TSTP Solution File: LAT039-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT039-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 05:59:04 EDT 2022
% Result : Unsatisfiable 0.41s 0.57s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of clauses : 93 ( 52 unt; 0 nHn; 48 RR)
% Number of literals : 152 ( 151 equ; 61 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 175 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_join,axiom,
join(X,X) = X ).
cnf(absorption1,axiom,
meet(X,join(X,Y)) = X ).
cnf(absorption2,axiom,
join(X,meet(X,Y)) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(associativity_of_meet,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ).
cnf(dist_join,hypothesis,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).
cnf(dist_meet,hypothesis,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
cnf(lhs,hypothesis,
join(xx,yy) = yy ).
cnf(rhs,negated_conjecture,
join(xx,meet(yy,zz)) != meet(yy,join(xx,zz)) ).
cnf(refute_0_0,plain,
meet(join(X_49,X_51),join(X_49,X_50)) = meet(join(X_49,X_50),join(X_49,X_51)),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(join(X_49,X_51))),bind(Y,$fot(join(X_49,X_50)))]]) ).
cnf(refute_0_1,plain,
join(X_49,meet(X_50,X_51)) = meet(join(X_49,X_50),join(X_49,X_51)),
inference(subst,[],[dist_join:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(X_51))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_4,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( join(X_49,meet(X_50,X_51)) != meet(join(X_49,X_50),join(X_49,X_51))
| meet(join(X_49,X_50),join(X_49,X_51)) = join(X_49,meet(X_50,X_51)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_49,meet(X_50,X_51)))),bind(Y0,$fot(meet(join(X_49,X_50),join(X_49,X_51))))]]) ).
cnf(refute_0_6,plain,
meet(join(X_49,X_50),join(X_49,X_51)) = join(X_49,meet(X_50,X_51)),
inference(resolve,[$cnf( $equal(join(X_49,meet(X_50,X_51)),meet(join(X_49,X_50),join(X_49,X_51))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( meet(join(X_49,X_50),join(X_49,X_51)) != join(X_49,meet(X_50,X_51))
| meet(join(X_49,X_51),join(X_49,X_50)) != meet(join(X_49,X_50),join(X_49,X_51))
| meet(join(X_49,X_51),join(X_49,X_50)) = join(X_49,meet(X_50,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_49,X_51),join(X_49,X_50)),meet(join(X_49,X_50),join(X_49,X_51))) ),[1],$fot(join(X_49,meet(X_50,X_51)))]]) ).
cnf(refute_0_8,plain,
( meet(join(X_49,X_51),join(X_49,X_50)) != meet(join(X_49,X_50),join(X_49,X_51))
| meet(join(X_49,X_51),join(X_49,X_50)) = join(X_49,meet(X_50,X_51)) ),
inference(resolve,[$cnf( $equal(meet(join(X_49,X_50),join(X_49,X_51)),join(X_49,meet(X_50,X_51))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
meet(join(X_49,X_51),join(X_49,X_50)) = join(X_49,meet(X_50,X_51)),
inference(resolve,[$cnf( $equal(meet(join(X_49,X_51),join(X_49,X_50)),meet(join(X_49,X_50),join(X_49,X_51))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( join(X,meet(Y,Z)) != meet(join(X,Y),join(X,Z))
| meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X,meet(Y,Z)))),bind(Y0,$fot(meet(join(X,Y),join(X,Z))))]]) ).
cnf(refute_0_11,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),meet(join(X,Y),join(X,Z))) )],[dist_join,refute_0_10]) ).
cnf(refute_0_12,plain,
meet(join(X_49,X_51),join(X_49,X_50)) = join(X_49,meet(X_51,X_50)),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_49)),bind(Y,$fot(X_51)),bind(Z,$fot(X_50))]]) ).
cnf(refute_0_13,plain,
( meet(join(X_49,X_51),join(X_49,X_50)) != join(X_49,meet(X_50,X_51))
| meet(join(X_49,X_51),join(X_49,X_50)) != join(X_49,meet(X_51,X_50))
| join(X_49,meet(X_51,X_50)) = join(X_49,meet(X_50,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_49,X_51),join(X_49,X_50)),join(X_49,meet(X_50,X_51))) ),[0],$fot(join(X_49,meet(X_51,X_50)))]]) ).
cnf(refute_0_14,plain,
( meet(join(X_49,X_51),join(X_49,X_50)) != join(X_49,meet(X_50,X_51))
| join(X_49,meet(X_51,X_50)) = join(X_49,meet(X_50,X_51)) ),
inference(resolve,[$cnf( $equal(meet(join(X_49,X_51),join(X_49,X_50)),join(X_49,meet(X_51,X_50))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(X_49,meet(X_51,X_50)) = join(X_49,meet(X_50,X_51)),
inference(resolve,[$cnf( $equal(meet(join(X_49,X_51),join(X_49,X_50)),join(X_49,meet(X_50,X_51))) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( join(X_49,meet(X_51,X_50)) != join(X_49,meet(X_50,X_51))
| join(X_49,meet(X_50,X_51)) = join(X_49,meet(X_51,X_50)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_49,meet(X_51,X_50)))),bind(Y0,$fot(join(X_49,meet(X_50,X_51))))]]) ).
cnf(refute_0_17,plain,
join(X_49,meet(X_50,X_51)) = join(X_49,meet(X_51,X_50)),
inference(resolve,[$cnf( $equal(join(X_49,meet(X_51,X_50)),join(X_49,meet(X_50,X_51))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
join(xx,meet(zz,yy)) = join(xx,meet(yy,zz)),
inference(subst,[],[refute_0_17:[bind(X_49,$fot(xx)),bind(X_50,$fot(zz)),bind(X_51,$fot(yy))]]) ).
cnf(refute_0_19,plain,
join(xx,meet(X_50,yy)) = meet(join(xx,X_50),join(xx,yy)),
inference(subst,[],[dist_join:[bind(X,$fot(xx)),bind(Y,$fot(X_50)),bind(Z,$fot(yy))]]) ).
cnf(refute_0_20,plain,
( join(xx,meet(X_50,yy)) != meet(join(xx,X_50),join(xx,yy))
| join(xx,yy) != yy
| join(xx,meet(X_50,yy)) = meet(join(xx,X_50),yy) ),
introduced(tautology,[equality,[$cnf( $equal(join(xx,meet(X_50,yy)),meet(join(xx,X_50),join(xx,yy))) ),[1,1],$fot(yy)]]) ).
cnf(refute_0_21,plain,
( join(xx,meet(X_50,yy)) != meet(join(xx,X_50),join(xx,yy))
| join(xx,meet(X_50,yy)) = meet(join(xx,X_50),yy) ),
inference(resolve,[$cnf( $equal(join(xx,yy),yy) )],[lhs,refute_0_20]) ).
cnf(refute_0_22,plain,
join(xx,meet(X_50,yy)) = meet(join(xx,X_50),yy),
inference(resolve,[$cnf( $equal(join(xx,meet(X_50,yy)),meet(join(xx,X_50),join(xx,yy))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( join(X,meet(X,Y)) != X
| meet(X,Y) != meet(Y,X)
| join(X,meet(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).
cnf(refute_0_24,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_23]) ).
cnf(refute_0_25,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_24]) ).
cnf(refute_0_26,plain,
join(meet(X_14,Y),meet(Y,meet(X_14,Y))) = meet(X_14,Y),
inference(subst,[],[refute_0_25:[bind(X,$fot(meet(X_14,Y)))]]) ).
cnf(refute_0_27,plain,
( join(X,Y) != join(Y,X)
| meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,Y)),X) ),[0,1],$fot(join(Y,X))]]) ).
cnf(refute_0_28,plain,
( meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_27]) ).
cnf(refute_0_29,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_28]) ).
cnf(refute_0_30,plain,
meet(meet(X_13,Y),join(X_13,meet(X_13,Y))) = meet(X_13,Y),
inference(subst,[],[refute_0_29:[bind(X,$fot(meet(X_13,Y))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_31,plain,
join(X_13,meet(X_13,Y)) = X_13,
inference(subst,[],[absorption2:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_32,plain,
( join(X_13,meet(X_13,Y)) != X_13
| meet(meet(X_13,Y),join(X_13,meet(X_13,Y))) != meet(X_13,Y)
| meet(meet(X_13,Y),X_13) = meet(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_13,Y),join(X_13,meet(X_13,Y))),meet(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_33,plain,
( meet(meet(X_13,Y),join(X_13,meet(X_13,Y))) != meet(X_13,Y)
| meet(meet(X_13,Y),X_13) = meet(X_13,Y) ),
inference(resolve,[$cnf( $equal(join(X_13,meet(X_13,Y)),X_13) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
meet(meet(X_13,Y),X_13) = meet(X_13,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_13,Y),join(X_13,meet(X_13,Y))),meet(X_13,Y)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
meet(meet(X_13,Y),X_13) = meet(X_13,meet(Y,X_13)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_36,plain,
( meet(meet(X_13,Y),X_13) != meet(X_13,Y)
| meet(meet(X_13,Y),X_13) != meet(X_13,meet(Y,X_13))
| meet(X_13,meet(Y,X_13)) = meet(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_13,Y),X_13),meet(X_13,Y)) ),[0],$fot(meet(X_13,meet(Y,X_13)))]]) ).
cnf(refute_0_37,plain,
( meet(meet(X_13,Y),X_13) != meet(X_13,Y)
| meet(X_13,meet(Y,X_13)) = meet(X_13,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_13,Y),X_13),meet(X_13,meet(Y,X_13))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
meet(X_13,meet(Y,X_13)) = meet(X_13,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_13,Y),X_13),meet(X_13,Y)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
meet(Y,meet(X_14,Y)) = meet(Y,X_14),
inference(subst,[],[refute_0_38:[bind(Y,$fot(X_14)),bind(X_13,$fot(Y))]]) ).
cnf(refute_0_40,plain,
( join(meet(X_14,Y),meet(Y,meet(X_14,Y))) != meet(X_14,Y)
| meet(Y,meet(X_14,Y)) != meet(Y,X_14)
| join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_14,Y),meet(Y,meet(X_14,Y))),meet(X_14,Y)) ),[0,1],$fot(meet(Y,X_14))]]) ).
cnf(refute_0_41,plain,
( join(meet(X_14,Y),meet(Y,meet(X_14,Y))) != meet(X_14,Y)
| join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y) ),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_14,Y)),meet(Y,X_14)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y),
inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,meet(X_14,Y))),meet(X_14,Y)) )],[refute_0_26,refute_0_41]) ).
cnf(refute_0_43,plain,
join(X_14,X_14) = X_14,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
meet(Y,join(X_14,X_14)) = meet(Y,join(X_14,X_14)),
introduced(tautology,[refl,[$fot(meet(Y,join(X_14,X_14)))]]) ).
cnf(refute_0_45,plain,
( join(X_14,X_14) != X_14
| meet(Y,join(X_14,X_14)) != meet(Y,join(X_14,X_14))
| meet(Y,join(X_14,X_14)) = meet(Y,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,join(X_14,X_14))) ),[1,1],$fot(X_14)]]) ).
cnf(refute_0_46,plain,
( join(X_14,X_14) != X_14
| meet(Y,join(X_14,X_14)) = meet(Y,X_14) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,join(X_14,X_14))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
meet(Y,join(X_14,X_14)) = meet(Y,X_14),
inference(resolve,[$cnf( $equal(join(X_14,X_14),X_14) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
meet(X_37,join(X_38,X_39)) = join(meet(X_37,X_38),meet(X_37,X_39)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_49,plain,
meet(X_38,X_37) = meet(X_37,X_38),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_38)),bind(Y,$fot(X_37))]]) ).
cnf(refute_0_50,plain,
( meet(X_38,X_37) != meet(X_37,X_38)
| meet(X_37,X_38) = meet(X_38,X_37) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_38,X_37))),bind(Y0,$fot(meet(X_37,X_38)))]]) ).
cnf(refute_0_51,plain,
meet(X_37,X_38) = meet(X_38,X_37),
inference(resolve,[$cnf( $equal(meet(X_38,X_37),meet(X_37,X_38)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( meet(X_37,X_38) != meet(X_38,X_37)
| meet(X_37,join(X_38,X_39)) != join(meet(X_37,X_38),meet(X_37,X_39))
| meet(X_37,join(X_38,X_39)) = join(meet(X_38,X_37),meet(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_37,join(X_38,X_39)),join(meet(X_37,X_38),meet(X_37,X_39))) ),[1,0],$fot(meet(X_38,X_37))]]) ).
cnf(refute_0_53,plain,
( meet(X_37,join(X_38,X_39)) != join(meet(X_37,X_38),meet(X_37,X_39))
| meet(X_37,join(X_38,X_39)) = join(meet(X_38,X_37),meet(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(meet(X_37,X_38),meet(X_38,X_37)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
meet(X_37,join(X_38,X_39)) = join(meet(X_38,X_37),meet(X_37,X_39)),
inference(resolve,[$cnf( $equal(meet(X_37,join(X_38,X_39)),join(meet(X_37,X_38),meet(X_37,X_39))) )],[refute_0_48,refute_0_53]) ).
cnf(refute_0_55,plain,
( meet(X_37,join(X_38,X_39)) != join(meet(X_38,X_37),meet(X_37,X_39))
| join(meet(X_38,X_37),meet(X_37,X_39)) = meet(X_37,join(X_38,X_39)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_37,join(X_38,X_39)))),bind(Y0,$fot(join(meet(X_38,X_37),meet(X_37,X_39))))]]) ).
cnf(refute_0_56,plain,
join(meet(X_38,X_37),meet(X_37,X_39)) = meet(X_37,join(X_38,X_39)),
inference(resolve,[$cnf( $equal(meet(X_37,join(X_38,X_39)),join(meet(X_38,X_37),meet(X_37,X_39))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,join(X_14,X_14)),
inference(subst,[],[refute_0_56:[bind(X_37,$fot(Y)),bind(X_38,$fot(X_14)),bind(X_39,$fot(X_14))]]) ).
cnf(refute_0_58,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_59,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_58]) ).
cnf(refute_0_60,plain,
( join(meet(X_14,Y),meet(Y,X_14)) != meet(Y,join(X_14,X_14))
| meet(Y,join(X_14,X_14)) != meet(Y,X_14)
| join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(join(meet(X_14,Y),meet(Y,X_14)))),bind(Y0,$fot(meet(Y,join(X_14,X_14)))),bind(Z0,$fot(meet(Y,X_14)))]]) ).
cnf(refute_0_61,plain,
( meet(Y,join(X_14,X_14)) != meet(Y,X_14)
| join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14) ),
inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(Y,join(X_14,X_14))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14),
inference(resolve,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,X_14)) )],[refute_0_47,refute_0_61]) ).
cnf(refute_0_63,plain,
( join(meet(X_14,Y),meet(Y,X_14)) != meet(Y,X_14)
| join(meet(X_14,Y),meet(Y,X_14)) != meet(X_14,Y)
| meet(Y,X_14) = meet(X_14,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(X_14,Y)) ),[0],$fot(meet(Y,X_14))]]) ).
cnf(refute_0_64,plain,
( join(meet(X_14,Y),meet(Y,X_14)) != meet(X_14,Y)
| meet(Y,X_14) = meet(X_14,Y) ),
inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(Y,X_14)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
meet(Y,X_14) = meet(X_14,Y),
inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(X_14,Y)) )],[refute_0_42,refute_0_64]) ).
cnf(refute_0_66,plain,
( meet(Y,X_14) != meet(X_14,Y)
| meet(X_14,Y) = meet(Y,X_14) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(Y,X_14))),bind(Y0,$fot(meet(X_14,Y)))]]) ).
cnf(refute_0_67,plain,
meet(X_14,Y) = meet(Y,X_14),
inference(resolve,[$cnf( $equal(meet(Y,X_14),meet(X_14,Y)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
meet(join(xx,X_50),yy) = meet(yy,join(xx,X_50)),
inference(subst,[],[refute_0_67:[bind(Y,$fot(yy)),bind(X_14,$fot(join(xx,X_50)))]]) ).
cnf(refute_0_69,plain,
( join(xx,meet(X_50,yy)) != meet(join(xx,X_50),yy)
| meet(join(xx,X_50),yy) != meet(yy,join(xx,X_50))
| join(xx,meet(X_50,yy)) = meet(yy,join(xx,X_50)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(xx,meet(X_50,yy)),meet(yy,join(xx,X_50))) ),[0],$fot(meet(join(xx,X_50),yy))]]) ).
cnf(refute_0_70,plain,
( join(xx,meet(X_50,yy)) != meet(join(xx,X_50),yy)
| join(xx,meet(X_50,yy)) = meet(yy,join(xx,X_50)) ),
inference(resolve,[$cnf( $equal(meet(join(xx,X_50),yy),meet(yy,join(xx,X_50))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
join(xx,meet(X_50,yy)) = meet(yy,join(xx,X_50)),
inference(resolve,[$cnf( $equal(join(xx,meet(X_50,yy)),meet(join(xx,X_50),yy)) )],[refute_0_22,refute_0_70]) ).
cnf(refute_0_72,plain,
( join(xx,meet(X_50,yy)) != meet(yy,join(xx,X_50))
| meet(yy,join(xx,X_50)) = join(xx,meet(X_50,yy)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(xx,meet(X_50,yy)))),bind(Y0,$fot(meet(yy,join(xx,X_50))))]]) ).
cnf(refute_0_73,plain,
meet(yy,join(xx,X_50)) = join(xx,meet(X_50,yy)),
inference(resolve,[$cnf( $equal(join(xx,meet(X_50,yy)),meet(yy,join(xx,X_50))) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
meet(yy,join(xx,zz)) = join(xx,meet(zz,yy)),
inference(subst,[],[refute_0_73:[bind(X_50,$fot(zz))]]) ).
cnf(refute_0_75,plain,
( join(xx,meet(zz,yy)) != join(xx,meet(yy,zz))
| meet(yy,join(xx,zz)) != join(xx,meet(zz,yy))
| meet(yy,join(xx,zz)) = join(xx,meet(yy,zz)) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(meet(yy,join(xx,zz)))),bind(Y0,$fot(join(xx,meet(zz,yy)))),bind(Z0,$fot(join(xx,meet(yy,zz))))]]) ).
cnf(refute_0_76,plain,
( join(xx,meet(zz,yy)) != join(xx,meet(yy,zz))
| meet(yy,join(xx,zz)) = join(xx,meet(yy,zz)) ),
inference(resolve,[$cnf( $equal(meet(yy,join(xx,zz)),join(xx,meet(zz,yy))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(yy,join(xx,zz)) = join(xx,meet(yy,zz)),
inference(resolve,[$cnf( $equal(join(xx,meet(zz,yy)),join(xx,meet(yy,zz))) )],[refute_0_18,refute_0_76]) ).
cnf(refute_0_78,plain,
( join(xx,meet(yy,zz)) != join(xx,meet(yy,zz))
| meet(yy,join(xx,zz)) != join(xx,meet(yy,zz))
| join(xx,meet(yy,zz)) = meet(yy,join(xx,zz)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(xx,meet(yy,zz)),meet(yy,join(xx,zz))) ),[1],$fot(join(xx,meet(yy,zz)))]]) ).
cnf(refute_0_79,plain,
( join(xx,meet(yy,zz)) != join(xx,meet(yy,zz))
| join(xx,meet(yy,zz)) = meet(yy,join(xx,zz)) ),
inference(resolve,[$cnf( $equal(meet(yy,join(xx,zz)),join(xx,meet(yy,zz))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
join(xx,meet(yy,zz)) != join(xx,meet(yy,zz)),
inference(resolve,[$cnf( $equal(join(xx,meet(yy,zz)),meet(yy,join(xx,zz))) )],[refute_0_79,rhs]) ).
cnf(refute_0_81,plain,
join(xx,meet(yy,zz)) = join(xx,meet(yy,zz)),
introduced(tautology,[refl,[$fot(join(xx,meet(yy,zz)))]]) ).
cnf(refute_0_82,plain,
$false,
inference(resolve,[$cnf( $equal(join(xx,meet(yy,zz)),join(xx,meet(yy,zz))) )],[refute_0_81,refute_0_80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LAT039-1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Thu Jun 30 10:37:34 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.41/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.41/0.57
% 0.41/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.41/0.58
%------------------------------------------------------------------------------