TSTP Solution File: LAT028-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:58:59 EDT 2022
% Result : Unsatisfiable 1.67s 1.84s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 68
% Syntax : Number of clauses : 261 ( 139 unt; 0 nHn; 126 RR)
% Number of literals : 438 ( 437 equ; 179 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 609 ( 55 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_meet,axiom,
meet(X,X) = X ).
cnf(idempotence_of_join,axiom,
join(X,X) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(wal_1,axiom,
meet(meet(join(X,Y),join(Z,Y)),Y) = Y ).
cnf(wal_2,axiom,
join(join(meet(X,Y),meet(Z,Y)),Y) = Y ).
cnf(idempotence_of_meet2,axiom,
meet2(X,X) = X ).
cnf(commutativity_of_meet2,axiom,
meet2(X,Y) = meet2(Y,X) ).
cnf(wal_1_2,axiom,
meet2(meet2(join(X,Y),join(Z,Y)),Y) = Y ).
cnf(wal_2_2,axiom,
join(join(meet2(X,Y),meet2(Z,Y)),Y) = Y ).
cnf(name,negated_conjecture,
meet(a,b) != meet2(a,b) ).
cnf(refute_0_0,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_1,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_2,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( meet(X,Y) != meet(Y,X)
| meet(Y,X) = meet(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,Y))),bind(Y0,$fot(meet(Y,X)))]]) ).
cnf(refute_0_4,plain,
meet(Y,X) = meet(X,Y),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_3]) ).
cnf(refute_0_5,plain,
meet(meet(join(X,Y),join(Z,Y)),Y) = meet(Y,meet(join(X,Y),join(Z,Y))),
inference(subst,[],[refute_0_4:[bind(X,$fot(Y)),bind(Y,$fot(meet(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_6,plain,
( meet(meet(join(X,Y),join(Z,Y)),Y) != Y
| meet(meet(join(X,Y),join(Z,Y)),Y) != meet(Y,meet(join(X,Y),join(Z,Y)))
| meet(Y,meet(join(X,Y),join(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),Y) ),[0],$fot(meet(Y,meet(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_7,plain,
( meet(meet(join(X,Y),join(Z,Y)),Y) != Y
| meet(Y,meet(join(X,Y),join(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),meet(Y,meet(join(X,Y),join(Z,Y)))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
meet(Y,meet(join(X,Y),join(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(meet(meet(join(X,Y),join(Z,Y)),Y),Y) )],[wal_1,refute_0_7]) ).
cnf(refute_0_9,plain,
meet(meet2(X,X_48),meet(join(X,meet2(X,X_48)),join(Z,meet2(X,X_48)))) = meet2(X,X_48),
inference(subst,[],[refute_0_8:[bind(Y,$fot(meet2(X,X_48)))]]) ).
cnf(refute_0_10,plain,
( join(X,Y) != join(Y,X)
| join(Y,X) = join(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).
cnf(refute_0_11,plain,
join(Y,X) = join(X,Y),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_10]) ).
cnf(refute_0_12,plain,
join(join(meet2(X,Y),meet2(Z,Y)),Y) = join(Y,join(meet2(X,Y),meet2(Z,Y))),
inference(subst,[],[refute_0_11:[bind(X,$fot(Y)),bind(Y,$fot(join(meet2(X,Y),meet2(Z,Y))))]]) ).
cnf(refute_0_13,plain,
( join(join(meet2(X,Y),meet2(Z,Y)),Y) != Y
| join(join(meet2(X,Y),meet2(Z,Y)),Y) != join(Y,join(meet2(X,Y),meet2(Z,Y)))
| join(Y,join(meet2(X,Y),meet2(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet2(X,Y),meet2(Z,Y)),Y),Y) ),[0],$fot(join(Y,join(meet2(X,Y),meet2(Z,Y))))]]) ).
cnf(refute_0_14,plain,
( join(join(meet2(X,Y),meet2(Z,Y)),Y) != Y
| join(Y,join(meet2(X,Y),meet2(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(join(join(meet2(X,Y),meet2(Z,Y)),Y),join(Y,join(meet2(X,Y),meet2(Z,Y)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(Y,join(meet2(X,Y),meet2(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(join(join(meet2(X,Y),meet2(Z,Y)),Y),Y) )],[wal_2_2,refute_0_14]) ).
cnf(refute_0_16,plain,
join(X_31,join(meet2(X_30,X_31),meet2(X_31,X_31))) = X_31,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_30)),bind(Y,$fot(X_31)),bind(Z,$fot(X_31))]]) ).
cnf(refute_0_17,plain,
meet2(X_31,X_31) = X_31,
inference(subst,[],[idempotence_of_meet2:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_18,plain,
( join(X_31,join(meet2(X_30,X_31),meet2(X_31,X_31))) != X_31
| meet2(X_31,X_31) != X_31
| join(X_31,join(meet2(X_30,X_31),X_31)) = X_31 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),meet2(X_31,X_31))),X_31) ),[0,1,1],$fot(X_31)]]) ).
cnf(refute_0_19,plain,
( join(X_31,join(meet2(X_30,X_31),meet2(X_31,X_31))) != X_31
| join(X_31,join(meet2(X_30,X_31),X_31)) = X_31 ),
inference(resolve,[$cnf( $equal(meet2(X_31,X_31),X_31) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
join(X_31,join(meet2(X_30,X_31),X_31)) = X_31,
inference(resolve,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),meet2(X_31,X_31))),X_31) )],[refute_0_16,refute_0_19]) ).
cnf(refute_0_21,plain,
join(meet2(X_30,X_31),X_31) = join(X_31,meet2(X_30,X_31)),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_31)),bind(Y,$fot(meet2(X_30,X_31)))]]) ).
cnf(refute_0_22,plain,
join(join(meet(X,Y),meet(Z,Y)),Y) = join(Y,join(meet(X,Y),meet(Z,Y))),
inference(subst,[],[refute_0_11:[bind(X,$fot(Y)),bind(Y,$fot(join(meet(X,Y),meet(Z,Y))))]]) ).
cnf(refute_0_23,plain,
( join(join(meet(X,Y),meet(Z,Y)),Y) != Y
| join(join(meet(X,Y),meet(Z,Y)),Y) != join(Y,join(meet(X,Y),meet(Z,Y)))
| join(Y,join(meet(X,Y),meet(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),Y) ),[0],$fot(join(Y,join(meet(X,Y),meet(Z,Y))))]]) ).
cnf(refute_0_24,plain,
( join(join(meet(X,Y),meet(Z,Y)),Y) != Y
| join(Y,join(meet(X,Y),meet(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),join(Y,join(meet(X,Y),meet(Z,Y)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
join(Y,join(meet(X,Y),meet(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(join(join(meet(X,Y),meet(Z,Y)),Y),Y) )],[wal_2,refute_0_24]) ).
cnf(refute_0_26,plain,
join(X_17,join(meet(X_18,X_17),meet(X_18,X_17))) = X_17,
inference(subst,[],[refute_0_25:[bind(X,$fot(X_18)),bind(Y,$fot(X_17)),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_27,plain,
join(meet(X_18,X_17),meet(X_18,X_17)) = meet(X_18,X_17),
inference(subst,[],[idempotence_of_join:[bind(X,$fot(meet(X_18,X_17)))]]) ).
cnf(refute_0_28,plain,
( join(X_17,join(meet(X_18,X_17),meet(X_18,X_17))) != X_17
| join(meet(X_18,X_17),meet(X_18,X_17)) != meet(X_18,X_17)
| join(X_17,meet(X_18,X_17)) = X_17 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_17,join(meet(X_18,X_17),meet(X_18,X_17))),X_17) ),[0,1],$fot(meet(X_18,X_17))]]) ).
cnf(refute_0_29,plain,
( join(X_17,join(meet(X_18,X_17),meet(X_18,X_17))) != X_17
| join(X_17,meet(X_18,X_17)) = X_17 ),
inference(resolve,[$cnf( $equal(join(meet(X_18,X_17),meet(X_18,X_17)),meet(X_18,X_17)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
join(X_17,meet(X_18,X_17)) = X_17,
inference(resolve,[$cnf( $equal(join(X_17,join(meet(X_18,X_17),meet(X_18,X_17))),X_17) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
join(join(X_11,X_20),meet(X_20,join(X_11,X_20))) = join(X_11,X_20),
inference(subst,[],[refute_0_30:[bind(X_17,$fot(join(X_11,X_20))),bind(X_18,$fot(X_20))]]) ).
cnf(refute_0_32,plain,
meet(X_10,meet(join(X_11,X_10),join(X_11,X_10))) = X_10,
inference(subst,[],[refute_0_8:[bind(X,$fot(X_11)),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_33,plain,
meet(join(X_11,X_10),join(X_11,X_10)) = join(X_11,X_10),
inference(subst,[],[idempotence_of_meet:[bind(X,$fot(join(X_11,X_10)))]]) ).
cnf(refute_0_34,plain,
( meet(X_10,meet(join(X_11,X_10),join(X_11,X_10))) != X_10
| meet(join(X_11,X_10),join(X_11,X_10)) != join(X_11,X_10)
| meet(X_10,join(X_11,X_10)) = X_10 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_10,meet(join(X_11,X_10),join(X_11,X_10))),X_10) ),[0,1],$fot(join(X_11,X_10))]]) ).
cnf(refute_0_35,plain,
( meet(X_10,meet(join(X_11,X_10),join(X_11,X_10))) != X_10
| meet(X_10,join(X_11,X_10)) = X_10 ),
inference(resolve,[$cnf( $equal(meet(join(X_11,X_10),join(X_11,X_10)),join(X_11,X_10)) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(X_10,join(X_11,X_10)) = X_10,
inference(resolve,[$cnf( $equal(meet(X_10,meet(join(X_11,X_10),join(X_11,X_10))),X_10) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
meet(X_20,join(X_11,X_20)) = X_20,
inference(subst,[],[refute_0_36:[bind(X_10,$fot(X_20))]]) ).
cnf(refute_0_38,plain,
( join(join(X_11,X_20),meet(X_20,join(X_11,X_20))) != join(X_11,X_20)
| meet(X_20,join(X_11,X_20)) != X_20
| join(join(X_11,X_20),X_20) = join(X_11,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_11,X_20),meet(X_20,join(X_11,X_20))),join(X_11,X_20)) ),[0,1],$fot(X_20)]]) ).
cnf(refute_0_39,plain,
( join(join(X_11,X_20),meet(X_20,join(X_11,X_20))) != join(X_11,X_20)
| join(join(X_11,X_20),X_20) = join(X_11,X_20) ),
inference(resolve,[$cnf( $equal(meet(X_20,join(X_11,X_20)),X_20) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
join(join(X_11,X_20),X_20) = join(X_11,X_20),
inference(resolve,[$cnf( $equal(join(join(X_11,X_20),meet(X_20,join(X_11,X_20))),join(X_11,X_20)) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
join(join(X_11,X_20),X_20) = join(X_20,join(X_11,X_20)),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_20)),bind(Y,$fot(join(X_11,X_20)))]]) ).
cnf(refute_0_42,plain,
( join(join(X_11,X_20),X_20) != join(X_11,X_20)
| join(join(X_11,X_20),X_20) != join(X_20,join(X_11,X_20))
| join(X_20,join(X_11,X_20)) = join(X_11,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_11,X_20),X_20),join(X_11,X_20)) ),[0],$fot(join(X_20,join(X_11,X_20)))]]) ).
cnf(refute_0_43,plain,
( join(join(X_11,X_20),X_20) != join(X_11,X_20)
| join(X_20,join(X_11,X_20)) = join(X_11,X_20) ),
inference(resolve,[$cnf( $equal(join(join(X_11,X_20),X_20),join(X_20,join(X_11,X_20))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
join(X_20,join(X_11,X_20)) = join(X_11,X_20),
inference(resolve,[$cnf( $equal(join(join(X_11,X_20),X_20),join(X_11,X_20)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
join(X_31,join(meet2(X_30,X_31),X_31)) = join(meet2(X_30,X_31),X_31),
inference(subst,[],[refute_0_44:[bind(X_11,$fot(meet2(X_30,X_31))),bind(X_20,$fot(X_31))]]) ).
cnf(refute_0_46,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_47,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_46]) ).
cnf(refute_0_48,plain,
( join(X_31,join(meet2(X_30,X_31),X_31)) != join(meet2(X_30,X_31),X_31)
| join(meet2(X_30,X_31),X_31) != join(X_31,meet2(X_30,X_31))
| join(X_31,join(meet2(X_30,X_31),X_31)) = join(X_31,meet2(X_30,X_31)) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(join(X_31,join(meet2(X_30,X_31),X_31)))),bind(Y0,$fot(join(meet2(X_30,X_31),X_31))),bind(Z0,$fot(join(X_31,meet2(X_30,X_31))))]]) ).
cnf(refute_0_49,plain,
( join(meet2(X_30,X_31),X_31) != join(X_31,meet2(X_30,X_31))
| join(X_31,join(meet2(X_30,X_31),X_31)) = join(X_31,meet2(X_30,X_31)) ),
inference(resolve,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),X_31)),join(meet2(X_30,X_31),X_31)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
join(X_31,join(meet2(X_30,X_31),X_31)) = join(X_31,meet2(X_30,X_31)),
inference(resolve,[$cnf( $equal(join(meet2(X_30,X_31),X_31),join(X_31,meet2(X_30,X_31))) )],[refute_0_21,refute_0_49]) ).
cnf(refute_0_51,plain,
( join(X_31,join(meet2(X_30,X_31),X_31)) != X_31
| join(X_31,join(meet2(X_30,X_31),X_31)) != join(X_31,meet2(X_30,X_31))
| join(X_31,meet2(X_30,X_31)) = X_31 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),X_31)),X_31) ),[0],$fot(join(X_31,meet2(X_30,X_31)))]]) ).
cnf(refute_0_52,plain,
( join(X_31,join(meet2(X_30,X_31),X_31)) != X_31
| join(X_31,meet2(X_30,X_31)) = X_31 ),
inference(resolve,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),X_31)),join(X_31,meet2(X_30,X_31))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
join(X_31,meet2(X_30,X_31)) = X_31,
inference(resolve,[$cnf( $equal(join(X_31,join(meet2(X_30,X_31),X_31)),X_31) )],[refute_0_20,refute_0_52]) ).
cnf(refute_0_54,plain,
join(X_34,meet2(X_33,X_34)) = X_34,
inference(subst,[],[refute_0_53:[bind(X_30,$fot(X_33)),bind(X_31,$fot(X_34))]]) ).
cnf(refute_0_55,plain,
meet2(X_34,X_33) = meet2(X_33,X_34),
inference(subst,[],[commutativity_of_meet2:[bind(X,$fot(X_34)),bind(Y,$fot(X_33))]]) ).
cnf(refute_0_56,plain,
( meet2(X_34,X_33) != meet2(X_33,X_34)
| meet2(X_33,X_34) = meet2(X_34,X_33) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet2(X_34,X_33))),bind(Y0,$fot(meet2(X_33,X_34)))]]) ).
cnf(refute_0_57,plain,
meet2(X_33,X_34) = meet2(X_34,X_33),
inference(resolve,[$cnf( $equal(meet2(X_34,X_33),meet2(X_33,X_34)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( join(X_34,meet2(X_33,X_34)) != X_34
| meet2(X_33,X_34) != meet2(X_34,X_33)
| join(X_34,meet2(X_34,X_33)) = X_34 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_34,meet2(X_33,X_34)),X_34) ),[0,1],$fot(meet2(X_34,X_33))]]) ).
cnf(refute_0_59,plain,
( join(X_34,meet2(X_33,X_34)) != X_34
| join(X_34,meet2(X_34,X_33)) = X_34 ),
inference(resolve,[$cnf( $equal(meet2(X_33,X_34),meet2(X_34,X_33)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
join(X_34,meet2(X_34,X_33)) = X_34,
inference(resolve,[$cnf( $equal(join(X_34,meet2(X_33,X_34)),X_34) )],[refute_0_54,refute_0_59]) ).
cnf(refute_0_61,plain,
join(X,meet2(X,X_48)) = X,
inference(subst,[],[refute_0_60:[bind(X_33,$fot(X_48)),bind(X_34,$fot(X))]]) ).
cnf(refute_0_62,plain,
( join(X,meet2(X,X_48)) != X
| meet(meet2(X,X_48),meet(join(X,meet2(X,X_48)),join(Z,meet2(X,X_48)))) != meet2(X,X_48)
| meet(meet2(X,X_48),meet(X,join(Z,meet2(X,X_48)))) = meet2(X,X_48) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X,X_48),meet(join(X,meet2(X,X_48)),join(Z,meet2(X,X_48)))),meet2(X,X_48)) ),[0,1,0],$fot(X)]]) ).
cnf(refute_0_63,plain,
( meet(meet2(X,X_48),meet(join(X,meet2(X,X_48)),join(Z,meet2(X,X_48)))) != meet2(X,X_48)
| meet(meet2(X,X_48),meet(X,join(Z,meet2(X,X_48)))) = meet2(X,X_48) ),
inference(resolve,[$cnf( $equal(join(X,meet2(X,X_48)),X) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
meet(meet2(X,X_48),meet(X,join(Z,meet2(X,X_48)))) = meet2(X,X_48),
inference(resolve,[$cnf( $equal(meet(meet2(X,X_48),meet(join(X,meet2(X,X_48)),join(Z,meet2(X,X_48)))),meet2(X,X_48)) )],[refute_0_9,refute_0_63]) ).
cnf(refute_0_65,plain,
meet(meet2(X_208,X_210),meet(X_208,join(X_210,meet2(X_208,X_210)))) = meet2(X_208,X_210),
inference(subst,[],[refute_0_64:[bind(X,$fot(X_208)),bind(Z,$fot(X_210)),bind(X_48,$fot(X_210))]]) ).
cnf(refute_0_66,plain,
join(X_210,meet2(X_208,X_210)) = X_210,
inference(subst,[],[refute_0_53:[bind(X_30,$fot(X_208)),bind(X_31,$fot(X_210))]]) ).
cnf(refute_0_67,plain,
( join(X_210,meet2(X_208,X_210)) != X_210
| meet(meet2(X_208,X_210),meet(X_208,join(X_210,meet2(X_208,X_210)))) != meet2(X_208,X_210)
| meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet2(X_208,X_210) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,join(X_210,meet2(X_208,X_210)))),meet2(X_208,X_210)) ),[0,1,1],$fot(X_210)]]) ).
cnf(refute_0_68,plain,
( meet(meet2(X_208,X_210),meet(X_208,join(X_210,meet2(X_208,X_210)))) != meet2(X_208,X_210)
| meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet2(X_208,X_210) ),
inference(resolve,[$cnf( $equal(join(X_210,meet2(X_208,X_210)),X_210) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet2(X_208,X_210),
inference(resolve,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,join(X_210,meet2(X_208,X_210)))),meet2(X_208,X_210)) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
meet(meet2(X_33,X_11),join(X_11,meet2(X_33,X_11))) = meet2(X_33,X_11),
inference(subst,[],[refute_0_36:[bind(X_10,$fot(meet2(X_33,X_11)))]]) ).
cnf(refute_0_71,plain,
join(X_11,meet2(X_33,X_11)) = X_11,
inference(subst,[],[refute_0_53:[bind(X_30,$fot(X_33)),bind(X_31,$fot(X_11))]]) ).
cnf(refute_0_72,plain,
( join(X_11,meet2(X_33,X_11)) != X_11
| meet(meet2(X_33,X_11),join(X_11,meet2(X_33,X_11))) != meet2(X_33,X_11)
| meet(meet2(X_33,X_11),X_11) = meet2(X_33,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_33,X_11),join(X_11,meet2(X_33,X_11))),meet2(X_33,X_11)) ),[0,1],$fot(X_11)]]) ).
cnf(refute_0_73,plain,
( meet(meet2(X_33,X_11),join(X_11,meet2(X_33,X_11))) != meet2(X_33,X_11)
| meet(meet2(X_33,X_11),X_11) = meet2(X_33,X_11) ),
inference(resolve,[$cnf( $equal(join(X_11,meet2(X_33,X_11)),X_11) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
meet(meet2(X_33,X_11),X_11) = meet2(X_33,X_11),
inference(resolve,[$cnf( $equal(meet(meet2(X_33,X_11),join(X_11,meet2(X_33,X_11))),meet2(X_33,X_11)) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
meet(meet2(X_33,X_11),X_11) = meet(X_11,meet2(X_33,X_11)),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_11)),bind(Y,$fot(meet2(X_33,X_11)))]]) ).
cnf(refute_0_76,plain,
( meet(meet2(X_33,X_11),X_11) != meet(X_11,meet2(X_33,X_11))
| meet(meet2(X_33,X_11),X_11) != meet2(X_33,X_11)
| meet(X_11,meet2(X_33,X_11)) = meet2(X_33,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_33,X_11),X_11),meet2(X_33,X_11)) ),[0],$fot(meet(X_11,meet2(X_33,X_11)))]]) ).
cnf(refute_0_77,plain,
( meet(meet2(X_33,X_11),X_11) != meet2(X_33,X_11)
| meet(X_11,meet2(X_33,X_11)) = meet2(X_33,X_11) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_33,X_11),X_11),meet(X_11,meet2(X_33,X_11))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
meet(X_11,meet2(X_33,X_11)) = meet2(X_33,X_11),
inference(resolve,[$cnf( $equal(meet(meet2(X_33,X_11),X_11),meet2(X_33,X_11)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
meet(meet2(X_110,X_109),meet2(meet(X_110,X_109),meet2(X_110,X_109))) = meet2(meet(X_110,X_109),meet2(X_110,X_109)),
inference(subst,[],[refute_0_78:[bind(X_11,$fot(meet2(X_110,X_109))),bind(X_33,$fot(meet(X_110,X_109)))]]) ).
cnf(refute_0_80,plain,
( meet2(X,Y) != meet2(Y,X)
| meet2(Y,X) = meet2(X,Y) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet2(X,Y))),bind(Y0,$fot(meet2(Y,X)))]]) ).
cnf(refute_0_81,plain,
meet2(Y,X) = meet2(X,Y),
inference(resolve,[$cnf( $equal(meet2(X,Y),meet2(Y,X)) )],[commutativity_of_meet2,refute_0_80]) ).
cnf(refute_0_82,plain,
meet2(meet2(join(X,Y),join(Z,Y)),Y) = meet2(Y,meet2(join(X,Y),join(Z,Y))),
inference(subst,[],[refute_0_81:[bind(X,$fot(Y)),bind(Y,$fot(meet2(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_83,plain,
( meet2(meet2(join(X,Y),join(Z,Y)),Y) != Y
| meet2(meet2(join(X,Y),join(Z,Y)),Y) != meet2(Y,meet2(join(X,Y),join(Z,Y)))
| meet2(Y,meet2(join(X,Y),join(Z,Y))) = Y ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet2(join(X,Y),join(Z,Y)),Y),Y) ),[0],$fot(meet2(Y,meet2(join(X,Y),join(Z,Y))))]]) ).
cnf(refute_0_84,plain,
( meet2(meet2(join(X,Y),join(Z,Y)),Y) != Y
| meet2(Y,meet2(join(X,Y),join(Z,Y))) = Y ),
inference(resolve,[$cnf( $equal(meet2(meet2(join(X,Y),join(Z,Y)),Y),meet2(Y,meet2(join(X,Y),join(Z,Y)))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
meet2(Y,meet2(join(X,Y),join(Z,Y))) = Y,
inference(resolve,[$cnf( $equal(meet2(meet2(join(X,Y),join(Z,Y)),Y),Y) )],[wal_1_2,refute_0_84]) ).
cnf(refute_0_86,plain,
meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),join(X_25,meet(X_25,X_20)))) = meet(X_25,X_20),
inference(subst,[],[refute_0_85:[bind(X,$fot(X_23)),bind(Y,$fot(meet(X_25,X_20))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_87,plain,
join(X_19,meet(X_20,X_19)) = X_19,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(X_19)),bind(X_18,$fot(X_20))]]) ).
cnf(refute_0_88,plain,
meet(X_19,X_20) = meet(X_20,X_19),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_19)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_89,plain,
( meet(X_19,X_20) != meet(X_20,X_19)
| meet(X_20,X_19) = meet(X_19,X_20) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_19,X_20))),bind(Y0,$fot(meet(X_20,X_19)))]]) ).
cnf(refute_0_90,plain,
meet(X_20,X_19) = meet(X_19,X_20),
inference(resolve,[$cnf( $equal(meet(X_19,X_20),meet(X_20,X_19)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( join(X_19,meet(X_20,X_19)) != X_19
| meet(X_20,X_19) != meet(X_19,X_20)
| join(X_19,meet(X_19,X_20)) = X_19 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_19,meet(X_20,X_19)),X_19) ),[0,1],$fot(meet(X_19,X_20))]]) ).
cnf(refute_0_92,plain,
( join(X_19,meet(X_20,X_19)) != X_19
| join(X_19,meet(X_19,X_20)) = X_19 ),
inference(resolve,[$cnf( $equal(meet(X_20,X_19),meet(X_19,X_20)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
join(X_19,meet(X_19,X_20)) = X_19,
inference(resolve,[$cnf( $equal(join(X_19,meet(X_20,X_19)),X_19) )],[refute_0_87,refute_0_92]) ).
cnf(refute_0_94,plain,
join(X_25,meet(X_25,X_20)) = X_25,
inference(subst,[],[refute_0_93:[bind(X_19,$fot(X_25))]]) ).
cnf(refute_0_95,plain,
( join(X_25,meet(X_25,X_20)) != X_25
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),join(X_25,meet(X_25,X_20)))) != meet(X_25,X_20)
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet(X_25,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),join(X_25,meet(X_25,X_20)))),meet(X_25,X_20)) ),[0,1,1],$fot(X_25)]]) ).
cnf(refute_0_96,plain,
( meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),join(X_25,meet(X_25,X_20)))) != meet(X_25,X_20)
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet(X_25,X_20) ),
inference(resolve,[$cnf( $equal(join(X_25,meet(X_25,X_20)),X_25) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet(X_25,X_20),
inference(resolve,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),join(X_25,meet(X_25,X_20)))),meet(X_25,X_20)) )],[refute_0_86,refute_0_96]) ).
cnf(refute_0_98,plain,
meet2(join(X_23,meet(X_25,X_20)),X_25) = meet2(X_25,join(X_23,meet(X_25,X_20))),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_25)),bind(Y,$fot(join(X_23,meet(X_25,X_20))))]]) ).
cnf(refute_0_99,plain,
meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),
introduced(tautology,[refl,[$fot(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)))]]) ).
cnf(refute_0_100,plain,
( meet2(join(X_23,meet(X_25,X_20)),X_25) != meet2(X_25,join(X_23,meet(X_25,X_20)))
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) != meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25))
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25))) ),[1,1],$fot(meet2(X_25,join(X_23,meet(X_25,X_20))))]]) ).
cnf(refute_0_101,plain,
( meet2(join(X_23,meet(X_25,X_20)),X_25) != meet2(X_25,join(X_23,meet(X_25,X_20)))
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) = meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))),
inference(resolve,[$cnf( $equal(meet2(join(X_23,meet(X_25,X_20)),X_25),meet2(X_25,join(X_23,meet(X_25,X_20)))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) != meet(X_25,X_20)
| meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) != meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20))))
| meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))) = meet(X_25,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),meet(X_25,X_20)) ),[0],$fot(meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))))]]) ).
cnf(refute_0_104,plain,
( meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)) != meet(X_25,X_20)
| meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))) = meet(X_25,X_20) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
meet2(meet(X_25,X_20),meet2(X_25,join(X_23,meet(X_25,X_20)))) = meet(X_25,X_20),
inference(resolve,[$cnf( $equal(meet2(meet(X_25,X_20),meet2(join(X_23,meet(X_25,X_20)),X_25)),meet(X_25,X_20)) )],[refute_0_97,refute_0_104]) ).
cnf(refute_0_106,plain,
meet2(meet(X_108,X_106),meet2(X_108,join(X_106,meet(X_108,X_106)))) = meet(X_108,X_106),
inference(subst,[],[refute_0_105:[bind(X_20,$fot(X_106)),bind(X_23,$fot(X_106)),bind(X_25,$fot(X_108))]]) ).
cnf(refute_0_107,plain,
join(X_106,meet(X_108,X_106)) = X_106,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(X_106)),bind(X_18,$fot(X_108))]]) ).
cnf(refute_0_108,plain,
( join(X_106,meet(X_108,X_106)) != X_106
| meet2(meet(X_108,X_106),meet2(X_108,join(X_106,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_108,X_106),meet2(X_108,X_106)) = meet(X_108,X_106) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_106,meet(X_108,X_106)))),meet(X_108,X_106)) ),[0,1,1],$fot(X_106)]]) ).
cnf(refute_0_109,plain,
( meet2(meet(X_108,X_106),meet2(X_108,join(X_106,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_108,X_106),meet2(X_108,X_106)) = meet(X_108,X_106) ),
inference(resolve,[$cnf( $equal(join(X_106,meet(X_108,X_106)),X_106) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
meet2(meet(X_108,X_106),meet2(X_108,X_106)) = meet(X_108,X_106),
inference(resolve,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_106,meet(X_108,X_106)))),meet(X_108,X_106)) )],[refute_0_106,refute_0_109]) ).
cnf(refute_0_111,plain,
meet2(meet(X_110,X_109),meet2(X_110,X_109)) = meet(X_110,X_109),
inference(subst,[],[refute_0_110:[bind(X_106,$fot(X_109)),bind(X_108,$fot(X_110))]]) ).
cnf(refute_0_112,plain,
( meet(meet2(X_110,X_109),meet2(meet(X_110,X_109),meet2(X_110,X_109))) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet2(meet(X_110,X_109),meet2(X_110,X_109)) != meet(X_110,X_109)
| meet(meet2(X_110,X_109),meet(X_110,X_109)) = meet2(meet(X_110,X_109),meet2(X_110,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_110,X_109),meet2(meet(X_110,X_109),meet2(X_110,X_109))),meet2(meet(X_110,X_109),meet2(X_110,X_109))) ),[0,1],$fot(meet(X_110,X_109))]]) ).
cnf(refute_0_113,plain,
( meet(meet2(X_110,X_109),meet2(meet(X_110,X_109),meet2(X_110,X_109))) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet2(X_110,X_109),meet(X_110,X_109)) = meet2(meet(X_110,X_109),meet2(X_110,X_109)) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_110,X_109),meet2(X_110,X_109)),meet(X_110,X_109)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
meet(meet2(X_110,X_109),meet(X_110,X_109)) = meet2(meet(X_110,X_109),meet2(X_110,X_109)),
inference(resolve,[$cnf( $equal(meet(meet2(X_110,X_109),meet2(meet(X_110,X_109),meet2(X_110,X_109))),meet2(meet(X_110,X_109),meet2(X_110,X_109))) )],[refute_0_79,refute_0_113]) ).
cnf(refute_0_115,plain,
meet(meet2(X_110,X_109),meet(X_110,X_109)) = meet(meet(X_110,X_109),meet2(X_110,X_109)),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_110,X_109))),bind(Y,$fot(meet2(X_110,X_109)))]]) ).
cnf(refute_0_116,plain,
( meet(meet2(X_110,X_109),meet(X_110,X_109)) != meet(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet2(X_110,X_109),meet(X_110,X_109)) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet2(meet(X_110,X_109),meet2(X_110,X_109)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_110,X_109),meet(X_110,X_109)),meet2(meet(X_110,X_109),meet2(X_110,X_109))) ),[0],$fot(meet(meet(X_110,X_109),meet2(X_110,X_109)))]]) ).
cnf(refute_0_117,plain,
( meet(meet2(X_110,X_109),meet(X_110,X_109)) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet2(meet(X_110,X_109),meet2(X_110,X_109)) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_110,X_109),meet(X_110,X_109)),meet(meet(X_110,X_109),meet2(X_110,X_109))) )],[refute_0_115,refute_0_116]) ).
cnf(refute_0_118,plain,
( meet(meet(X_110,X_109),meet2(X_110,X_109)) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet2(meet(X_110,X_109),meet2(X_110,X_109)) != meet(X_110,X_109)
| meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet(X_110,X_109) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(meet(X_110,X_109),meet2(X_110,X_109)),meet(X_110,X_109)) ),[0],$fot(meet2(meet(X_110,X_109),meet2(X_110,X_109)))]]) ).
cnf(refute_0_119,plain,
( meet(meet(X_110,X_109),meet2(X_110,X_109)) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet(X_110,X_109) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_110,X_109),meet2(X_110,X_109)),meet(X_110,X_109)) )],[refute_0_111,refute_0_118]) ).
cnf(refute_0_120,plain,
( meet(meet2(X_110,X_109),meet(X_110,X_109)) != meet2(meet(X_110,X_109),meet2(X_110,X_109))
| meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet(X_110,X_109) ),
inference(resolve,[$cnf( $equal(meet(meet(X_110,X_109),meet2(X_110,X_109)),meet2(meet(X_110,X_109),meet2(X_110,X_109))) )],[refute_0_117,refute_0_119]) ).
cnf(refute_0_121,plain,
meet(meet(X_110,X_109),meet2(X_110,X_109)) = meet(X_110,X_109),
inference(resolve,[$cnf( $equal(meet(meet2(X_110,X_109),meet(X_110,X_109)),meet2(meet(X_110,X_109),meet2(X_110,X_109))) )],[refute_0_114,refute_0_120]) ).
cnf(refute_0_122,plain,
meet(meet(X_208,X_210),meet2(X_208,X_210)) = meet(X_208,X_210),
inference(subst,[],[refute_0_121:[bind(X_109,$fot(X_210)),bind(X_110,$fot(X_208))]]) ).
cnf(refute_0_123,plain,
meet2(X_109,X_110) = meet2(X_110,X_109),
inference(subst,[],[commutativity_of_meet2:[bind(X,$fot(X_109)),bind(Y,$fot(X_110))]]) ).
cnf(refute_0_124,plain,
( meet2(X_109,X_110) != meet2(X_110,X_109)
| meet2(X_110,X_109) = meet2(X_109,X_110) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet2(X_109,X_110))),bind(Y0,$fot(meet2(X_110,X_109)))]]) ).
cnf(refute_0_125,plain,
meet2(X_110,X_109) = meet2(X_109,X_110),
inference(resolve,[$cnf( $equal(meet2(X_109,X_110),meet2(X_110,X_109)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
( meet2(X_110,X_109) != meet2(X_109,X_110)
| meet2(meet(X_110,X_109),meet2(X_110,X_109)) != meet(X_110,X_109)
| meet2(meet(X_110,X_109),meet2(X_109,X_110)) = meet(X_110,X_109) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_110,X_109),meet2(X_110,X_109)),meet(X_110,X_109)) ),[0,1],$fot(meet2(X_109,X_110))]]) ).
cnf(refute_0_127,plain,
( meet2(meet(X_110,X_109),meet2(X_110,X_109)) != meet(X_110,X_109)
| meet2(meet(X_110,X_109),meet2(X_109,X_110)) = meet(X_110,X_109) ),
inference(resolve,[$cnf( $equal(meet2(X_110,X_109),meet2(X_109,X_110)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
meet2(meet(X_110,X_109),meet2(X_109,X_110)) = meet(X_110,X_109),
inference(resolve,[$cnf( $equal(meet2(meet(X_110,X_109),meet2(X_110,X_109)),meet(X_110,X_109)) )],[refute_0_111,refute_0_127]) ).
cnf(refute_0_129,plain,
meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),
inference(subst,[],[refute_0_128:[bind(X_109,$fot(meet(X_147,X_149))),bind(X_110,$fot(meet2(X_149,join(X_148,meet(X_149,X_147)))))]]) ).
cnf(refute_0_130,plain,
meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))) = meet(X_108,X_106),
inference(subst,[],[refute_0_105:[bind(X_20,$fot(X_106)),bind(X_23,$fot(X_107)),bind(X_25,$fot(X_108))]]) ).
cnf(refute_0_131,plain,
meet(X_106,X_108) = meet(X_108,X_106),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_106)),bind(Y,$fot(X_108))]]) ).
cnf(refute_0_132,plain,
( meet(X_106,X_108) != meet(X_108,X_106)
| meet(X_108,X_106) = meet(X_106,X_108) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_106,X_108))),bind(Y0,$fot(meet(X_108,X_106)))]]) ).
cnf(refute_0_133,plain,
meet(X_108,X_106) = meet(X_106,X_108),
inference(resolve,[$cnf( $equal(meet(X_106,X_108),meet(X_108,X_106)) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( meet(X_108,X_106) != meet(X_106,X_108)
| meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_106,X_108),meet2(X_108,join(X_107,meet(X_108,X_106)))) = meet(X_108,X_106) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))),meet(X_108,X_106)) ),[0,0],$fot(meet(X_106,X_108))]]) ).
cnf(refute_0_135,plain,
( meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_106,X_108),meet2(X_108,join(X_107,meet(X_108,X_106)))) = meet(X_108,X_106) ),
inference(resolve,[$cnf( $equal(meet(X_108,X_106),meet(X_106,X_108)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
meet2(meet(X_106,X_108),meet2(X_108,join(X_107,meet(X_108,X_106)))) = meet(X_108,X_106),
inference(resolve,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))),meet(X_108,X_106)) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) = meet(X_149,X_147),
inference(subst,[],[refute_0_136:[bind(X_106,$fot(X_147)),bind(X_107,$fot(X_148)),bind(X_108,$fot(X_149))]]) ).
cnf(refute_0_138,plain,
( meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) != meet(X_149,X_147)
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) ),[0,1],$fot(meet(X_149,X_147))]]) ).
cnf(refute_0_139,plain,
( meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))),meet(X_149,X_147)) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),
inference(resolve,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet2(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) )],[refute_0_129,refute_0_139]) ).
cnf(refute_0_141,plain,
meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_147,X_149))),bind(Y,$fot(meet2(X_149,join(X_148,meet(X_149,X_147)))))]]) ).
cnf(refute_0_142,plain,
meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) = meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))),
introduced(tautology,[refl,[$fot(meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))))]]) ).
cnf(refute_0_143,plain,
( meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) != meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)))
| meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))),meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)))) ),[1,1],$fot(meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))]]) ).
cnf(refute_0_144,plain,
( meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))),meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),
inference(resolve,[$cnf( $equal(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))),
inference(subst,[],[refute_0_81:[bind(X,$fot(meet(X_149,X_147))),bind(Y,$fot(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))))]]) ).
cnf(refute_0_147,plain,
( meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) != meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) != meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)))),bind(Y0,$fot(meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))))),bind(Z0,$fot(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))))]]) ).
cnf(refute_0_148,plain,
( meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) != meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) ),
inference(resolve,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)),meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))),meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
( meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) != meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) ),[0],$fot(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))))]]) ).
cnf(refute_0_151,plain,
( meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) ),
inference(resolve,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)),meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
( meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) ),[1],$fot(meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))]]) ).
cnf(refute_0_153,plain,
( meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) )],[refute_0_141,refute_0_152]) ).
cnf(refute_0_154,plain,
( meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)) != meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) )],[refute_0_151,refute_0_153]) ).
cnf(refute_0_155,plain,
meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))),
inference(resolve,[$cnf( $equal(meet2(meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149)),meet(X_149,X_147)),meet(meet2(X_149,join(X_148,meet(X_149,X_147))),meet(X_147,X_149))) )],[refute_0_140,refute_0_154]) ).
cnf(refute_0_156,plain,
( meet(X_108,X_106) != meet(X_106,X_108)
| meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_106,X_108)))) = meet(X_108,X_106) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))),meet(X_108,X_106)) ),[0,1,1,1],$fot(meet(X_106,X_108))]]) ).
cnf(refute_0_157,plain,
( meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))) != meet(X_108,X_106)
| meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_106,X_108)))) = meet(X_108,X_106) ),
inference(resolve,[$cnf( $equal(meet(X_108,X_106),meet(X_106,X_108)) )],[refute_0_133,refute_0_156]) ).
cnf(refute_0_158,plain,
meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_106,X_108)))) = meet(X_108,X_106),
inference(resolve,[$cnf( $equal(meet2(meet(X_108,X_106),meet2(X_108,join(X_107,meet(X_108,X_106)))),meet(X_108,X_106)) )],[refute_0_130,refute_0_157]) ).
cnf(refute_0_159,plain,
meet2(meet(X_146,X_144),meet2(X_146,join(meet(X_144,X_146),meet(X_144,X_146)))) = meet(X_146,X_144),
inference(subst,[],[refute_0_158:[bind(X_106,$fot(X_144)),bind(X_107,$fot(meet(X_144,X_146))),bind(X_108,$fot(X_146))]]) ).
cnf(refute_0_160,plain,
join(meet(X_144,X_146),meet(X_144,X_146)) = meet(X_144,X_146),
inference(subst,[],[idempotence_of_join:[bind(X,$fot(meet(X_144,X_146)))]]) ).
cnf(refute_0_161,plain,
( join(meet(X_144,X_146),meet(X_144,X_146)) != meet(X_144,X_146)
| meet2(meet(X_146,X_144),meet2(X_146,join(meet(X_144,X_146),meet(X_144,X_146)))) != meet(X_146,X_144)
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet(X_146,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,join(meet(X_144,X_146),meet(X_144,X_146)))),meet(X_146,X_144)) ),[0,1,1],$fot(meet(X_144,X_146))]]) ).
cnf(refute_0_162,plain,
( meet2(meet(X_146,X_144),meet2(X_146,join(meet(X_144,X_146),meet(X_144,X_146)))) != meet(X_146,X_144)
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet(X_146,X_144) ),
inference(resolve,[$cnf( $equal(join(meet(X_144,X_146),meet(X_144,X_146)),meet(X_144,X_146)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet(X_146,X_144),
inference(resolve,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,join(meet(X_144,X_146),meet(X_144,X_146)))),meet(X_146,X_144)) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
meet2(X_24,meet2(join(X_25,X_24),join(X_25,X_24))) = X_24,
inference(subst,[],[refute_0_85:[bind(X,$fot(X_25)),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_165,plain,
meet2(join(X_25,X_24),join(X_25,X_24)) = join(X_25,X_24),
inference(subst,[],[idempotence_of_meet2:[bind(X,$fot(join(X_25,X_24)))]]) ).
cnf(refute_0_166,plain,
( meet2(X_24,meet2(join(X_25,X_24),join(X_25,X_24))) != X_24
| meet2(join(X_25,X_24),join(X_25,X_24)) != join(X_25,X_24)
| meet2(X_24,join(X_25,X_24)) = X_24 ),
introduced(tautology,[equality,[$cnf( $equal(meet2(X_24,meet2(join(X_25,X_24),join(X_25,X_24))),X_24) ),[0,1],$fot(join(X_25,X_24))]]) ).
cnf(refute_0_167,plain,
( meet2(X_24,meet2(join(X_25,X_24),join(X_25,X_24))) != X_24
| meet2(X_24,join(X_25,X_24)) = X_24 ),
inference(resolve,[$cnf( $equal(meet2(join(X_25,X_24),join(X_25,X_24)),join(X_25,X_24)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
meet2(X_24,join(X_25,X_24)) = X_24,
inference(resolve,[$cnf( $equal(meet2(X_24,meet2(join(X_25,X_24),join(X_25,X_24))),X_24) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
meet2(meet(X_18,X_27),join(X_27,meet(X_18,X_27))) = meet(X_18,X_27),
inference(subst,[],[refute_0_168:[bind(X_24,$fot(meet(X_18,X_27))),bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_170,plain,
join(X_27,meet(X_18,X_27)) = X_27,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(X_27))]]) ).
cnf(refute_0_171,plain,
( join(X_27,meet(X_18,X_27)) != X_27
| meet2(meet(X_18,X_27),join(X_27,meet(X_18,X_27))) != meet(X_18,X_27)
| meet2(meet(X_18,X_27),X_27) = meet(X_18,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_18,X_27),join(X_27,meet(X_18,X_27))),meet(X_18,X_27)) ),[0,1],$fot(X_27)]]) ).
cnf(refute_0_172,plain,
( meet2(meet(X_18,X_27),join(X_27,meet(X_18,X_27))) != meet(X_18,X_27)
| meet2(meet(X_18,X_27),X_27) = meet(X_18,X_27) ),
inference(resolve,[$cnf( $equal(join(X_27,meet(X_18,X_27)),X_27) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
meet2(meet(X_18,X_27),X_27) = meet(X_18,X_27),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_27),join(X_27,meet(X_18,X_27))),meet(X_18,X_27)) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
meet2(meet(X_18,X_27),X_27) = meet2(X_27,meet(X_18,X_27)),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_27)),bind(Y,$fot(meet(X_18,X_27)))]]) ).
cnf(refute_0_175,plain,
( meet2(meet(X_18,X_27),X_27) != meet(X_18,X_27)
| meet2(meet(X_18,X_27),X_27) != meet2(X_27,meet(X_18,X_27))
| meet2(X_27,meet(X_18,X_27)) = meet(X_18,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_18,X_27),X_27),meet(X_18,X_27)) ),[0],$fot(meet2(X_27,meet(X_18,X_27)))]]) ).
cnf(refute_0_176,plain,
( meet2(meet(X_18,X_27),X_27) != meet(X_18,X_27)
| meet2(X_27,meet(X_18,X_27)) = meet(X_18,X_27) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_27),X_27),meet2(X_27,meet(X_18,X_27))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
meet2(X_27,meet(X_18,X_27)) = meet(X_18,X_27),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_27),X_27),meet(X_18,X_27)) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
meet2(X_146,meet(X_144,X_146)) = meet(X_144,X_146),
inference(subst,[],[refute_0_177:[bind(X_18,$fot(X_144)),bind(X_27,$fot(X_146))]]) ).
cnf(refute_0_179,plain,
meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),
introduced(tautology,[refl,[$fot(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))))]]) ).
cnf(refute_0_180,plain,
( meet2(X_146,meet(X_144,X_146)) != meet(X_144,X_146)
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) != meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146)))
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet2(meet(X_146,X_144),meet(X_144,X_146)) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146)))) ),[1,1],$fot(meet(X_144,X_146))]]) ).
cnf(refute_0_181,plain,
( meet2(X_146,meet(X_144,X_146)) != meet(X_144,X_146)
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet2(meet(X_146,X_144),meet(X_144,X_146)) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) = meet2(meet(X_146,X_144),meet(X_144,X_146)),
inference(resolve,[$cnf( $equal(meet2(X_146,meet(X_144,X_146)),meet(X_144,X_146)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
( meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) != meet(X_146,X_144)
| meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) != meet2(meet(X_146,X_144),meet(X_144,X_146))
| meet2(meet(X_146,X_144),meet(X_144,X_146)) = meet(X_146,X_144) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),meet(X_146,X_144)) ),[0],$fot(meet2(meet(X_146,X_144),meet(X_144,X_146)))]]) ).
cnf(refute_0_184,plain,
( meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))) != meet(X_146,X_144)
| meet2(meet(X_146,X_144),meet(X_144,X_146)) = meet(X_146,X_144) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),meet2(meet(X_146,X_144),meet(X_144,X_146))) )],[refute_0_182,refute_0_183]) ).
cnf(refute_0_185,plain,
meet2(meet(X_146,X_144),meet(X_144,X_146)) = meet(X_146,X_144),
inference(resolve,[$cnf( $equal(meet2(meet(X_146,X_144),meet2(X_146,meet(X_144,X_146))),meet(X_146,X_144)) )],[refute_0_163,refute_0_184]) ).
cnf(refute_0_186,plain,
meet2(meet(X_149,X_147),meet(X_147,X_149)) = meet(X_149,X_147),
inference(subst,[],[refute_0_185:[bind(X_144,$fot(X_147)),bind(X_146,$fot(X_149))]]) ).
cnf(refute_0_187,plain,
meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),
inference(subst,[],[refute_0_78:[bind(X_11,$fot(meet2(X_115,join(X_114,meet(X_113,X_115))))),bind(X_33,$fot(meet(X_113,X_115)))]]) ).
cnf(refute_0_188,plain,
meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),join(X_25,meet(X_18,X_25)))) = meet(X_18,X_25),
inference(subst,[],[refute_0_85:[bind(X,$fot(X_23)),bind(Y,$fot(meet(X_18,X_25))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_189,plain,
join(X_25,meet(X_18,X_25)) = X_25,
inference(subst,[],[refute_0_30:[bind(X_17,$fot(X_25))]]) ).
cnf(refute_0_190,plain,
( join(X_25,meet(X_18,X_25)) != X_25
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),join(X_25,meet(X_18,X_25)))) != meet(X_18,X_25)
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet(X_18,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),join(X_25,meet(X_18,X_25)))),meet(X_18,X_25)) ),[0,1,1],$fot(X_25)]]) ).
cnf(refute_0_191,plain,
( meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),join(X_25,meet(X_18,X_25)))) != meet(X_18,X_25)
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet(X_18,X_25) ),
inference(resolve,[$cnf( $equal(join(X_25,meet(X_18,X_25)),X_25) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet(X_18,X_25),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),join(X_25,meet(X_18,X_25)))),meet(X_18,X_25)) )],[refute_0_188,refute_0_191]) ).
cnf(refute_0_193,plain,
meet2(join(X_23,meet(X_18,X_25)),X_25) = meet2(X_25,join(X_23,meet(X_18,X_25))),
inference(subst,[],[refute_0_81:[bind(X,$fot(X_25)),bind(Y,$fot(join(X_23,meet(X_18,X_25))))]]) ).
cnf(refute_0_194,plain,
meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),
introduced(tautology,[refl,[$fot(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)))]]) ).
cnf(refute_0_195,plain,
( meet2(join(X_23,meet(X_18,X_25)),X_25) != meet2(X_25,join(X_23,meet(X_18,X_25)))
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) != meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25))
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25))) ),[1,1],$fot(meet2(X_25,join(X_23,meet(X_18,X_25))))]]) ).
cnf(refute_0_196,plain,
( meet2(join(X_23,meet(X_18,X_25)),X_25) != meet2(X_25,join(X_23,meet(X_18,X_25)))
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) = meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))),
inference(resolve,[$cnf( $equal(meet2(join(X_23,meet(X_18,X_25)),X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) )],[refute_0_193,refute_0_196]) ).
cnf(refute_0_198,plain,
( meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) != meet(X_18,X_25)
| meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) != meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25))))
| meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) = meet(X_18,X_25) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),meet(X_18,X_25)) ),[0],$fot(meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))))]]) ).
cnf(refute_0_199,plain,
( meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)) != meet(X_18,X_25)
| meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) = meet(X_18,X_25) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25))))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
meet2(meet(X_18,X_25),meet2(X_25,join(X_23,meet(X_18,X_25)))) = meet(X_18,X_25),
inference(resolve,[$cnf( $equal(meet2(meet(X_18,X_25),meet2(join(X_23,meet(X_18,X_25)),X_25)),meet(X_18,X_25)) )],[refute_0_192,refute_0_199]) ).
cnf(refute_0_201,plain,
meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet(X_113,X_115),
inference(subst,[],[refute_0_200:[bind(X_18,$fot(X_113)),bind(X_23,$fot(X_114)),bind(X_25,$fot(X_115))]]) ).
cnf(refute_0_202,plain,
( meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) != meet(X_113,X_115)
| meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) ),[0,1],$fot(meet(X_113,X_115))]]) ).
cnf(refute_0_203,plain,
( meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),meet(X_113,X_115)) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),
inference(resolve,[$cnf( $equal(meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) )],[refute_0_187,refute_0_203]) ).
cnf(refute_0_205,plain,
meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) = meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_113,X_115))),bind(Y,$fot(meet2(X_115,join(X_114,meet(X_113,X_115)))))]]) ).
cnf(refute_0_206,plain,
( meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) != meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) ),[0],$fot(meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))))]]) ).
cnf(refute_0_207,plain,
( meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)),meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
( meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) != meet(X_113,X_115)
| meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet(X_113,X_115) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),meet(X_113,X_115)) ),[0],$fot(meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))))]]) ).
cnf(refute_0_209,plain,
( meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet(X_113,X_115) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),meet(X_113,X_115)) )],[refute_0_201,refute_0_208]) ).
cnf(refute_0_210,plain,
( meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)) != meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))
| meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet(X_113,X_115) ),
inference(resolve,[$cnf( $equal(meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) )],[refute_0_207,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115)))) = meet(X_113,X_115),
inference(resolve,[$cnf( $equal(meet(meet2(X_115,join(X_114,meet(X_113,X_115))),meet(X_113,X_115)),meet2(meet(X_113,X_115),meet2(X_115,join(X_114,meet(X_113,X_115))))) )],[refute_0_204,refute_0_210]) ).
cnf(refute_0_212,plain,
meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_150,X_152)))) = meet(X_150,X_152),
inference(subst,[],[refute_0_211:[bind(X_113,$fot(X_150)),bind(X_114,$fot(X_151)),bind(X_115,$fot(X_152))]]) ).
cnf(refute_0_213,plain,
meet(X_152,X_150) = meet(X_150,X_152),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_152)),bind(Y,$fot(X_150))]]) ).
cnf(refute_0_214,plain,
( meet(X_152,X_150) != meet(X_150,X_152)
| meet(X_150,X_152) = meet(X_152,X_150) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_152,X_150))),bind(Y0,$fot(meet(X_150,X_152)))]]) ).
cnf(refute_0_215,plain,
meet(X_150,X_152) = meet(X_152,X_150),
inference(resolve,[$cnf( $equal(meet(X_152,X_150),meet(X_150,X_152)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( meet(X_150,X_152) != meet(X_152,X_150)
| meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_150,X_152)))) != meet(X_150,X_152)
| meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_152,X_150)))) = meet(X_150,X_152) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_150,X_152)))),meet(X_150,X_152)) ),[0,1,1,1],$fot(meet(X_152,X_150))]]) ).
cnf(refute_0_217,plain,
( meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_150,X_152)))) != meet(X_150,X_152)
| meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_152,X_150)))) = meet(X_150,X_152) ),
inference(resolve,[$cnf( $equal(meet(X_150,X_152),meet(X_152,X_150)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_152,X_150)))) = meet(X_150,X_152),
inference(resolve,[$cnf( $equal(meet(meet(X_150,X_152),meet2(X_152,join(X_151,meet(X_150,X_152)))),meet(X_150,X_152)) )],[refute_0_212,refute_0_217]) ).
cnf(refute_0_219,plain,
meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) = meet(X_147,X_149),
inference(subst,[],[refute_0_218:[bind(X_150,$fot(X_147)),bind(X_151,$fot(X_148)),bind(X_152,$fot(X_149))]]) ).
cnf(refute_0_220,plain,
meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),
introduced(tautology,[refl,[$fot(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))))]]) ).
cnf(refute_0_221,plain,
( meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) != meet(X_147,X_149)
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet2(meet(X_149,X_147),meet(X_147,X_149)) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))) ),[1,1],$fot(meet(X_147,X_149))]]) ).
cnf(refute_0_222,plain,
( meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) != meet(X_147,X_149)
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet2(meet(X_149,X_147),meet(X_147,X_149)) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet2(meet(X_149,X_147),meet(X_147,X_149)),
inference(resolve,[$cnf( $equal(meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))),meet(X_147,X_149)) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
( meet2(meet(X_149,X_147),meet(X_147,X_149)) != meet(X_149,X_147)
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet2(meet(X_149,X_147),meet(X_147,X_149))
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(X_149,X_147) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))))),bind(Y0,$fot(meet2(meet(X_149,X_147),meet(X_147,X_149)))),bind(Z0,$fot(meet(X_149,X_147)))]]) ).
cnf(refute_0_225,plain,
( meet2(meet(X_149,X_147),meet(X_147,X_149)) != meet(X_149,X_147)
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(X_149,X_147) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet2(meet(X_149,X_147),meet(X_147,X_149))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) = meet(X_149,X_147),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(X_147,X_149)),meet(X_149,X_147)) )],[refute_0_186,refute_0_225]) ).
cnf(refute_0_227,plain,
( meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(X_149,X_147)
| meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet(X_149,X_147) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) ),[0],$fot(meet(X_149,X_147))]]) ).
cnf(refute_0_228,plain,
( meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet(X_149,X_147) = meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) ),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(X_149,X_147)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
( meet(X_149,X_147) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))) != meet(X_147,X_149)
| meet(X_149,X_147) = meet(X_147,X_149) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X_149,X_147),meet(X_147,X_149)) ),[0],$fot(meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))))]]) ).
cnf(refute_0_230,plain,
( meet(X_149,X_147) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet(X_149,X_147) = meet(X_147,X_149) ),
inference(resolve,[$cnf( $equal(meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147)))),meet(X_147,X_149)) )],[refute_0_219,refute_0_229]) ).
cnf(refute_0_231,plain,
( meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) != meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))
| meet(X_149,X_147) = meet(X_147,X_149) ),
inference(resolve,[$cnf( $equal(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) )],[refute_0_228,refute_0_230]) ).
cnf(refute_0_232,plain,
meet(X_149,X_147) = meet(X_147,X_149),
inference(resolve,[$cnf( $equal(meet2(meet(X_149,X_147),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))),meet(meet(X_147,X_149),meet2(X_149,join(X_148,meet(X_149,X_147))))) )],[refute_0_155,refute_0_231]) ).
cnf(refute_0_233,plain,
( meet(X_149,X_147) != meet(X_147,X_149)
| meet(X_147,X_149) = meet(X_149,X_147) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_149,X_147))),bind(Y0,$fot(meet(X_147,X_149)))]]) ).
cnf(refute_0_234,plain,
meet(X_147,X_149) = meet(X_149,X_147),
inference(resolve,[$cnf( $equal(meet(X_149,X_147),meet(X_147,X_149)) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet(meet(X_208,X_210),meet2(X_208,X_210)),
inference(subst,[],[refute_0_234:[bind(X_147,$fot(meet2(X_208,X_210))),bind(X_149,$fot(meet(X_208,X_210)))]]) ).
cnf(refute_0_236,plain,
( meet(meet(X_208,X_210),meet2(X_208,X_210)) != meet(X_208,X_210)
| meet(meet2(X_208,X_210),meet(X_208,X_210)) != meet(meet(X_208,X_210),meet2(X_208,X_210))
| meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet(X_208,X_210) ),
inference(subst,[],[refute_0_47:[bind(X0,$fot(meet(meet2(X_208,X_210),meet(X_208,X_210)))),bind(Y0,$fot(meet(meet(X_208,X_210),meet2(X_208,X_210)))),bind(Z0,$fot(meet(X_208,X_210)))]]) ).
cnf(refute_0_237,plain,
( meet(meet(X_208,X_210),meet2(X_208,X_210)) != meet(X_208,X_210)
| meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet(X_208,X_210) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,X_210)),meet(meet(X_208,X_210),meet2(X_208,X_210))) )],[refute_0_235,refute_0_236]) ).
cnf(refute_0_238,plain,
meet(meet2(X_208,X_210),meet(X_208,X_210)) = meet(X_208,X_210),
inference(resolve,[$cnf( $equal(meet(meet(X_208,X_210),meet2(X_208,X_210)),meet(X_208,X_210)) )],[refute_0_122,refute_0_237]) ).
cnf(refute_0_239,plain,
( meet(meet2(X_208,X_210),meet(X_208,X_210)) != meet(X_208,X_210)
| meet(meet2(X_208,X_210),meet(X_208,X_210)) != meet2(X_208,X_210)
| meet(X_208,X_210) = meet2(X_208,X_210) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,X_210)),meet2(X_208,X_210)) ),[0],$fot(meet(X_208,X_210))]]) ).
cnf(refute_0_240,plain,
( meet(meet2(X_208,X_210),meet(X_208,X_210)) != meet2(X_208,X_210)
| meet(X_208,X_210) = meet2(X_208,X_210) ),
inference(resolve,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,X_210)),meet(X_208,X_210)) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
meet(X_208,X_210) = meet2(X_208,X_210),
inference(resolve,[$cnf( $equal(meet(meet2(X_208,X_210),meet(X_208,X_210)),meet2(X_208,X_210)) )],[refute_0_69,refute_0_240]) ).
cnf(refute_0_242,plain,
( meet(X_208,X_210) != meet2(X_208,X_210)
| meet2(X_208,X_210) = meet(X_208,X_210) ),
inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_208,X_210))),bind(Y0,$fot(meet2(X_208,X_210)))]]) ).
cnf(refute_0_243,plain,
meet2(X_208,X_210) = meet(X_208,X_210),
inference(resolve,[$cnf( $equal(meet(X_208,X_210),meet2(X_208,X_210)) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
meet2(a,b) = meet(a,b),
inference(subst,[],[refute_0_243:[bind(X_208,$fot(a)),bind(X_210,$fot(b))]]) ).
cnf(refute_0_245,plain,
( meet(a,b) != meet(a,b)
| meet2(a,b) != meet(a,b)
| meet(a,b) = meet2(a,b) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(a,b),meet2(a,b)) ),[1],$fot(meet(a,b))]]) ).
cnf(refute_0_246,plain,
( meet(a,b) != meet(a,b)
| meet(a,b) = meet2(a,b) ),
inference(resolve,[$cnf( $equal(meet2(a,b),meet(a,b)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
meet(a,b) != meet(a,b),
inference(resolve,[$cnf( $equal(meet(a,b),meet2(a,b)) )],[refute_0_246,name]) ).
cnf(refute_0_248,plain,
meet(a,b) = meet(a,b),
introduced(tautology,[refl,[$fot(meet(a,b))]]) ).
cnf(refute_0_249,plain,
$false,
inference(resolve,[$cnf( $equal(meet(a,b),meet(a,b)) )],[refute_0_248,refute_0_247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT028-1 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 29 23:49:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.67/1.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.67/1.84
% 1.67/1.84 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.67/1.87
%------------------------------------------------------------------------------