies(implies(truth,X_27),X_27),implies(X_27,X_27)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
truth = implies(X_27,X_27),
inference(resolve,[$cnf( $equal(truth,implies(implies(truth,X_27),X_27)) )],[refute_0_52,refute_0_59]) ).
cnf(refute_0_61,plain,
( truth != implies(X_27,X_27)
| implies(X_27,X_27) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(X_27,X_27)))]]) ).
cnf(refute_0_62,plain,
implies(X_27,X_27) = truth,
inference(resolve,[$cnf( $equal(truth,implies(X_27,X_27)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
implies(X_26,X_26) = truth,
inference(subst,[],[refute_0_62:[bind(X_27,$fot(X_26))]]) ).
cnf(refute_0_64,plain,
implies(X_26,implies(X_26,X_26)) = implies(X_26,implies(X_26,X_26)),
introduced(tautology,[refl,[$fot(implies(X_26,implies(X_26,X_26)))]]) ).
cnf(refute_0_65,plain,
( implies(X_26,X_26) != truth
| implies(X_26,implies(X_26,X_26)) != implies(X_26,implies(X_26,X_26))
| implies(X_26,implies(X_26,X_26)) = implies(X_26,truth) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,implies(X_26,X_26)),implies(X_26,implies(X_26,X_26))) ),[1,1],$fot(truth)]]) ).
cnf(refute_0_66,plain,
( implies(X_26,X_26) != truth
| implies(X_26,implies(X_26,X_26)) = implies(X_26,truth) ),
inference(resolve,[$cnf( $equal(implies(X_26,implies(X_26,X_26)),implies(X_26,implies(X_26,X_26))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
implies(X_26,implies(X_26,X_26)) = implies(X_26,truth),
inference(resolve,[$cnf( $equal(implies(X_26,X_26),truth) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( implies(X_26,implies(X_26,X_26)) != implies(X_26,truth)
| implies(X_26,implies(X_26,X_26)) != truth
| implies(X_26,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_26,implies(X_26,X_26)),truth) ),[0],$fot(implies(X_26,truth))]]) ).
cnf(refute_0_69,plain,
( implies(X_26,implies(X_26,X_26)) != truth
| implies(X_26,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(X_26,implies(X_26,X_26)),implies(X_26,truth)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
implies(X_26,truth) = truth,
inference(resolve,[$cnf( $equal(implies(X_26,implies(X_26,X_26)),truth) )],[refute_0_47,refute_0_69]) ).
cnf(refute_0_71,plain,
implies(not(X),truth) = truth,
inference(subst,[],[refute_0_70:[bind(X_26,$fot(not(X)))]]) ).
cnf(refute_0_72,plain,
( implies(not(X),truth) != truth
| or(X,truth) != implies(not(X),truth)
| or(X,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,truth),implies(not(X),truth)) ),[1],$fot(truth)]]) ).
cnf(refute_0_73,plain,
( or(X,truth) != implies(not(X),truth)
| or(X,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),truth) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
or(X,truth) = truth,
inference(resolve,[$cnf( $equal(or(X,truth),implies(not(X),truth)) )],[refute_0_22,refute_0_73]) ).
cnf(refute_0_75,plain,
or(truth,X_2) = or(X_2,truth),
inference(subst,[],[or_commutativity:[bind(X,$fot(truth)),bind(Y,$fot(X_2))]]) ).
cnf(refute_0_76,plain,
( or(truth,X_2) != implies(falsehood,X_2)
| or(truth,X_2) != or(X_2,truth)
| or(X_2,truth) = implies(falsehood,X_2) ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_2),implies(falsehood,X_2)) ),[0],$fot(or(X_2,truth))]]) ).
cnf(refute_0_77,plain,
( or(truth,X_2) != implies(falsehood,X_2)
| or(X_2,truth) = implies(falsehood,X_2) ),
inference(resolve,[$cnf( $equal(or(truth,X_2),or(X_2,truth)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
or(X_2,truth) = implies(falsehood,X_2),
inference(resolve,[$cnf( $equal(or(truth,X_2),implies(falsehood,X_2)) )],[refute_0_21,refute_0_77]) ).
cnf(refute_0_79,plain,
or(X,truth) = implies(falsehood,X),
inference(subst,[],[refute_0_78:[bind(X_2,$fot(X))]]) ).
cnf(refute_0_80,plain,
( or(X,truth) != implies(falsehood,X)
| or(X,truth) != truth
| implies(falsehood,X) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,truth),truth) ),[0],$fot(implies(falsehood,X))]]) ).
cnf(refute_0_81,plain,
( or(X,truth) != truth
| implies(falsehood,X) = truth ),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
implies(falsehood,X) = truth,
inference(resolve,[$cnf( $equal(or(X,truth),truth) )],[refute_0_74,refute_0_81]) ).
cnf(refute_0_83,plain,
implies(falsehood,X_2) = truth,
inference(subst,[],[refute_0_82:[bind(X,$fot(X_2))]]) ).
cnf(refute_0_84,plain,
( implies(falsehood,X_2) != truth
| or(truth,X_2) != implies(falsehood,X_2)
| or(truth,X_2) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(truth,X_2),implies(falsehood,X_2)) ),[1],$fot(truth)]]) ).
cnf(refute_0_85,plain,
( or(truth,X_2) != implies(falsehood,X_2)
| or(truth,X_2) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,X_2),truth) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
or(truth,X_2) = truth,
inference(resolve,[$cnf( $equal(or(truth,X_2),implies(falsehood,X_2)) )],[refute_0_21,refute_0_85]) ).
cnf(refute_0_87,plain,
or(truth,X_17) = truth,
inference(subst,[],[refute_0_86:[bind(X_2,$fot(X_17))]]) ).
cnf(refute_0_88,plain,
( implies(or(truth,X_17),X_17) != implies(implies(X_17,not(truth)),not(truth))
| or(truth,X_17) != truth
| implies(truth,X_17) = implies(implies(X_17,not(truth)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(truth,X_17),X_17),implies(implies(X_17,not(truth)),not(truth))) ),[0,0],$fot(truth)]]) ).
cnf(refute_0_89,plain,
( implies(or(truth,X_17),X_17) != implies(implies(X_17,not(truth)),not(truth))
| implies(truth,X_17) = implies(implies(X_17,not(truth)),not(truth)) ),
inference(resolve,[$cnf( $equal(or(truth,X_17),truth) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
implies(truth,X_17) = implies(implies(X_17,not(truth)),not(truth)),
inference(resolve,[$cnf( $equal(implies(or(truth,X_17),X_17),implies(implies(X_17,not(truth)),not(truth))) )],[refute_0_17,refute_0_89]) ).
cnf(refute_0_91,plain,
( implies(truth,X_17) != X_17
| implies(truth,X_17) != implies(implies(X_17,not(truth)),not(truth))
| X_17 = implies(implies(X_17,not(truth)),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,X_17),implies(implies(X_17,not(truth)),not(truth))) ),[0],$fot(X_17)]]) ).
cnf(refute_0_92,plain,
( implies(truth,X_17) != implies(implies(X_17,not(truth)),not(truth))
| X_17 = implies(implies(X_17,not(truth)),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(truth,X_17),X_17) )],[refute_0_38,refute_0_91]) ).
cnf(refute_0_93,plain,
implies(implies(X_17,falsehood),not(truth)) = implies(implies(X_17,falsehood),not(truth)),
introduced(tautology,[refl,[$fot(implies(implies(X_17,falsehood),not(truth)))]]) ).
cnf(refute_0_94,plain,
( implies(implies(X_17,falsehood),not(truth)) != implies(implies(X_17,falsehood),not(truth))
| not(truth) != falsehood
| implies(implies(X_17,falsehood),not(truth)) = implies(implies(X_17,falsehood),falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,falsehood),not(truth)),implies(implies(X_17,falsehood),not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_95,plain,
( not(truth) != falsehood
| implies(implies(X_17,falsehood),not(truth)) = implies(implies(X_17,falsehood),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,falsehood),not(truth)),implies(implies(X_17,falsehood),not(truth))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
implies(implies(X_17,falsehood),not(truth)) = implies(implies(X_17,falsehood),falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_95]) ).
cnf(refute_0_97,plain,
implies(X_17,not(truth)) = implies(X_17,not(truth)),
introduced(tautology,[refl,[$fot(implies(X_17,not(truth)))]]) ).
cnf(refute_0_98,plain,
( implies(X_17,not(truth)) != implies(X_17,not(truth))
| not(truth) != falsehood
| implies(X_17,not(truth)) = implies(X_17,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_17,not(truth)),implies(X_17,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_99,plain,
( not(truth) != falsehood
| implies(X_17,not(truth)) = implies(X_17,falsehood) ),
inference(resolve,[$cnf( $equal(implies(X_17,not(truth)),implies(X_17,not(truth))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(X_17,not(truth)) = implies(X_17,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_99]) ).
cnf(refute_0_101,plain,
implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,not(truth)),not(truth)),
introduced(tautology,[refl,[$fot(implies(implies(X_17,not(truth)),not(truth)))]]) ).
cnf(refute_0_102,plain,
( implies(X_17,not(truth)) != implies(X_17,falsehood)
| implies(implies(X_17,not(truth)),not(truth)) != implies(implies(X_17,not(truth)),not(truth))
| implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),not(truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(X_17,not(truth)),not(truth)),implies(implies(X_17,not(truth)),not(truth))) ),[1,0],$fot(implies(X_17,falsehood))]]) ).
cnf(refute_0_103,plain,
( implies(X_17,not(truth)) != implies(X_17,falsehood)
| implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),not(truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(truth)),not(truth)),implies(implies(X_17,not(truth)),not(truth))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),not(truth)),
inference(resolve,[$cnf( $equal(implies(X_17,not(truth)),implies(X_17,falsehood)) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_106,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_105]) ).
cnf(refute_0_107,plain,
( implies(implies(X_17,falsehood),not(truth)) != implies(implies(X_17,falsehood),falsehood)
| implies(implies(X_17,not(truth)),not(truth)) != implies(implies(X_17,falsehood),not(truth))
| implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),falsehood) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(X_17,not(truth)),not(truth)))),bind(Y0,$fot(implies(implies(X_17,falsehood),not(truth)))),bind(Z0,$fot(implies(implies(X_17,falsehood),falsehood)))]]) ).
cnf(refute_0_108,plain,
( implies(implies(X_17,falsehood),not(truth)) != implies(implies(X_17,falsehood),falsehood)
| implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(truth)),not(truth)),implies(implies(X_17,falsehood),not(truth))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(implies(X_17,not(truth)),not(truth)) = implies(implies(X_17,falsehood),falsehood),
inference(resolve,[$cnf( $equal(implies(implies(X_17,falsehood),not(truth)),implies(implies(X_17,falsehood),falsehood)) )],[refute_0_96,refute_0_108]) ).
cnf(refute_0_110,plain,
( X_17 != implies(implies(X_17,not(truth)),not(truth))
| implies(implies(X_17,not(truth)),not(truth)) != implies(implies(X_17,falsehood),falsehood)
| X_17 = implies(implies(X_17,falsehood),falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_17,implies(implies(X_17,falsehood),falsehood)) ),[0],$fot(implies(implies(X_17,not(truth)),not(truth)))]]) ).
cnf(refute_0_111,plain,
( X_17 != implies(implies(X_17,not(truth)),not(truth))
| X_17 = implies(implies(X_17,falsehood),falsehood) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,not(truth)),not(truth)),implies(implies(X_17,falsehood),falsehood)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( implies(truth,X_17) != implies(implies(X_17,not(truth)),not(truth))
| X_17 = implies(implies(X_17,falsehood),falsehood) ),
inference(resolve,[$cnf( $equal(X_17,implies(implies(X_17,not(truth)),not(truth))) )],[refute_0_92,refute_0_111]) ).
cnf(refute_0_113,plain,
X_17 = implies(implies(X_17,falsehood),falsehood),
inference(resolve,[$cnf( $equal(implies(truth,X_17),implies(implies(X_17,not(truth)),not(truth))) )],[refute_0_90,refute_0_112]) ).
cnf(refute_0_114,plain,
implies(or(X,falsehood),falsehood) = implies(implies(falsehood,not(X)),not(X)),
inference(subst,[],[refute_0_16:[bind(X_17,$fot(falsehood))]]) ).
cnf(refute_0_115,plain,
implies(falsehood,not(X)) = truth,
inference(subst,[],[refute_0_82:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_116,plain,
( implies(falsehood,not(X)) != truth
| implies(or(X,falsehood),falsehood) != implies(implies(falsehood,not(X)),not(X))
| implies(or(X,falsehood),falsehood) = implies(truth,not(X)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(implies(falsehood,not(X)),not(X))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_117,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( $equal(implies(falsehood,not(X)),truth) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
implies(or(X,falsehood),falsehood) = implies(truth,not(X)),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(implies(falsehood,not(X)),not(X))) )],[refute_0_114,refute_0_117]) ).
cnf(refute_0_119,plain,
implies(truth,not(X)) = not(X),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(X)))]]) ).
cnf(refute_0_120,plain,
( implies(or(X,falsehood),falsehood) != implies(truth,not(X))
| implies(truth,not(X)) != not(X)
| implies(or(X,falsehood),falsehood) = not(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(or(X,falsehood),falsehood),not(X)) ),[0],$fot(implies(truth,not(X)))]]) ).
cnf(refute_0_121,plain,
( implies(or(X,falsehood),falsehood) != implies(truth,not(X))
| implies(or(X,falsehood),falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(truth,not(X)),not(X)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
implies(or(X,falsehood),falsehood) = not(X),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(truth,not(X))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
or(or(falsehood,falsehood),Y) = implies(not(or(falsehood,falsehood)),Y),
inference(subst,[],[or_definition:[bind(X,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_124,plain,
and(X_13,truth) = not(or(not(X_13),not(truth))),
inference(subst,[],[and_definition:[bind(X,$fot(X_13)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_125,plain,
( and(X_13,truth) != not(or(not(X_13),not(truth)))
| not(truth) != falsehood
| and(X_13,truth) = not(or(not(X_13),falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X_13,truth),not(or(not(X_13),not(truth)))) ),[1,0,1],$fot(falsehood)]]) ).
cnf(refute_0_126,plain,
( and(X_13,truth) != not(or(not(X_13),not(truth)))
| and(X_13,truth) = not(or(not(X_13),falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_125]) ).
cnf(refute_0_127,plain,
and(X_13,truth) = not(or(not(X_13),falsehood)),
inference(resolve,[$cnf( $equal(and(X_13,truth),not(or(not(X_13),not(truth)))) )],[refute_0_124,refute_0_126]) ).
cnf(refute_0_128,plain,
( or(X,Y) != or(Y,X)
| or(Y,X) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(or(Y,X)))]]) ).
cnf(refute_0_129,plain,
or(Y,X) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),or(Y,X)) )],[or_commutativity,refute_0_128]) ).
cnf(refute_0_130,plain,
or(not(X_13),falsehood) = or(falsehood,not(X_13)),
inference(subst,[],[refute_0_129:[bind(X,$fot(falsehood)),bind(Y,$fot(not(X_13)))]]) ).
cnf(refute_0_131,plain,
not(or(not(X_13),falsehood)) = not(or(not(X_13),falsehood)),
introduced(tautology,[refl,[$fot(not(or(not(X_13),falsehood)))]]) ).
cnf(refute_0_132,plain,
( not(or(not(X_13),falsehood)) != not(or(not(X_13),falsehood))
| or(not(X_13),falsehood) != or(falsehood,not(X_13))
| not(or(not(X_13),falsehood)) = not(or(falsehood,not(X_13))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X_13),falsehood)),not(or(not(X_13),falsehood))) ),[1,0],$fot(or(falsehood,not(X_13)))]]) ).
cnf(refute_0_133,plain,
( or(not(X_13),falsehood) != or(falsehood,not(X_13))
| not(or(not(X_13),falsehood)) = not(or(falsehood,not(X_13))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_13),falsehood)),not(or(not(X_13),falsehood))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
not(or(not(X_13),falsehood)) = not(or(falsehood,not(X_13))),
inference(resolve,[$cnf( $equal(or(not(X_13),falsehood),or(falsehood,not(X_13))) )],[refute_0_130,refute_0_133]) ).
cnf(refute_0_135,plain,
( and(X_13,truth) != not(or(not(X_13),falsehood))
| not(or(not(X_13),falsehood)) != not(or(falsehood,not(X_13)))
| and(X_13,truth) = not(or(falsehood,not(X_13))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_13,truth),not(or(falsehood,not(X_13)))) ),[0],$fot(not(or(not(X_13),falsehood)))]]) ).
cnf(refute_0_136,plain,
( and(X_13,truth) != not(or(not(X_13),falsehood))
| and(X_13,truth) = not(or(falsehood,not(X_13))) ),
inference(resolve,[$cnf( $equal(not(or(not(X_13),falsehood)),not(or(falsehood,not(X_13)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
and(X_13,truth) = not(or(falsehood,not(X_13))),
inference(resolve,[$cnf( $equal(and(X_13,truth),not(or(not(X_13),falsehood))) )],[refute_0_127,refute_0_136]) ).
cnf(refute_0_138,plain,
and(truth,truth) = not(or(falsehood,not(truth))),
inference(subst,[],[refute_0_137:[bind(X_13,$fot(truth))]]) ).
cnf(refute_0_139,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_140,plain,
( and(truth,truth) != not(or(falsehood,not(truth)))
| and(truth,truth) = not(or(falsehood,falsehood)) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_139]) ).
cnf(refute_0_141,plain,
and(truth,truth) = not(or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,not(truth)))) )],[refute_0_138,refute_0_140]) ).
cnf(refute_0_142,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) = and(truth,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,truth))),bind(Y0,$fot(not(or(falsehood,falsehood))))]]) ).
cnf(refute_0_143,plain,
not(or(falsehood,falsehood)) = and(truth,truth),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( not(or(falsehood,falsehood)) != and(truth,truth)
| or(or(falsehood,falsehood),Y) != implies(not(or(falsehood,falsehood)),Y)
| or(or(falsehood,falsehood),Y) = implies(and(truth,truth),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),Y),implies(not(or(falsehood,falsehood)),Y)) ),[1,0],$fot(and(truth,truth))]]) ).
cnf(refute_0_145,plain,
( or(or(falsehood,falsehood),Y) != implies(not(or(falsehood,falsehood)),Y)
| or(or(falsehood,falsehood),Y) = implies(and(truth,truth),Y) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
or(or(falsehood,falsehood),Y) = implies(and(truth,truth),Y),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),Y),implies(not(or(falsehood,falsehood)),Y)) )],[refute_0_123,refute_0_145]) ).
cnf(refute_0_147,plain,
or(or(falsehood,falsehood),Y) = or(falsehood,or(falsehood,Y)),
inference(subst,[],[or_associativity:[bind(X,$fot(falsehood)),bind(Y,$fot(falsehood)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_148,plain,
( or(or(falsehood,falsehood),Y) != implies(and(truth,truth),Y)
| or(or(falsehood,falsehood),Y) != or(falsehood,or(falsehood,Y))
| or(falsehood,or(falsehood,Y)) = implies(and(truth,truth),Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(or(falsehood,falsehood),Y),implies(and(truth,truth),Y)) ),[0],$fot(or(falsehood,or(falsehood,Y)))]]) ).
cnf(refute_0_149,plain,
( or(or(falsehood,falsehood),Y) != implies(and(truth,truth),Y)
| or(falsehood,or(falsehood,Y)) = implies(and(truth,truth),Y) ),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),Y),or(falsehood,or(falsehood,Y))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
or(falsehood,or(falsehood,Y)) = implies(and(truth,truth),Y),
inference(resolve,[$cnf( $equal(or(or(falsehood,falsehood),Y),implies(and(truth,truth),Y)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
or(falsehood,or(falsehood,X_34)) = implies(and(truth,truth),X_34),
inference(subst,[],[refute_0_150:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_152,plain,
or(X_34,falsehood) = or(falsehood,X_34),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_34)),bind(Y,$fot(falsehood))]]) ).
cnf(refute_0_153,plain,
( or(X_34,falsehood) != or(falsehood,X_34)
| or(falsehood,X_34) = or(X_34,falsehood) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_34,falsehood))),bind(Y0,$fot(or(falsehood,X_34)))]]) ).
cnf(refute_0_154,plain,
or(falsehood,X_34) = or(X_34,falsehood),
inference(resolve,[$cnf( $equal(or(X_34,falsehood),or(falsehood,X_34)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( or(falsehood,X_34) != or(X_34,falsehood)
| or(falsehood,or(falsehood,X_34)) != implies(and(truth,truth),X_34)
| or(falsehood,or(X_34,falsehood)) = implies(and(truth,truth),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,X_34)),implies(and(truth,truth),X_34)) ),[0,1],$fot(or(X_34,falsehood))]]) ).
cnf(refute_0_156,plain,
( or(falsehood,or(falsehood,X_34)) != implies(and(truth,truth),X_34)
| or(falsehood,or(X_34,falsehood)) = implies(and(truth,truth),X_34) ),
inference(resolve,[$cnf( $equal(or(falsehood,X_34),or(X_34,falsehood)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
or(falsehood,or(X_34,falsehood)) = implies(and(truth,truth),X_34),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,X_34)),implies(and(truth,truth),X_34)) )],[refute_0_151,refute_0_156]) ).
cnf(refute_0_158,plain,
( or(X,Y) != implies(not(X),Y)
| implies(not(X),Y) = or(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X,Y))),bind(Y0,$fot(implies(not(X),Y)))]]) ).
cnf(refute_0_159,plain,
implies(not(X),Y) = or(X,Y),
inference(resolve,[$cnf( $equal(or(X,Y),implies(not(X),Y)) )],[or_definition,refute_0_158]) ).
cnf(refute_0_160,plain,
implies(not(falsehood),X_34) = or(falsehood,X_34),
inference(subst,[],[refute_0_159:[bind(X,$fot(falsehood)),bind(Y,$fot(X_34))]]) ).
cnf(refute_0_161,plain,
or(falsehood,falsehood) = implies(implies(or(falsehood,falsehood),falsehood),falsehood),
inference(subst,[],[refute_0_113:[bind(X_17,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_162,plain,
implies(not(X),not(Y)) = or(X,not(Y)),
inference(subst,[],[refute_0_159:[bind(Y,$fot(not(Y)))]]) ).
cnf(refute_0_163,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(implies(not(X),not(Y)),implies(Y,X)),
introduced(tautology,[refl,[$fot(implies(implies(not(X),not(Y)),implies(Y,X)))]]) ).
cnf(refute_0_164,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_165,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( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(implies(not(X),not(Y)),implies(Y,X))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
implies(implies(not(X),not(Y)),implies(Y,X)) = implies(or(X,not(Y)),implies(Y,X)),
inference(resolve,[$cnf( $equal(implies(not(X),not(Y)),or(X,not(Y))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != implies(or(X,not(Y)),implies(Y,X))
| implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
introduced(tautology,[equality,[$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_168,plain,
( implies(implies(not(X),not(Y)),implies(Y,X)) != truth
| implies(or(X,not(Y)),implies(Y,X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),implies(or(X,not(Y)),implies(Y,X))) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
implies(or(X,not(Y)),implies(Y,X)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(not(X),not(Y)),implies(Y,X)),truth) )],[wajsberg_4,refute_0_168]) ).
cnf(refute_0_170,plain,
implies(or(X_36,not(truth)),implies(truth,X_36)) = truth,
inference(subst,[],[refute_0_169:[bind(X,$fot(X_36)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_171,plain,
implies(truth,X_36) = X_36,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_36))]]) ).
cnf(refute_0_172,plain,
( implies(or(X_36,not(truth)),implies(truth,X_36)) != truth
| implies(truth,X_36) != X_36
| implies(or(X_36,not(truth)),X_36) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_36,not(truth)),implies(truth,X_36)),truth) ),[0,1],$fot(X_36)]]) ).
cnf(refute_0_173,plain,
( implies(or(X_36,not(truth)),implies(truth,X_36)) != truth
| implies(or(X_36,not(truth)),X_36) = truth ),
inference(resolve,[$cnf( $equal(implies(truth,X_36),X_36) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
implies(or(X_36,not(truth)),X_36) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_36,not(truth)),implies(truth,X_36)),truth) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
or(X_36,not(truth)) = or(X_36,not(truth)),
introduced(tautology,[refl,[$fot(or(X_36,not(truth)))]]) ).
cnf(refute_0_176,plain,
( not(truth) != falsehood
| or(X_36,not(truth)) != or(X_36,not(truth))
| or(X_36,not(truth)) = or(X_36,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(X_36,not(truth)),or(X_36,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_177,plain,
( not(truth) != falsehood
| or(X_36,not(truth)) = or(X_36,falsehood) ),
inference(resolve,[$cnf( $equal(or(X_36,not(truth)),or(X_36,not(truth))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
or(X_36,not(truth)) = or(X_36,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_177]) ).
cnf(refute_0_179,plain,
implies(or(X_36,not(truth)),X_36) = implies(or(X_36,not(truth)),X_36),
introduced(tautology,[refl,[$fot(implies(or(X_36,not(truth)),X_36))]]) ).
cnf(refute_0_180,plain,
( implies(or(X_36,not(truth)),X_36) != implies(or(X_36,not(truth)),X_36)
| or(X_36,not(truth)) != or(X_36,falsehood)
| implies(or(X_36,not(truth)),X_36) = implies(or(X_36,falsehood),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_36,not(truth)),X_36),implies(or(X_36,not(truth)),X_36)) ),[1,0],$fot(or(X_36,falsehood))]]) ).
cnf(refute_0_181,plain,
( or(X_36,not(truth)) != or(X_36,falsehood)
| implies(or(X_36,not(truth)),X_36) = implies(or(X_36,falsehood),X_36) ),
inference(resolve,[$cnf( $equal(implies(or(X_36,not(truth)),X_36),implies(or(X_36,not(truth)),X_36)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
implies(or(X_36,not(truth)),X_36) = implies(or(X_36,falsehood),X_36),
inference(resolve,[$cnf( $equal(or(X_36,not(truth)),or(X_36,falsehood)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( implies(or(X_36,not(truth)),X_36) != implies(or(X_36,falsehood),X_36)
| implies(or(X_36,not(truth)),X_36) != truth
| implies(or(X_36,falsehood),X_36) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_36,not(truth)),X_36),truth) ),[0],$fot(implies(or(X_36,falsehood),X_36))]]) ).
cnf(refute_0_184,plain,
( implies(or(X_36,not(truth)),X_36) != truth
| implies(or(X_36,falsehood),X_36) = truth ),
inference(resolve,[$cnf( $equal(implies(or(X_36,not(truth)),X_36),implies(or(X_36,falsehood),X_36)) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
implies(or(X_36,falsehood),X_36) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_36,not(truth)),X_36),truth) )],[refute_0_174,refute_0_184]) ).
cnf(refute_0_186,plain,
implies(or(falsehood,falsehood),falsehood) = truth,
inference(subst,[],[refute_0_185:[bind(X_36,$fot(falsehood))]]) ).
cnf(refute_0_187,plain,
( implies(or(falsehood,falsehood),falsehood) != truth
| or(falsehood,falsehood) != implies(implies(or(falsehood,falsehood),falsehood),falsehood)
| or(falsehood,falsehood) = implies(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,falsehood),implies(implies(or(falsehood,falsehood),falsehood),falsehood)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_188,plain,
( or(falsehood,falsehood) != implies(implies(or(falsehood,falsehood),falsehood),falsehood)
| or(falsehood,falsehood) = implies(truth,falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,falsehood),falsehood),truth) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
or(falsehood,falsehood) = implies(truth,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),implies(implies(or(falsehood,falsehood),falsehood),falsehood)) )],[refute_0_161,refute_0_188]) ).
cnf(refute_0_190,plain,
implies(truth,falsehood) = falsehood,
inference(subst,[],[wajsberg_1:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_191,plain,
( implies(truth,falsehood) != falsehood
| or(falsehood,falsehood) != implies(truth,falsehood)
| or(falsehood,falsehood) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,falsehood),implies(truth,falsehood)) ),[1],$fot(falsehood)]]) ).
cnf(refute_0_192,plain,
( or(falsehood,falsehood) != implies(truth,falsehood)
| or(falsehood,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(implies(truth,falsehood),falsehood) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
or(falsehood,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),implies(truth,falsehood)) )],[refute_0_189,refute_0_192]) ).
cnf(refute_0_194,plain,
not(or(falsehood,falsehood)) = not(or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(not(or(falsehood,falsehood)))]]) ).
cnf(refute_0_195,plain,
( not(or(falsehood,falsehood)) != not(or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_196,plain,
( or(falsehood,falsehood) != falsehood
| not(or(falsehood,falsehood)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(or(falsehood,falsehood))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
not(or(falsehood,falsehood)) = not(falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| not(or(falsehood,falsehood)) != not(falsehood)
| and(truth,truth) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,truth),not(falsehood)) ),[0],$fot(not(or(falsehood,falsehood)))]]) ).
cnf(refute_0_199,plain,
( and(truth,truth) != not(or(falsehood,falsehood))
| and(truth,truth) = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),not(falsehood)) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
and(truth,truth) = not(falsehood),
inference(resolve,[$cnf( $equal(and(truth,truth),not(or(falsehood,falsehood))) )],[refute_0_141,refute_0_199]) ).
cnf(refute_0_201,plain,
implies(and(truth,truth),X_34) = implies(and(truth,truth),X_34),
introduced(tautology,[refl,[$fot(implies(and(truth,truth),X_34))]]) ).
cnf(refute_0_202,plain,
( and(truth,truth) != not(falsehood)
| implies(and(truth,truth),X_34) != implies(and(truth,truth),X_34)
| implies(and(truth,truth),X_34) = implies(not(falsehood),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(implies(and(truth,truth),X_34),implies(and(truth,truth),X_34)) ),[1,0],$fot(not(falsehood))]]) ).
cnf(refute_0_203,plain,
( and(truth,truth) != not(falsehood)
| implies(and(truth,truth),X_34) = implies(not(falsehood),X_34) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_34),implies(and(truth,truth),X_34)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
implies(and(truth,truth),X_34) = implies(not(falsehood),X_34),
inference(resolve,[$cnf( $equal(and(truth,truth),not(falsehood)) )],[refute_0_200,refute_0_203]) ).
cnf(refute_0_205,plain,
( implies(and(truth,truth),X_34) != implies(not(falsehood),X_34)
| implies(not(falsehood),X_34) != or(falsehood,X_34)
| implies(and(truth,truth),X_34) = or(falsehood,X_34) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(and(truth,truth),X_34))),bind(Y0,$fot(implies(not(falsehood),X_34))),bind(Z0,$fot(or(falsehood,X_34)))]]) ).
cnf(refute_0_206,plain,
( implies(not(falsehood),X_34) != or(falsehood,X_34)
| implies(and(truth,truth),X_34) = or(falsehood,X_34) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_34),implies(not(falsehood),X_34)) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
implies(and(truth,truth),X_34) = or(falsehood,X_34),
inference(resolve,[$cnf( $equal(implies(not(falsehood),X_34),or(falsehood,X_34)) )],[refute_0_160,refute_0_206]) ).
cnf(refute_0_208,plain,
( implies(and(truth,truth),X_34) != or(falsehood,X_34)
| or(falsehood,or(X_34,falsehood)) != implies(and(truth,truth),X_34)
| or(falsehood,or(X_34,falsehood)) = or(falsehood,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_34,falsehood)),implies(and(truth,truth),X_34)) ),[1],$fot(or(falsehood,X_34))]]) ).
cnf(refute_0_209,plain,
( or(falsehood,or(X_34,falsehood)) != implies(and(truth,truth),X_34)
| or(falsehood,or(X_34,falsehood)) = or(falsehood,X_34) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),X_34),or(falsehood,X_34)) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
or(falsehood,or(X_34,falsehood)) = or(falsehood,X_34),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_34,falsehood)),implies(and(truth,truth),X_34)) )],[refute_0_157,refute_0_209]) ).
cnf(refute_0_211,plain,
or(falsehood,Y) = implies(not(falsehood),Y),
inference(subst,[],[or_definition:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_212,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(implies(and(truth,truth),not(falsehood)),not(falsehood)),
inference(subst,[],[wajsberg_3:[bind(X,$fot(not(falsehood))),bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_213,plain,
or(falsehood,or(falsehood,not(falsehood))) = implies(and(truth,truth),not(falsehood)),
inference(subst,[],[refute_0_150:[bind(Y,$fot(not(falsehood)))]]) ).
cnf(refute_0_214,plain,
or(X,not(X)) = implies(not(X),not(X)),
inference(subst,[],[or_definition:[bind(Y,$fot(not(X)))]]) ).
cnf(refute_0_215,plain,
implies(not(X),not(X)) = implies(implies(not(X),truth),truth),
inference(subst,[],[refute_0_41:[bind(X_17,$fot(not(X)))]]) ).
cnf(refute_0_216,plain,
( implies(not(X),not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) ),[1],$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_217,plain,
( or(X,not(X)) != implies(not(X),not(X))
| or(X,not(X)) = implies(implies(not(X),truth),truth) ),
inference(resolve,[$cnf( $equal(implies(not(X),not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
or(X,not(X)) = implies(implies(not(X),truth),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(not(X),not(X))) )],[refute_0_214,refute_0_217]) ).
cnf(refute_0_219,plain,
implies(not(X),truth) = or(X,truth),
inference(subst,[],[refute_0_159:[bind(Y,$fot(truth))]]) ).
cnf(refute_0_220,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_106:[bind(X0,$fot(implies(not(X),truth))),bind(Y0,$fot(or(X,truth))),bind(Z0,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_221,plain,
( or(X,truth) != implies(falsehood,X)
| implies(not(X),truth) = implies(falsehood,X) ),
inference(resolve,[$cnf( $equal(implies(not(X),truth),or(X,truth)) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
implies(not(X),truth) = implies(falsehood,X),
inference(resolve,[$cnf( $equal(or(X,truth),implies(falsehood,X)) )],[refute_0_79,refute_0_221]) ).
cnf(refute_0_223,plain,
implies(implies(not(X),truth),truth) = implies(implies(not(X),truth),truth),
introduced(tautology,[refl,[$fot(implies(implies(not(X),truth),truth))]]) ).
cnf(refute_0_224,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_225,plain,
( implies(not(X),truth) != implies(falsehood,X)
| implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(not(X),truth),truth)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
implies(implies(not(X),truth),truth) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(implies(not(X),truth),implies(falsehood,X)) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
( implies(implies(not(X),truth),truth) != implies(implies(falsehood,X),truth)
| or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) ),[1],$fot(implies(implies(falsehood,X),truth))]]) ).
cnf(refute_0_228,plain,
( or(X,not(X)) != implies(implies(not(X),truth),truth)
| or(X,not(X)) = implies(implies(falsehood,X),truth) ),
inference(resolve,[$cnf( $equal(implies(implies(not(X),truth),truth),implies(implies(falsehood,X),truth)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
or(X,not(X)) = implies(implies(falsehood,X),truth),
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(not(X),truth),truth)) )],[refute_0_218,refute_0_228]) ).
cnf(refute_0_230,plain,
implies(implies(falsehood,X),truth) = truth,
inference(subst,[],[refute_0_70:[bind(X_26,$fot(implies(falsehood,X)))]]) ).
cnf(refute_0_231,plain,
( implies(implies(falsehood,X),truth) != truth
| or(X,not(X)) != implies(implies(falsehood,X),truth)
| or(X,not(X)) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) ),[1],$fot(truth)]]) ).
cnf(refute_0_232,plain,
( or(X,not(X)) != implies(implies(falsehood,X),truth)
| or(X,not(X)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X),truth),truth) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
or(X,not(X)) = truth,
inference(resolve,[$cnf( $equal(or(X,not(X)),implies(implies(falsehood,X),truth)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
or(falsehood,not(falsehood)) = truth,
inference(subst,[],[refute_0_233:[bind(X,$fot(falsehood))]]) ).
cnf(refute_0_235,plain,
( or(falsehood,not(falsehood)) != truth
| or(falsehood,or(falsehood,not(falsehood))) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) = implies(and(truth,truth),not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(falsehood,not(falsehood))),implies(and(truth,truth),not(falsehood))) ),[0,1],$fot(truth)]]) ).
cnf(refute_0_236,plain,
( or(falsehood,or(falsehood,not(falsehood))) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) = implies(and(truth,truth),not(falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
or(falsehood,truth) = implies(and(truth,truth),not(falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,or(falsehood,not(falsehood))),implies(and(truth,truth),not(falsehood))) )],[refute_0_213,refute_0_236]) ).
cnf(refute_0_238,plain,
( implies(falsehood,X_2) != truth
| or(X_2,truth) != implies(falsehood,X_2)
| or(X_2,truth) = truth ),
introduced(tautology,[equality,[$cnf( $equal(or(X_2,truth),implies(falsehood,X_2)) ),[1],$fot(truth)]]) ).
cnf(refute_0_239,plain,
( or(X_2,truth) != implies(falsehood,X_2)
| or(X_2,truth) = truth ),
inference(resolve,[$cnf( $equal(implies(falsehood,X_2),truth) )],[refute_0_83,refute_0_238]) ).
cnf(refute_0_240,plain,
or(X_2,truth) = truth,
inference(resolve,[$cnf( $equal(or(X_2,truth),implies(falsehood,X_2)) )],[refute_0_78,refute_0_239]) ).
cnf(refute_0_241,plain,
or(falsehood,truth) = truth,
inference(subst,[],[refute_0_240:[bind(X_2,$fot(falsehood))]]) ).
cnf(refute_0_242,plain,
( or(falsehood,truth) != implies(and(truth,truth),not(falsehood))
| or(falsehood,truth) != truth
| truth = implies(and(truth,truth),not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,truth),implies(and(truth,truth),not(falsehood))) ),[0],$fot(truth)]]) ).
cnf(refute_0_243,plain,
( or(falsehood,truth) != implies(and(truth,truth),not(falsehood))
| truth = implies(and(truth,truth),not(falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,truth),truth) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
truth = implies(and(truth,truth),not(falsehood)),
inference(resolve,[$cnf( $equal(or(falsehood,truth),implies(and(truth,truth),not(falsehood))) )],[refute_0_237,refute_0_243]) ).
cnf(refute_0_245,plain,
( truth != implies(and(truth,truth),not(falsehood))
| implies(and(truth,truth),not(falsehood)) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(implies(and(truth,truth),not(falsehood))))]]) ).
cnf(refute_0_246,plain,
implies(and(truth,truth),not(falsehood)) = truth,
inference(resolve,[$cnf( $equal(truth,implies(and(truth,truth),not(falsehood))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( implies(and(truth,truth),not(falsehood)) != truth
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_248,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
inference(resolve,[$cnf( $equal(implies(and(truth,truth),not(falsehood)),truth) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) )],[refute_0_212,refute_0_248]) ).
cnf(refute_0_250,plain,
or(and(truth,truth),falsehood) = or(falsehood,and(truth,truth)),
inference(subst,[],[refute_0_129:[bind(X,$fot(falsehood)),bind(Y,$fot(and(truth,truth)))]]) ).
cnf(refute_0_251,plain,
implies(or(and(truth,truth),falsehood),and(truth,truth)) = implies(or(and(truth,truth),falsehood),and(truth,truth)),
introduced(tautology,[refl,[$fot(implies(or(and(truth,truth),falsehood),and(truth,truth)))]]) ).
cnf(refute_0_252,plain,
( implies(or(and(truth,truth),falsehood),and(truth,truth)) != implies(or(and(truth,truth),falsehood),and(truth,truth))
| or(and(truth,truth),falsehood) != or(falsehood,and(truth,truth))
| implies(or(and(truth,truth),falsehood),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(and(truth,truth),falsehood),and(truth,truth)),implies(or(and(truth,truth),falsehood),and(truth,truth))) ),[1,0],$fot(or(falsehood,and(truth,truth)))]]) ).
cnf(refute_0_253,plain,
( or(and(truth,truth),falsehood) != or(falsehood,and(truth,truth))
| implies(or(and(truth,truth),falsehood),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(or(and(truth,truth),falsehood),and(truth,truth)),implies(or(and(truth,truth),falsehood),and(truth,truth))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
implies(or(and(truth,truth),falsehood),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)),
inference(resolve,[$cnf( $equal(or(and(truth,truth),falsehood),or(falsehood,and(truth,truth))) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
implies(or(X_23,X_24),X_24) = implies(implies(X_24,not(X_23)),not(X_23)),
inference(subst,[],[refute_0_16:[bind(X,$fot(X_23)),bind(X_17,$fot(X_24))]]) ).
cnf(refute_0_256,plain,
or(X_24,X_23) = or(X_23,X_24),
inference(subst,[],[or_commutativity:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_257,plain,
( or(X_24,X_23) != or(X_23,X_24)
| or(X_23,X_24) = or(X_24,X_23) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(X_24,X_23))),bind(Y0,$fot(or(X_23,X_24)))]]) ).
cnf(refute_0_258,plain,
or(X_23,X_24) = or(X_24,X_23),
inference(resolve,[$cnf( $equal(or(X_24,X_23),or(X_23,X_24)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
( implies(or(X_23,X_24),X_24) != implies(implies(X_24,not(X_23)),not(X_23))
| or(X_23,X_24) != or(X_24,X_23)
| implies(or(X_24,X_23),X_24) = implies(implies(X_24,not(X_23)),not(X_23)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_23,X_24),X_24),implies(implies(X_24,not(X_23)),not(X_23))) ),[0,0],$fot(or(X_24,X_23))]]) ).
cnf(refute_0_260,plain,
( implies(or(X_23,X_24),X_24) != implies(implies(X_24,not(X_23)),not(X_23))
| implies(or(X_24,X_23),X_24) = implies(implies(X_24,not(X_23)),not(X_23)) ),
inference(resolve,[$cnf( $equal(or(X_23,X_24),or(X_24,X_23)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
implies(or(X_24,X_23),X_24) = implies(implies(X_24,not(X_23)),not(X_23)),
inference(resolve,[$cnf( $equal(implies(or(X_23,X_24),X_24),implies(implies(X_24,not(X_23)),not(X_23))) )],[refute_0_255,refute_0_260]) ).
cnf(refute_0_262,plain,
( implies(or(X_24,X_23),X_24) != implies(implies(X_24,not(X_23)),not(X_23))
| implies(implies(X_24,not(X_23)),not(X_23)) = implies(or(X_24,X_23),X_24) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(or(X_24,X_23),X_24))),bind(Y0,$fot(implies(implies(X_24,not(X_23)),not(X_23))))]]) ).
cnf(refute_0_263,plain,
implies(implies(X_24,not(X_23)),not(X_23)) = implies(or(X_24,X_23),X_24),
inference(resolve,[$cnf( $equal(implies(or(X_24,X_23),X_24),implies(implies(X_24,not(X_23)),not(X_23))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) = implies(or(and(truth,truth),falsehood),and(truth,truth)),
inference(subst,[],[refute_0_263:[bind(X_23,$fot(falsehood)),bind(X_24,$fot(and(truth,truth)))]]) ).
cnf(refute_0_265,plain,
( implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) != implies(or(and(truth,truth),falsehood),and(truth,truth))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(implies(and(truth,truth),not(falsehood)),not(falsehood))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(and(truth,truth),falsehood),and(truth,truth)) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)))),bind(Y0,$fot(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)))),bind(Z0,$fot(implies(or(and(truth,truth),falsehood),and(truth,truth))))]]) ).
cnf(refute_0_266,plain,
( implies(implies(and(truth,truth),not(falsehood)),not(falsehood)) != implies(or(and(truth,truth),falsehood),and(truth,truth))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(and(truth,truth),falsehood),and(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(implies(and(truth,truth),not(falsehood)),not(falsehood))) )],[refute_0_212,refute_0_265]) ).
cnf(refute_0_267,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(and(truth,truth),falsehood),and(truth,truth)),
inference(resolve,[$cnf( $equal(implies(implies(and(truth,truth),not(falsehood)),not(falsehood)),implies(or(and(truth,truth),falsehood),and(truth,truth))) )],[refute_0_264,refute_0_266]) ).
cnf(refute_0_268,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(or(and(truth,truth),falsehood),and(truth,truth))
| implies(or(and(truth,truth),falsehood),and(truth,truth)) != implies(or(falsehood,and(truth,truth)),and(truth,truth))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)))),bind(Y0,$fot(implies(or(and(truth,truth),falsehood),and(truth,truth)))),bind(Z0,$fot(implies(or(falsehood,and(truth,truth)),and(truth,truth))))]]) ).
cnf(refute_0_269,plain,
( implies(or(and(truth,truth),falsehood),and(truth,truth)) != implies(or(falsehood,and(truth,truth)),and(truth,truth))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(or(and(truth,truth),falsehood),and(truth,truth))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) = implies(or(falsehood,and(truth,truth)),and(truth,truth)),
inference(resolve,[$cnf( $equal(implies(or(and(truth,truth),falsehood),and(truth,truth)),implies(or(falsehood,and(truth,truth)),and(truth,truth))) )],[refute_0_254,refute_0_269]) ).
cnf(refute_0_271,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(or(falsehood,and(truth,truth)),and(truth,truth))
| implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(truth,not(falsehood))) ),[0],$fot(implies(or(falsehood,and(truth,truth)),and(truth,truth)))]]) ).
cnf(refute_0_272,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) = implies(truth,not(falsehood)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(or(falsehood,and(truth,truth)),and(truth,truth))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
implies(truth,not(falsehood)) = not(falsehood),
inference(subst,[],[wajsberg_1:[bind(X,$fot(not(falsehood)))]]) ).
cnf(refute_0_274,plain,
( implies(or(falsehood,and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(truth,not(falsehood)) != not(falsehood)
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),not(falsehood)) ),[0],$fot(implies(truth,not(falsehood)))]]) ).
cnf(refute_0_275,plain,
( implies(or(falsehood,and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(implies(truth,not(falsehood)),not(falsehood)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
( implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)) != implies(truth,not(falsehood))
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) = not(falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),implies(truth,not(falsehood))) )],[refute_0_272,refute_0_275]) ).
cnf(refute_0_277,plain,
implies(or(falsehood,and(truth,truth)),and(truth,truth)) = not(falsehood),
inference(resolve,[$cnf( $equal(implies(implies(not(falsehood),and(truth,truth)),and(truth,truth)),implies(truth,not(falsehood))) )],[refute_0_249,refute_0_276]) ).
cnf(refute_0_278,plain,
implies(or(X_38,falsehood),X_38) = truth,
inference(subst,[],[refute_0_185:[bind(X_36,$fot(X_38))]]) ).
cnf(refute_0_279,plain,
or(falsehood,X_38) = or(X_38,falsehood),
inference(subst,[],[or_commutativity:[bind(X,$fot(falsehood)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_280,plain,
( or(falsehood,X_38) != or(X_38,falsehood)
| or(X_38,falsehood) = or(falsehood,X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(or(falsehood,X_38))),bind(Y0,$fot(or(X_38,falsehood)))]]) ).
cnf(refute_0_281,plain,
or(X_38,falsehood) = or(falsehood,X_38),
inference(resolve,[$cnf( $equal(or(falsehood,X_38),or(X_38,falsehood)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( implies(or(X_38,falsehood),X_38) != truth
| or(X_38,falsehood) != or(falsehood,X_38)
| implies(or(falsehood,X_38),X_38) = truth ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X_38,falsehood),X_38),truth) ),[0,0],$fot(or(falsehood,X_38))]]) ).
cnf(refute_0_283,plain,
( implies(or(X_38,falsehood),X_38) != truth
| implies(or(falsehood,X_38),X_38) = truth ),
inference(resolve,[$cnf( $equal(or(X_38,falsehood),or(falsehood,X_38)) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
implies(or(falsehood,X_38),X_38) = truth,
inference(resolve,[$cnf( $equal(implies(or(X_38,falsehood),X_38),truth) )],[refute_0_278,refute_0_283]) ).
cnf(refute_0_285,plain,
implies(or(falsehood,and(truth,truth)),and(truth,truth)) = truth,
inference(subst,[],[refute_0_284:[bind(X_38,$fot(and(truth,truth)))]]) ).
cnf(refute_0_286,plain,
( implies(or(falsehood,and(truth,truth)),and(truth,truth)) != not(falsehood)
| implies(or(falsehood,and(truth,truth)),and(truth,truth)) != truth
| truth = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),not(falsehood)) ),[0],$fot(truth)]]) ).
cnf(refute_0_287,plain,
( implies(or(falsehood,and(truth,truth)),and(truth,truth)) != not(falsehood)
| truth = not(falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),truth) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
truth = not(falsehood),
inference(resolve,[$cnf( $equal(implies(or(falsehood,and(truth,truth)),and(truth,truth)),not(falsehood)) )],[refute_0_277,refute_0_287]) ).
cnf(refute_0_289,plain,
( truth != not(falsehood)
| not(falsehood) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(not(falsehood)))]]) ).
cnf(refute_0_290,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(truth,not(falsehood)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
( not(falsehood) != truth
| or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_292,plain,
( or(falsehood,Y) != implies(not(falsehood),Y)
| or(falsehood,Y) = implies(truth,Y) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
or(falsehood,Y) = implies(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(not(falsehood),Y)) )],[refute_0_211,refute_0_292]) ).
cnf(refute_0_294,plain,
implies(truth,Y) = Y,
inference(subst,[],[wajsberg_1:[bind(X,$fot(Y))]]) ).
cnf(refute_0_295,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_296,plain,
( or(falsehood,Y) != implies(truth,Y)
| or(falsehood,Y) = Y ),
inference(resolve,[$cnf( $equal(implies(truth,Y),Y) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
or(falsehood,Y) = Y,
inference(resolve,[$cnf( $equal(or(falsehood,Y),implies(truth,Y)) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
or(falsehood,or(X_34,falsehood)) = or(X_34,falsehood),
inference(subst,[],[refute_0_297:[bind(Y,$fot(or(X_34,falsehood)))]]) ).
cnf(refute_0_299,plain,
( or(falsehood,or(X_34,falsehood)) != or(X_34,falsehood)
| or(falsehood,or(X_34,falsehood)) != or(falsehood,X_34)
| or(X_34,falsehood) = or(falsehood,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,or(X_34,falsehood)),or(falsehood,X_34)) ),[0],$fot(or(X_34,falsehood))]]) ).
cnf(refute_0_300,plain,
( or(falsehood,or(X_34,falsehood)) != or(falsehood,X_34)
| or(X_34,falsehood) = or(falsehood,X_34) ),
inference(resolve,[$cnf( $equal(or(falsehood,or(X_34,falsehood)),or(X_34,falsehood)) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
or(falsehood,X_34) = X_34,
inference(subst,[],[refute_0_297:[bind(Y,$fot(X_34))]]) ).
cnf(refute_0_302,plain,
( or(X_34,falsehood) != or(falsehood,X_34)
| or(falsehood,X_34) != X_34
| or(X_34,falsehood) = X_34 ),
introduced(tautology,[equality,[$cnf( ~ $equal(or(X_34,falsehood),X_34) ),[0],$fot(or(falsehood,X_34))]]) ).
cnf(refute_0_303,plain,
( or(X_34,falsehood) != or(falsehood,X_34)
| or(X_34,falsehood) = X_34 ),
inference(resolve,[$cnf( $equal(or(falsehood,X_34),X_34) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( or(falsehood,or(X_34,falsehood)) != or(falsehood,X_34)
| or(X_34,falsehood) = X_34 ),
inference(resolve,[$cnf( $equal(or(X_34,falsehood),or(falsehood,X_34)) )],[refute_0_300,refute_0_303]) ).
cnf(refute_0_305,plain,
or(X_34,falsehood) = X_34,
inference(resolve,[$cnf( $equal(or(falsehood,or(X_34,falsehood)),or(falsehood,X_34)) )],[refute_0_210,refute_0_304]) ).
cnf(refute_0_306,plain,
or(X,falsehood) = X,
inference(subst,[],[refute_0_305:[bind(X_34,$fot(X))]]) ).
cnf(refute_0_307,plain,
implies(or(X,falsehood),falsehood) = implies(or(X,falsehood),falsehood),
introduced(tautology,[refl,[$fot(implies(or(X,falsehood),falsehood))]]) ).
cnf(refute_0_308,plain,
( implies(or(X,falsehood),falsehood) != implies(or(X,falsehood),falsehood)
| or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) ),[1,0],$fot(X)]]) ).
cnf(refute_0_309,plain,
( or(X,falsehood) != X
| implies(or(X,falsehood),falsehood) = implies(X,falsehood) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(or(X,falsehood),falsehood)) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
implies(or(X,falsehood),falsehood) = implies(X,falsehood),
inference(resolve,[$cnf( $equal(or(X,falsehood),X) )],[refute_0_306,refute_0_309]) ).
cnf(refute_0_311,plain,
( implies(or(X,falsehood),falsehood) != implies(X,falsehood)
| implies(or(X,falsehood),falsehood) != not(X)
| implies(X,falsehood) = not(X) ),
introduced(tautology,[equality,[$cnf( $equal(implies(or(X,falsehood),falsehood),not(X)) ),[0],$fot(implies(X,falsehood))]]) ).
cnf(refute_0_312,plain,
( implies(or(X,falsehood),falsehood) != not(X)
| implies(X,falsehood) = not(X) ),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),implies(X,falsehood)) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
implies(X,falsehood) = not(X),
inference(resolve,[$cnf( $equal(implies(or(X,falsehood),falsehood),not(X)) )],[refute_0_122,refute_0_312]) ).
cnf(refute_0_314,plain,
implies(X_17,falsehood) = not(X_17),
inference(subst,[],[refute_0_313:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_315,plain,
not(implies(X_17,falsehood)) = not(implies(X_17,falsehood)),
introduced(tautology,[refl,[$fot(not(implies(X_17,falsehood)))]]) ).
cnf(refute_0_316,plain,
( implies(X_17,falsehood) != not(X_17)
| not(implies(X_17,falsehood)) != not(implies(X_17,falsehood))
| not(implies(X_17,falsehood)) = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( $equal(not(implies(X_17,falsehood)),not(implies(X_17,falsehood))) ),[1,0],$fot(not(X_17))]]) ).
cnf(refute_0_317,plain,
( implies(X_17,falsehood) != not(X_17)
| not(implies(X_17,falsehood)) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(not(implies(X_17,falsehood)),not(implies(X_17,falsehood))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
not(implies(X_17,falsehood)) = not(not(X_17)),
inference(resolve,[$cnf( $equal(implies(X_17,falsehood),not(X_17)) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
implies(implies(X_17,falsehood),falsehood) = not(implies(X_17,falsehood)),
inference(subst,[],[refute_0_313:[bind(X,$fot(implies(X_17,falsehood)))]]) ).
cnf(refute_0_320,plain,
( implies(implies(X_17,falsehood),falsehood) != not(implies(X_17,falsehood))
| not(implies(X_17,falsehood)) != not(not(X_17))
| implies(implies(X_17,falsehood),falsehood) = not(not(X_17)) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(X_17,falsehood),falsehood))),bind(Y0,$fot(not(implies(X_17,falsehood)))),bind(Z0,$fot(not(not(X_17))))]]) ).
cnf(refute_0_321,plain,
( not(implies(X_17,falsehood)) != not(not(X_17))
| implies(implies(X_17,falsehood),falsehood) = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,falsehood),falsehood),not(implies(X_17,falsehood))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
implies(implies(X_17,falsehood),falsehood) = not(not(X_17)),
inference(resolve,[$cnf( $equal(not(implies(X_17,falsehood)),not(not(X_17))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( X_17 != implies(implies(X_17,falsehood),falsehood)
| implies(implies(X_17,falsehood),falsehood) != not(not(X_17))
| X_17 = not(not(X_17)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_17,not(not(X_17))) ),[0],$fot(implies(implies(X_17,falsehood),falsehood))]]) ).
cnf(refute_0_324,plain,
( X_17 != implies(implies(X_17,falsehood),falsehood)
| X_17 = not(not(X_17)) ),
inference(resolve,[$cnf( $equal(implies(implies(X_17,falsehood),falsehood),not(not(X_17))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
X_17 = not(not(X_17)),
inference(resolve,[$cnf( $equal(X_17,implies(implies(X_17,falsehood),falsehood)) )],[refute_0_113,refute_0_324]) ).
cnf(refute_0_326,plain,
X_41 = not(not(X_41)),
inference(subst,[],[refute_0_325:[bind(X_17,$fot(X_41))]]) ).
cnf(refute_0_327,plain,
( X_41 != not(not(X_41))
| not(not(X_41)) = X_41 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_41)),bind(Y0,$fot(not(not(X_41))))]]) ).
cnf(refute_0_328,plain,
not(not(X_41)) = X_41,
inference(resolve,[$cnf( $equal(X_41,not(not(X_41))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
( not(not(X_41)) != X_41
| or(not(X_41),Y) != implies(not(not(X_41)),Y)
| or(not(X_41),Y) = implies(X_41,Y) ),
introduced(tautology,[equality,[$cnf( $equal(or(not(X_41),Y),implies(not(not(X_41)),Y)) ),[1,0],$fot(X_41)]]) ).
cnf(refute_0_330,plain,
( or(not(X_41),Y) != implies(not(not(X_41)),Y)
| or(not(X_41),Y) = implies(X_41,Y) ),
inference(resolve,[$cnf( $equal(not(not(X_41)),X_41) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
or(not(X_41),Y) = implies(X_41,Y),
inference(resolve,[$cnf( $equal(or(not(X_41),Y),implies(not(not(X_41)),Y)) )],[refute_0_9,refute_0_330]) ).
cnf(refute_0_332,plain,
or(not(implies(X,Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(subst,[],[refute_0_331:[bind(Y,$fot(and(not(X),Y))),bind(X_41,$fot(implies(X,Y)))]]) ).
cnf(refute_0_333,plain,
and(X,not(X_41)) = not(or(not(X),not(not(X_41)))),
inference(subst,[],[and_definition:[bind(Y,$fot(not(X_41)))]]) ).
cnf(refute_0_334,plain,
( and(X,not(X_41)) != not(or(not(X),not(not(X_41))))
| not(not(X_41)) != X_41
| and(X,not(X_41)) = not(or(not(X),X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(and(X,not(X_41)),not(or(not(X),not(not(X_41))))) ),[1,0,1],$fot(X_41)]]) ).
cnf(refute_0_335,plain,
( and(X,not(X_41)) != not(or(not(X),not(not(X_41))))
| and(X,not(X_41)) = not(or(not(X),X_41)) ),
inference(resolve,[$cnf( $equal(not(not(X_41)),X_41) )],[refute_0_328,refute_0_334]) ).
cnf(refute_0_336,plain,
and(X,not(X_41)) = not(or(not(X),X_41)),
inference(resolve,[$cnf( $equal(and(X,not(X_41)),not(or(not(X),not(not(X_41))))) )],[refute_0_333,refute_0_335]) ).
cnf(refute_0_337,plain,
or(not(X),X_41) = implies(X,X_41),
inference(subst,[],[refute_0_331:[bind(Y,$fot(X_41)),bind(X_41,$fot(X))]]) ).
cnf(refute_0_338,plain,
not(or(not(X),X_41)) = not(or(not(X),X_41)),
introduced(tautology,[refl,[$fot(not(or(not(X),X_41)))]]) ).
cnf(refute_0_339,plain,
( not(or(not(X),X_41)) != not(or(not(X),X_41))
| or(not(X),X_41) != implies(X,X_41)
| not(or(not(X),X_41)) = not(implies(X,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(not(X),X_41)),not(or(not(X),X_41))) ),[1,0],$fot(implies(X,X_41))]]) ).
cnf(refute_0_340,plain,
( or(not(X),X_41) != implies(X,X_41)
| not(or(not(X),X_41)) = not(implies(X,X_41)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_41)),not(or(not(X),X_41))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
not(or(not(X),X_41)) = not(implies(X,X_41)),
inference(resolve,[$cnf( $equal(or(not(X),X_41),implies(X,X_41)) )],[refute_0_337,refute_0_340]) ).
cnf(refute_0_342,plain,
( and(X,not(X_41)) != not(or(not(X),X_41))
| not(or(not(X),X_41)) != not(implies(X,X_41))
| and(X,not(X_41)) = not(implies(X,X_41)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X,not(X_41)),not(implies(X,X_41))) ),[0],$fot(not(or(not(X),X_41)))]]) ).
cnf(refute_0_343,plain,
( and(X,not(X_41)) != not(or(not(X),X_41))
| and(X,not(X_41)) = not(implies(X,X_41)) ),
inference(resolve,[$cnf( $equal(not(or(not(X),X_41)),not(implies(X,X_41))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
and(X,not(X_41)) = not(implies(X,X_41)),
inference(resolve,[$cnf( $equal(and(X,not(X_41)),not(or(not(X),X_41))) )],[refute_0_336,refute_0_343]) ).
cnf(refute_0_345,plain,
and(X,not(Y)) = not(implies(X,Y)),
inference(subst,[],[refute_0_344:[bind(X_41,$fot(Y))]]) ).
cnf(refute_0_346,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(and(X,not(Y)),and(not(X),Y)),
introduced(tautology,[refl,[$fot(or(and(X,not(Y)),and(not(X),Y)))]]) ).
cnf(refute_0_347,plain,
( and(X,not(Y)) != not(implies(X,Y))
| or(and(X,not(Y)),and(not(X),Y)) != or(and(X,not(Y)),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)) ),
introduced(tautology,[equality,[$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_348,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( $equal(or(and(X,not(Y)),and(not(X),Y)),or(and(X,not(Y)),and(not(X),Y))) )],[refute_0_346,refute_0_347]) ).
cnf(refute_0_349,plain,
or(and(X,not(Y)),and(not(X),Y)) = or(not(implies(X,Y)),and(not(X),Y)),
inference(resolve,[$cnf( $equal(and(X,not(Y)),not(implies(X,Y))) )],[refute_0_345,refute_0_348]) ).
cnf(refute_0_350,plain,
( or(and(X,not(Y)),and(not(X),Y)) != or(not(implies(X,Y)),and(not(X),Y))
| or(not(implies(X,Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)) ),
inference(subst,[],[refute_0_106:[bind(X0,$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_351,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( $equal(or(and(X,not(Y)),and(not(X),Y)),or(not(implies(X,Y)),and(not(X),Y))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
or(and(X,not(Y)),and(not(X),Y)) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(or(not(implies(X,Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_332,refute_0_351]) ).
cnf(refute_0_353,plain,
( or(and(X,not(Y)),and(not(X),Y)) != implies(implies(X,Y),and(not(X),Y))
| xor(X,Y) != or(and(X,not(Y)),and(not(X),Y))
| xor(X,Y) = implies(implies(X,Y),and(not(X),Y)) ),
introduced(tautology,[equality,[$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_354,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( $equal(or(and(X,not(Y)),and(not(X),Y)),implies(implies(X,Y),and(not(X),Y))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
xor(X,Y) = implies(implies(X,Y),and(not(X),Y)),
inference(resolve,[$cnf( $equal(xor(X,Y),or(and(X,not(Y)),and(not(X),Y))) )],[xor_definition,refute_0_354]) ).
cnf(refute_0_356,plain,
xor(falsehood,X_57) = implies(implies(falsehood,X_57),and(not(falsehood),X_57)),
inference(subst,[],[refute_0_355:[bind(X,$fot(falsehood)),bind(Y,$fot(X_57))]]) ).
cnf(refute_0_357,plain,
( not(falsehood) != truth
| xor(falsehood,X_57) != implies(implies(falsehood,X_57),and(not(falsehood),X_57))
| xor(falsehood,X_57) = implies(implies(falsehood,X_57),and(truth,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,X_57),implies(implies(falsehood,X_57),and(not(falsehood),X_57))) ),[1,1,0],$fot(truth)]]) ).
cnf(refute_0_358,plain,
( xor(falsehood,X_57) != implies(implies(falsehood,X_57),and(not(falsehood),X_57))
| xor(falsehood,X_57) = implies(implies(falsehood,X_57),and(truth,X_57)) ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_290,refute_0_357]) ).
cnf(refute_0_359,plain,
xor(falsehood,X_57) = implies(implies(falsehood,X_57),and(truth,X_57)),
inference(resolve,[$cnf( $equal(xor(falsehood,X_57),implies(implies(falsehood,X_57),and(not(falsehood),X_57))) )],[refute_0_356,refute_0_358]) ).
cnf(refute_0_360,plain,
implies(truth,X_57) = X_57,
inference(subst,[],[wajsberg_1:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_361,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(not(or(falsehood,and(truth,truth))),not(Y))),
inference(subst,[],[and_definition:[bind(X,$fot(or(falsehood,and(truth,truth))))]]) ).
cnf(refute_0_362,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,not(or(falsehood,falsehood)))),
inference(subst,[],[refute_0_137:[bind(X_13,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_363,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| not(or(falsehood,falsehood)) != and(truth,truth)
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) ),[1,0,1],$fot(and(truth,truth))]]) ).
cnf(refute_0_364,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,not(or(falsehood,falsehood))))
| and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,falsehood)),and(truth,truth)) )],[refute_0_143,refute_0_363]) ).
cnf(refute_0_365,plain,
and(or(falsehood,falsehood),truth) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,not(or(falsehood,falsehood))))) )],[refute_0_362,refute_0_364]) ).
cnf(refute_0_366,plain,
( and(X,Y) != and(Y,X)
| and(Y,X) = and(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X,Y))),bind(Y0,$fot(and(Y,X)))]]) ).
cnf(refute_0_367,plain,
and(Y,X) = and(X,Y),
inference(resolve,[$cnf( $equal(and(X,Y),and(Y,X)) )],[and_commutativity,refute_0_366]) ).
cnf(refute_0_368,plain,
and(or(falsehood,falsehood),truth) = and(truth,or(falsehood,falsehood)),
inference(subst,[],[refute_0_367:[bind(X,$fot(truth)),bind(Y,$fot(or(falsehood,falsehood)))]]) ).
cnf(refute_0_369,plain,
( and(or(falsehood,falsehood),truth) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) ),[0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_370,plain,
( and(or(falsehood,falsehood),truth) != not(or(falsehood,and(truth,truth)))
| and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),and(truth,or(falsehood,falsehood))) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
and(truth,or(falsehood,falsehood)) = not(or(falsehood,and(truth,truth))),
inference(resolve,[$cnf( $equal(and(or(falsehood,falsehood),truth),not(or(falsehood,and(truth,truth)))) )],[refute_0_365,refute_0_370]) ).
cnf(refute_0_372,plain,
( and(truth,or(falsehood,falsehood)) != not(or(falsehood,and(truth,truth)))
| not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(not(or(falsehood,and(truth,truth)))))]]) ).
cnf(refute_0_373,plain,
not(or(falsehood,and(truth,truth))) = and(truth,or(falsehood,falsehood)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),not(or(falsehood,and(truth,truth)))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| not(or(falsehood,and(truth,truth))) != and(truth,or(falsehood,falsehood))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) ),[1,0,0],$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_375,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(not(or(falsehood,and(truth,truth))),not(Y)))
| and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,and(truth,truth))),and(truth,or(falsehood,falsehood))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
and(or(falsehood,and(truth,truth)),Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(not(or(falsehood,and(truth,truth))),not(Y)))) )],[refute_0_361,refute_0_375]) ).
cnf(refute_0_377,plain,
or(falsehood,and(truth,truth)) = or(falsehood,and(truth,truth)),
introduced(tautology,[refl,[$fot(or(falsehood,and(truth,truth)))]]) ).
cnf(refute_0_378,plain,
( and(truth,truth) != not(falsehood)
| or(falsehood,and(truth,truth)) != or(falsehood,and(truth,truth))
| or(falsehood,and(truth,truth)) = or(falsehood,not(falsehood)) ),
introduced(tautology,[equality,[$cnf( $equal(or(falsehood,and(truth,truth)),or(falsehood,and(truth,truth))) ),[1,1],$fot(not(falsehood))]]) ).
cnf(refute_0_379,plain,
( and(truth,truth) != not(falsehood)
| or(falsehood,and(truth,truth)) = or(falsehood,not(falsehood)) ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),or(falsehood,and(truth,truth))) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
or(falsehood,and(truth,truth)) = or(falsehood,not(falsehood)),
inference(resolve,[$cnf( $equal(and(truth,truth),not(falsehood)) )],[refute_0_200,refute_0_379]) ).
cnf(refute_0_381,plain,
( or(falsehood,and(truth,truth)) != or(falsehood,not(falsehood))
| or(falsehood,not(falsehood)) != truth
| or(falsehood,and(truth,truth)) = truth ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(or(falsehood,and(truth,truth)))),bind(Y0,$fot(or(falsehood,not(falsehood)))),bind(Z0,$fot(truth))]]) ).
cnf(refute_0_382,plain,
( or(falsehood,not(falsehood)) != truth
| or(falsehood,and(truth,truth)) = truth ),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),or(falsehood,not(falsehood))) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
or(falsehood,and(truth,truth)) = truth,
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_234,refute_0_382]) ).
cnf(refute_0_384,plain,
and(or(falsehood,and(truth,truth)),Y) = and(or(falsehood,and(truth,truth)),Y),
introduced(tautology,[refl,[$fot(and(or(falsehood,and(truth,truth)),Y))]]) ).
cnf(refute_0_385,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(or(falsehood,and(truth,truth)),Y)
| or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_386,plain,
( or(falsehood,and(truth,truth)) != truth
| and(or(falsehood,and(truth,truth)),Y) = and(truth,Y) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(or(falsehood,and(truth,truth)),Y)) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
and(or(falsehood,and(truth,truth)),Y) = and(truth,Y),
inference(resolve,[$cnf( $equal(or(falsehood,and(truth,truth)),truth) )],[refute_0_383,refute_0_386]) ).
cnf(refute_0_388,plain,
( and(or(falsehood,and(truth,truth)),Y) != and(truth,Y)
| and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[0],$fot(and(truth,Y))]]) ).
cnf(refute_0_389,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = not(or(and(truth,or(falsehood,falsehood)),not(Y))) ),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),and(truth,Y)) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
( and(X_13,truth) != not(or(falsehood,not(X_13)))
| not(or(falsehood,not(X_13))) = and(X_13,truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and(X_13,truth))),bind(Y0,$fot(not(or(falsehood,not(X_13)))))]]) ).
cnf(refute_0_391,plain,
not(or(falsehood,not(X_13))) = and(X_13,truth),
inference(resolve,[$cnf( $equal(and(X_13,truth),not(or(falsehood,not(X_13)))) )],[refute_0_137,refute_0_390]) ).
cnf(refute_0_392,plain,
not(or(falsehood,not(Y))) = and(Y,truth),
inference(subst,[],[refute_0_391:[bind(X_13,$fot(Y))]]) ).
cnf(refute_0_393,plain,
and(falsehood,truth) = not(or(falsehood,not(falsehood))),
inference(subst,[],[refute_0_137:[bind(X_13,$fot(falsehood))]]) ).
cnf(refute_0_394,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| or(falsehood,not(falsehood)) != truth
| and(falsehood,truth) = not(truth) ),
introduced(tautology,[equality,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_395,plain,
( and(falsehood,truth) != not(or(falsehood,not(falsehood)))
| and(falsehood,truth) = not(truth) ),
inference(resolve,[$cnf( $equal(or(falsehood,not(falsehood)),truth) )],[refute_0_234,refute_0_394]) ).
cnf(refute_0_396,plain,
and(falsehood,truth) = not(truth),
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(or(falsehood,not(falsehood)))) )],[refute_0_393,refute_0_395]) ).
cnf(refute_0_397,plain,
( and(falsehood,truth) != not(truth)
| not(truth) != falsehood
| and(falsehood,truth) = falsehood ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(falsehood,truth),falsehood) ),[0],$fot(not(truth))]]) ).
cnf(refute_0_398,plain,
( and(falsehood,truth) != not(truth)
| and(falsehood,truth) = falsehood ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_397]) ).
cnf(refute_0_399,plain,
and(falsehood,truth) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),not(truth)) )],[refute_0_396,refute_0_398]) ).
cnf(refute_0_400,plain,
and(truth,falsehood) = and(falsehood,truth),
inference(subst,[],[refute_0_367:[bind(X,$fot(falsehood)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_401,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) != and(falsehood,truth)
| and(truth,falsehood) = falsehood ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(and(truth,falsehood))),bind(Y0,$fot(and(falsehood,truth))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_402,plain,
( and(falsehood,truth) != falsehood
| and(truth,falsehood) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,falsehood),and(falsehood,truth)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
and(truth,falsehood) = falsehood,
inference(resolve,[$cnf( $equal(and(falsehood,truth),falsehood) )],[refute_0_399,refute_0_402]) ).
cnf(refute_0_404,plain,
and(truth,or(falsehood,falsehood)) = and(truth,or(falsehood,falsehood)),
introduced(tautology,[refl,[$fot(and(truth,or(falsehood,falsehood)))]]) ).
cnf(refute_0_405,plain,
( and(truth,or(falsehood,falsehood)) != and(truth,or(falsehood,falsehood))
| or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_406,plain,
( or(falsehood,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = and(truth,falsehood) ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,or(falsehood,falsehood))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
and(truth,or(falsehood,falsehood)) = and(truth,falsehood),
inference(resolve,[$cnf( $equal(or(falsehood,falsehood),falsehood) )],[refute_0_193,refute_0_406]) ).
cnf(refute_0_408,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) != and(truth,falsehood)
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(and(truth,or(falsehood,falsehood)))),bind(Y0,$fot(and(truth,falsehood))),bind(Z0,$fot(falsehood))]]) ).
cnf(refute_0_409,plain,
( and(truth,falsehood) != falsehood
| and(truth,or(falsehood,falsehood)) = falsehood ),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),and(truth,falsehood)) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
and(truth,or(falsehood,falsehood)) = falsehood,
inference(resolve,[$cnf( $equal(and(truth,falsehood),falsehood) )],[refute_0_403,refute_0_409]) ).
cnf(refute_0_411,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(and(truth,or(falsehood,falsehood)),not(Y)),
introduced(tautology,[refl,[$fot(or(and(truth,or(falsehood,falsehood)),not(Y)))]]) ).
cnf(refute_0_412,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) != or(and(truth,or(falsehood,falsehood)),not(Y))
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_413,plain,
( and(truth,or(falsehood,falsehood)) != falsehood
| or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)) ),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(and(truth,or(falsehood,falsehood)),not(Y))) )],[refute_0_411,refute_0_412]) ).
cnf(refute_0_414,plain,
or(and(truth,or(falsehood,falsehood)),not(Y)) = or(falsehood,not(Y)),
inference(resolve,[$cnf( $equal(and(truth,or(falsehood,falsehood)),falsehood) )],[refute_0_410,refute_0_413]) ).
cnf(refute_0_415,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(and(truth,or(falsehood,falsehood)),not(Y))),
introduced(tautology,[refl,[$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_416,plain,
( not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) ),[1,0],$fot(or(falsehood,not(Y)))]]) ).
cnf(refute_0_417,plain,
( or(and(truth,or(falsehood,falsehood)),not(Y)) != or(falsehood,not(Y))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = not(or(falsehood,not(Y))),
inference(resolve,[$cnf( $equal(or(and(truth,or(falsehood,falsehood)),not(Y)),or(falsehood,not(Y))) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
( not(or(and(truth,or(falsehood,falsehood)),not(Y))) != not(or(falsehood,not(Y)))
| not(or(falsehood,not(Y))) != and(Y,truth)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))),bind(Y0,$fot(not(or(falsehood,not(Y))))),bind(Z0,$fot(and(Y,truth)))]]) ).
cnf(refute_0_420,plain,
( not(or(falsehood,not(Y))) != and(Y,truth)
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),not(or(falsehood,not(Y)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
not(or(and(truth,or(falsehood,falsehood)),not(Y))) = and(Y,truth),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(Y))),and(Y,truth)) )],[refute_0_392,refute_0_420]) ).
cnf(refute_0_422,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| not(or(and(truth,or(falsehood,falsehood)),not(Y))) != and(Y,truth)
| and(truth,Y) = and(Y,truth) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(truth,Y),and(Y,truth)) ),[0],$fot(not(or(and(truth,or(falsehood,falsehood)),not(Y))))]]) ).
cnf(refute_0_423,plain,
( and(truth,Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(not(or(and(truth,or(falsehood,falsehood)),not(Y))),and(Y,truth)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
( and(or(falsehood,and(truth,truth)),Y) != not(or(and(truth,or(falsehood,falsehood)),not(Y)))
| and(truth,Y) = and(Y,truth) ),
inference(resolve,[$cnf( $equal(and(truth,Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_389,refute_0_423]) ).
cnf(refute_0_425,plain,
and(truth,Y) = and(Y,truth),
inference(resolve,[$cnf( $equal(and(or(falsehood,and(truth,truth)),Y),not(or(and(truth,or(falsehood,falsehood)),not(Y)))) )],[refute_0_376,refute_0_424]) ).
cnf(refute_0_426,plain,
or(falsehood,not(X_13)) = not(X_13),
inference(subst,[],[refute_0_297:[bind(Y,$fot(not(X_13)))]]) ).
cnf(refute_0_427,plain,
not(or(falsehood,not(X_13))) = not(or(falsehood,not(X_13))),
introduced(tautology,[refl,[$fot(not(or(falsehood,not(X_13))))]]) ).
cnf(refute_0_428,plain,
( not(or(falsehood,not(X_13))) != not(or(falsehood,not(X_13)))
| or(falsehood,not(X_13)) != not(X_13)
| not(or(falsehood,not(X_13))) = not(not(X_13)) ),
introduced(tautology,[equality,[$cnf( $equal(not(or(falsehood,not(X_13))),not(or(falsehood,not(X_13)))) ),[1,0],$fot(not(X_13))]]) ).
cnf(refute_0_429,plain,
( or(falsehood,not(X_13)) != not(X_13)
| not(or(falsehood,not(X_13))) = not(not(X_13)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_13))),not(or(falsehood,not(X_13)))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
not(or(falsehood,not(X_13))) = not(not(X_13)),
inference(resolve,[$cnf( $equal(or(falsehood,not(X_13)),not(X_13)) )],[refute_0_426,refute_0_429]) ).
cnf(refute_0_431,plain,
( and(X_13,truth) != not(or(falsehood,not(X_13)))
| not(or(falsehood,not(X_13))) != not(not(X_13))
| and(X_13,truth) = not(not(X_13)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_13,truth),not(not(X_13))) ),[0],$fot(not(or(falsehood,not(X_13))))]]) ).
cnf(refute_0_432,plain,
( and(X_13,truth) != not(or(falsehood,not(X_13)))
| and(X_13,truth) = not(not(X_13)) ),
inference(resolve,[$cnf( $equal(not(or(falsehood,not(X_13))),not(not(X_13))) )],[refute_0_430,refute_0_431]) ).
cnf(refute_0_433,plain,
and(X_13,truth) = not(not(X_13)),
inference(resolve,[$cnf( $equal(and(X_13,truth),not(or(falsehood,not(X_13)))) )],[refute_0_137,refute_0_432]) ).
cnf(refute_0_434,plain,
( X_17 != not(not(X_17))
| not(not(X_17)) = X_17 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_17)),bind(Y0,$fot(not(not(X_17))))]]) ).
cnf(refute_0_435,plain,
not(not(X_17)) = X_17,
inference(resolve,[$cnf( $equal(X_17,not(not(X_17))) )],[refute_0_325,refute_0_434]) ).
cnf(refute_0_436,plain,
not(not(X_13)) = X_13,
inference(subst,[],[refute_0_435:[bind(X_17,$fot(X_13))]]) ).
cnf(refute_0_437,plain,
( and(X_13,truth) != not(not(X_13))
| not(not(X_13)) != X_13
| and(X_13,truth) = X_13 ),
introduced(tautology,[equality,[$cnf( ~ $equal(and(X_13,truth),X_13) ),[0],$fot(not(not(X_13)))]]) ).
cnf(refute_0_438,plain,
( and(X_13,truth) != not(not(X_13))
| and(X_13,truth) = X_13 ),
inference(resolve,[$cnf( $equal(not(not(X_13)),X_13) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
and(X_13,truth) = X_13,
inference(resolve,[$cnf( $equal(and(X_13,truth),not(not(X_13))) )],[refute_0_433,refute_0_438]) ).
cnf(refute_0_440,plain,
and(Y,truth) = Y,
inference(subst,[],[refute_0_439:[bind(X_13,$fot(Y))]]) ).
cnf(refute_0_441,plain,
( and(Y,truth) != Y
| and(truth,Y) != and(Y,truth)
| and(truth,Y) = Y ),
introduced(tautology,[equality,[$cnf( $equal(and(truth,Y),and(Y,truth)) ),[1],$fot(Y)]]) ).
cnf(refute_0_442,plain,
( and(truth,Y) != and(Y,truth)
| and(truth,Y) = Y ),
inference(resolve,[$cnf( $equal(and(Y,truth),Y) )],[refute_0_440,refute_0_441]) ).
cnf(refute_0_443,plain,
and(truth,Y) = Y,
inference(resolve,[$cnf( $equal(and(truth,Y),and(Y,truth)) )],[refute_0_425,refute_0_442]) ).
cnf(refute_0_444,plain,
and(truth,X_57) = X_57,
inference(subst,[],[refute_0_443:[bind(Y,$fot(X_57))]]) ).
cnf(refute_0_445,plain,
implies(truth,and(truth,X_57)) = implies(truth,and(truth,X_57)),
introduced(tautology,[refl,[$fot(implies(truth,and(truth,X_57)))]]) ).
cnf(refute_0_446,plain,
( and(truth,X_57) != X_57
| implies(truth,and(truth,X_57)) != implies(truth,and(truth,X_57))
| implies(truth,and(truth,X_57)) = implies(truth,X_57) ),
introduced(tautology,[equality,[$cnf( $equal(implies(truth,and(truth,X_57)),implies(truth,and(truth,X_57))) ),[1,1],$fot(X_57)]]) ).
cnf(refute_0_447,plain,
( and(truth,X_57) != X_57
| implies(truth,and(truth,X_57)) = implies(truth,X_57) ),
inference(resolve,[$cnf( $equal(implies(truth,and(truth,X_57)),implies(truth,and(truth,X_57))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
implies(truth,and(truth,X_57)) = implies(truth,X_57),
inference(resolve,[$cnf( $equal(and(truth,X_57),X_57) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
implies(falsehood,X_57) = truth,
inference(subst,[],[refute_0_82:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_450,plain,
implies(implies(falsehood,X_57),and(truth,X_57)) = implies(implies(falsehood,X_57),and(truth,X_57)),
introduced(tautology,[refl,[$fot(implies(implies(falsehood,X_57),and(truth,X_57)))]]) ).
cnf(refute_0_451,plain,
( implies(falsehood,X_57) != truth
| implies(implies(falsehood,X_57),and(truth,X_57)) != implies(implies(falsehood,X_57),and(truth,X_57))
| implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,and(truth,X_57)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(implies(falsehood,X_57),and(truth,X_57)),implies(implies(falsehood,X_57),and(truth,X_57))) ),[1,0],$fot(truth)]]) ).
cnf(refute_0_452,plain,
( implies(falsehood,X_57) != truth
| implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,and(truth,X_57)) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_57),and(truth,X_57)),implies(implies(falsehood,X_57),and(truth,X_57))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,and(truth,X_57)),
inference(resolve,[$cnf( $equal(implies(falsehood,X_57),truth) )],[refute_0_449,refute_0_452]) ).
cnf(refute_0_454,plain,
( implies(implies(falsehood,X_57),and(truth,X_57)) != implies(truth,and(truth,X_57))
| implies(truth,and(truth,X_57)) != implies(truth,X_57)
| implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,X_57) ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(falsehood,X_57),and(truth,X_57)))),bind(Y0,$fot(implies(truth,and(truth,X_57)))),bind(Z0,$fot(implies(truth,X_57)))]]) ).
cnf(refute_0_455,plain,
( implies(truth,and(truth,X_57)) != implies(truth,X_57)
| implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,X_57) ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_57),and(truth,X_57)),implies(truth,and(truth,X_57))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
implies(implies(falsehood,X_57),and(truth,X_57)) = implies(truth,X_57),
inference(resolve,[$cnf( $equal(implies(truth,and(truth,X_57)),implies(truth,X_57)) )],[refute_0_448,refute_0_455]) ).
cnf(refute_0_457,plain,
( implies(implies(falsehood,X_57),and(truth,X_57)) != implies(truth,X_57)
| implies(truth,X_57) != X_57
| implies(implies(falsehood,X_57),and(truth,X_57)) = X_57 ),
inference(subst,[],[refute_0_106:[bind(X0,$fot(implies(implies(falsehood,X_57),and(truth,X_57)))),bind(Y0,$fot(implies(truth,X_57))),bind(Z0,$fot(X_57))]]) ).
cnf(refute_0_458,plain,
( implies(truth,X_57) != X_57
| implies(implies(falsehood,X_57),and(truth,X_57)) = X_57 ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_57),and(truth,X_57)),implies(truth,X_57)) )],[refute_0_456,refute_0_457]) ).
cnf(refute_0_459,plain,
implies(implies(falsehood,X_57),and(truth,X_57)) = X_57,
inference(resolve,[$cnf( $equal(implies(truth,X_57),X_57) )],[refute_0_360,refute_0_458]) ).
cnf(refute_0_460,plain,
( implies(implies(falsehood,X_57),and(truth,X_57)) != X_57
| xor(falsehood,X_57) != implies(implies(falsehood,X_57),and(truth,X_57))
| xor(falsehood,X_57) = X_57 ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,X_57),implies(implies(falsehood,X_57),and(truth,X_57))) ),[1],$fot(X_57)]]) ).
cnf(refute_0_461,plain,
( xor(falsehood,X_57) != implies(implies(falsehood,X_57),and(truth,X_57))
| xor(falsehood,X_57) = X_57 ),
inference(resolve,[$cnf( $equal(implies(implies(falsehood,X_57),and(truth,X_57)),X_57) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
xor(falsehood,X_57) = X_57,
inference(resolve,[$cnf( $equal(xor(falsehood,X_57),implies(implies(falsehood,X_57),and(truth,X_57))) )],[refute_0_359,refute_0_461]) ).
cnf(refute_0_463,plain,
xor(falsehood,x) = x,
inference(subst,[],[refute_0_462:[bind(X_57,$fot(x))]]) ).
cnf(refute_0_464,plain,
( x != x
| xor(falsehood,x) != x
| xor(falsehood,x) = x ),
introduced(tautology,[equality,[$cnf( $equal(xor(falsehood,x),x) ),[0,1],$fot(x)]]) ).
cnf(refute_0_465,plain,
( x != x
| xor(falsehood,x) = x ),
inference(resolve,[$cnf( $equal(xor(falsehood,x),x) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
x != x,
inference(resolve,[$cnf( $equal(xor(falsehood,x),x) )],[refute_0_465,refute_0_8]) ).
cnf(refute_0_467,plain,
x = x,
introduced(tautology,[refl,[$fot(x)]]) ).
cnf(refute_0_468,plain,
$false,
inference(resolve,[$cnf( $equal(x,x) )],[refute_0_467,refute_0_466]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL154-1 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n029.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sun Jul 3 12:21:56 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.38/0.54 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.38/0.54
% 0.38/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.40/0.59
%------------------------------------------------------------------------------