TSTP Solution File: LCL164-1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:50:07 EDT 2022
% Result : Unsatisfiable 0.22s 0.45s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 40
% Syntax : Number of clauses : 150 ( 77 unt; 0 nHn; 87 RR)
% Number of literals : 254 ( 253 equ; 106 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 170 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1,axiom,
not(X) = xor(X,truth) ).
cnf(axiom_2,axiom,
xor(X,falsehood) = X ).
cnf(axiom_6,axiom,
and_star(xor(truth,X),X) = falsehood ).
cnf(axiom_7,axiom,
xor(X,xor(truth,Y)) = xor(xor(X,truth),Y) ).
cnf(xor_commutativity,axiom,
xor(X,Y) = xor(Y,X) ).
cnf(and_star_commutativity,axiom,
and_star(X,Y) = and_star(Y,X) ).
cnf(false_definition,axiom,
not(truth) = falsehood ).
cnf(implies_definition,axiom,
implies(X,Y) = xor(truth,and_star(X,xor(truth,Y))) ).
cnf(prove_wajsberg_axiom,negated_conjecture,
implies(implies(not(x),not(y)),implies(y,x)) != truth ).
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( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( not(X) != xor(X,truth)
| xor(X,truth) = not(X) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X))),bind(Y0,$fot(xor(X,truth)))]]) ).
cnf(refute_0_4,plain,
xor(X,truth) = not(X),
inference(resolve,[$cnf( $equal(not(X),xor(X,truth)) )],[axiom_1,refute_0_3]) ).
cnf(refute_0_5,plain,
xor(xor(X,truth),Y) = xor(xor(X,truth),Y),
introduced(tautology,[refl,[$fot(xor(xor(X,truth),Y))]]) ).
cnf(refute_0_6,plain,
( xor(X,truth) != not(X)
| xor(xor(X,truth),Y) != xor(xor(X,truth),Y)
| xor(xor(X,truth),Y) = xor(not(X),Y) ),
introduced(tautology,[equality,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) ),[1,0],$fot(not(X))]]) ).
cnf(refute_0_7,plain,
( xor(X,truth) != not(X)
| xor(xor(X,truth),Y) = xor(not(X),Y) ),
inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(xor(X,truth),Y)) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
xor(xor(X,truth),Y) = xor(not(X),Y),
inference(resolve,[$cnf( $equal(xor(X,truth),not(X)) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
| xor(xor(X,truth),Y) != xor(not(X),Y)
| xor(X,xor(truth,Y)) = xor(not(X),Y) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X,xor(truth,Y)),xor(not(X),Y)) ),[0],$fot(xor(xor(X,truth),Y))]]) ).
cnf(refute_0_10,plain,
( xor(X,xor(truth,Y)) != xor(xor(X,truth),Y)
| xor(X,xor(truth,Y)) = xor(not(X),Y) ),
inference(resolve,[$cnf( $equal(xor(xor(X,truth),Y),xor(not(X),Y)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
xor(X,xor(truth,Y)) = xor(not(X),Y),
inference(resolve,[$cnf( $equal(xor(X,xor(truth,Y)),xor(xor(X,truth),Y)) )],[axiom_7,refute_0_10]) ).
cnf(refute_0_12,plain,
xor(X_6,xor(truth,truth)) = xor(not(X_6),truth),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_6)),bind(Y,$fot(truth))]]) ).
cnf(refute_0_13,plain,
not(truth) = xor(truth,truth),
inference(subst,[],[axiom_1:[bind(X,$fot(truth))]]) ).
cnf(refute_0_14,plain,
( not(truth) != xor(truth,truth)
| xor(truth,truth) = not(truth) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(truth))),bind(Y0,$fot(xor(truth,truth)))]]) ).
cnf(refute_0_15,plain,
xor(truth,truth) = not(truth),
inference(resolve,[$cnf( $equal(not(truth),xor(truth,truth)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(truth,truth) != not(truth)
| xor(X_6,not(truth)) = xor(not(X_6),truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) ),[0,1],$fot(not(truth))]]) ).
cnf(refute_0_17,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(X_6,not(truth)) = xor(not(X_6),truth) ),
inference(resolve,[$cnf( $equal(xor(truth,truth),not(truth)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
xor(X_6,not(truth)) = xor(not(X_6),truth),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_17]) ).
cnf(refute_0_19,plain,
xor(X_6,falsehood) = X_6,
inference(subst,[],[axiom_2:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_20,plain,
xor(X_6,not(truth)) = xor(X_6,not(truth)),
introduced(tautology,[refl,[$fot(xor(X_6,not(truth)))]]) ).
cnf(refute_0_21,plain,
( not(truth) != falsehood
| xor(X_6,not(truth)) != xor(X_6,not(truth))
| xor(X_6,not(truth)) = xor(X_6,falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) ),[1,1],$fot(falsehood)]]) ).
cnf(refute_0_22,plain,
( not(truth) != falsehood
| xor(X_6,not(truth)) = xor(X_6,falsehood) ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,not(truth))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
xor(X_6,not(truth)) = xor(X_6,falsehood),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_22]) ).
cnf(refute_0_24,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_24]) ).
cnf(refute_0_26,plain,
( xor(X_6,falsehood) != X_6
| xor(X_6,not(truth)) != xor(X_6,falsehood)
| xor(X_6,not(truth)) = X_6 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(xor(X_6,not(truth)))),bind(Y0,$fot(xor(X_6,falsehood))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_27,plain,
( xor(X_6,falsehood) != X_6
| xor(X_6,not(truth)) = X_6 ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(X_6,falsehood)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
xor(X_6,not(truth)) = X_6,
inference(resolve,[$cnf( $equal(xor(X_6,falsehood),X_6) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
( xor(X_6,not(truth)) != X_6
| xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(not(X_6),truth) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) ),[0],$fot(X_6)]]) ).
cnf(refute_0_30,plain,
( xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(not(X_6),truth) ),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),X_6) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( xor(X,Y) != xor(Y,X)
| xor(Y,X) = xor(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(xor(X,Y))),bind(Y0,$fot(xor(Y,X)))]]) ).
cnf(refute_0_32,plain,
xor(Y,X) = xor(X,Y),
inference(resolve,[$cnf( $equal(xor(X,Y),xor(Y,X)) )],[xor_commutativity,refute_0_31]) ).
cnf(refute_0_33,plain,
xor(not(X_6),truth) = xor(truth,not(X_6)),
inference(subst,[],[refute_0_32:[bind(X,$fot(truth)),bind(Y,$fot(not(X_6)))]]) ).
cnf(refute_0_34,plain,
( X_6 != xor(not(X_6),truth)
| xor(not(X_6),truth) != xor(truth,not(X_6))
| X_6 = xor(truth,not(X_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_6,xor(truth,not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).
cnf(refute_0_35,plain,
( X_6 != xor(not(X_6),truth)
| X_6 = xor(truth,not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( xor(X_6,not(truth)) != xor(not(X_6),truth)
| X_6 = xor(truth,not(X_6)) ),
inference(resolve,[$cnf( $equal(X_6,xor(not(X_6),truth)) )],[refute_0_30,refute_0_35]) ).
cnf(refute_0_37,plain,
X_6 = xor(truth,not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,not(truth)),xor(not(X_6),truth)) )],[refute_0_18,refute_0_36]) ).
cnf(refute_0_38,plain,
not(X_6) = xor(truth,not(not(X_6))),
inference(subst,[],[refute_0_37:[bind(X_6,$fot(not(X_6)))]]) ).
cnf(refute_0_39,plain,
not(not(X_6)) = xor(not(X_6),truth),
inference(subst,[],[axiom_1:[bind(X,$fot(not(X_6)))]]) ).
cnf(refute_0_40,plain,
( not(not(X_6)) != xor(not(X_6),truth)
| xor(not(X_6),truth) = not(not(X_6)) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(not(X_6)))),bind(Y0,$fot(xor(not(X_6),truth)))]]) ).
cnf(refute_0_41,plain,
xor(not(X_6),truth) = not(not(X_6)),
inference(resolve,[$cnf( $equal(not(not(X_6)),xor(not(X_6),truth)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(not(X_6),truth) != not(not(X_6))
| xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(xor(not(X_6),truth))]]) ).
cnf(refute_0_43,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(X_6,xor(truth,truth)) = not(not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),not(not(X_6))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
xor(X_6,xor(truth,truth)) = not(not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_43]) ).
cnf(refute_0_45,plain,
( X_6 != xor(truth,not(X_6))
| xor(truth,not(X_6)) = X_6 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(xor(truth,not(X_6))))]]) ).
cnf(refute_0_46,plain,
xor(truth,not(X_6)) = X_6,
inference(resolve,[$cnf( $equal(X_6,xor(truth,not(X_6))) )],[refute_0_37,refute_0_45]) ).
cnf(refute_0_47,plain,
( xor(not(X_6),truth) != xor(truth,not(X_6))
| xor(truth,not(X_6)) != X_6
| xor(not(X_6),truth) = X_6 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(xor(not(X_6),truth))),bind(Y0,$fot(xor(truth,not(X_6)))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_48,plain,
( xor(truth,not(X_6)) != X_6
| xor(not(X_6),truth) = X_6 ),
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),xor(truth,not(X_6))) )],[refute_0_33,refute_0_47]) ).
cnf(refute_0_49,plain,
xor(not(X_6),truth) = X_6,
inference(resolve,[$cnf( $equal(xor(truth,not(X_6)),X_6) )],[refute_0_46,refute_0_48]) ).
cnf(refute_0_50,plain,
( xor(X_6,xor(truth,truth)) != xor(not(X_6),truth)
| xor(not(X_6),truth) != X_6
| xor(X_6,xor(truth,truth)) = X_6 ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(xor(X_6,xor(truth,truth)))),bind(Y0,$fot(xor(not(X_6),truth))),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_51,plain,
( xor(not(X_6),truth) != X_6
| xor(X_6,xor(truth,truth)) = X_6 ),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),xor(not(X_6),truth)) )],[refute_0_12,refute_0_50]) ).
cnf(refute_0_52,plain,
xor(X_6,xor(truth,truth)) = X_6,
inference(resolve,[$cnf( $equal(xor(not(X_6),truth),X_6) )],[refute_0_49,refute_0_51]) ).
cnf(refute_0_53,plain,
( xor(X_6,xor(truth,truth)) != X_6
| xor(X_6,xor(truth,truth)) != not(not(X_6))
| X_6 = not(not(X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) ),[0],$fot(X_6)]]) ).
cnf(refute_0_54,plain,
( xor(X_6,xor(truth,truth)) != not(not(X_6))
| X_6 = not(not(X_6)) ),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),X_6) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
X_6 = not(not(X_6)),
inference(resolve,[$cnf( $equal(xor(X_6,xor(truth,truth)),not(not(X_6))) )],[refute_0_44,refute_0_54]) ).
cnf(refute_0_56,plain,
( X_6 != not(not(X_6))
| not(not(X_6)) = X_6 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_6)),bind(Y0,$fot(not(not(X_6))))]]) ).
cnf(refute_0_57,plain,
not(not(X_6)) = X_6,
inference(resolve,[$cnf( $equal(X_6,not(not(X_6))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( not(X_6) != xor(truth,not(not(X_6)))
| not(not(X_6)) != X_6
| not(X_6) = xor(truth,X_6) ),
introduced(tautology,[equality,[$cnf( $equal(not(X_6),xor(truth,not(not(X_6)))) ),[1,1],$fot(X_6)]]) ).
cnf(refute_0_59,plain,
( not(X_6) != xor(truth,not(not(X_6)))
| not(X_6) = xor(truth,X_6) ),
inference(resolve,[$cnf( $equal(not(not(X_6)),X_6) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
not(X_6) = xor(truth,X_6),
inference(resolve,[$cnf( $equal(not(X_6),xor(truth,not(not(X_6)))) )],[refute_0_38,refute_0_59]) ).
cnf(refute_0_61,plain,
( not(X_6) != xor(truth,X_6)
| xor(truth,X_6) = not(X_6) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(not(X_6))),bind(Y0,$fot(xor(truth,X_6)))]]) ).
cnf(refute_0_62,plain,
xor(truth,X_6) = not(X_6),
inference(resolve,[$cnf( $equal(not(X_6),xor(truth,X_6)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
xor(truth,Y) = not(Y),
inference(subst,[],[refute_0_62:[bind(X_6,$fot(Y))]]) ).
cnf(refute_0_64,plain,
and_star(X,xor(truth,Y)) = and_star(X,xor(truth,Y)),
introduced(tautology,[refl,[$fot(and_star(X,xor(truth,Y)))]]) ).
cnf(refute_0_65,plain,
( and_star(X,xor(truth,Y)) != and_star(X,xor(truth,Y))
| xor(truth,Y) != not(Y)
| and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) ),[1,1],$fot(not(Y))]]) ).
cnf(refute_0_66,plain,
( xor(truth,Y) != not(Y)
| and_star(X,xor(truth,Y)) = and_star(X,not(Y)) ),
inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,xor(truth,Y))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
and_star(X,xor(truth,Y)) = and_star(X,not(Y)),
inference(resolve,[$cnf( $equal(xor(truth,Y),not(Y)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
not(and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
introduced(tautology,[refl,[$fot(not(and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_69,plain,
( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
| not(and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
| not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) ),[1,0],$fot(and_star(X,not(Y)))]]) ).
cnf(refute_0_70,plain,
( and_star(X,xor(truth,Y)) != and_star(X,not(Y))
| not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
not(and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(and_star(X,xor(truth,Y)),and_star(X,not(Y))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,xor(truth,Y))),
inference(subst,[],[refute_0_62:[bind(X_6,$fot(and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_73,plain,
( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,xor(truth,Y)))
| xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(xor(truth,and_star(X,xor(truth,Y))))),bind(Y0,$fot(not(and_star(X,xor(truth,Y))))),bind(Z,$fot(not(and_star(X,not(Y)))))]]) ).
cnf(refute_0_74,plain,
( not(and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,xor(truth,Y)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
xor(truth,and_star(X,xor(truth,Y))) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(not(and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
| xor(truth,and_star(X,xor(truth,Y))) != not(and_star(X,not(Y)))
| implies(X,Y) = not(and_star(X,not(Y))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X,Y),not(and_star(X,not(Y)))) ),[0],$fot(xor(truth,and_star(X,xor(truth,Y))))]]) ).
cnf(refute_0_77,plain,
( implies(X,Y) != xor(truth,and_star(X,xor(truth,Y)))
| implies(X,Y) = not(and_star(X,not(Y))) ),
inference(resolve,[$cnf( $equal(xor(truth,and_star(X,xor(truth,Y))),not(and_star(X,not(Y)))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
implies(X,Y) = not(and_star(X,not(Y))),
inference(resolve,[$cnf( $equal(implies(X,Y),xor(truth,and_star(X,xor(truth,Y)))) )],[implies_definition,refute_0_77]) ).
cnf(refute_0_79,plain,
implies(X_38,X_38) = not(and_star(X_38,not(X_38))),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_38)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_80,plain,
( and_star(X,Y) != and_star(Y,X)
| and_star(Y,X) = and_star(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and_star(X,Y))),bind(Y0,$fot(and_star(Y,X)))]]) ).
cnf(refute_0_81,plain,
and_star(Y,X) = and_star(X,Y),
inference(resolve,[$cnf( $equal(and_star(X,Y),and_star(Y,X)) )],[and_star_commutativity,refute_0_80]) ).
cnf(refute_0_82,plain,
and_star(xor(truth,X),X) = and_star(X,xor(truth,X)),
inference(subst,[],[refute_0_81:[bind(Y,$fot(xor(truth,X)))]]) ).
cnf(refute_0_83,plain,
( and_star(xor(truth,X),X) != and_star(X,xor(truth,X))
| and_star(xor(truth,X),X) != falsehood
| and_star(X,xor(truth,X)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(xor(truth,X),X),falsehood) ),[0],$fot(and_star(X,xor(truth,X)))]]) ).
cnf(refute_0_84,plain,
( and_star(xor(truth,X),X) != falsehood
| and_star(X,xor(truth,X)) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),X),and_star(X,xor(truth,X))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
and_star(X,xor(truth,X)) = falsehood,
inference(resolve,[$cnf( $equal(and_star(xor(truth,X),X),falsehood) )],[axiom_6,refute_0_84]) ).
cnf(refute_0_86,plain,
and_star(not(X_12),xor(truth,not(X_12))) = falsehood,
inference(subst,[],[refute_0_85:[bind(X,$fot(not(X_12)))]]) ).
cnf(refute_0_87,plain,
X_12 = xor(truth,not(X_12)),
inference(subst,[],[refute_0_37:[bind(X_6,$fot(X_12))]]) ).
cnf(refute_0_88,plain,
( X_12 != xor(truth,not(X_12))
| xor(truth,not(X_12)) = X_12 ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_12)),bind(Y0,$fot(xor(truth,not(X_12))))]]) ).
cnf(refute_0_89,plain,
xor(truth,not(X_12)) = X_12,
inference(resolve,[$cnf( $equal(X_12,xor(truth,not(X_12))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( and_star(not(X_12),xor(truth,not(X_12))) != falsehood
| xor(truth,not(X_12)) != X_12
| and_star(not(X_12),X_12) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_12),xor(truth,not(X_12))),falsehood) ),[0,1],$fot(X_12)]]) ).
cnf(refute_0_91,plain,
( and_star(not(X_12),xor(truth,not(X_12))) != falsehood
| and_star(not(X_12),X_12) = falsehood ),
inference(resolve,[$cnf( $equal(xor(truth,not(X_12)),X_12) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
and_star(not(X_12),X_12) = falsehood,
inference(resolve,[$cnf( $equal(and_star(not(X_12),xor(truth,not(X_12))),falsehood) )],[refute_0_86,refute_0_91]) ).
cnf(refute_0_93,plain,
and_star(not(X_12),X_12) = and_star(X_12,not(X_12)),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_12)),bind(Y,$fot(not(X_12)))]]) ).
cnf(refute_0_94,plain,
( and_star(not(X_12),X_12) != and_star(X_12,not(X_12))
| and_star(not(X_12),X_12) != falsehood
| and_star(X_12,not(X_12)) = falsehood ),
introduced(tautology,[equality,[$cnf( $equal(and_star(not(X_12),X_12),falsehood) ),[0],$fot(and_star(X_12,not(X_12)))]]) ).
cnf(refute_0_95,plain,
( and_star(not(X_12),X_12) != falsehood
| and_star(X_12,not(X_12)) = falsehood ),
inference(resolve,[$cnf( $equal(and_star(not(X_12),X_12),and_star(X_12,not(X_12))) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
and_star(X_12,not(X_12)) = falsehood,
inference(resolve,[$cnf( $equal(and_star(not(X_12),X_12),falsehood) )],[refute_0_92,refute_0_95]) ).
cnf(refute_0_97,plain,
and_star(X_38,not(X_38)) = falsehood,
inference(subst,[],[refute_0_96:[bind(X_12,$fot(X_38))]]) ).
cnf(refute_0_98,plain,
( and_star(X_38,not(X_38)) != falsehood
| implies(X_38,X_38) != not(and_star(X_38,not(X_38)))
| implies(X_38,X_38) = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_38,X_38),not(and_star(X_38,not(X_38)))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_99,plain,
( implies(X_38,X_38) != not(and_star(X_38,not(X_38)))
| implies(X_38,X_38) = not(falsehood) ),
inference(resolve,[$cnf( $equal(and_star(X_38,not(X_38)),falsehood) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
implies(X_38,X_38) = not(falsehood),
inference(resolve,[$cnf( $equal(implies(X_38,X_38),not(and_star(X_38,not(X_38)))) )],[refute_0_79,refute_0_99]) ).
cnf(refute_0_101,plain,
truth = not(not(truth)),
inference(subst,[],[refute_0_55:[bind(X_6,$fot(truth))]]) ).
cnf(refute_0_102,plain,
( not(truth) != falsehood
| truth != not(not(truth))
| truth = not(falsehood) ),
introduced(tautology,[equality,[$cnf( $equal(truth,not(not(truth))) ),[1,0],$fot(falsehood)]]) ).
cnf(refute_0_103,plain,
( truth != not(not(truth))
| truth = not(falsehood) ),
inference(resolve,[$cnf( $equal(not(truth),falsehood) )],[false_definition,refute_0_102]) ).
cnf(refute_0_104,plain,
truth = not(falsehood),
inference(resolve,[$cnf( $equal(truth,not(not(truth))) )],[refute_0_101,refute_0_103]) ).
cnf(refute_0_105,plain,
( truth != not(falsehood)
| not(falsehood) = truth ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(truth)),bind(Y0,$fot(not(falsehood)))]]) ).
cnf(refute_0_106,plain,
not(falsehood) = truth,
inference(resolve,[$cnf( $equal(truth,not(falsehood)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( implies(X_38,X_38) != not(falsehood)
| not(falsehood) != truth
| implies(X_38,X_38) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(X_38,X_38),truth) ),[0],$fot(not(falsehood))]]) ).
cnf(refute_0_108,plain,
( implies(X_38,X_38) != not(falsehood)
| implies(X_38,X_38) = truth ),
inference(resolve,[$cnf( $equal(not(falsehood),truth) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
implies(X_38,X_38) = truth,
inference(resolve,[$cnf( $equal(implies(X_38,X_38),not(falsehood)) )],[refute_0_100,refute_0_108]) ).
cnf(refute_0_110,plain,
implies(implies(y,x),implies(y,x)) = truth,
inference(subst,[],[refute_0_109:[bind(X_38,$fot(implies(y,x)))]]) ).
cnf(refute_0_111,plain,
implies(X_37,X_38) = not(and_star(X_37,not(X_38))),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_37)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_112,plain,
and_star(not(X_38),X_37) = and_star(X_37,not(X_38)),
inference(subst,[],[and_star_commutativity:[bind(X,$fot(not(X_38))),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_113,plain,
( and_star(not(X_38),X_37) != and_star(X_37,not(X_38))
| and_star(X_37,not(X_38)) = and_star(not(X_38),X_37) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(and_star(not(X_38),X_37))),bind(Y0,$fot(and_star(X_37,not(X_38))))]]) ).
cnf(refute_0_114,plain,
and_star(X_37,not(X_38)) = and_star(not(X_38),X_37),
inference(resolve,[$cnf( $equal(and_star(not(X_38),X_37),and_star(X_37,not(X_38))) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
( and_star(X_37,not(X_38)) != and_star(not(X_38),X_37)
| implies(X_37,X_38) != not(and_star(X_37,not(X_38)))
| implies(X_37,X_38) = not(and_star(not(X_38),X_37)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_37,X_38),not(and_star(X_37,not(X_38)))) ),[1,0],$fot(and_star(not(X_38),X_37))]]) ).
cnf(refute_0_116,plain,
( implies(X_37,X_38) != not(and_star(X_37,not(X_38)))
| implies(X_37,X_38) = not(and_star(not(X_38),X_37)) ),
inference(resolve,[$cnf( $equal(and_star(X_37,not(X_38)),and_star(not(X_38),X_37)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
implies(X_37,X_38) = not(and_star(not(X_38),X_37)),
inference(resolve,[$cnf( $equal(implies(X_37,X_38),not(and_star(X_37,not(X_38)))) )],[refute_0_111,refute_0_116]) ).
cnf(refute_0_118,plain,
( implies(X_37,X_38) != not(and_star(not(X_38),X_37))
| not(and_star(not(X_38),X_37)) = implies(X_37,X_38) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(implies(X_37,X_38))),bind(Y0,$fot(not(and_star(not(X_38),X_37))))]]) ).
cnf(refute_0_119,plain,
not(and_star(not(X_38),X_37)) = implies(X_37,X_38),
inference(resolve,[$cnf( $equal(implies(X_37,X_38),not(and_star(not(X_38),X_37))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
not(and_star(not(x),y)) = implies(y,x),
inference(subst,[],[refute_0_119:[bind(X_37,$fot(y)),bind(X_38,$fot(x))]]) ).
cnf(refute_0_121,plain,
implies(X_37,not(X_6)) = not(and_star(X_37,not(not(X_6)))),
inference(subst,[],[refute_0_78:[bind(X,$fot(X_37)),bind(Y,$fot(not(X_6)))]]) ).
cnf(refute_0_122,plain,
( implies(X_37,not(X_6)) != not(and_star(X_37,not(not(X_6))))
| not(not(X_6)) != X_6
| implies(X_37,not(X_6)) = not(and_star(X_37,X_6)) ),
introduced(tautology,[equality,[$cnf( $equal(implies(X_37,not(X_6)),not(and_star(X_37,not(not(X_6))))) ),[1,0,1],$fot(X_6)]]) ).
cnf(refute_0_123,plain,
( implies(X_37,not(X_6)) != not(and_star(X_37,not(not(X_6))))
| implies(X_37,not(X_6)) = not(and_star(X_37,X_6)) ),
inference(resolve,[$cnf( $equal(not(not(X_6)),X_6) )],[refute_0_57,refute_0_122]) ).
cnf(refute_0_124,plain,
implies(X_37,not(X_6)) = not(and_star(X_37,X_6)),
inference(resolve,[$cnf( $equal(implies(X_37,not(X_6)),not(and_star(X_37,not(not(X_6))))) )],[refute_0_121,refute_0_123]) ).
cnf(refute_0_125,plain,
implies(not(x),not(y)) = not(and_star(not(x),y)),
inference(subst,[],[refute_0_124:[bind(X_37,$fot(not(x))),bind(X_6,$fot(y))]]) ).
cnf(refute_0_126,plain,
( implies(not(x),not(y)) != not(and_star(not(x),y))
| not(and_star(not(x),y)) != implies(y,x)
| implies(not(x),not(y)) = implies(y,x) ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(implies(not(x),not(y)))),bind(Y0,$fot(not(and_star(not(x),y)))),bind(Z,$fot(implies(y,x)))]]) ).
cnf(refute_0_127,plain,
( not(and_star(not(x),y)) != implies(y,x)
| implies(not(x),not(y)) = implies(y,x) ),
inference(resolve,[$cnf( $equal(implies(not(x),not(y)),not(and_star(not(x),y))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
implies(not(x),not(y)) = implies(y,x),
inference(resolve,[$cnf( $equal(not(and_star(not(x),y)),implies(y,x)) )],[refute_0_120,refute_0_127]) ).
cnf(refute_0_129,plain,
implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(not(x),not(y)),implies(y,x)),
introduced(tautology,[refl,[$fot(implies(implies(not(x),not(y)),implies(y,x)))]]) ).
cnf(refute_0_130,plain,
( implies(implies(not(x),not(y)),implies(y,x)) != implies(implies(not(x),not(y)),implies(y,x))
| implies(not(x),not(y)) != implies(y,x)
| implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(y,x),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(implies(y,x))]]) ).
cnf(refute_0_131,plain,
( implies(not(x),not(y)) != implies(y,x)
| implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(y,x),implies(y,x)) ),
inference(resolve,[$cnf( $equal(implies(implies(not(x),not(y)),implies(y,x)),implies(implies(not(x),not(y)),implies(y,x))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
implies(implies(not(x),not(y)),implies(y,x)) = implies(implies(y,x),implies(y,x)),
inference(resolve,[$cnf( $equal(implies(not(x),not(y)),implies(y,x)) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( implies(implies(not(x),not(y)),implies(y,x)) != implies(implies(y,x),implies(y,x))
| implies(implies(y,x),implies(y,x)) != truth
| implies(implies(not(x),not(y)),implies(y,x)) = truth ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(implies(implies(not(x),not(y)),implies(y,x)))),bind(Y0,$fot(implies(implies(y,x),implies(y,x)))),bind(Z,$fot(truth))]]) ).
cnf(refute_0_134,plain,
( implies(implies(y,x),implies(y,x)) != truth
| implies(implies(not(x),not(y)),implies(y,x)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(x),not(y)),implies(y,x)),implies(implies(y,x),implies(y,x))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
implies(implies(not(x),not(y)),implies(y,x)) = truth,
inference(resolve,[$cnf( $equal(implies(implies(y,x),implies(y,x)),truth) )],[refute_0_110,refute_0_134]) ).
cnf(refute_0_136,plain,
( implies(implies(not(x),not(y)),implies(y,x)) != truth
| truth != truth
| implies(implies(not(x),not(y)),implies(y,x)) = truth ),
introduced(tautology,[equality,[$cnf( ~ $equal(implies(implies(not(x),not(y)),implies(y,x)),truth) ),[0],$fot(truth)]]) ).
cnf(refute_0_137,plain,
( truth != truth
| implies(implies(not(x),not(y)),implies(y,x)) = truth ),
inference(resolve,[$cnf( $equal(implies(implies(not(x),not(y)),implies(y,x)),truth) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
truth != truth,
inference(resolve,[$cnf( $equal(implies(implies(not(x),not(y)),implies(y,x)),truth) )],[refute_0_137,prove_wajsberg_axiom]) ).
cnf(refute_0_139,plain,
truth = truth,
introduced(tautology,[refl,[$fot(truth)]]) ).
cnf(refute_0_140,plain,
$false,
inference(resolve,[$cnf( $equal(truth,truth) )],[refute_0_139,refute_0_138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL164-1 : TPTP v8.1.0. Released v1.0.0.
% 0.15/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.35 % Computer : n026.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 07:37:21 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.22/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.45
% 0.22/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.22/0.47
%------------------------------------------------------------------------------