TSTP Solution File: LAT037-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 05:59:03 EDT 2022
% Result : Unsatisfiable 1.40s 1.56s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 88
% Syntax : Number of clauses : 379 ( 202 unt; 0 nHn; 185 RR)
% Number of literals : 635 ( 634 equ; 257 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 : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 694 ( 45 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_meet,axiom,
meet(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(associativity_of_join,axiom,
join(join(X,Y),Z) = join(X,join(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(x_meet_0,axiom,
meet(X,n0) = n0 ).
cnf(x_join_0,axiom,
join(X,n0) = X ).
cnf(x_meet_1,axiom,
meet(X,n1) = X ).
cnf(lhs1,axiom,
join(xx,yy) = n1 ).
cnf(lhs2,axiom,
join(xx,zz) = n1 ).
cnf(lhs3,axiom,
meet(xx,yy) = n0 ).
cnf(lhs4,axiom,
meet(xx,zz) = n0 ).
cnf(rhs,negated_conjecture,
yy != zz ).
cnf(refute_0_0,plain,
join(X_82,meet(X_83,X_84)) = meet(join(X_82,X_83),join(X_82,X_84)),
inference(subst,[],[dist_join:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_1,plain,
join(X_84,X_82) = join(X_82,X_84),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_84)),bind(Y,$fot(X_82))]]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( join(X_84,X_82) != join(X_82,X_84)
| join(X_82,X_84) = join(X_84,X_82) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_84,X_82))),bind(Y0,$fot(join(X_82,X_84)))]]) ).
cnf(refute_0_6,plain,
join(X_82,X_84) = join(X_84,X_82),
inference(resolve,[$cnf( $equal(join(X_84,X_82),join(X_82,X_84)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( join(X_82,X_84) != join(X_84,X_82)
| join(X_82,meet(X_83,X_84)) != meet(join(X_82,X_83),join(X_82,X_84))
| join(X_82,meet(X_83,X_84)) = meet(join(X_82,X_83),join(X_84,X_82)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,meet(X_83,X_84)),meet(join(X_82,X_83),join(X_82,X_84))) ),[1,1],$fot(join(X_84,X_82))]]) ).
cnf(refute_0_8,plain,
( join(X_82,meet(X_83,X_84)) != meet(join(X_82,X_83),join(X_82,X_84))
| join(X_82,meet(X_83,X_84)) = meet(join(X_82,X_83),join(X_84,X_82)) ),
inference(resolve,[$cnf( $equal(join(X_82,X_84),join(X_84,X_82)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
join(X_82,meet(X_83,X_84)) = meet(join(X_82,X_83),join(X_84,X_82)),
inference(resolve,[$cnf( $equal(join(X_82,meet(X_83,X_84)),meet(join(X_82,X_83),join(X_82,X_84))) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
join(zz,meet(X_83,xx)) = meet(join(zz,X_83),join(xx,zz)),
inference(subst,[],[refute_0_9:[bind(X_82,$fot(zz)),bind(X_84,$fot(xx))]]) ).
cnf(refute_0_11,plain,
join(zz,meet(X_162,xx)) = meet(join(zz,X_162),join(xx,zz)),
inference(subst,[],[refute_0_9:[bind(X_82,$fot(zz)),bind(X_83,$fot(X_162)),bind(X_84,$fot(xx))]]) ).
cnf(refute_0_12,plain,
( join(xx,zz) != n1
| join(zz,meet(X_162,xx)) != meet(join(zz,X_162),join(xx,zz))
| join(zz,meet(X_162,xx)) = meet(join(zz,X_162),n1) ),
introduced(tautology,[equality,[$cnf( $equal(join(zz,meet(X_162,xx)),meet(join(zz,X_162),join(xx,zz))) ),[1,1],$fot(n1)]]) ).
cnf(refute_0_13,plain,
( join(zz,meet(X_162,xx)) != meet(join(zz,X_162),join(xx,zz))
| join(zz,meet(X_162,xx)) = meet(join(zz,X_162),n1) ),
inference(resolve,[$cnf( $equal(join(xx,zz),n1) )],[lhs2,refute_0_12]) ).
cnf(refute_0_14,plain,
join(zz,meet(X_162,xx)) = meet(join(zz,X_162),n1),
inference(resolve,[$cnf( $equal(join(zz,meet(X_162,xx)),meet(join(zz,X_162),join(xx,zz))) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
meet(X,n1) = meet(n1,X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(n1))]]) ).
cnf(refute_0_16,plain,
( meet(X,n1) != X
| meet(X,n1) != meet(n1,X)
| meet(n1,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,n1),X) ),[0],$fot(meet(n1,X))]]) ).
cnf(refute_0_17,plain,
( meet(X,n1) != X
| meet(n1,X) = X ),
inference(resolve,[$cnf( $equal(meet(X,n1),meet(n1,X)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
meet(n1,X) = X,
inference(resolve,[$cnf( $equal(meet(X,n1),X) )],[x_meet_1,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(n1,join(zz,X_162)) = join(zz,X_162),
inference(subst,[],[refute_0_18:[bind(X,$fot(join(zz,X_162)))]]) ).
cnf(refute_0_20,plain,
join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = meet(join(meet(X_22,X_14),meet(X_14,X_22)),join(meet(X_22,X_14),X_84)),
inference(subst,[],[dist_join:[bind(X,$fot(meet(X_22,X_14))),bind(Y,$fot(meet(X_14,X_22))),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_21,plain,
join(X_13,meet(X_13,X_14)) = X_13,
inference(subst,[],[absorption2:[bind(X,$fot(X_13)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_22,plain,
meet(X_14,X_13) = meet(X_13,X_14),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_14)),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_23,plain,
( meet(X_14,X_13) != meet(X_13,X_14)
| meet(X_13,X_14) = meet(X_14,X_13) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_14,X_13))),bind(Y0,$fot(meet(X_13,X_14)))]]) ).
cnf(refute_0_24,plain,
meet(X_13,X_14) = meet(X_14,X_13),
inference(resolve,[$cnf( $equal(meet(X_14,X_13),meet(X_13,X_14)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( join(X_13,meet(X_13,X_14)) != X_13
| meet(X_13,X_14) != meet(X_14,X_13)
| join(X_13,meet(X_14,X_13)) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_13,meet(X_13,X_14)),X_13) ),[0,1],$fot(meet(X_14,X_13))]]) ).
cnf(refute_0_26,plain,
( join(X_13,meet(X_13,X_14)) != X_13
| join(X_13,meet(X_14,X_13)) = X_13 ),
inference(resolve,[$cnf( $equal(meet(X_13,X_14),meet(X_14,X_13)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
join(X_13,meet(X_14,X_13)) = X_13,
inference(resolve,[$cnf( $equal(join(X_13,meet(X_13,X_14)),X_13) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
join(meet(X_22,X_14),meet(X_14,meet(X_22,X_14))) = meet(X_22,X_14),
inference(subst,[],[refute_0_27:[bind(X_13,$fot(meet(X_22,X_14)))]]) ).
cnf(refute_0_29,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_30,plain,
( meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_29]) ).
cnf(refute_0_31,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_30]) ).
cnf(refute_0_32,plain,
meet(meet(X_21,Y),join(X_21,meet(X_21,Y))) = meet(X_21,Y),
inference(subst,[],[refute_0_31:[bind(X,$fot(meet(X_21,Y))),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_33,plain,
join(X_21,meet(X_21,Y)) = X_21,
inference(subst,[],[absorption2:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_34,plain,
( join(X_21,meet(X_21,Y)) != X_21
| meet(meet(X_21,Y),join(X_21,meet(X_21,Y))) != meet(X_21,Y)
| meet(meet(X_21,Y),X_21) = meet(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_21,Y),join(X_21,meet(X_21,Y))),meet(X_21,Y)) ),[0,1],$fot(X_21)]]) ).
cnf(refute_0_35,plain,
( meet(meet(X_21,Y),join(X_21,meet(X_21,Y))) != meet(X_21,Y)
| meet(meet(X_21,Y),X_21) = meet(X_21,Y) ),
inference(resolve,[$cnf( $equal(join(X_21,meet(X_21,Y)),X_21) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(meet(X_21,Y),X_21) = meet(X_21,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_21,Y),join(X_21,meet(X_21,Y))),meet(X_21,Y)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
meet(meet(X_21,Y),X_21) = meet(X_21,meet(Y,X_21)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_21)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_38,plain,
( meet(meet(X_21,Y),X_21) != meet(X_21,Y)
| meet(meet(X_21,Y),X_21) != meet(X_21,meet(Y,X_21))
| meet(X_21,meet(Y,X_21)) = meet(X_21,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_21,Y),X_21),meet(X_21,Y)) ),[0],$fot(meet(X_21,meet(Y,X_21)))]]) ).
cnf(refute_0_39,plain,
( meet(meet(X_21,Y),X_21) != meet(X_21,Y)
| meet(X_21,meet(Y,X_21)) = meet(X_21,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_21,Y),X_21),meet(X_21,meet(Y,X_21))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
meet(X_21,meet(Y,X_21)) = meet(X_21,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_21,Y),X_21),meet(X_21,Y)) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
meet(X_14,meet(X_22,X_14)) = meet(X_14,X_22),
inference(subst,[],[refute_0_40:[bind(Y,$fot(X_22)),bind(X_21,$fot(X_14))]]) ).
cnf(refute_0_42,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_14))) != meet(X_22,X_14)
| meet(X_14,meet(X_22,X_14)) != meet(X_14,X_22)
| join(meet(X_22,X_14),meet(X_14,X_22)) = meet(X_22,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_14))),meet(X_22,X_14)) ),[0,1],$fot(meet(X_14,X_22))]]) ).
cnf(refute_0_43,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_14))) != meet(X_22,X_14)
| join(meet(X_22,X_14),meet(X_14,X_22)) = meet(X_22,X_14) ),
inference(resolve,[$cnf( $equal(meet(X_14,meet(X_22,X_14)),meet(X_14,X_22)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
join(meet(X_22,X_14),meet(X_14,X_22)) = meet(X_22,X_14),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_14))),meet(X_22,X_14)) )],[refute_0_28,refute_0_43]) ).
cnf(refute_0_45,plain,
( join(meet(X_22,X_14),meet(X_14,X_22)) != meet(X_22,X_14)
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != meet(join(meet(X_22,X_14),meet(X_14,X_22)),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),meet(join(meet(X_22,X_14),meet(X_14,X_22)),join(meet(X_22,X_14),X_84))) ),[1,0],$fot(meet(X_22,X_14))]]) ).
cnf(refute_0_46,plain,
( join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != meet(join(meet(X_22,X_14),meet(X_14,X_22)),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,X_22)),meet(X_22,X_14)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),meet(join(meet(X_22,X_14),meet(X_14,X_22)),join(meet(X_22,X_14),X_84))) )],[refute_0_20,refute_0_46]) ).
cnf(refute_0_48,plain,
meet(meet(X_14,X_22),X_84) = meet(X_14,meet(X_22,X_84)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_14)),bind(Y,$fot(X_22)),bind(Z,$fot(X_84))]]) ).
cnf(refute_0_49,plain,
join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),
introduced(tautology,[refl,[$fot(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)))]]) ).
cnf(refute_0_50,plain,
( join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84))
| meet(meet(X_14,X_22),X_84) != meet(X_14,meet(X_22,X_84))
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84))) ),[1,1],$fot(meet(X_14,meet(X_22,X_84)))]]) ).
cnf(refute_0_51,plain,
( meet(meet(X_14,X_22),X_84) != meet(X_14,meet(X_22,X_84))
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) = join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),
inference(resolve,[$cnf( $equal(meet(meet(X_14,X_22),X_84),meet(X_14,meet(X_22,X_84))) )],[refute_0_48,refute_0_51]) ).
cnf(refute_0_53,plain,
( join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84)))
| join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))) ),[0],$fot(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))))]]) ).
cnf(refute_0_54,plain,
( join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84)))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)) = meet(X_51,X_52),
inference(subst,[],[absorption1:[bind(X,$fot(meet(X_51,X_52)))]]) ).
cnf(refute_0_56,plain,
meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)) = meet(X_51,meet(X_52,join(meet(X_51,X_52),Y))),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(join(meet(X_51,X_52),Y)))]]) ).
cnf(refute_0_57,plain,
( meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)) != meet(X_51,X_52)
| meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)) != meet(X_51,meet(X_52,join(meet(X_51,X_52),Y)))
| meet(X_51,meet(X_52,join(meet(X_51,X_52),Y))) = meet(X_51,X_52) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)),meet(X_51,X_52)) ),[0],$fot(meet(X_51,meet(X_52,join(meet(X_51,X_52),Y))))]]) ).
cnf(refute_0_58,plain,
( meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)) != meet(X_51,X_52)
| meet(X_51,meet(X_52,join(meet(X_51,X_52),Y))) = meet(X_51,X_52) ),
inference(resolve,[$cnf( $equal(meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)),meet(X_51,meet(X_52,join(meet(X_51,X_52),Y)))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
meet(X_51,meet(X_52,join(meet(X_51,X_52),Y))) = meet(X_51,X_52),
inference(resolve,[$cnf( $equal(meet(meet(X_51,X_52),join(meet(X_51,X_52),Y)),meet(X_51,X_52)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))) = meet(X_22,X_14),
inference(subst,[],[refute_0_59:[bind(Y,$fot(X_84)),bind(X_51,$fot(X_22)),bind(X_52,$fot(X_14))]]) ).
cnf(refute_0_61,plain,
meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) = meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_22)),bind(Y,$fot(X_14)),bind(Z,$fot(join(meet(X_22,X_14),X_84)))]]) ).
cnf(refute_0_62,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_63,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_4,refute_0_62]) ).
cnf(refute_0_64,plain,
( meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))) != meet(X_22,X_14)
| meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) != meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84)))
| meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) = meet(X_22,X_14) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)))),bind(Y0,$fot(meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))))),bind(Z0,$fot(meet(X_22,X_14)))]]) ).
cnf(refute_0_65,plain,
( meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))) != meet(X_22,X_14)
| meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) = meet(X_22,X_14) ),
inference(resolve,[$cnf( $equal(meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)),meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84)))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) = meet(X_22,X_14),
inference(resolve,[$cnf( $equal(meet(X_22,meet(X_14,join(meet(X_22,X_14),X_84))),meet(X_22,X_14)) )],[refute_0_60,refute_0_65]) ).
cnf(refute_0_67,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))
| meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)) != meet(X_22,X_14)
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_22,X_14) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(X_22,X_14)) ),[0],$fot(meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)))]]) ).
cnf(refute_0_68,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_22,X_14) ),
inference(resolve,[$cnf( $equal(meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84)),meet(X_22,X_14)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)) != meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_22,X_14) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))) )],[refute_0_54,refute_0_68]) ).
cnf(refute_0_70,plain,
join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_22,X_14),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(meet(X_14,X_22),X_84)),meet(meet(X_22,X_14),join(meet(X_22,X_14),X_84))) )],[refute_0_47,refute_0_69]) ).
cnf(refute_0_71,plain,
join(X_22,meet(X_22,X_84)) = X_22,
inference(subst,[],[absorption2:[bind(X,$fot(X_22)),bind(Y,$fot(X_84))]]) ).
cnf(refute_0_72,plain,
meet(X_14,join(X_22,meet(X_22,X_84))) = meet(X_14,join(X_22,meet(X_22,X_84))),
introduced(tautology,[refl,[$fot(meet(X_14,join(X_22,meet(X_22,X_84))))]]) ).
cnf(refute_0_73,plain,
( join(X_22,meet(X_22,X_84)) != X_22
| meet(X_14,join(X_22,meet(X_22,X_84))) != meet(X_14,join(X_22,meet(X_22,X_84)))
| meet(X_14,join(X_22,meet(X_22,X_84))) = meet(X_14,X_22) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_14,join(X_22,meet(X_22,X_84))),meet(X_14,join(X_22,meet(X_22,X_84)))) ),[1,1],$fot(X_22)]]) ).
cnf(refute_0_74,plain,
( join(X_22,meet(X_22,X_84)) != X_22
| meet(X_14,join(X_22,meet(X_22,X_84))) = meet(X_14,X_22) ),
inference(resolve,[$cnf( $equal(meet(X_14,join(X_22,meet(X_22,X_84))),meet(X_14,join(X_22,meet(X_22,X_84)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
meet(X_14,join(X_22,meet(X_22,X_84))) = meet(X_14,X_22),
inference(resolve,[$cnf( $equal(join(X_22,meet(X_22,X_84)),X_22) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
meet(X_93,join(X_94,X_95)) = join(meet(X_93,X_94),meet(X_93,X_95)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_93)),bind(Y,$fot(X_94)),bind(Z,$fot(X_95))]]) ).
cnf(refute_0_77,plain,
meet(X_94,X_93) = meet(X_93,X_94),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_94)),bind(Y,$fot(X_93))]]) ).
cnf(refute_0_78,plain,
( meet(X_94,X_93) != meet(X_93,X_94)
| meet(X_93,X_94) = meet(X_94,X_93) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_94,X_93))),bind(Y0,$fot(meet(X_93,X_94)))]]) ).
cnf(refute_0_79,plain,
meet(X_93,X_94) = meet(X_94,X_93),
inference(resolve,[$cnf( $equal(meet(X_94,X_93),meet(X_93,X_94)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
( meet(X_93,X_94) != meet(X_94,X_93)
| meet(X_93,join(X_94,X_95)) != join(meet(X_93,X_94),meet(X_93,X_95))
| meet(X_93,join(X_94,X_95)) = join(meet(X_94,X_93),meet(X_93,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_93,join(X_94,X_95)),join(meet(X_93,X_94),meet(X_93,X_95))) ),[1,0],$fot(meet(X_94,X_93))]]) ).
cnf(refute_0_81,plain,
( meet(X_93,join(X_94,X_95)) != join(meet(X_93,X_94),meet(X_93,X_95))
| meet(X_93,join(X_94,X_95)) = join(meet(X_94,X_93),meet(X_93,X_95)) ),
inference(resolve,[$cnf( $equal(meet(X_93,X_94),meet(X_94,X_93)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
meet(X_93,join(X_94,X_95)) = join(meet(X_94,X_93),meet(X_93,X_95)),
inference(resolve,[$cnf( $equal(meet(X_93,join(X_94,X_95)),join(meet(X_93,X_94),meet(X_93,X_95))) )],[refute_0_76,refute_0_81]) ).
cnf(refute_0_83,plain,
( meet(X_93,join(X_94,X_95)) != join(meet(X_94,X_93),meet(X_93,X_95))
| join(meet(X_94,X_93),meet(X_93,X_95)) = meet(X_93,join(X_94,X_95)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_93,join(X_94,X_95)))),bind(Y0,$fot(join(meet(X_94,X_93),meet(X_93,X_95))))]]) ).
cnf(refute_0_84,plain,
join(meet(X_94,X_93),meet(X_93,X_95)) = meet(X_93,join(X_94,X_95)),
inference(resolve,[$cnf( $equal(meet(X_93,join(X_94,X_95)),join(meet(X_94,X_93),meet(X_93,X_95))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_14,join(X_22,meet(X_22,X_84))),
inference(subst,[],[refute_0_84:[bind(X_93,$fot(X_14)),bind(X_94,$fot(X_22)),bind(X_95,$fot(meet(X_22,X_84)))]]) ).
cnf(refute_0_86,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(X_14,join(X_22,meet(X_22,X_84)))
| meet(X_14,join(X_22,meet(X_22,X_84))) != meet(X_14,X_22)
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_14,X_22) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))))),bind(Y0,$fot(meet(X_14,join(X_22,meet(X_22,X_84))))),bind(Z0,$fot(meet(X_14,X_22)))]]) ).
cnf(refute_0_87,plain,
( meet(X_14,join(X_22,meet(X_22,X_84))) != meet(X_14,X_22)
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_14,X_22) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(X_14,join(X_22,meet(X_22,X_84)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) = meet(X_14,X_22),
inference(resolve,[$cnf( $equal(meet(X_14,join(X_22,meet(X_22,X_84))),meet(X_14,X_22)) )],[refute_0_75,refute_0_87]) ).
cnf(refute_0_89,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(X_14,X_22)
| join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(X_22,X_14)
| meet(X_14,X_22) = meet(X_22,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(X_22,X_14)) ),[0],$fot(meet(X_14,X_22))]]) ).
cnf(refute_0_90,plain,
( join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))) != meet(X_22,X_14)
| meet(X_14,X_22) = meet(X_22,X_14) ),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(X_14,X_22)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
meet(X_14,X_22) = meet(X_22,X_14),
inference(resolve,[$cnf( $equal(join(meet(X_22,X_14),meet(X_14,meet(X_22,X_84))),meet(X_22,X_14)) )],[refute_0_70,refute_0_90]) ).
cnf(refute_0_92,plain,
( meet(X_14,X_22) != meet(X_22,X_14)
| meet(X_22,X_14) = meet(X_14,X_22) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_14,X_22))),bind(Y0,$fot(meet(X_22,X_14)))]]) ).
cnf(refute_0_93,plain,
meet(X_22,X_14) = meet(X_14,X_22),
inference(resolve,[$cnf( $equal(meet(X_14,X_22),meet(X_22,X_14)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
meet(join(zz,X_162),n1) = meet(n1,join(zz,X_162)),
inference(subst,[],[refute_0_93:[bind(X_14,$fot(n1)),bind(X_22,$fot(join(zz,X_162)))]]) ).
cnf(refute_0_95,plain,
( meet(join(zz,X_162),n1) != meet(n1,join(zz,X_162))
| meet(n1,join(zz,X_162)) != join(zz,X_162)
| meet(join(zz,X_162),n1) = join(zz,X_162) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(join(zz,X_162),n1))),bind(Y0,$fot(meet(n1,join(zz,X_162)))),bind(Z0,$fot(join(zz,X_162)))]]) ).
cnf(refute_0_96,plain,
( meet(n1,join(zz,X_162)) != join(zz,X_162)
| meet(join(zz,X_162),n1) = join(zz,X_162) ),
inference(resolve,[$cnf( $equal(meet(join(zz,X_162),n1),meet(n1,join(zz,X_162))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
meet(join(zz,X_162),n1) = join(zz,X_162),
inference(resolve,[$cnf( $equal(meet(n1,join(zz,X_162)),join(zz,X_162)) )],[refute_0_19,refute_0_96]) ).
cnf(refute_0_98,plain,
( join(zz,meet(X_162,xx)) != meet(join(zz,X_162),n1)
| meet(join(zz,X_162),n1) != join(zz,X_162)
| join(zz,meet(X_162,xx)) = join(zz,X_162) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zz,meet(X_162,xx)),join(zz,X_162)) ),[0],$fot(meet(join(zz,X_162),n1))]]) ).
cnf(refute_0_99,plain,
( join(zz,meet(X_162,xx)) != meet(join(zz,X_162),n1)
| join(zz,meet(X_162,xx)) = join(zz,X_162) ),
inference(resolve,[$cnf( $equal(meet(join(zz,X_162),n1),join(zz,X_162)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
join(zz,meet(X_162,xx)) = join(zz,X_162),
inference(resolve,[$cnf( $equal(join(zz,meet(X_162,xx)),meet(join(zz,X_162),n1)) )],[refute_0_14,refute_0_99]) ).
cnf(refute_0_101,plain,
join(zz,meet(X_83,xx)) = join(zz,X_83),
inference(subst,[],[refute_0_100:[bind(X_162,$fot(X_83))]]) ).
cnf(refute_0_102,plain,
( join(zz,meet(X_83,xx)) != join(zz,X_83)
| join(zz,meet(X_83,xx)) != meet(join(zz,X_83),join(xx,zz))
| join(zz,X_83) = meet(join(zz,X_83),join(xx,zz)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zz,meet(X_83,xx)),meet(join(zz,X_83),join(xx,zz))) ),[0],$fot(join(zz,X_83))]]) ).
cnf(refute_0_103,plain,
( join(zz,meet(X_83,xx)) != meet(join(zz,X_83),join(xx,zz))
| join(zz,X_83) = meet(join(zz,X_83),join(xx,zz)) ),
inference(resolve,[$cnf( $equal(join(zz,meet(X_83,xx)),join(zz,X_83)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
join(zz,X_83) = meet(join(zz,X_83),join(xx,zz)),
inference(resolve,[$cnf( $equal(join(zz,meet(X_83,xx)),meet(join(zz,X_83),join(xx,zz))) )],[refute_0_10,refute_0_103]) ).
cnf(refute_0_105,plain,
join(X_83,X_82) = join(X_82,X_83),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_83)),bind(Y,$fot(X_82))]]) ).
cnf(refute_0_106,plain,
( join(X_83,X_82) != join(X_82,X_83)
| join(X_82,X_83) = join(X_83,X_82) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_83,X_82))),bind(Y0,$fot(join(X_82,X_83)))]]) ).
cnf(refute_0_107,plain,
join(X_82,X_83) = join(X_83,X_82),
inference(resolve,[$cnf( $equal(join(X_83,X_82),join(X_82,X_83)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( join(X_82,X_83) != join(X_83,X_82)
| join(X_82,meet(X_83,X_84)) != meet(join(X_82,X_83),join(X_82,X_84))
| join(X_82,meet(X_83,X_84)) = meet(join(X_83,X_82),join(X_82,X_84)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_82,meet(X_83,X_84)),meet(join(X_82,X_83),join(X_82,X_84))) ),[1,0],$fot(join(X_83,X_82))]]) ).
cnf(refute_0_109,plain,
( join(X_82,meet(X_83,X_84)) != meet(join(X_82,X_83),join(X_82,X_84))
| join(X_82,meet(X_83,X_84)) = meet(join(X_83,X_82),join(X_82,X_84)) ),
inference(resolve,[$cnf( $equal(join(X_82,X_83),join(X_83,X_82)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
join(X_82,meet(X_83,X_84)) = meet(join(X_83,X_82),join(X_82,X_84)),
inference(resolve,[$cnf( $equal(join(X_82,meet(X_83,X_84)),meet(join(X_82,X_83),join(X_82,X_84))) )],[refute_0_0,refute_0_109]) ).
cnf(refute_0_111,plain,
( join(X_82,meet(X_83,X_84)) != meet(join(X_83,X_82),join(X_82,X_84))
| meet(join(X_83,X_82),join(X_82,X_84)) = join(X_82,meet(X_83,X_84)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_82,meet(X_83,X_84)))),bind(Y0,$fot(meet(join(X_83,X_82),join(X_82,X_84))))]]) ).
cnf(refute_0_112,plain,
meet(join(X_83,X_82),join(X_82,X_84)) = join(X_82,meet(X_83,X_84)),
inference(resolve,[$cnf( $equal(join(X_82,meet(X_83,X_84)),meet(join(X_83,X_82),join(X_82,X_84))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
meet(join(xx,zz),join(zz,X_83)) = join(zz,meet(xx,X_83)),
inference(subst,[],[refute_0_112:[bind(X_82,$fot(zz)),bind(X_83,$fot(xx)),bind(X_84,$fot(X_83))]]) ).
cnf(refute_0_114,plain,
meet(join(zz,X_83),join(xx,zz)) = meet(join(xx,zz),join(zz,X_83)),
inference(subst,[],[refute_0_93:[bind(X_14,$fot(join(xx,zz))),bind(X_22,$fot(join(zz,X_83)))]]) ).
cnf(refute_0_115,plain,
( meet(join(xx,zz),join(zz,X_83)) != join(zz,meet(xx,X_83))
| meet(join(zz,X_83),join(xx,zz)) != meet(join(xx,zz),join(zz,X_83))
| meet(join(zz,X_83),join(xx,zz)) = join(zz,meet(xx,X_83)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(join(zz,X_83),join(xx,zz)))),bind(Y0,$fot(meet(join(xx,zz),join(zz,X_83)))),bind(Z0,$fot(join(zz,meet(xx,X_83))))]]) ).
cnf(refute_0_116,plain,
( meet(join(xx,zz),join(zz,X_83)) != join(zz,meet(xx,X_83))
| meet(join(zz,X_83),join(xx,zz)) = join(zz,meet(xx,X_83)) ),
inference(resolve,[$cnf( $equal(meet(join(zz,X_83),join(xx,zz)),meet(join(xx,zz),join(zz,X_83))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
meet(join(zz,X_83),join(xx,zz)) = join(zz,meet(xx,X_83)),
inference(resolve,[$cnf( $equal(meet(join(xx,zz),join(zz,X_83)),join(zz,meet(xx,X_83))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( join(zz,X_83) != meet(join(zz,X_83),join(xx,zz))
| meet(join(zz,X_83),join(xx,zz)) != join(zz,meet(xx,X_83))
| join(zz,X_83) = join(zz,meet(xx,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zz,X_83),join(zz,meet(xx,X_83))) ),[0],$fot(meet(join(zz,X_83),join(xx,zz)))]]) ).
cnf(refute_0_119,plain,
( join(zz,X_83) != meet(join(zz,X_83),join(xx,zz))
| join(zz,X_83) = join(zz,meet(xx,X_83)) ),
inference(resolve,[$cnf( $equal(meet(join(zz,X_83),join(xx,zz)),join(zz,meet(xx,X_83))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
join(zz,X_83) = join(zz,meet(xx,X_83)),
inference(resolve,[$cnf( $equal(join(zz,X_83),meet(join(zz,X_83),join(xx,zz))) )],[refute_0_104,refute_0_119]) ).
cnf(refute_0_121,plain,
join(zz,meet(X_52,zz)) = join(zz,meet(xx,meet(X_52,zz))),
inference(subst,[],[refute_0_120:[bind(X_83,$fot(meet(X_52,zz)))]]) ).
cnf(refute_0_122,plain,
join(X_13,meet(meet(X_51,X_52),X_13)) = X_13,
inference(subst,[],[refute_0_27:[bind(X_14,$fot(meet(X_51,X_52)))]]) ).
cnf(refute_0_123,plain,
meet(meet(X_51,X_52),X_13) = meet(X_51,meet(X_52,X_13)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_124,plain,
( join(X_13,meet(meet(X_51,X_52),X_13)) != X_13
| meet(meet(X_51,X_52),X_13) != meet(X_51,meet(X_52,X_13))
| join(X_13,meet(X_51,meet(X_52,X_13))) = X_13 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_13,meet(meet(X_51,X_52),X_13)),X_13) ),[0,1],$fot(meet(X_51,meet(X_52,X_13)))]]) ).
cnf(refute_0_125,plain,
( join(X_13,meet(meet(X_51,X_52),X_13)) != X_13
| join(X_13,meet(X_51,meet(X_52,X_13))) = X_13 ),
inference(resolve,[$cnf( $equal(meet(meet(X_51,X_52),X_13),meet(X_51,meet(X_52,X_13))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
join(X_13,meet(X_51,meet(X_52,X_13))) = X_13,
inference(resolve,[$cnf( $equal(join(X_13,meet(meet(X_51,X_52),X_13)),X_13) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
join(zz,meet(xx,meet(X_52,zz))) = zz,
inference(subst,[],[refute_0_126:[bind(X_13,$fot(zz)),bind(X_51,$fot(xx))]]) ).
cnf(refute_0_128,plain,
( join(zz,meet(X_52,zz)) != join(zz,meet(xx,meet(X_52,zz)))
| join(zz,meet(xx,meet(X_52,zz))) != zz
| join(zz,meet(X_52,zz)) = zz ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zz,meet(X_52,zz)),zz) ),[0],$fot(join(zz,meet(xx,meet(X_52,zz))))]]) ).
cnf(refute_0_129,plain,
( join(zz,meet(X_52,zz)) != join(zz,meet(xx,meet(X_52,zz)))
| join(zz,meet(X_52,zz)) = zz ),
inference(resolve,[$cnf( $equal(join(zz,meet(xx,meet(X_52,zz))),zz) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(zz,meet(X_52,zz)) = zz,
inference(resolve,[$cnf( $equal(join(zz,meet(X_52,zz)),join(zz,meet(xx,meet(X_52,zz)))) )],[refute_0_121,refute_0_129]) ).
cnf(refute_0_131,plain,
join(yy,meet(X_83,xx)) = meet(join(yy,X_83),join(xx,yy)),
inference(subst,[],[refute_0_9:[bind(X_82,$fot(yy)),bind(X_84,$fot(xx))]]) ).
cnf(refute_0_132,plain,
join(yy,meet(X_162,xx)) = meet(join(yy,X_162),join(xx,yy)),
inference(subst,[],[refute_0_9:[bind(X_82,$fot(yy)),bind(X_83,$fot(X_162)),bind(X_84,$fot(xx))]]) ).
cnf(refute_0_133,plain,
( join(xx,yy) != n1
| join(yy,meet(X_162,xx)) != meet(join(yy,X_162),join(xx,yy))
| join(yy,meet(X_162,xx)) = meet(join(yy,X_162),n1) ),
introduced(tautology,[equality,[$cnf( $equal(join(yy,meet(X_162,xx)),meet(join(yy,X_162),join(xx,yy))) ),[1,1],$fot(n1)]]) ).
cnf(refute_0_134,plain,
( join(yy,meet(X_162,xx)) != meet(join(yy,X_162),join(xx,yy))
| join(yy,meet(X_162,xx)) = meet(join(yy,X_162),n1) ),
inference(resolve,[$cnf( $equal(join(xx,yy),n1) )],[lhs1,refute_0_133]) ).
cnf(refute_0_135,plain,
join(yy,meet(X_162,xx)) = meet(join(yy,X_162),n1),
inference(resolve,[$cnf( $equal(join(yy,meet(X_162,xx)),meet(join(yy,X_162),join(xx,yy))) )],[refute_0_132,refute_0_134]) ).
cnf(refute_0_136,plain,
meet(n1,join(yy,X_162)) = join(yy,X_162),
inference(subst,[],[refute_0_18:[bind(X,$fot(join(yy,X_162)))]]) ).
cnf(refute_0_137,plain,
meet(join(yy,X_162),n1) = meet(n1,join(yy,X_162)),
inference(subst,[],[refute_0_93:[bind(X_14,$fot(n1)),bind(X_22,$fot(join(yy,X_162)))]]) ).
cnf(refute_0_138,plain,
( meet(join(yy,X_162),n1) != meet(n1,join(yy,X_162))
| meet(n1,join(yy,X_162)) != join(yy,X_162)
| meet(join(yy,X_162),n1) = join(yy,X_162) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(join(yy,X_162),n1))),bind(Y0,$fot(meet(n1,join(yy,X_162)))),bind(Z0,$fot(join(yy,X_162)))]]) ).
cnf(refute_0_139,plain,
( meet(n1,join(yy,X_162)) != join(yy,X_162)
| meet(join(yy,X_162),n1) = join(yy,X_162) ),
inference(resolve,[$cnf( $equal(meet(join(yy,X_162),n1),meet(n1,join(yy,X_162))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
meet(join(yy,X_162),n1) = join(yy,X_162),
inference(resolve,[$cnf( $equal(meet(n1,join(yy,X_162)),join(yy,X_162)) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
( join(yy,meet(X_162,xx)) != meet(join(yy,X_162),n1)
| meet(join(yy,X_162),n1) != join(yy,X_162)
| join(yy,meet(X_162,xx)) = join(yy,X_162) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(yy,meet(X_162,xx)),join(yy,X_162)) ),[0],$fot(meet(join(yy,X_162),n1))]]) ).
cnf(refute_0_142,plain,
( join(yy,meet(X_162,xx)) != meet(join(yy,X_162),n1)
| join(yy,meet(X_162,xx)) = join(yy,X_162) ),
inference(resolve,[$cnf( $equal(meet(join(yy,X_162),n1),join(yy,X_162)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
join(yy,meet(X_162,xx)) = join(yy,X_162),
inference(resolve,[$cnf( $equal(join(yy,meet(X_162,xx)),meet(join(yy,X_162),n1)) )],[refute_0_135,refute_0_142]) ).
cnf(refute_0_144,plain,
join(yy,meet(X_83,xx)) = join(yy,X_83),
inference(subst,[],[refute_0_143:[bind(X_162,$fot(X_83))]]) ).
cnf(refute_0_145,plain,
( join(yy,meet(X_83,xx)) != join(yy,X_83)
| join(yy,meet(X_83,xx)) != meet(join(yy,X_83),join(xx,yy))
| join(yy,X_83) = meet(join(yy,X_83),join(xx,yy)) ),
introduced(tautology,[equality,[$cnf( $equal(join(yy,meet(X_83,xx)),meet(join(yy,X_83),join(xx,yy))) ),[0],$fot(join(yy,X_83))]]) ).
cnf(refute_0_146,plain,
( join(yy,meet(X_83,xx)) != meet(join(yy,X_83),join(xx,yy))
| join(yy,X_83) = meet(join(yy,X_83),join(xx,yy)) ),
inference(resolve,[$cnf( $equal(join(yy,meet(X_83,xx)),join(yy,X_83)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
join(yy,X_83) = meet(join(yy,X_83),join(xx,yy)),
inference(resolve,[$cnf( $equal(join(yy,meet(X_83,xx)),meet(join(yy,X_83),join(xx,yy))) )],[refute_0_131,refute_0_146]) ).
cnf(refute_0_148,plain,
meet(join(xx,yy),join(yy,X_83)) = join(yy,meet(xx,X_83)),
inference(subst,[],[refute_0_112:[bind(X_82,$fot(yy)),bind(X_83,$fot(xx)),bind(X_84,$fot(X_83))]]) ).
cnf(refute_0_149,plain,
meet(join(yy,X_83),join(xx,yy)) = meet(join(xx,yy),join(yy,X_83)),
inference(subst,[],[refute_0_93:[bind(X_14,$fot(join(xx,yy))),bind(X_22,$fot(join(yy,X_83)))]]) ).
cnf(refute_0_150,plain,
( meet(join(xx,yy),join(yy,X_83)) != join(yy,meet(xx,X_83))
| meet(join(yy,X_83),join(xx,yy)) != meet(join(xx,yy),join(yy,X_83))
| meet(join(yy,X_83),join(xx,yy)) = join(yy,meet(xx,X_83)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(join(yy,X_83),join(xx,yy)))),bind(Y0,$fot(meet(join(xx,yy),join(yy,X_83)))),bind(Z0,$fot(join(yy,meet(xx,X_83))))]]) ).
cnf(refute_0_151,plain,
( meet(join(xx,yy),join(yy,X_83)) != join(yy,meet(xx,X_83))
| meet(join(yy,X_83),join(xx,yy)) = join(yy,meet(xx,X_83)) ),
inference(resolve,[$cnf( $equal(meet(join(yy,X_83),join(xx,yy)),meet(join(xx,yy),join(yy,X_83))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
meet(join(yy,X_83),join(xx,yy)) = join(yy,meet(xx,X_83)),
inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(yy,X_83)),join(yy,meet(xx,X_83))) )],[refute_0_148,refute_0_151]) ).
cnf(refute_0_153,plain,
( join(yy,X_83) != meet(join(yy,X_83),join(xx,yy))
| meet(join(yy,X_83),join(xx,yy)) != join(yy,meet(xx,X_83))
| join(yy,X_83) = join(yy,meet(xx,X_83)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(yy,X_83),join(yy,meet(xx,X_83))) ),[0],$fot(meet(join(yy,X_83),join(xx,yy)))]]) ).
cnf(refute_0_154,plain,
( join(yy,X_83) != meet(join(yy,X_83),join(xx,yy))
| join(yy,X_83) = join(yy,meet(xx,X_83)) ),
inference(resolve,[$cnf( $equal(meet(join(yy,X_83),join(xx,yy)),join(yy,meet(xx,X_83))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
join(yy,X_83) = join(yy,meet(xx,X_83)),
inference(resolve,[$cnf( $equal(join(yy,X_83),meet(join(yy,X_83),join(xx,yy))) )],[refute_0_147,refute_0_154]) ).
cnf(refute_0_156,plain,
join(yy,meet(X_55,zz)) = join(yy,meet(xx,meet(X_55,zz))),
inference(subst,[],[refute_0_155:[bind(X_83,$fot(meet(X_55,zz)))]]) ).
cnf(refute_0_157,plain,
meet(meet(xx,zz),X_53) = meet(xx,meet(zz,X_53)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(xx)),bind(Y,$fot(zz)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_158,plain,
( meet(meet(xx,zz),X_53) != meet(xx,meet(zz,X_53))
| meet(xx,zz) != n0
| meet(n0,X_53) = meet(xx,meet(zz,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(xx,zz),X_53),meet(xx,meet(zz,X_53))) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_159,plain,
( meet(meet(xx,zz),X_53) != meet(xx,meet(zz,X_53))
| meet(n0,X_53) = meet(xx,meet(zz,X_53)) ),
inference(resolve,[$cnf( $equal(meet(xx,zz),n0) )],[lhs4,refute_0_158]) ).
cnf(refute_0_160,plain,
meet(n0,X_53) = meet(xx,meet(zz,X_53)),
inference(resolve,[$cnf( $equal(meet(meet(xx,zz),X_53),meet(xx,meet(zz,X_53))) )],[refute_0_157,refute_0_159]) ).
cnf(refute_0_161,plain,
meet(X,n0) = meet(n0,X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(n0))]]) ).
cnf(refute_0_162,plain,
( meet(X,n0) != meet(n0,X)
| meet(X,n0) != n0
| meet(n0,X) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,n0),n0) ),[0],$fot(meet(n0,X))]]) ).
cnf(refute_0_163,plain,
( meet(X,n0) != n0
| meet(n0,X) = n0 ),
inference(resolve,[$cnf( $equal(meet(X,n0),meet(n0,X)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
meet(n0,X) = n0,
inference(resolve,[$cnf( $equal(meet(X,n0),n0) )],[x_meet_0,refute_0_163]) ).
cnf(refute_0_165,plain,
meet(n0,X_53) = n0,
inference(subst,[],[refute_0_164:[bind(X,$fot(X_53))]]) ).
cnf(refute_0_166,plain,
( meet(n0,X_53) != meet(xx,meet(zz,X_53))
| meet(n0,X_53) != n0
| n0 = meet(xx,meet(zz,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(n0,X_53),meet(xx,meet(zz,X_53))) ),[0],$fot(n0)]]) ).
cnf(refute_0_167,plain,
( meet(n0,X_53) != meet(xx,meet(zz,X_53))
| n0 = meet(xx,meet(zz,X_53)) ),
inference(resolve,[$cnf( $equal(meet(n0,X_53),n0) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
n0 = meet(xx,meet(zz,X_53)),
inference(resolve,[$cnf( $equal(meet(n0,X_53),meet(xx,meet(zz,X_53))) )],[refute_0_160,refute_0_167]) ).
cnf(refute_0_169,plain,
n0 = meet(xx,meet(zz,X_55)),
inference(subst,[],[refute_0_168:[bind(X_53,$fot(X_55))]]) ).
cnf(refute_0_170,plain,
meet(X_55,zz) = meet(zz,X_55),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_55)),bind(Y,$fot(zz))]]) ).
cnf(refute_0_171,plain,
( meet(X_55,zz) != meet(zz,X_55)
| meet(zz,X_55) = meet(X_55,zz) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(meet(X_55,zz))),bind(Y0,$fot(meet(zz,X_55)))]]) ).
cnf(refute_0_172,plain,
meet(zz,X_55) = meet(X_55,zz),
inference(resolve,[$cnf( $equal(meet(X_55,zz),meet(zz,X_55)) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( meet(zz,X_55) != meet(X_55,zz)
| n0 != meet(xx,meet(zz,X_55))
| n0 = meet(xx,meet(X_55,zz)) ),
introduced(tautology,[equality,[$cnf( $equal(n0,meet(xx,meet(zz,X_55))) ),[1,1],$fot(meet(X_55,zz))]]) ).
cnf(refute_0_174,plain,
( n0 != meet(xx,meet(zz,X_55))
| n0 = meet(xx,meet(X_55,zz)) ),
inference(resolve,[$cnf( $equal(meet(zz,X_55),meet(X_55,zz)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
n0 = meet(xx,meet(X_55,zz)),
inference(resolve,[$cnf( $equal(n0,meet(xx,meet(zz,X_55))) )],[refute_0_169,refute_0_174]) ).
cnf(refute_0_176,plain,
( n0 != meet(xx,meet(X_55,zz))
| meet(xx,meet(X_55,zz)) = n0 ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(n0)),bind(Y0,$fot(meet(xx,meet(X_55,zz))))]]) ).
cnf(refute_0_177,plain,
meet(xx,meet(X_55,zz)) = n0,
inference(resolve,[$cnf( $equal(n0,meet(xx,meet(X_55,zz))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( join(yy,meet(X_55,zz)) != join(yy,meet(xx,meet(X_55,zz)))
| meet(xx,meet(X_55,zz)) != n0
| join(yy,meet(X_55,zz)) = join(yy,n0) ),
introduced(tautology,[equality,[$cnf( $equal(join(yy,meet(X_55,zz)),join(yy,meet(xx,meet(X_55,zz)))) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_179,plain,
( join(yy,meet(X_55,zz)) != join(yy,meet(xx,meet(X_55,zz)))
| join(yy,meet(X_55,zz)) = join(yy,n0) ),
inference(resolve,[$cnf( $equal(meet(xx,meet(X_55,zz)),n0) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
join(yy,meet(X_55,zz)) = join(yy,n0),
inference(resolve,[$cnf( $equal(join(yy,meet(X_55,zz)),join(yy,meet(xx,meet(X_55,zz)))) )],[refute_0_156,refute_0_179]) ).
cnf(refute_0_181,plain,
join(X,n0) = join(n0,X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(n0))]]) ).
cnf(refute_0_182,plain,
( join(X,n0) != X
| join(X,n0) != join(n0,X)
| join(n0,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,n0),X) ),[0],$fot(join(n0,X))]]) ).
cnf(refute_0_183,plain,
( join(X,n0) != X
| join(n0,X) = X ),
inference(resolve,[$cnf( $equal(join(X,n0),join(n0,X)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
join(n0,X) = X,
inference(resolve,[$cnf( $equal(join(X,n0),X) )],[x_join_0,refute_0_183]) ).
cnf(refute_0_185,plain,
join(n0,yy) = yy,
inference(subst,[],[refute_0_184:[bind(X,$fot(yy))]]) ).
cnf(refute_0_186,plain,
join(join(X_94,yy),meet(X_101,meet(xx,join(X_94,yy)))) = join(X_94,yy),
inference(subst,[],[refute_0_126:[bind(X_13,$fot(join(X_94,yy))),bind(X_51,$fot(X_101)),bind(X_52,$fot(xx))]]) ).
cnf(refute_0_187,plain,
meet(xx,join(X_94,yy)) = join(meet(xx,X_94),meet(xx,yy)),
inference(subst,[],[dist_meet:[bind(X,$fot(xx)),bind(Y,$fot(X_94)),bind(Z,$fot(yy))]]) ).
cnf(refute_0_188,plain,
( meet(xx,join(X_94,yy)) != join(meet(xx,X_94),meet(xx,yy))
| meet(xx,yy) != n0
| meet(xx,join(X_94,yy)) = join(meet(xx,X_94),n0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(X_94,yy)),join(meet(xx,X_94),meet(xx,yy))) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_189,plain,
( meet(xx,join(X_94,yy)) != join(meet(xx,X_94),meet(xx,yy))
| meet(xx,join(X_94,yy)) = join(meet(xx,X_94),n0) ),
inference(resolve,[$cnf( $equal(meet(xx,yy),n0) )],[lhs3,refute_0_188]) ).
cnf(refute_0_190,plain,
meet(xx,join(X_94,yy)) = join(meet(xx,X_94),n0),
inference(resolve,[$cnf( $equal(meet(xx,join(X_94,yy)),join(meet(xx,X_94),meet(xx,yy))) )],[refute_0_187,refute_0_189]) ).
cnf(refute_0_191,plain,
join(n0,meet(xx,X_94)) = meet(xx,X_94),
inference(subst,[],[refute_0_184:[bind(X,$fot(meet(xx,X_94)))]]) ).
cnf(refute_0_192,plain,
meet(join(X_24,Y),join(Y,join(X_24,Y))) = join(X_24,Y),
inference(subst,[],[refute_0_31:[bind(X,$fot(join(X_24,Y)))]]) ).
cnf(refute_0_193,plain,
join(join(X_16,Y),meet(X_16,join(X_16,Y))) = join(X_16,Y),
inference(subst,[],[refute_0_27:[bind(X_13,$fot(join(X_16,Y))),bind(X_14,$fot(X_16))]]) ).
cnf(refute_0_194,plain,
meet(X_16,join(X_16,Y)) = X_16,
inference(subst,[],[absorption1:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_195,plain,
( join(join(X_16,Y),meet(X_16,join(X_16,Y))) != join(X_16,Y)
| meet(X_16,join(X_16,Y)) != X_16
| join(join(X_16,Y),X_16) = join(X_16,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_16,Y),meet(X_16,join(X_16,Y))),join(X_16,Y)) ),[0,1],$fot(X_16)]]) ).
cnf(refute_0_196,plain,
( join(join(X_16,Y),meet(X_16,join(X_16,Y))) != join(X_16,Y)
| join(join(X_16,Y),X_16) = join(X_16,Y) ),
inference(resolve,[$cnf( $equal(meet(X_16,join(X_16,Y)),X_16) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
join(join(X_16,Y),X_16) = join(X_16,Y),
inference(resolve,[$cnf( $equal(join(join(X_16,Y),meet(X_16,join(X_16,Y))),join(X_16,Y)) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
join(join(X_16,Y),X_16) = join(X_16,join(Y,X_16)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_16)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_199,plain,
( join(join(X_16,Y),X_16) != join(X_16,Y)
| join(join(X_16,Y),X_16) != join(X_16,join(Y,X_16))
| join(X_16,join(Y,X_16)) = join(X_16,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_16,Y),X_16),join(X_16,Y)) ),[0],$fot(join(X_16,join(Y,X_16)))]]) ).
cnf(refute_0_200,plain,
( join(join(X_16,Y),X_16) != join(X_16,Y)
| join(X_16,join(Y,X_16)) = join(X_16,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_16,Y),X_16),join(X_16,join(Y,X_16))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
join(X_16,join(Y,X_16)) = join(X_16,Y),
inference(resolve,[$cnf( $equal(join(join(X_16,Y),X_16),join(X_16,Y)) )],[refute_0_197,refute_0_200]) ).
cnf(refute_0_202,plain,
join(Y,join(X_24,Y)) = join(Y,X_24),
inference(subst,[],[refute_0_201:[bind(Y,$fot(X_24)),bind(X_16,$fot(Y))]]) ).
cnf(refute_0_203,plain,
( join(Y,join(X_24,Y)) != join(Y,X_24)
| meet(join(X_24,Y),join(Y,join(X_24,Y))) != join(X_24,Y)
| meet(join(X_24,Y),join(Y,X_24)) = join(X_24,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_24,Y),join(Y,join(X_24,Y))),join(X_24,Y)) ),[0,1],$fot(join(Y,X_24))]]) ).
cnf(refute_0_204,plain,
( meet(join(X_24,Y),join(Y,join(X_24,Y))) != join(X_24,Y)
| meet(join(X_24,Y),join(Y,X_24)) = join(X_24,Y) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_24,Y)),join(Y,X_24)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
meet(join(X_24,Y),join(Y,X_24)) = join(X_24,Y),
inference(resolve,[$cnf( $equal(meet(join(X_24,Y),join(Y,join(X_24,Y))),join(X_24,Y)) )],[refute_0_192,refute_0_204]) ).
cnf(refute_0_206,plain,
meet(X_24,X_24) = X_24,
inference(subst,[],[idempotence_of_meet:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_207,plain,
join(Y,meet(X_24,X_24)) = join(Y,meet(X_24,X_24)),
introduced(tautology,[refl,[$fot(join(Y,meet(X_24,X_24)))]]) ).
cnf(refute_0_208,plain,
( join(Y,meet(X_24,X_24)) != join(Y,meet(X_24,X_24))
| meet(X_24,X_24) != X_24
| join(Y,meet(X_24,X_24)) = join(Y,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(Y,meet(X_24,X_24)),join(Y,meet(X_24,X_24))) ),[1,1],$fot(X_24)]]) ).
cnf(refute_0_209,plain,
( meet(X_24,X_24) != X_24
| join(Y,meet(X_24,X_24)) = join(Y,X_24) ),
inference(resolve,[$cnf( $equal(join(Y,meet(X_24,X_24)),join(Y,meet(X_24,X_24))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
join(Y,meet(X_24,X_24)) = join(Y,X_24),
inference(resolve,[$cnf( $equal(meet(X_24,X_24),X_24) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(join(X_24,Y),join(Y,X_24)) = join(Y,meet(X_24,X_24)),
inference(subst,[],[refute_0_112:[bind(X_82,$fot(Y)),bind(X_83,$fot(X_24)),bind(X_84,$fot(X_24))]]) ).
cnf(refute_0_212,plain,
( join(Y,meet(X_24,X_24)) != join(Y,X_24)
| meet(join(X_24,Y),join(Y,X_24)) != join(Y,meet(X_24,X_24))
| meet(join(X_24,Y),join(Y,X_24)) = join(Y,X_24) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(meet(join(X_24,Y),join(Y,X_24)))),bind(Y0,$fot(join(Y,meet(X_24,X_24)))),bind(Z0,$fot(join(Y,X_24)))]]) ).
cnf(refute_0_213,plain,
( join(Y,meet(X_24,X_24)) != join(Y,X_24)
| meet(join(X_24,Y),join(Y,X_24)) = join(Y,X_24) ),
inference(resolve,[$cnf( $equal(meet(join(X_24,Y),join(Y,X_24)),join(Y,meet(X_24,X_24))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
meet(join(X_24,Y),join(Y,X_24)) = join(Y,X_24),
inference(resolve,[$cnf( $equal(join(Y,meet(X_24,X_24)),join(Y,X_24)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( meet(join(X_24,Y),join(Y,X_24)) != join(Y,X_24)
| meet(join(X_24,Y),join(Y,X_24)) != join(X_24,Y)
| join(Y,X_24) = join(X_24,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_24,Y),join(Y,X_24)),join(X_24,Y)) ),[0],$fot(join(Y,X_24))]]) ).
cnf(refute_0_216,plain,
( meet(join(X_24,Y),join(Y,X_24)) != join(X_24,Y)
| join(Y,X_24) = join(X_24,Y) ),
inference(resolve,[$cnf( $equal(meet(join(X_24,Y),join(Y,X_24)),join(Y,X_24)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
join(Y,X_24) = join(X_24,Y),
inference(resolve,[$cnf( $equal(meet(join(X_24,Y),join(Y,X_24)),join(X_24,Y)) )],[refute_0_205,refute_0_216]) ).
cnf(refute_0_218,plain,
( join(Y,X_24) != join(X_24,Y)
| join(X_24,Y) = join(Y,X_24) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(Y,X_24))),bind(Y0,$fot(join(X_24,Y)))]]) ).
cnf(refute_0_219,plain,
join(X_24,Y) = join(Y,X_24),
inference(resolve,[$cnf( $equal(join(Y,X_24),join(X_24,Y)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
join(meet(xx,X_94),n0) = join(n0,meet(xx,X_94)),
inference(subst,[],[refute_0_219:[bind(Y,$fot(n0)),bind(X_24,$fot(meet(xx,X_94)))]]) ).
cnf(refute_0_221,plain,
( join(meet(xx,X_94),n0) != join(n0,meet(xx,X_94))
| join(n0,meet(xx,X_94)) != meet(xx,X_94)
| join(meet(xx,X_94),n0) = meet(xx,X_94) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(meet(xx,X_94),n0))),bind(Y0,$fot(join(n0,meet(xx,X_94)))),bind(Z0,$fot(meet(xx,X_94)))]]) ).
cnf(refute_0_222,plain,
( join(n0,meet(xx,X_94)) != meet(xx,X_94)
| join(meet(xx,X_94),n0) = meet(xx,X_94) ),
inference(resolve,[$cnf( $equal(join(meet(xx,X_94),n0),join(n0,meet(xx,X_94))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
join(meet(xx,X_94),n0) = meet(xx,X_94),
inference(resolve,[$cnf( $equal(join(n0,meet(xx,X_94)),meet(xx,X_94)) )],[refute_0_191,refute_0_222]) ).
cnf(refute_0_224,plain,
( join(meet(xx,X_94),n0) != meet(xx,X_94)
| meet(xx,join(X_94,yy)) != join(meet(xx,X_94),n0)
| meet(xx,join(X_94,yy)) = meet(xx,X_94) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(X_94,yy)),join(meet(xx,X_94),n0)) ),[1],$fot(meet(xx,X_94))]]) ).
cnf(refute_0_225,plain,
( meet(xx,join(X_94,yy)) != join(meet(xx,X_94),n0)
| meet(xx,join(X_94,yy)) = meet(xx,X_94) ),
inference(resolve,[$cnf( $equal(join(meet(xx,X_94),n0),meet(xx,X_94)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
meet(xx,join(X_94,yy)) = meet(xx,X_94),
inference(resolve,[$cnf( $equal(meet(xx,join(X_94,yy)),join(meet(xx,X_94),n0)) )],[refute_0_190,refute_0_225]) ).
cnf(refute_0_227,plain,
( join(join(X_94,yy),meet(X_101,meet(xx,join(X_94,yy)))) != join(X_94,yy)
| meet(xx,join(X_94,yy)) != meet(xx,X_94)
| join(join(X_94,yy),meet(X_101,meet(xx,X_94))) = join(X_94,yy) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_94,yy),meet(X_101,meet(xx,join(X_94,yy)))),join(X_94,yy)) ),[0,1,1],$fot(meet(xx,X_94))]]) ).
cnf(refute_0_228,plain,
( join(join(X_94,yy),meet(X_101,meet(xx,join(X_94,yy)))) != join(X_94,yy)
| join(join(X_94,yy),meet(X_101,meet(xx,X_94))) = join(X_94,yy) ),
inference(resolve,[$cnf( $equal(meet(xx,join(X_94,yy)),meet(xx,X_94)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
join(join(X_94,yy),meet(X_101,meet(xx,X_94))) = join(X_94,yy),
inference(resolve,[$cnf( $equal(join(join(X_94,yy),meet(X_101,meet(xx,join(X_94,yy)))),join(X_94,yy)) )],[refute_0_186,refute_0_228]) ).
cnf(refute_0_230,plain,
join(join(X_94,yy),meet(X_101,meet(xx,X_94))) = join(X_94,join(yy,meet(X_101,meet(xx,X_94)))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_94)),bind(Y,$fot(yy)),bind(Z,$fot(meet(X_101,meet(xx,X_94))))]]) ).
cnf(refute_0_231,plain,
( join(join(X_94,yy),meet(X_101,meet(xx,X_94))) != join(X_94,join(yy,meet(X_101,meet(xx,X_94))))
| join(join(X_94,yy),meet(X_101,meet(xx,X_94))) != join(X_94,yy)
| join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) = join(X_94,yy) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_94,yy),meet(X_101,meet(xx,X_94))),join(X_94,yy)) ),[0],$fot(join(X_94,join(yy,meet(X_101,meet(xx,X_94)))))]]) ).
cnf(refute_0_232,plain,
( join(join(X_94,yy),meet(X_101,meet(xx,X_94))) != join(X_94,yy)
| join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) = join(X_94,yy) ),
inference(resolve,[$cnf( $equal(join(join(X_94,yy),meet(X_101,meet(xx,X_94))),join(X_94,join(yy,meet(X_101,meet(xx,X_94))))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) = join(X_94,yy),
inference(resolve,[$cnf( $equal(join(join(X_94,yy),meet(X_101,meet(xx,X_94))),join(X_94,yy)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
join(X,join(X_32,X_33)) = join(join(X_32,X_33),X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_32,X_33)))]]) ).
cnf(refute_0_235,plain,
join(join(X_32,X_33),X) = join(X_32,join(X_33,X)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_32)),bind(Y,$fot(X_33)),bind(Z,$fot(X))]]) ).
cnf(refute_0_236,plain,
( join(X,join(X_32,X_33)) != join(join(X_32,X_33),X)
| join(join(X_32,X_33),X) != join(X_32,join(X_33,X))
| join(X,join(X_32,X_33)) = join(X_32,join(X_33,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_32,X_33)),join(X_32,join(X_33,X))) ),[0],$fot(join(join(X_32,X_33),X))]]) ).
cnf(refute_0_237,plain,
( join(X,join(X_32,X_33)) != join(join(X_32,X_33),X)
| join(X,join(X_32,X_33)) = join(X_32,join(X_33,X)) ),
inference(resolve,[$cnf( $equal(join(join(X_32,X_33),X),join(X_32,join(X_33,X))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
join(X,join(X_32,X_33)) = join(X_32,join(X_33,X)),
inference(resolve,[$cnf( $equal(join(X,join(X_32,X_33)),join(join(X_32,X_33),X)) )],[refute_0_234,refute_0_237]) ).
cnf(refute_0_239,plain,
join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) = join(X_111,join(X_112,meet(X_51,meet(X_52,X_112)))),
inference(subst,[],[refute_0_238:[bind(X,$fot(meet(X_51,meet(X_52,X_112)))),bind(X_32,$fot(X_111)),bind(X_33,$fot(X_112))]]) ).
cnf(refute_0_240,plain,
join(X_112,meet(X_51,meet(X_52,X_112))) = X_112,
inference(subst,[],[refute_0_126:[bind(X_13,$fot(X_112))]]) ).
cnf(refute_0_241,plain,
( join(X_112,meet(X_51,meet(X_52,X_112))) != X_112
| join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) != join(X_111,join(X_112,meet(X_51,meet(X_52,X_112))))
| join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) = join(X_111,X_112) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)),join(X_111,join(X_112,meet(X_51,meet(X_52,X_112))))) ),[1,1],$fot(X_112)]]) ).
cnf(refute_0_242,plain,
( join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) != join(X_111,join(X_112,meet(X_51,meet(X_52,X_112))))
| join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) = join(X_111,X_112) ),
inference(resolve,[$cnf( $equal(join(X_112,meet(X_51,meet(X_52,X_112))),X_112) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) = join(X_111,X_112),
inference(resolve,[$cnf( $equal(join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)),join(X_111,join(X_112,meet(X_51,meet(X_52,X_112))))) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
join(X_110,join(X_111,X_112)) = join(X_111,join(X_112,X_110)),
inference(subst,[],[refute_0_238:[bind(X,$fot(X_110)),bind(X_32,$fot(X_111)),bind(X_33,$fot(X_112))]]) ).
cnf(refute_0_245,plain,
join(X_112,X_111) = join(X_111,X_112),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_112)),bind(Y,$fot(X_111))]]) ).
cnf(refute_0_246,plain,
( join(X_112,X_111) != join(X_111,X_112)
| join(X_111,X_112) = join(X_112,X_111) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_112,X_111))),bind(Y0,$fot(join(X_111,X_112)))]]) ).
cnf(refute_0_247,plain,
join(X_111,X_112) = join(X_112,X_111),
inference(resolve,[$cnf( $equal(join(X_112,X_111),join(X_111,X_112)) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
( join(X_110,join(X_111,X_112)) != join(X_111,join(X_112,X_110))
| join(X_111,X_112) != join(X_112,X_111)
| join(X_110,join(X_112,X_111)) = join(X_111,join(X_112,X_110)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_110,join(X_111,X_112)),join(X_111,join(X_112,X_110))) ),[0,1],$fot(join(X_112,X_111))]]) ).
cnf(refute_0_249,plain,
( join(X_110,join(X_111,X_112)) != join(X_111,join(X_112,X_110))
| join(X_110,join(X_112,X_111)) = join(X_111,join(X_112,X_110)) ),
inference(resolve,[$cnf( $equal(join(X_111,X_112),join(X_112,X_111)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
join(X_110,join(X_112,X_111)) = join(X_111,join(X_112,X_110)),
inference(resolve,[$cnf( $equal(join(X_110,join(X_111,X_112)),join(X_111,join(X_112,X_110))) )],[refute_0_244,refute_0_249]) ).
cnf(refute_0_251,plain,
( join(X_110,join(X_112,X_111)) != join(X_111,join(X_112,X_110))
| join(X_111,join(X_112,X_110)) = join(X_110,join(X_112,X_111)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_110,join(X_112,X_111)))),bind(Y0,$fot(join(X_111,join(X_112,X_110))))]]) ).
cnf(refute_0_252,plain,
join(X_111,join(X_112,X_110)) = join(X_110,join(X_112,X_111)),
inference(resolve,[$cnf( $equal(join(X_110,join(X_112,X_111)),join(X_111,join(X_112,X_110))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) = join(X_112,join(X_111,meet(X_51,meet(X_52,X_112)))),
inference(subst,[],[refute_0_252:[bind(X_110,$fot(X_112)),bind(X_111,$fot(meet(X_51,meet(X_52,X_112)))),bind(X_112,$fot(X_111))]]) ).
cnf(refute_0_254,plain,
( join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) != join(X_111,X_112)
| join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) != join(X_112,join(X_111,meet(X_51,meet(X_52,X_112))))
| join(X_112,join(X_111,meet(X_51,meet(X_52,X_112)))) = join(X_111,X_112) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)),join(X_111,X_112)) ),[0],$fot(join(X_112,join(X_111,meet(X_51,meet(X_52,X_112)))))]]) ).
cnf(refute_0_255,plain,
( join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)) != join(X_111,X_112)
| join(X_112,join(X_111,meet(X_51,meet(X_52,X_112)))) = join(X_111,X_112) ),
inference(resolve,[$cnf( $equal(join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)),join(X_112,join(X_111,meet(X_51,meet(X_52,X_112))))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
join(X_112,join(X_111,meet(X_51,meet(X_52,X_112)))) = join(X_111,X_112),
inference(resolve,[$cnf( $equal(join(meet(X_51,meet(X_52,X_112)),join(X_111,X_112)),join(X_111,X_112)) )],[refute_0_243,refute_0_255]) ).
cnf(refute_0_257,plain,
join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) = join(yy,X_94),
inference(subst,[],[refute_0_256:[bind(X_111,$fot(yy)),bind(X_112,$fot(X_94)),bind(X_51,$fot(X_101)),bind(X_52,$fot(xx))]]) ).
cnf(refute_0_258,plain,
( join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) != join(X_94,yy)
| join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) != join(yy,X_94)
| join(yy,X_94) = join(X_94,yy) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_94,join(yy,meet(X_101,meet(xx,X_94)))),join(X_94,yy)) ),[0],$fot(join(yy,X_94))]]) ).
cnf(refute_0_259,plain,
( join(X_94,join(yy,meet(X_101,meet(xx,X_94)))) != join(X_94,yy)
| join(yy,X_94) = join(X_94,yy) ),
inference(resolve,[$cnf( $equal(join(X_94,join(yy,meet(X_101,meet(xx,X_94)))),join(yy,X_94)) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
join(yy,X_94) = join(X_94,yy),
inference(resolve,[$cnf( $equal(join(X_94,join(yy,meet(X_101,meet(xx,X_94)))),join(X_94,yy)) )],[refute_0_233,refute_0_259]) ).
cnf(refute_0_261,plain,
join(yy,n0) = join(n0,yy),
inference(subst,[],[refute_0_260:[bind(X_94,$fot(n0))]]) ).
cnf(refute_0_262,plain,
( join(n0,yy) != yy
| join(yy,n0) != join(n0,yy)
| join(yy,n0) = yy ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(yy,n0))),bind(Y0,$fot(join(n0,yy))),bind(Z0,$fot(yy))]]) ).
cnf(refute_0_263,plain,
( join(n0,yy) != yy
| join(yy,n0) = yy ),
inference(resolve,[$cnf( $equal(join(yy,n0),join(n0,yy)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
join(yy,n0) = yy,
inference(resolve,[$cnf( $equal(join(n0,yy),yy) )],[refute_0_185,refute_0_263]) ).
cnf(refute_0_265,plain,
( join(yy,meet(X_55,zz)) != join(yy,n0)
| join(yy,n0) != yy
| join(yy,meet(X_55,zz)) = yy ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(yy,meet(X_55,zz)),yy) ),[0],$fot(join(yy,n0))]]) ).
cnf(refute_0_266,plain,
( join(yy,meet(X_55,zz)) != join(yy,n0)
| join(yy,meet(X_55,zz)) = yy ),
inference(resolve,[$cnf( $equal(join(yy,n0),yy) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
join(yy,meet(X_55,zz)) = yy,
inference(resolve,[$cnf( $equal(join(yy,meet(X_55,zz)),join(yy,n0)) )],[refute_0_180,refute_0_266]) ).
cnf(refute_0_268,plain,
join(yy,meet(X_52,zz)) = yy,
inference(subst,[],[refute_0_267:[bind(X_55,$fot(X_52))]]) ).
cnf(refute_0_269,plain,
join(zz,join(yy,X_95)) = join(zz,meet(xx,join(yy,X_95))),
inference(subst,[],[refute_0_120:[bind(X_83,$fot(join(yy,X_95)))]]) ).
cnf(refute_0_270,plain,
meet(xx,join(yy,X_95)) = join(meet(xx,yy),meet(xx,X_95)),
inference(subst,[],[dist_meet:[bind(X,$fot(xx)),bind(Y,$fot(yy)),bind(Z,$fot(X_95))]]) ).
cnf(refute_0_271,plain,
( meet(xx,join(yy,X_95)) != join(meet(xx,yy),meet(xx,X_95))
| meet(xx,yy) != n0
| meet(xx,join(yy,X_95)) = join(n0,meet(xx,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(yy,X_95)),join(meet(xx,yy),meet(xx,X_95))) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_272,plain,
( meet(xx,join(yy,X_95)) != join(meet(xx,yy),meet(xx,X_95))
| meet(xx,join(yy,X_95)) = join(n0,meet(xx,X_95)) ),
inference(resolve,[$cnf( $equal(meet(xx,yy),n0) )],[lhs3,refute_0_271]) ).
cnf(refute_0_273,plain,
meet(xx,join(yy,X_95)) = join(n0,meet(xx,X_95)),
inference(resolve,[$cnf( $equal(meet(xx,join(yy,X_95)),join(meet(xx,yy),meet(xx,X_95))) )],[refute_0_270,refute_0_272]) ).
cnf(refute_0_274,plain,
join(n0,meet(xx,X_95)) = meet(xx,X_95),
inference(subst,[],[refute_0_184:[bind(X,$fot(meet(xx,X_95)))]]) ).
cnf(refute_0_275,plain,
( join(n0,meet(xx,X_95)) != meet(xx,X_95)
| meet(xx,join(yy,X_95)) != join(n0,meet(xx,X_95))
| meet(xx,join(yy,X_95)) = meet(xx,X_95) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(yy,X_95)),join(n0,meet(xx,X_95))) ),[1],$fot(meet(xx,X_95))]]) ).
cnf(refute_0_276,plain,
( meet(xx,join(yy,X_95)) != join(n0,meet(xx,X_95))
| meet(xx,join(yy,X_95)) = meet(xx,X_95) ),
inference(resolve,[$cnf( $equal(join(n0,meet(xx,X_95)),meet(xx,X_95)) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
meet(xx,join(yy,X_95)) = meet(xx,X_95),
inference(resolve,[$cnf( $equal(meet(xx,join(yy,X_95)),join(n0,meet(xx,X_95))) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( join(zz,join(yy,X_95)) != join(zz,meet(xx,join(yy,X_95)))
| meet(xx,join(yy,X_95)) != meet(xx,X_95)
| join(zz,join(yy,X_95)) = join(zz,meet(xx,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zz,join(yy,X_95)),join(zz,meet(xx,join(yy,X_95)))) ),[1,1],$fot(meet(xx,X_95))]]) ).
cnf(refute_0_279,plain,
( join(zz,join(yy,X_95)) != join(zz,meet(xx,join(yy,X_95)))
| join(zz,join(yy,X_95)) = join(zz,meet(xx,X_95)) ),
inference(resolve,[$cnf( $equal(meet(xx,join(yy,X_95)),meet(xx,X_95)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
join(zz,join(yy,X_95)) = join(zz,meet(xx,X_95)),
inference(resolve,[$cnf( $equal(join(zz,join(yy,X_95)),join(zz,meet(xx,join(yy,X_95)))) )],[refute_0_269,refute_0_279]) ).
cnf(refute_0_281,plain,
join(yy,join(zz,X_95)) = join(yy,meet(xx,join(zz,X_95))),
inference(subst,[],[refute_0_155:[bind(X_83,$fot(join(zz,X_95)))]]) ).
cnf(refute_0_282,plain,
meet(xx,join(zz,X_95)) = join(meet(xx,zz),meet(xx,X_95)),
inference(subst,[],[dist_meet:[bind(X,$fot(xx)),bind(Y,$fot(zz)),bind(Z,$fot(X_95))]]) ).
cnf(refute_0_283,plain,
( meet(xx,join(zz,X_95)) != join(meet(xx,zz),meet(xx,X_95))
| meet(xx,zz) != n0
| meet(xx,join(zz,X_95)) = join(n0,meet(xx,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(zz,X_95)),join(meet(xx,zz),meet(xx,X_95))) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_284,plain,
( meet(xx,join(zz,X_95)) != join(meet(xx,zz),meet(xx,X_95))
| meet(xx,join(zz,X_95)) = join(n0,meet(xx,X_95)) ),
inference(resolve,[$cnf( $equal(meet(xx,zz),n0) )],[lhs4,refute_0_283]) ).
cnf(refute_0_285,plain,
meet(xx,join(zz,X_95)) = join(n0,meet(xx,X_95)),
inference(resolve,[$cnf( $equal(meet(xx,join(zz,X_95)),join(meet(xx,zz),meet(xx,X_95))) )],[refute_0_282,refute_0_284]) ).
cnf(refute_0_286,plain,
( join(n0,meet(xx,X_95)) != meet(xx,X_95)
| meet(xx,join(zz,X_95)) != join(n0,meet(xx,X_95))
| meet(xx,join(zz,X_95)) = meet(xx,X_95) ),
introduced(tautology,[equality,[$cnf( $equal(meet(xx,join(zz,X_95)),join(n0,meet(xx,X_95))) ),[1],$fot(meet(xx,X_95))]]) ).
cnf(refute_0_287,plain,
( meet(xx,join(zz,X_95)) != join(n0,meet(xx,X_95))
| meet(xx,join(zz,X_95)) = meet(xx,X_95) ),
inference(resolve,[$cnf( $equal(join(n0,meet(xx,X_95)),meet(xx,X_95)) )],[refute_0_274,refute_0_286]) ).
cnf(refute_0_288,plain,
meet(xx,join(zz,X_95)) = meet(xx,X_95),
inference(resolve,[$cnf( $equal(meet(xx,join(zz,X_95)),join(n0,meet(xx,X_95))) )],[refute_0_285,refute_0_287]) ).
cnf(refute_0_289,plain,
( join(yy,join(zz,X_95)) != join(yy,meet(xx,join(zz,X_95)))
| meet(xx,join(zz,X_95)) != meet(xx,X_95)
| join(yy,join(zz,X_95)) = join(yy,meet(xx,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,X_95)),join(yy,meet(xx,join(zz,X_95)))) ),[1,1],$fot(meet(xx,X_95))]]) ).
cnf(refute_0_290,plain,
( join(yy,join(zz,X_95)) != join(yy,meet(xx,join(zz,X_95)))
| join(yy,join(zz,X_95)) = join(yy,meet(xx,X_95)) ),
inference(resolve,[$cnf( $equal(meet(xx,join(zz,X_95)),meet(xx,X_95)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
join(yy,join(zz,X_95)) = join(yy,meet(xx,X_95)),
inference(resolve,[$cnf( $equal(join(yy,join(zz,X_95)),join(yy,meet(xx,join(zz,X_95)))) )],[refute_0_281,refute_0_290]) ).
cnf(refute_0_292,plain,
( join(yy,X_83) != join(yy,meet(xx,X_83))
| join(yy,meet(xx,X_83)) = join(yy,X_83) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(yy,X_83))),bind(Y0,$fot(join(yy,meet(xx,X_83))))]]) ).
cnf(refute_0_293,plain,
join(yy,meet(xx,X_83)) = join(yy,X_83),
inference(resolve,[$cnf( $equal(join(yy,X_83),join(yy,meet(xx,X_83))) )],[refute_0_155,refute_0_292]) ).
cnf(refute_0_294,plain,
join(yy,meet(xx,X_95)) = join(yy,X_95),
inference(subst,[],[refute_0_293:[bind(X_83,$fot(X_95))]]) ).
cnf(refute_0_295,plain,
( join(yy,join(zz,X_95)) != join(yy,meet(xx,X_95))
| join(yy,meet(xx,X_95)) != join(yy,X_95)
| join(yy,join(zz,X_95)) = join(yy,X_95) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(yy,join(zz,X_95)),join(yy,X_95)) ),[0],$fot(join(yy,meet(xx,X_95)))]]) ).
cnf(refute_0_296,plain,
( join(yy,join(zz,X_95)) != join(yy,meet(xx,X_95))
| join(yy,join(zz,X_95)) = join(yy,X_95) ),
inference(resolve,[$cnf( $equal(join(yy,meet(xx,X_95)),join(yy,X_95)) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
join(yy,join(zz,X_95)) = join(yy,X_95),
inference(resolve,[$cnf( $equal(join(yy,join(zz,X_95)),join(yy,meet(xx,X_95))) )],[refute_0_291,refute_0_296]) ).
cnf(refute_0_298,plain,
join(join(X_112,X_24),join(X_111,X_112)) = join(X_111,join(X_112,join(X_112,X_24))),
inference(subst,[],[refute_0_238:[bind(X,$fot(join(X_112,X_24))),bind(X_32,$fot(X_111)),bind(X_33,$fot(X_112))]]) ).
cnf(refute_0_299,plain,
join(X_25,join(X_24,X_25)) = join(X_25,X_24),
inference(subst,[],[refute_0_201:[bind(Y,$fot(X_24)),bind(X_16,$fot(X_25))]]) ).
cnf(refute_0_300,plain,
join(X_25,X_24) = join(X_24,X_25),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_301,plain,
( join(X_25,X_24) != join(X_24,X_25)
| join(X_24,X_25) = join(X_25,X_24) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_25,X_24))),bind(Y0,$fot(join(X_24,X_25)))]]) ).
cnf(refute_0_302,plain,
join(X_24,X_25) = join(X_25,X_24),
inference(resolve,[$cnf( $equal(join(X_25,X_24),join(X_24,X_25)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
( join(X_24,X_25) != join(X_25,X_24)
| join(X_25,join(X_24,X_25)) != join(X_25,X_24)
| join(X_25,join(X_25,X_24)) = join(X_25,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_25,join(X_24,X_25)),join(X_25,X_24)) ),[0,1],$fot(join(X_25,X_24))]]) ).
cnf(refute_0_304,plain,
( join(X_25,join(X_24,X_25)) != join(X_25,X_24)
| join(X_25,join(X_25,X_24)) = join(X_25,X_24) ),
inference(resolve,[$cnf( $equal(join(X_24,X_25),join(X_25,X_24)) )],[refute_0_302,refute_0_303]) ).
cnf(refute_0_305,plain,
join(X_25,join(X_25,X_24)) = join(X_25,X_24),
inference(resolve,[$cnf( $equal(join(X_25,join(X_24,X_25)),join(X_25,X_24)) )],[refute_0_299,refute_0_304]) ).
cnf(refute_0_306,plain,
join(X_112,join(X_112,X_24)) = join(X_112,X_24),
inference(subst,[],[refute_0_305:[bind(X_25,$fot(X_112))]]) ).
cnf(refute_0_307,plain,
( join(X_112,join(X_112,X_24)) != join(X_112,X_24)
| join(join(X_112,X_24),join(X_111,X_112)) != join(X_111,join(X_112,join(X_112,X_24)))
| join(join(X_112,X_24),join(X_111,X_112)) = join(X_111,join(X_112,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_111,join(X_112,join(X_112,X_24)))) ),[1,1],$fot(join(X_112,X_24))]]) ).
cnf(refute_0_308,plain,
( join(join(X_112,X_24),join(X_111,X_112)) != join(X_111,join(X_112,join(X_112,X_24)))
| join(join(X_112,X_24),join(X_111,X_112)) = join(X_111,join(X_112,X_24)) ),
inference(resolve,[$cnf( $equal(join(X_112,join(X_112,X_24)),join(X_112,X_24)) )],[refute_0_306,refute_0_307]) ).
cnf(refute_0_309,plain,
join(join(X_112,X_24),join(X_111,X_112)) = join(X_111,join(X_112,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_111,join(X_112,join(X_112,X_24)))) )],[refute_0_298,refute_0_308]) ).
cnf(refute_0_310,plain,
join(join(X_32,join(Y,X_32)),X_34) = join(X_32,join(join(Y,X_32),X_34)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_32)),bind(Y,$fot(join(Y,X_32))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_311,plain,
join(X_32,join(Y,X_32)) = join(X_32,Y),
inference(subst,[],[refute_0_201:[bind(X_16,$fot(X_32))]]) ).
cnf(refute_0_312,plain,
( join(X_32,join(Y,X_32)) != join(X_32,Y)
| join(join(X_32,join(Y,X_32)),X_34) != join(X_32,join(join(Y,X_32),X_34))
| join(join(X_32,Y),X_34) = join(X_32,join(join(Y,X_32),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_32,join(Y,X_32)),X_34),join(X_32,join(join(Y,X_32),X_34))) ),[0,0],$fot(join(X_32,Y))]]) ).
cnf(refute_0_313,plain,
( join(join(X_32,join(Y,X_32)),X_34) != join(X_32,join(join(Y,X_32),X_34))
| join(join(X_32,Y),X_34) = join(X_32,join(join(Y,X_32),X_34)) ),
inference(resolve,[$cnf( $equal(join(X_32,join(Y,X_32)),join(X_32,Y)) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
join(join(X_32,Y),X_34) = join(X_32,join(join(Y,X_32),X_34)),
inference(resolve,[$cnf( $equal(join(join(X_32,join(Y,X_32)),X_34),join(X_32,join(join(Y,X_32),X_34))) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
join(join(X_32,Y),X_34) = join(X_32,join(Y,X_34)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_32)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_316,plain,
( join(join(X_32,Y),X_34) != join(X_32,join(Y,X_34))
| join(join(X_32,Y),X_34) != join(X_32,join(join(Y,X_32),X_34))
| join(X_32,join(Y,X_34)) = join(X_32,join(join(Y,X_32),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_32,Y),X_34),join(X_32,join(join(Y,X_32),X_34))) ),[0],$fot(join(X_32,join(Y,X_34)))]]) ).
cnf(refute_0_317,plain,
( join(join(X_32,Y),X_34) != join(X_32,join(join(Y,X_32),X_34))
| join(X_32,join(Y,X_34)) = join(X_32,join(join(Y,X_32),X_34)) ),
inference(resolve,[$cnf( $equal(join(join(X_32,Y),X_34),join(X_32,join(Y,X_34))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
join(join(Y,X_32),X_34) = join(Y,join(X_32,X_34)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(Y)),bind(Y,$fot(X_32)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_319,plain,
join(X_32,join(join(Y,X_32),X_34)) = join(X_32,join(join(Y,X_32),X_34)),
introduced(tautology,[refl,[$fot(join(X_32,join(join(Y,X_32),X_34)))]]) ).
cnf(refute_0_320,plain,
( join(X_32,join(join(Y,X_32),X_34)) != join(X_32,join(join(Y,X_32),X_34))
| join(join(Y,X_32),X_34) != join(Y,join(X_32,X_34))
| join(X_32,join(join(Y,X_32),X_34)) = join(X_32,join(Y,join(X_32,X_34))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_32,join(join(Y,X_32),X_34)),join(X_32,join(join(Y,X_32),X_34))) ),[1,1],$fot(join(Y,join(X_32,X_34)))]]) ).
cnf(refute_0_321,plain,
( join(join(Y,X_32),X_34) != join(Y,join(X_32,X_34))
| join(X_32,join(join(Y,X_32),X_34)) = join(X_32,join(Y,join(X_32,X_34))) ),
inference(resolve,[$cnf( $equal(join(X_32,join(join(Y,X_32),X_34)),join(X_32,join(join(Y,X_32),X_34))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
join(X_32,join(join(Y,X_32),X_34)) = join(X_32,join(Y,join(X_32,X_34))),
inference(resolve,[$cnf( $equal(join(join(Y,X_32),X_34),join(Y,join(X_32,X_34))) )],[refute_0_318,refute_0_321]) ).
cnf(refute_0_323,plain,
( join(X_32,join(Y,X_34)) != join(X_32,join(join(Y,X_32),X_34))
| join(X_32,join(join(Y,X_32),X_34)) != join(X_32,join(Y,join(X_32,X_34)))
| join(X_32,join(Y,X_34)) = join(X_32,join(Y,join(X_32,X_34))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_32,join(Y,X_34)),join(X_32,join(Y,join(X_32,X_34)))) ),[0],$fot(join(X_32,join(join(Y,X_32),X_34)))]]) ).
cnf(refute_0_324,plain,
( join(X_32,join(Y,X_34)) != join(X_32,join(join(Y,X_32),X_34))
| join(X_32,join(Y,X_34)) = join(X_32,join(Y,join(X_32,X_34))) ),
inference(resolve,[$cnf( $equal(join(X_32,join(join(Y,X_32),X_34)),join(X_32,join(Y,join(X_32,X_34)))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
( join(join(X_32,Y),X_34) != join(X_32,join(join(Y,X_32),X_34))
| join(X_32,join(Y,X_34)) = join(X_32,join(Y,join(X_32,X_34))) ),
inference(resolve,[$cnf( $equal(join(X_32,join(Y,X_34)),join(X_32,join(join(Y,X_32),X_34))) )],[refute_0_317,refute_0_324]) ).
cnf(refute_0_326,plain,
join(X_32,join(Y,X_34)) = join(X_32,join(Y,join(X_32,X_34))),
inference(resolve,[$cnf( $equal(join(join(X_32,Y),X_34),join(X_32,join(join(Y,X_32),X_34))) )],[refute_0_314,refute_0_325]) ).
cnf(refute_0_327,plain,
( join(X_32,join(Y,X_34)) != join(X_32,join(Y,join(X_32,X_34)))
| join(X_32,join(Y,join(X_32,X_34))) = join(X_32,join(Y,X_34)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_32,join(Y,X_34)))),bind(Y0,$fot(join(X_32,join(Y,join(X_32,X_34)))))]]) ).
cnf(refute_0_328,plain,
join(X_32,join(Y,join(X_32,X_34))) = join(X_32,join(Y,X_34)),
inference(resolve,[$cnf( $equal(join(X_32,join(Y,X_34)),join(X_32,join(Y,join(X_32,X_34)))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
join(X_112,join(X_111,join(X_112,X_24))) = join(X_112,join(X_111,X_24)),
inference(subst,[],[refute_0_328:[bind(Y,$fot(X_111)),bind(X_32,$fot(X_112)),bind(X_34,$fot(X_24))]]) ).
cnf(refute_0_330,plain,
join(join(X_112,X_24),join(X_111,X_112)) = join(X_112,join(X_111,join(X_112,X_24))),
inference(subst,[],[refute_0_252:[bind(X_110,$fot(X_112)),bind(X_111,$fot(join(X_112,X_24))),bind(X_112,$fot(X_111))]]) ).
cnf(refute_0_331,plain,
( join(X_112,join(X_111,join(X_112,X_24))) != join(X_112,join(X_111,X_24))
| join(join(X_112,X_24),join(X_111,X_112)) != join(X_112,join(X_111,join(X_112,X_24)))
| join(join(X_112,X_24),join(X_111,X_112)) = join(X_112,join(X_111,X_24)) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(join(X_112,X_24),join(X_111,X_112)))),bind(Y0,$fot(join(X_112,join(X_111,join(X_112,X_24))))),bind(Z0,$fot(join(X_112,join(X_111,X_24))))]]) ).
cnf(refute_0_332,plain,
( join(X_112,join(X_111,join(X_112,X_24))) != join(X_112,join(X_111,X_24))
| join(join(X_112,X_24),join(X_111,X_112)) = join(X_112,join(X_111,X_24)) ),
inference(resolve,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_112,join(X_111,join(X_112,X_24)))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
join(join(X_112,X_24),join(X_111,X_112)) = join(X_112,join(X_111,X_24)),
inference(resolve,[$cnf( $equal(join(X_112,join(X_111,join(X_112,X_24))),join(X_112,join(X_111,X_24))) )],[refute_0_329,refute_0_332]) ).
cnf(refute_0_334,plain,
( join(join(X_112,X_24),join(X_111,X_112)) != join(X_111,join(X_112,X_24))
| join(join(X_112,X_24),join(X_111,X_112)) != join(X_112,join(X_111,X_24))
| join(X_112,join(X_111,X_24)) = join(X_111,join(X_112,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_111,join(X_112,X_24))) ),[0],$fot(join(X_112,join(X_111,X_24)))]]) ).
cnf(refute_0_335,plain,
( join(join(X_112,X_24),join(X_111,X_112)) != join(X_111,join(X_112,X_24))
| join(X_112,join(X_111,X_24)) = join(X_111,join(X_112,X_24)) ),
inference(resolve,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_112,join(X_111,X_24))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
join(X_112,join(X_111,X_24)) = join(X_111,join(X_112,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_112,X_24),join(X_111,X_112)),join(X_111,join(X_112,X_24))) )],[refute_0_309,refute_0_335]) ).
cnf(refute_0_337,plain,
( join(X_112,join(X_111,X_24)) != join(X_111,join(X_112,X_24))
| join(X_111,join(X_112,X_24)) = join(X_112,join(X_111,X_24)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(X_112,join(X_111,X_24)))),bind(Y0,$fot(join(X_111,join(X_112,X_24))))]]) ).
cnf(refute_0_338,plain,
join(X_111,join(X_112,X_24)) = join(X_112,join(X_111,X_24)),
inference(resolve,[$cnf( $equal(join(X_112,join(X_111,X_24)),join(X_111,join(X_112,X_24))) )],[refute_0_336,refute_0_337]) ).
cnf(refute_0_339,plain,
join(zz,join(yy,X_95)) = join(yy,join(zz,X_95)),
inference(subst,[],[refute_0_338:[bind(X_111,$fot(zz)),bind(X_112,$fot(yy)),bind(X_24,$fot(X_95))]]) ).
cnf(refute_0_340,plain,
( join(yy,join(zz,X_95)) != join(yy,X_95)
| join(zz,join(yy,X_95)) != join(yy,join(zz,X_95))
| join(zz,join(yy,X_95)) = join(yy,X_95) ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(zz,join(yy,X_95)))),bind(Y0,$fot(join(yy,join(zz,X_95)))),bind(Z0,$fot(join(yy,X_95)))]]) ).
cnf(refute_0_341,plain,
( join(yy,join(zz,X_95)) != join(yy,X_95)
| join(zz,join(yy,X_95)) = join(yy,X_95) ),
inference(resolve,[$cnf( $equal(join(zz,join(yy,X_95)),join(yy,join(zz,X_95))) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
join(zz,join(yy,X_95)) = join(yy,X_95),
inference(resolve,[$cnf( $equal(join(yy,join(zz,X_95)),join(yy,X_95)) )],[refute_0_297,refute_0_341]) ).
cnf(refute_0_343,plain,
( join(zz,join(yy,X_95)) != join(yy,X_95)
| join(zz,join(yy,X_95)) != join(zz,meet(xx,X_95))
| join(yy,X_95) = join(zz,meet(xx,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zz,join(yy,X_95)),join(zz,meet(xx,X_95))) ),[0],$fot(join(yy,X_95))]]) ).
cnf(refute_0_344,plain,
( join(zz,join(yy,X_95)) != join(zz,meet(xx,X_95))
| join(yy,X_95) = join(zz,meet(xx,X_95)) ),
inference(resolve,[$cnf( $equal(join(zz,join(yy,X_95)),join(yy,X_95)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
( join(zz,X_83) != join(zz,meet(xx,X_83))
| join(zz,meet(xx,X_83)) = join(zz,X_83) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(zz,X_83))),bind(Y0,$fot(join(zz,meet(xx,X_83))))]]) ).
cnf(refute_0_346,plain,
join(zz,meet(xx,X_83)) = join(zz,X_83),
inference(resolve,[$cnf( $equal(join(zz,X_83),join(zz,meet(xx,X_83))) )],[refute_0_120,refute_0_345]) ).
cnf(refute_0_347,plain,
join(zz,meet(xx,X_95)) = join(zz,X_95),
inference(subst,[],[refute_0_346:[bind(X_83,$fot(X_95))]]) ).
cnf(refute_0_348,plain,
( join(yy,X_95) != join(zz,meet(xx,X_95))
| join(zz,meet(xx,X_95)) != join(zz,X_95)
| join(yy,X_95) = join(zz,X_95) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(yy,X_95),join(zz,X_95)) ),[0],$fot(join(zz,meet(xx,X_95)))]]) ).
cnf(refute_0_349,plain,
( join(yy,X_95) != join(zz,meet(xx,X_95))
| join(yy,X_95) = join(zz,X_95) ),
inference(resolve,[$cnf( $equal(join(zz,meet(xx,X_95)),join(zz,X_95)) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
( join(zz,join(yy,X_95)) != join(zz,meet(xx,X_95))
| join(yy,X_95) = join(zz,X_95) ),
inference(resolve,[$cnf( $equal(join(yy,X_95),join(zz,meet(xx,X_95))) )],[refute_0_344,refute_0_349]) ).
cnf(refute_0_351,plain,
join(yy,X_95) = join(zz,X_95),
inference(resolve,[$cnf( $equal(join(zz,join(yy,X_95)),join(zz,meet(xx,X_95))) )],[refute_0_280,refute_0_350]) ).
cnf(refute_0_352,plain,
( join(yy,X_95) != join(zz,X_95)
| join(zz,X_95) = join(yy,X_95) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(join(yy,X_95))),bind(Y0,$fot(join(zz,X_95)))]]) ).
cnf(refute_0_353,plain,
join(zz,X_95) = join(yy,X_95),
inference(resolve,[$cnf( $equal(join(yy,X_95),join(zz,X_95)) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
join(zz,meet(X_52,zz)) = join(yy,meet(X_52,zz)),
inference(subst,[],[refute_0_353:[bind(X_95,$fot(meet(X_52,zz)))]]) ).
cnf(refute_0_355,plain,
( join(yy,meet(X_52,zz)) != yy
| join(zz,meet(X_52,zz)) != join(yy,meet(X_52,zz))
| join(zz,meet(X_52,zz)) = yy ),
inference(subst,[],[refute_0_63:[bind(X0,$fot(join(zz,meet(X_52,zz)))),bind(Y0,$fot(join(yy,meet(X_52,zz)))),bind(Z0,$fot(yy))]]) ).
cnf(refute_0_356,plain,
( join(yy,meet(X_52,zz)) != yy
| join(zz,meet(X_52,zz)) = yy ),
inference(resolve,[$cnf( $equal(join(zz,meet(X_52,zz)),join(yy,meet(X_52,zz))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
join(zz,meet(X_52,zz)) = yy,
inference(resolve,[$cnf( $equal(join(yy,meet(X_52,zz)),yy) )],[refute_0_268,refute_0_356]) ).
cnf(refute_0_358,plain,
( join(zz,meet(X_52,zz)) != yy
| join(zz,meet(X_52,zz)) != zz
| yy = zz ),
introduced(tautology,[equality,[$cnf( $equal(join(zz,meet(X_52,zz)),zz) ),[0],$fot(yy)]]) ).
cnf(refute_0_359,plain,
( join(zz,meet(X_52,zz)) != zz
| yy = zz ),
inference(resolve,[$cnf( $equal(join(zz,meet(X_52,zz)),yy) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
yy = zz,
inference(resolve,[$cnf( $equal(join(zz,meet(X_52,zz)),zz) )],[refute_0_130,refute_0_359]) ).
cnf(refute_0_361,plain,
$false,
inference(resolve,[$cnf( $equal(yy,zz) )],[refute_0_360,rhs]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT037-1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n019.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Thu Jun 30 13:11:23 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.40/1.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.40/1.56
% 1.40/1.56 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.40/1.59
%------------------------------------------------------------------------------