TSTP Solution File: LAT043-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 05:59:06 EDT 2022
% Result : Unsatisfiable 8.93s 9.11s
% Output : CNFRefutation 8.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 77
% Syntax : Number of clauses : 329 ( 176 unt; 0 nHn; 157 RR)
% Number of literals : 549 ( 548 equ; 222 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 638 ( 26 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(idempotence_of_join,axiom,
join(X,X) = X ).
cnf(absorption1,axiom,
meet(X,join(X,Y)) = X ).
cnf(absorption2,axiom,
join(X,meet(X,Y)) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(associativity_of_meet,axiom,
meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ).
cnf(associativity_of_join,axiom,
join(join(X,Y),Z) = join(X,join(Y,Z)) ).
cnf(distributivity,axiom,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
cnf(invertability1,axiom,
join(complement(X),X) = n1 ).
cnf(invertability2,axiom,
meet(complement(X),X) = n0 ).
cnf(invertability3,axiom,
complement(complement(X)) = X ).
cnf(prove_compatability_law,negated_conjecture,
complement(join(c,d)) != meet(complement(c),complement(d)) ).
cnf(refute_0_0,plain,
meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = join(meet(X_71,meet(X_47,complement(X_71))),meet(X_71,X_73)),
inference(subst,[],[distributivity:[bind(X,$fot(X_71)),bind(Y,$fot(meet(X_47,complement(X_71)))),bind(Z,$fot(X_73))]]) ).
cnf(refute_0_1,plain,
meet(X,meet(X_29,X_30)) = meet(meet(X_29,X_30),X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(meet(X_29,X_30)))]]) ).
cnf(refute_0_2,plain,
meet(meet(X_29,X_30),X) = meet(X_29,meet(X_30,X)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_29)),bind(Y,$fot(X_30)),bind(Z,$fot(X))]]) ).
cnf(refute_0_3,plain,
( meet(X,meet(X_29,X_30)) != meet(meet(X_29,X_30),X)
| meet(meet(X_29,X_30),X) != meet(X_29,meet(X_30,X))
| meet(X,meet(X_29,X_30)) = meet(X_29,meet(X_30,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X,meet(X_29,X_30)),meet(X_29,meet(X_30,X))) ),[0],$fot(meet(meet(X_29,X_30),X))]]) ).
cnf(refute_0_4,plain,
( meet(X,meet(X_29,X_30)) != meet(meet(X_29,X_30),X)
| meet(X,meet(X_29,X_30)) = meet(X_29,meet(X_30,X)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_29,X_30),X),meet(X_29,meet(X_30,X))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
meet(X,meet(X_29,X_30)) = meet(X_29,meet(X_30,X)),
inference(resolve,[$cnf( $equal(meet(X,meet(X_29,X_30)),meet(meet(X_29,X_30),X)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
meet(complement(X_48),meet(X_47,X_48)) = meet(X_47,meet(X_48,complement(X_48))),
inference(subst,[],[refute_0_5:[bind(X,$fot(complement(X_48))),bind(X_29,$fot(X_47)),bind(X_30,$fot(X_48))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_8,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_9,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( meet(X,Y) != meet(Y,X)
| meet(Y,X) = meet(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X,Y))),bind(Y0,$fot(meet(Y,X)))]]) ).
cnf(refute_0_11,plain,
meet(Y,X) = meet(X,Y),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_10]) ).
cnf(refute_0_12,plain,
meet(complement(X),X) = meet(X,complement(X)),
inference(subst,[],[refute_0_11:[bind(Y,$fot(complement(X)))]]) ).
cnf(refute_0_13,plain,
( meet(complement(X),X) != meet(X,complement(X))
| meet(complement(X),X) != n0
| meet(X,complement(X)) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X),X),n0) ),[0],$fot(meet(X,complement(X)))]]) ).
cnf(refute_0_14,plain,
( meet(complement(X),X) != n0
| meet(X,complement(X)) = n0 ),
inference(resolve,[$cnf( $equal(meet(complement(X),X),meet(X,complement(X))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
meet(X,complement(X)) = n0,
inference(resolve,[$cnf( $equal(meet(complement(X),X),n0) )],[invertability2,refute_0_14]) ).
cnf(refute_0_16,plain,
meet(X_48,complement(X_48)) = n0,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_48))]]) ).
cnf(refute_0_17,plain,
( meet(X_48,complement(X_48)) != n0
| meet(complement(X_48),meet(X_47,X_48)) != meet(X_47,meet(X_48,complement(X_48)))
| meet(complement(X_48),meet(X_47,X_48)) = meet(X_47,n0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_48),meet(X_47,X_48)),meet(X_47,meet(X_48,complement(X_48)))) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_18,plain,
( meet(complement(X_48),meet(X_47,X_48)) != meet(X_47,meet(X_48,complement(X_48)))
| meet(complement(X_48),meet(X_47,X_48)) = meet(X_47,n0) ),
inference(resolve,[$cnf( $equal(meet(X_48,complement(X_48)),n0) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(complement(X_48),meet(X_47,X_48)) = meet(X_47,n0),
inference(resolve,[$cnf( $equal(meet(complement(X_48),meet(X_47,X_48)),meet(X_47,meet(X_48,complement(X_48)))) )],[refute_0_6,refute_0_18]) ).
cnf(refute_0_20,plain,
meet(X_46,meet(X_47,X_48)) = meet(X_47,meet(X_48,X_46)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_46)),bind(X_29,$fot(X_47)),bind(X_30,$fot(X_48))]]) ).
cnf(refute_0_21,plain,
meet(X_48,X_47) = meet(X_47,X_48),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_48)),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_22,plain,
( meet(X_48,X_47) != meet(X_47,X_48)
| meet(X_47,X_48) = meet(X_48,X_47) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_48,X_47))),bind(Y0,$fot(meet(X_47,X_48)))]]) ).
cnf(refute_0_23,plain,
meet(X_47,X_48) = meet(X_48,X_47),
inference(resolve,[$cnf( $equal(meet(X_48,X_47),meet(X_47,X_48)) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( meet(X_46,meet(X_47,X_48)) != meet(X_47,meet(X_48,X_46))
| meet(X_47,X_48) != meet(X_48,X_47)
| meet(X_46,meet(X_48,X_47)) = meet(X_47,meet(X_48,X_46)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_46,meet(X_47,X_48)),meet(X_47,meet(X_48,X_46))) ),[0,1],$fot(meet(X_48,X_47))]]) ).
cnf(refute_0_25,plain,
( meet(X_46,meet(X_47,X_48)) != meet(X_47,meet(X_48,X_46))
| meet(X_46,meet(X_48,X_47)) = meet(X_47,meet(X_48,X_46)) ),
inference(resolve,[$cnf( $equal(meet(X_47,X_48),meet(X_48,X_47)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
meet(X_46,meet(X_48,X_47)) = meet(X_47,meet(X_48,X_46)),
inference(resolve,[$cnf( $equal(meet(X_46,meet(X_47,X_48)),meet(X_47,meet(X_48,X_46))) )],[refute_0_20,refute_0_25]) ).
cnf(refute_0_27,plain,
( meet(X_46,meet(X_48,X_47)) != meet(X_47,meet(X_48,X_46))
| meet(X_47,meet(X_48,X_46)) = meet(X_46,meet(X_48,X_47)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_46,meet(X_48,X_47)))),bind(Y0,$fot(meet(X_47,meet(X_48,X_46))))]]) ).
cnf(refute_0_28,plain,
meet(X_47,meet(X_48,X_46)) = meet(X_46,meet(X_48,X_47)),
inference(resolve,[$cnf( $equal(meet(X_46,meet(X_48,X_47)),meet(X_47,meet(X_48,X_46))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
meet(complement(X_48),meet(X_47,X_48)) = meet(X_48,meet(X_47,complement(X_48))),
inference(subst,[],[refute_0_28:[bind(X_46,$fot(X_48)),bind(X_47,$fot(complement(X_48))),bind(X_48,$fot(X_47))]]) ).
cnf(refute_0_30,plain,
( meet(complement(X_48),meet(X_47,X_48)) != meet(X_47,n0)
| meet(complement(X_48),meet(X_47,X_48)) != meet(X_48,meet(X_47,complement(X_48)))
| meet(X_48,meet(X_47,complement(X_48))) = meet(X_47,n0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_48),meet(X_47,X_48)),meet(X_47,n0)) ),[0],$fot(meet(X_48,meet(X_47,complement(X_48))))]]) ).
cnf(refute_0_31,plain,
( meet(complement(X_48),meet(X_47,X_48)) != meet(X_47,n0)
| meet(X_48,meet(X_47,complement(X_48))) = meet(X_47,n0) ),
inference(resolve,[$cnf( $equal(meet(complement(X_48),meet(X_47,X_48)),meet(X_48,meet(X_47,complement(X_48)))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
meet(X,n0) = meet(n0,X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(n0))]]) ).
cnf(refute_0_33,plain,
join(n0,meet(n0,Y)) = n0,
inference(subst,[],[absorption2:[bind(X,$fot(n0))]]) ).
cnf(refute_0_34,plain,
join(X_8,meet(X_8,complement(X_8))) = X_8,
inference(subst,[],[absorption2:[bind(X,$fot(X_8)),bind(Y,$fot(complement(X_8)))]]) ).
cnf(refute_0_35,plain,
meet(X_8,complement(X_8)) = n0,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_8))]]) ).
cnf(refute_0_36,plain,
( join(X_8,meet(X_8,complement(X_8))) != X_8
| meet(X_8,complement(X_8)) != n0
| join(X_8,n0) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_8,meet(X_8,complement(X_8))),X_8) ),[0,1],$fot(n0)]]) ).
cnf(refute_0_37,plain,
( join(X_8,meet(X_8,complement(X_8))) != X_8
| join(X_8,n0) = X_8 ),
inference(resolve,[$cnf( $equal(meet(X_8,complement(X_8)),n0) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
join(X_8,n0) = X_8,
inference(resolve,[$cnf( $equal(join(X_8,meet(X_8,complement(X_8))),X_8) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
join(X_8,n0) = join(n0,X_8),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_8)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_40,plain,
( join(X_8,n0) != X_8
| join(X_8,n0) != join(n0,X_8)
| join(n0,X_8) = X_8 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_8,n0),X_8) ),[0],$fot(join(n0,X_8))]]) ).
cnf(refute_0_41,plain,
( join(X_8,n0) != X_8
| join(n0,X_8) = X_8 ),
inference(resolve,[$cnf( $equal(join(X_8,n0),join(n0,X_8)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
join(n0,X_8) = X_8,
inference(resolve,[$cnf( $equal(join(X_8,n0),X_8) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
join(n0,meet(n0,Y)) = meet(n0,Y),
inference(subst,[],[refute_0_42:[bind(X_8,$fot(meet(n0,Y)))]]) ).
cnf(refute_0_44,plain,
( join(n0,meet(n0,Y)) != meet(n0,Y)
| join(n0,meet(n0,Y)) != n0
| meet(n0,Y) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(join(n0,meet(n0,Y)),n0) ),[0],$fot(meet(n0,Y))]]) ).
cnf(refute_0_45,plain,
( join(n0,meet(n0,Y)) != n0
| meet(n0,Y) = n0 ),
inference(resolve,[$cnf( $equal(join(n0,meet(n0,Y)),meet(n0,Y)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
meet(n0,Y) = n0,
inference(resolve,[$cnf( $equal(join(n0,meet(n0,Y)),n0) )],[refute_0_33,refute_0_45]) ).
cnf(refute_0_47,plain,
meet(n0,X) = n0,
inference(subst,[],[refute_0_46:[bind(Y,$fot(X))]]) ).
cnf(refute_0_48,plain,
( meet(X,n0) != meet(n0,X)
| meet(n0,X) != n0
| meet(X,n0) = n0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X,n0),n0) ),[0],$fot(meet(n0,X))]]) ).
cnf(refute_0_49,plain,
( meet(X,n0) != meet(n0,X)
| meet(X,n0) = n0 ),
inference(resolve,[$cnf( $equal(meet(n0,X),n0) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
meet(X,n0) = n0,
inference(resolve,[$cnf( $equal(meet(X,n0),meet(n0,X)) )],[refute_0_32,refute_0_49]) ).
cnf(refute_0_51,plain,
meet(X_47,n0) = n0,
inference(subst,[],[refute_0_50:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_52,plain,
( meet(X_47,n0) != n0
| meet(X_48,meet(X_47,complement(X_48))) != meet(X_47,n0)
| meet(X_48,meet(X_47,complement(X_48))) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_48,meet(X_47,complement(X_48))),meet(X_47,n0)) ),[1],$fot(n0)]]) ).
cnf(refute_0_53,plain,
( meet(X_48,meet(X_47,complement(X_48))) != meet(X_47,n0)
| meet(X_48,meet(X_47,complement(X_48))) = n0 ),
inference(resolve,[$cnf( $equal(meet(X_47,n0),n0) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( meet(complement(X_48),meet(X_47,X_48)) != meet(X_47,n0)
| meet(X_48,meet(X_47,complement(X_48))) = n0 ),
inference(resolve,[$cnf( $equal(meet(X_48,meet(X_47,complement(X_48))),meet(X_47,n0)) )],[refute_0_31,refute_0_53]) ).
cnf(refute_0_55,plain,
meet(X_48,meet(X_47,complement(X_48))) = n0,
inference(resolve,[$cnf( $equal(meet(complement(X_48),meet(X_47,X_48)),meet(X_47,n0)) )],[refute_0_19,refute_0_54]) ).
cnf(refute_0_56,plain,
meet(X_71,meet(X_47,complement(X_71))) = n0,
inference(subst,[],[refute_0_55:[bind(X_48,$fot(X_71))]]) ).
cnf(refute_0_57,plain,
( meet(X_71,join(meet(X_47,complement(X_71)),X_73)) != join(meet(X_71,meet(X_47,complement(X_71))),meet(X_71,X_73))
| meet(X_71,meet(X_47,complement(X_71))) != n0
| meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = join(n0,meet(X_71,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(meet(X_47,complement(X_71)),X_73)),join(meet(X_71,meet(X_47,complement(X_71))),meet(X_71,X_73))) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_58,plain,
( meet(X_71,join(meet(X_47,complement(X_71)),X_73)) != join(meet(X_71,meet(X_47,complement(X_71))),meet(X_71,X_73))
| meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = join(n0,meet(X_71,X_73)) ),
inference(resolve,[$cnf( $equal(meet(X_71,meet(X_47,complement(X_71))),n0) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = join(n0,meet(X_71,X_73)),
inference(resolve,[$cnf( $equal(meet(X_71,join(meet(X_47,complement(X_71)),X_73)),join(meet(X_71,meet(X_47,complement(X_71))),meet(X_71,X_73))) )],[refute_0_0,refute_0_58]) ).
cnf(refute_0_60,plain,
join(n0,meet(X_71,X_73)) = meet(X_71,X_73),
inference(subst,[],[refute_0_42:[bind(X_8,$fot(meet(X_71,X_73)))]]) ).
cnf(refute_0_61,plain,
( join(n0,meet(X_71,X_73)) != meet(X_71,X_73)
| meet(X_71,join(meet(X_47,complement(X_71)),X_73)) != join(n0,meet(X_71,X_73))
| meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = meet(X_71,X_73) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(meet(X_47,complement(X_71)),X_73)),join(n0,meet(X_71,X_73))) ),[1],$fot(meet(X_71,X_73))]]) ).
cnf(refute_0_62,plain,
( meet(X_71,join(meet(X_47,complement(X_71)),X_73)) != join(n0,meet(X_71,X_73))
| meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = meet(X_71,X_73) ),
inference(resolve,[$cnf( $equal(join(n0,meet(X_71,X_73)),meet(X_71,X_73)) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(X_71,join(meet(X_47,complement(X_71)),X_73)) = meet(X_71,X_73),
inference(resolve,[$cnf( $equal(meet(X_71,join(meet(X_47,complement(X_71)),X_73)),join(n0,meet(X_71,X_73))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
meet(X_243,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))) = meet(X_243,complement(join(complement(X_243),complement(X_242)))),
inference(subst,[],[refute_0_63:[bind(X_47,$fot(X_242)),bind(X_71,$fot(X_243)),bind(X_73,$fot(complement(join(complement(X_243),complement(X_242)))))]]) ).
cnf(refute_0_65,plain,
meet(X_71,join(complement(X_71),X_73)) = join(meet(X_71,complement(X_71)),meet(X_71,X_73)),
inference(subst,[],[distributivity:[bind(X,$fot(X_71)),bind(Y,$fot(complement(X_71))),bind(Z,$fot(X_73))]]) ).
cnf(refute_0_66,plain,
meet(X_71,complement(X_71)) = n0,
inference(subst,[],[refute_0_15:[bind(X,$fot(X_71))]]) ).
cnf(refute_0_67,plain,
( meet(X_71,complement(X_71)) != n0
| meet(X_71,join(complement(X_71),X_73)) != join(meet(X_71,complement(X_71)),meet(X_71,X_73))
| meet(X_71,join(complement(X_71),X_73)) = join(n0,meet(X_71,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(complement(X_71),X_73)),join(meet(X_71,complement(X_71)),meet(X_71,X_73))) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_68,plain,
( meet(X_71,join(complement(X_71),X_73)) != join(meet(X_71,complement(X_71)),meet(X_71,X_73))
| meet(X_71,join(complement(X_71),X_73)) = join(n0,meet(X_71,X_73)) ),
inference(resolve,[$cnf( $equal(meet(X_71,complement(X_71)),n0) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
meet(X_71,join(complement(X_71),X_73)) = join(n0,meet(X_71,X_73)),
inference(resolve,[$cnf( $equal(meet(X_71,join(complement(X_71),X_73)),join(meet(X_71,complement(X_71)),meet(X_71,X_73))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
( join(n0,meet(X_71,X_73)) != meet(X_71,X_73)
| meet(X_71,join(complement(X_71),X_73)) != join(n0,meet(X_71,X_73))
| meet(X_71,join(complement(X_71),X_73)) = meet(X_71,X_73) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(complement(X_71),X_73)),join(n0,meet(X_71,X_73))) ),[1],$fot(meet(X_71,X_73))]]) ).
cnf(refute_0_71,plain,
( meet(X_71,join(complement(X_71),X_73)) != join(n0,meet(X_71,X_73))
| meet(X_71,join(complement(X_71),X_73)) = meet(X_71,X_73) ),
inference(resolve,[$cnf( $equal(join(n0,meet(X_71,X_73)),meet(X_71,X_73)) )],[refute_0_60,refute_0_70]) ).
cnf(refute_0_72,plain,
meet(X_71,join(complement(X_71),X_73)) = meet(X_71,X_73),
inference(resolve,[$cnf( $equal(meet(X_71,join(complement(X_71),X_73)),join(n0,meet(X_71,X_73))) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
meet(X_74,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))) = meet(X_74,join(Y,complement(join(Y,complement(X_74))))),
inference(subst,[],[refute_0_72:[bind(X_71,$fot(X_74)),bind(X_73,$fot(join(Y,complement(join(Y,complement(X_74))))))]]) ).
cnf(refute_0_74,plain,
( join(X,meet(X,Y)) != X
| meet(X,Y) != meet(Y,X)
| join(X,meet(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).
cnf(refute_0_75,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_74]) ).
cnf(refute_0_76,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_75]) ).
cnf(refute_0_77,plain,
join(join(X_22,Y),meet(X_22,join(X_22,Y))) = join(X_22,Y),
inference(subst,[],[refute_0_76:[bind(X,$fot(join(X_22,Y))),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_78,plain,
meet(X_22,join(X_22,Y)) = X_22,
inference(subst,[],[absorption1:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_79,plain,
( join(join(X_22,Y),meet(X_22,join(X_22,Y))) != join(X_22,Y)
| meet(X_22,join(X_22,Y)) != X_22
| join(join(X_22,Y),X_22) = join(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_22,Y),meet(X_22,join(X_22,Y))),join(X_22,Y)) ),[0,1],$fot(X_22)]]) ).
cnf(refute_0_80,plain,
( join(join(X_22,Y),meet(X_22,join(X_22,Y))) != join(X_22,Y)
| join(join(X_22,Y),X_22) = join(X_22,Y) ),
inference(resolve,[$cnf( $equal(meet(X_22,join(X_22,Y)),X_22) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
join(join(X_22,Y),X_22) = join(X_22,Y),
inference(resolve,[$cnf( $equal(join(join(X_22,Y),meet(X_22,join(X_22,Y))),join(X_22,Y)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
join(join(X_22,Y),X_22) = join(X_22,join(Y,X_22)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_22)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_83,plain,
( join(join(X_22,Y),X_22) != join(X_22,Y)
| join(join(X_22,Y),X_22) != join(X_22,join(Y,X_22))
| join(X_22,join(Y,X_22)) = join(X_22,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_22,Y),X_22),join(X_22,Y)) ),[0],$fot(join(X_22,join(Y,X_22)))]]) ).
cnf(refute_0_84,plain,
( join(join(X_22,Y),X_22) != join(X_22,Y)
| join(X_22,join(Y,X_22)) = join(X_22,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_22,Y),X_22),join(X_22,join(Y,X_22))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
join(X_22,join(Y,X_22)) = join(X_22,Y),
inference(resolve,[$cnf( $equal(join(join(X_22,Y),X_22),join(X_22,Y)) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
join(join(X_41,complement(join(Y,X_41))),join(Y,join(X_41,complement(join(Y,X_41))))) = join(join(X_41,complement(join(Y,X_41))),Y),
inference(subst,[],[refute_0_85:[bind(X_22,$fot(join(X_41,complement(join(Y,X_41)))))]]) ).
cnf(refute_0_87,plain,
( join(X,Y) != join(Y,X)
| join(Y,X) = join(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).
cnf(refute_0_88,plain,
join(Y,X) = join(X,Y),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_87]) ).
cnf(refute_0_89,plain,
join(complement(X),X) = join(X,complement(X)),
inference(subst,[],[refute_0_88:[bind(Y,$fot(complement(X)))]]) ).
cnf(refute_0_90,plain,
( join(complement(X),X) != join(X,complement(X))
| join(complement(X),X) != n1
| join(X,complement(X)) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X),X),n1) ),[0],$fot(join(X,complement(X)))]]) ).
cnf(refute_0_91,plain,
( join(complement(X),X) != n1
| join(X,complement(X)) = n1 ),
inference(resolve,[$cnf( $equal(join(complement(X),X),join(X,complement(X))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
join(X,complement(X)) = n1,
inference(resolve,[$cnf( $equal(join(complement(X),X),n1) )],[invertability1,refute_0_91]) ).
cnf(refute_0_93,plain,
join(join(X_37,X_38),complement(join(X_37,X_38))) = n1,
inference(subst,[],[refute_0_92:[bind(X,$fot(join(X_37,X_38)))]]) ).
cnf(refute_0_94,plain,
join(join(X_37,X_38),complement(join(X_37,X_38))) = join(X_37,join(X_38,complement(join(X_37,X_38)))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(complement(join(X_37,X_38))))]]) ).
cnf(refute_0_95,plain,
( join(join(X_37,X_38),complement(join(X_37,X_38))) != join(X_37,join(X_38,complement(join(X_37,X_38))))
| join(join(X_37,X_38),complement(join(X_37,X_38))) != n1
| join(X_37,join(X_38,complement(join(X_37,X_38)))) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_37,X_38),complement(join(X_37,X_38))),n1) ),[0],$fot(join(X_37,join(X_38,complement(join(X_37,X_38)))))]]) ).
cnf(refute_0_96,plain,
( join(join(X_37,X_38),complement(join(X_37,X_38))) != n1
| join(X_37,join(X_38,complement(join(X_37,X_38)))) = n1 ),
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),complement(join(X_37,X_38))),join(X_37,join(X_38,complement(join(X_37,X_38))))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
join(X_37,join(X_38,complement(join(X_37,X_38)))) = n1,
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),complement(join(X_37,X_38))),n1) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
join(Y,join(X_41,complement(join(Y,X_41)))) = n1,
inference(subst,[],[refute_0_97:[bind(X_37,$fot(Y)),bind(X_38,$fot(X_41))]]) ).
cnf(refute_0_99,plain,
( join(Y,join(X_41,complement(join(Y,X_41)))) != n1
| join(join(X_41,complement(join(Y,X_41))),join(Y,join(X_41,complement(join(Y,X_41))))) != join(join(X_41,complement(join(Y,X_41))),Y)
| join(join(X_41,complement(join(Y,X_41))),n1) = join(join(X_41,complement(join(Y,X_41))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),join(Y,join(X_41,complement(join(Y,X_41))))),join(join(X_41,complement(join(Y,X_41))),Y)) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_100,plain,
( join(join(X_41,complement(join(Y,X_41))),join(Y,join(X_41,complement(join(Y,X_41))))) != join(join(X_41,complement(join(Y,X_41))),Y)
| join(join(X_41,complement(join(Y,X_41))),n1) = join(join(X_41,complement(join(Y,X_41))),Y) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_41,complement(join(Y,X_41)))),n1) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
join(join(X_41,complement(join(Y,X_41))),n1) = join(join(X_41,complement(join(Y,X_41))),Y),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),join(Y,join(X_41,complement(join(Y,X_41))))),join(join(X_41,complement(join(Y,X_41))),Y)) )],[refute_0_86,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(n1,join(n1,Y)) = n1,
inference(subst,[],[absorption1:[bind(X,$fot(n1))]]) ).
cnf(refute_0_103,plain,
meet(X_5,join(X_5,complement(X_5))) = X_5,
inference(subst,[],[absorption1:[bind(X,$fot(X_5)),bind(Y,$fot(complement(X_5)))]]) ).
cnf(refute_0_104,plain,
join(X_5,complement(X_5)) = n1,
inference(subst,[],[refute_0_92:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_105,plain,
( join(X_5,complement(X_5)) != n1
| meet(X_5,join(X_5,complement(X_5))) != X_5
| meet(X_5,n1) = X_5 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_5,join(X_5,complement(X_5))),X_5) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_106,plain,
( meet(X_5,join(X_5,complement(X_5))) != X_5
| meet(X_5,n1) = X_5 ),
inference(resolve,[$cnf( $equal(join(X_5,complement(X_5)),n1) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
meet(X_5,n1) = X_5,
inference(resolve,[$cnf( $equal(meet(X_5,join(X_5,complement(X_5))),X_5) )],[refute_0_103,refute_0_106]) ).
cnf(refute_0_108,plain,
meet(X_5,n1) = meet(n1,X_5),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_5)),bind(Y,$fot(n1))]]) ).
cnf(refute_0_109,plain,
( meet(X_5,n1) != X_5
| meet(X_5,n1) != meet(n1,X_5)
| meet(n1,X_5) = X_5 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_5,n1),X_5) ),[0],$fot(meet(n1,X_5))]]) ).
cnf(refute_0_110,plain,
( meet(X_5,n1) != X_5
| meet(n1,X_5) = X_5 ),
inference(resolve,[$cnf( $equal(meet(X_5,n1),meet(n1,X_5)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
meet(n1,X_5) = X_5,
inference(resolve,[$cnf( $equal(meet(X_5,n1),X_5) )],[refute_0_107,refute_0_110]) ).
cnf(refute_0_112,plain,
meet(n1,join(n1,Y)) = join(n1,Y),
inference(subst,[],[refute_0_111:[bind(X_5,$fot(join(n1,Y)))]]) ).
cnf(refute_0_113,plain,
( meet(n1,join(n1,Y)) != join(n1,Y)
| meet(n1,join(n1,Y)) != n1
| join(n1,Y) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(meet(n1,join(n1,Y)),n1) ),[0],$fot(join(n1,Y))]]) ).
cnf(refute_0_114,plain,
( meet(n1,join(n1,Y)) != n1
| join(n1,Y) = n1 ),
inference(resolve,[$cnf( $equal(meet(n1,join(n1,Y)),join(n1,Y)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
join(n1,Y) = n1,
inference(resolve,[$cnf( $equal(meet(n1,join(n1,Y)),n1) )],[refute_0_102,refute_0_114]) ).
cnf(refute_0_116,plain,
join(n1,Y) = join(Y,n1),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(n1))]]) ).
cnf(refute_0_117,plain,
( join(n1,Y) != join(Y,n1)
| join(n1,Y) != n1
| join(Y,n1) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(join(n1,Y),n1) ),[0],$fot(join(Y,n1))]]) ).
cnf(refute_0_118,plain,
( join(n1,Y) != n1
| join(Y,n1) = n1 ),
inference(resolve,[$cnf( $equal(join(n1,Y),join(Y,n1)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
join(Y,n1) = n1,
inference(resolve,[$cnf( $equal(join(n1,Y),n1) )],[refute_0_115,refute_0_118]) ).
cnf(refute_0_120,plain,
join(join(X_41,complement(join(Y,X_41))),n1) = n1,
inference(subst,[],[refute_0_119:[bind(Y,$fot(join(X_41,complement(join(Y,X_41)))))]]) ).
cnf(refute_0_121,plain,
( join(join(X_41,complement(join(Y,X_41))),n1) != join(join(X_41,complement(join(Y,X_41))),Y)
| join(join(X_41,complement(join(Y,X_41))),n1) != n1
| n1 = join(join(X_41,complement(join(Y,X_41))),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),n1),join(join(X_41,complement(join(Y,X_41))),Y)) ),[0],$fot(n1)]]) ).
cnf(refute_0_122,plain,
( join(join(X_41,complement(join(Y,X_41))),n1) != join(join(X_41,complement(join(Y,X_41))),Y)
| n1 = join(join(X_41,complement(join(Y,X_41))),Y) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),n1),n1) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
join(join(X_37,X_38),X_39) = join(X_37,join(X_38,X_39)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_124,plain,
join(X_39,X_38) = join(X_38,X_39),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_39)),bind(Y,$fot(X_38))]]) ).
cnf(refute_0_125,plain,
( join(X_39,X_38) != join(X_38,X_39)
| join(X_38,X_39) = join(X_39,X_38) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_39,X_38))),bind(Y0,$fot(join(X_38,X_39)))]]) ).
cnf(refute_0_126,plain,
join(X_38,X_39) = join(X_39,X_38),
inference(resolve,[$cnf( $equal(join(X_39,X_38),join(X_38,X_39)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
( join(X_38,X_39) != join(X_39,X_38)
| join(join(X_37,X_38),X_39) != join(X_37,join(X_38,X_39))
| join(join(X_37,X_38),X_39) = join(X_37,join(X_39,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_37,X_38),X_39),join(X_37,join(X_38,X_39))) ),[1,1],$fot(join(X_39,X_38))]]) ).
cnf(refute_0_128,plain,
( join(join(X_37,X_38),X_39) != join(X_37,join(X_38,X_39))
| join(join(X_37,X_38),X_39) = join(X_37,join(X_39,X_38)) ),
inference(resolve,[$cnf( $equal(join(X_38,X_39),join(X_39,X_38)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
join(join(X_37,X_38),X_39) = join(X_37,join(X_39,X_38)),
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),X_39),join(X_37,join(X_38,X_39))) )],[refute_0_123,refute_0_128]) ).
cnf(refute_0_130,plain,
( join(join(X_37,X_38),X_39) != join(X_37,join(X_38,X_39))
| join(join(X_37,X_38),X_39) != join(X_37,join(X_39,X_38))
| join(X_37,join(X_38,X_39)) = join(X_37,join(X_39,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_37,X_38),X_39),join(X_37,join(X_39,X_38))) ),[0],$fot(join(X_37,join(X_38,X_39)))]]) ).
cnf(refute_0_131,plain,
( join(join(X_37,X_38),X_39) != join(X_37,join(X_39,X_38))
| join(X_37,join(X_38,X_39)) = join(X_37,join(X_39,X_38)) ),
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),X_39),join(X_37,join(X_38,X_39))) )],[refute_0_123,refute_0_130]) ).
cnf(refute_0_132,plain,
join(X_37,join(X_38,X_39)) = join(X_37,join(X_39,X_38)),
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),X_39),join(X_37,join(X_39,X_38))) )],[refute_0_129,refute_0_131]) ).
cnf(refute_0_133,plain,
( join(X_37,join(X_38,X_39)) != join(X_37,join(X_39,X_38))
| join(X_37,join(X_39,X_38)) = join(X_37,join(X_38,X_39)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_37,join(X_38,X_39)))),bind(Y0,$fot(join(X_37,join(X_39,X_38))))]]) ).
cnf(refute_0_134,plain,
join(X_37,join(X_39,X_38)) = join(X_37,join(X_38,X_39)),
inference(resolve,[$cnf( $equal(join(X_37,join(X_38,X_39)),join(X_37,join(X_39,X_38))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
join(X_41,join(complement(join(Y,X_41)),Y)) = join(X_41,join(Y,complement(join(Y,X_41)))),
inference(subst,[],[refute_0_134:[bind(X_37,$fot(X_41)),bind(X_38,$fot(Y)),bind(X_39,$fot(complement(join(Y,X_41))))]]) ).
cnf(refute_0_136,plain,
join(join(X_41,complement(join(Y,X_41))),Y) = join(X_41,join(complement(join(Y,X_41)),Y)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_41)),bind(Y,$fot(complement(join(Y,X_41)))),bind(Z,$fot(Y))]]) ).
cnf(refute_0_137,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_138,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_137]) ).
cnf(refute_0_139,plain,
( join(X_41,join(complement(join(Y,X_41)),Y)) != join(X_41,join(Y,complement(join(Y,X_41))))
| join(join(X_41,complement(join(Y,X_41))),Y) != join(X_41,join(complement(join(Y,X_41)),Y))
| join(join(X_41,complement(join(Y,X_41))),Y) = join(X_41,join(Y,complement(join(Y,X_41)))) ),
inference(subst,[],[refute_0_138:[bind(X0,$fot(join(join(X_41,complement(join(Y,X_41))),Y))),bind(Y0,$fot(join(X_41,join(complement(join(Y,X_41)),Y)))),bind(Z0,$fot(join(X_41,join(Y,complement(join(Y,X_41))))))]]) ).
cnf(refute_0_140,plain,
( join(X_41,join(complement(join(Y,X_41)),Y)) != join(X_41,join(Y,complement(join(Y,X_41))))
| join(join(X_41,complement(join(Y,X_41))),Y) = join(X_41,join(Y,complement(join(Y,X_41)))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),Y),join(X_41,join(complement(join(Y,X_41)),Y))) )],[refute_0_136,refute_0_139]) ).
cnf(refute_0_141,plain,
join(join(X_41,complement(join(Y,X_41))),Y) = join(X_41,join(Y,complement(join(Y,X_41)))),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(join(Y,X_41)),Y)),join(X_41,join(Y,complement(join(Y,X_41))))) )],[refute_0_135,refute_0_140]) ).
cnf(refute_0_142,plain,
( join(join(X_41,complement(join(Y,X_41))),Y) != join(X_41,join(Y,complement(join(Y,X_41))))
| n1 != join(join(X_41,complement(join(Y,X_41))),Y)
| n1 = join(X_41,join(Y,complement(join(Y,X_41)))) ),
introduced(tautology,[equality,[$cnf( $equal(n1,join(join(X_41,complement(join(Y,X_41))),Y)) ),[1],$fot(join(X_41,join(Y,complement(join(Y,X_41)))))]]) ).
cnf(refute_0_143,plain,
( n1 != join(join(X_41,complement(join(Y,X_41))),Y)
| n1 = join(X_41,join(Y,complement(join(Y,X_41)))) ),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),Y),join(X_41,join(Y,complement(join(Y,X_41))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( join(join(X_41,complement(join(Y,X_41))),n1) != join(join(X_41,complement(join(Y,X_41))),Y)
| n1 = join(X_41,join(Y,complement(join(Y,X_41)))) ),
inference(resolve,[$cnf( $equal(n1,join(join(X_41,complement(join(Y,X_41))),Y)) )],[refute_0_122,refute_0_143]) ).
cnf(refute_0_145,plain,
n1 = join(X_41,join(Y,complement(join(Y,X_41)))),
inference(resolve,[$cnf( $equal(join(join(X_41,complement(join(Y,X_41))),n1),join(join(X_41,complement(join(Y,X_41))),Y)) )],[refute_0_101,refute_0_144]) ).
cnf(refute_0_146,plain,
n1 = join(complement(X_74),join(Y,complement(join(Y,complement(X_74))))),
inference(subst,[],[refute_0_145:[bind(X_41,$fot(complement(X_74)))]]) ).
cnf(refute_0_147,plain,
( n1 != join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))
| join(complement(X_74),join(Y,complement(join(Y,complement(X_74))))) = n1 ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(n1)),bind(Y0,$fot(join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))))]]) ).
cnf(refute_0_148,plain,
join(complement(X_74),join(Y,complement(join(Y,complement(X_74))))) = n1,
inference(resolve,[$cnf( $equal(n1,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
( join(complement(X_74),join(Y,complement(join(Y,complement(X_74))))) != n1
| meet(X_74,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))) != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| meet(X_74,n1) = meet(X_74,join(Y,complement(join(Y,complement(X_74))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_74,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))),meet(X_74,join(Y,complement(join(Y,complement(X_74)))))) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_150,plain,
( meet(X_74,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))) != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| meet(X_74,n1) = meet(X_74,join(Y,complement(join(Y,complement(X_74))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_74),join(Y,complement(join(Y,complement(X_74))))),n1) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
meet(X_74,n1) = meet(X_74,join(Y,complement(join(Y,complement(X_74))))),
inference(resolve,[$cnf( $equal(meet(X_74,join(complement(X_74),join(Y,complement(join(Y,complement(X_74)))))),meet(X_74,join(Y,complement(join(Y,complement(X_74)))))) )],[refute_0_73,refute_0_150]) ).
cnf(refute_0_152,plain,
meet(X_74,n1) = X_74,
inference(subst,[],[refute_0_107:[bind(X_5,$fot(X_74))]]) ).
cnf(refute_0_153,plain,
( meet(X_74,n1) != X_74
| meet(X_74,n1) != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| X_74 = meet(X_74,join(Y,complement(join(Y,complement(X_74))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_74,n1),meet(X_74,join(Y,complement(join(Y,complement(X_74)))))) ),[0],$fot(X_74)]]) ).
cnf(refute_0_154,plain,
( meet(X_74,n1) != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| X_74 = meet(X_74,join(Y,complement(join(Y,complement(X_74))))) ),
inference(resolve,[$cnf( $equal(meet(X_74,n1),X_74) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
X_74 = meet(X_74,join(Y,complement(join(Y,complement(X_74))))),
inference(resolve,[$cnf( $equal(meet(X_74,n1),meet(X_74,join(Y,complement(join(Y,complement(X_74)))))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
meet(X,join(Y,complement(join(X_130,complement(X))))) = join(meet(X,Y),meet(X,complement(join(X_130,complement(X))))),
inference(subst,[],[distributivity:[bind(Z,$fot(complement(join(X_130,complement(X)))))]]) ).
cnf(refute_0_157,plain,
meet(X_71,join(X_72,complement(X_71))) = join(meet(X_71,X_72),meet(X_71,complement(X_71))),
inference(subst,[],[distributivity:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(Z,$fot(complement(X_71)))]]) ).
cnf(refute_0_158,plain,
( meet(X_71,complement(X_71)) != n0
| meet(X_71,join(X_72,complement(X_71))) != join(meet(X_71,X_72),meet(X_71,complement(X_71)))
| meet(X_71,join(X_72,complement(X_71))) = join(meet(X_71,X_72),n0) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(X_72,complement(X_71))),join(meet(X_71,X_72),meet(X_71,complement(X_71)))) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_159,plain,
( meet(X_71,join(X_72,complement(X_71))) != join(meet(X_71,X_72),meet(X_71,complement(X_71)))
| meet(X_71,join(X_72,complement(X_71))) = join(meet(X_71,X_72),n0) ),
inference(resolve,[$cnf( $equal(meet(X_71,complement(X_71)),n0) )],[refute_0_66,refute_0_158]) ).
cnf(refute_0_160,plain,
meet(X_71,join(X_72,complement(X_71))) = join(meet(X_71,X_72),n0),
inference(resolve,[$cnf( $equal(meet(X_71,join(X_72,complement(X_71))),join(meet(X_71,X_72),meet(X_71,complement(X_71)))) )],[refute_0_157,refute_0_159]) ).
cnf(refute_0_161,plain,
join(meet(X_71,X_72),n0) = meet(X_71,X_72),
inference(subst,[],[refute_0_38:[bind(X_8,$fot(meet(X_71,X_72)))]]) ).
cnf(refute_0_162,plain,
( join(meet(X_71,X_72),n0) != meet(X_71,X_72)
| meet(X_71,join(X_72,complement(X_71))) != join(meet(X_71,X_72),n0)
| meet(X_71,join(X_72,complement(X_71))) = meet(X_71,X_72) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(X_72,complement(X_71))),join(meet(X_71,X_72),n0)) ),[1],$fot(meet(X_71,X_72))]]) ).
cnf(refute_0_163,plain,
( meet(X_71,join(X_72,complement(X_71))) != join(meet(X_71,X_72),n0)
| meet(X_71,join(X_72,complement(X_71))) = meet(X_71,X_72) ),
inference(resolve,[$cnf( $equal(join(meet(X_71,X_72),n0),meet(X_71,X_72)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
meet(X_71,join(X_72,complement(X_71))) = meet(X_71,X_72),
inference(resolve,[$cnf( $equal(meet(X_71,join(X_72,complement(X_71))),join(meet(X_71,X_72),n0)) )],[refute_0_160,refute_0_163]) ).
cnf(refute_0_165,plain,
meet(complement(X),join(X_77,complement(complement(X)))) = meet(complement(X),X_77),
inference(subst,[],[refute_0_164:[bind(X_71,$fot(complement(X))),bind(X_72,$fot(X_77))]]) ).
cnf(refute_0_166,plain,
( complement(complement(X)) != X
| meet(complement(X),join(X_77,complement(complement(X)))) != meet(complement(X),X_77)
| meet(complement(X),join(X_77,X)) = meet(complement(X),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X),join(X_77,complement(complement(X)))),meet(complement(X),X_77)) ),[0,1,1],$fot(X)]]) ).
cnf(refute_0_167,plain,
( meet(complement(X),join(X_77,complement(complement(X)))) != meet(complement(X),X_77)
| meet(complement(X),join(X_77,X)) = meet(complement(X),X_77) ),
inference(resolve,[$cnf( $equal(complement(complement(X)),X) )],[invertability3,refute_0_166]) ).
cnf(refute_0_168,plain,
meet(complement(X),join(X_77,X)) = meet(complement(X),X_77),
inference(resolve,[$cnf( $equal(meet(complement(X),join(X_77,complement(complement(X)))),meet(complement(X),X_77)) )],[refute_0_165,refute_0_167]) ).
cnf(refute_0_169,plain,
meet(complement(join(X_105,complement(X_77))),join(X_77,join(X_105,complement(X_77)))) = meet(complement(join(X_105,complement(X_77))),X_77),
inference(subst,[],[refute_0_168:[bind(X,$fot(join(X_105,complement(X_77))))]]) ).
cnf(refute_0_170,plain,
join(X,join(X_37,X_38)) = join(join(X_37,X_38),X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_37,X_38)))]]) ).
cnf(refute_0_171,plain,
join(join(X_37,X_38),X) = join(X_37,join(X_38,X)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_37)),bind(Y,$fot(X_38)),bind(Z,$fot(X))]]) ).
cnf(refute_0_172,plain,
( join(X,join(X_37,X_38)) != join(join(X_37,X_38),X)
| join(join(X_37,X_38),X) != join(X_37,join(X_38,X))
| join(X,join(X_37,X_38)) = join(X_37,join(X_38,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_37,X_38)),join(X_37,join(X_38,X))) ),[0],$fot(join(join(X_37,X_38),X))]]) ).
cnf(refute_0_173,plain,
( join(X,join(X_37,X_38)) != join(join(X_37,X_38),X)
| join(X,join(X_37,X_38)) = join(X_37,join(X_38,X)) ),
inference(resolve,[$cnf( $equal(join(join(X_37,X_38),X),join(X_37,join(X_38,X))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
join(X,join(X_37,X_38)) = join(X_37,join(X_38,X)),
inference(resolve,[$cnf( $equal(join(X,join(X_37,X_38)),join(join(X_37,X_38),X)) )],[refute_0_170,refute_0_173]) ).
cnf(refute_0_175,plain,
join(complement(X_61),join(X_60,X_61)) = join(X_60,join(X_61,complement(X_61))),
inference(subst,[],[refute_0_174:[bind(X,$fot(complement(X_61))),bind(X_37,$fot(X_60)),bind(X_38,$fot(X_61))]]) ).
cnf(refute_0_176,plain,
join(X_61,complement(X_61)) = n1,
inference(subst,[],[refute_0_92:[bind(X,$fot(X_61))]]) ).
cnf(refute_0_177,plain,
( join(X_61,complement(X_61)) != n1
| join(complement(X_61),join(X_60,X_61)) != join(X_60,join(X_61,complement(X_61)))
| join(complement(X_61),join(X_60,X_61)) = join(X_60,n1) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_61),join(X_60,X_61)),join(X_60,join(X_61,complement(X_61)))) ),[1,1],$fot(n1)]]) ).
cnf(refute_0_178,plain,
( join(complement(X_61),join(X_60,X_61)) != join(X_60,join(X_61,complement(X_61)))
| join(complement(X_61),join(X_60,X_61)) = join(X_60,n1) ),
inference(resolve,[$cnf( $equal(join(X_61,complement(X_61)),n1) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
join(complement(X_61),join(X_60,X_61)) = join(X_60,n1),
inference(resolve,[$cnf( $equal(join(complement(X_61),join(X_60,X_61)),join(X_60,join(X_61,complement(X_61)))) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
join(X_59,join(X_60,X_61)) = join(X_60,join(X_61,X_59)),
inference(subst,[],[refute_0_174:[bind(X,$fot(X_59)),bind(X_37,$fot(X_60)),bind(X_38,$fot(X_61))]]) ).
cnf(refute_0_181,plain,
join(X_61,X_60) = join(X_60,X_61),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_61)),bind(Y,$fot(X_60))]]) ).
cnf(refute_0_182,plain,
( join(X_61,X_60) != join(X_60,X_61)
| join(X_60,X_61) = join(X_61,X_60) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_61,X_60))),bind(Y0,$fot(join(X_60,X_61)))]]) ).
cnf(refute_0_183,plain,
join(X_60,X_61) = join(X_61,X_60),
inference(resolve,[$cnf( $equal(join(X_61,X_60),join(X_60,X_61)) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
( join(X_59,join(X_60,X_61)) != join(X_60,join(X_61,X_59))
| join(X_60,X_61) != join(X_61,X_60)
| join(X_59,join(X_61,X_60)) = join(X_60,join(X_61,X_59)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_59,join(X_60,X_61)),join(X_60,join(X_61,X_59))) ),[0,1],$fot(join(X_61,X_60))]]) ).
cnf(refute_0_185,plain,
( join(X_59,join(X_60,X_61)) != join(X_60,join(X_61,X_59))
| join(X_59,join(X_61,X_60)) = join(X_60,join(X_61,X_59)) ),
inference(resolve,[$cnf( $equal(join(X_60,X_61),join(X_61,X_60)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
join(X_59,join(X_61,X_60)) = join(X_60,join(X_61,X_59)),
inference(resolve,[$cnf( $equal(join(X_59,join(X_60,X_61)),join(X_60,join(X_61,X_59))) )],[refute_0_180,refute_0_185]) ).
cnf(refute_0_187,plain,
( join(X_59,join(X_61,X_60)) != join(X_60,join(X_61,X_59))
| join(X_60,join(X_61,X_59)) = join(X_59,join(X_61,X_60)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_59,join(X_61,X_60)))),bind(Y0,$fot(join(X_60,join(X_61,X_59))))]]) ).
cnf(refute_0_188,plain,
join(X_60,join(X_61,X_59)) = join(X_59,join(X_61,X_60)),
inference(resolve,[$cnf( $equal(join(X_59,join(X_61,X_60)),join(X_60,join(X_61,X_59))) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
join(complement(X_61),join(X_60,X_61)) = join(X_61,join(X_60,complement(X_61))),
inference(subst,[],[refute_0_188:[bind(X_59,$fot(X_61)),bind(X_60,$fot(complement(X_61))),bind(X_61,$fot(X_60))]]) ).
cnf(refute_0_190,plain,
( join(complement(X_61),join(X_60,X_61)) != join(X_60,n1)
| join(complement(X_61),join(X_60,X_61)) != join(X_61,join(X_60,complement(X_61)))
| join(X_61,join(X_60,complement(X_61))) = join(X_60,n1) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_61),join(X_60,X_61)),join(X_60,n1)) ),[0],$fot(join(X_61,join(X_60,complement(X_61))))]]) ).
cnf(refute_0_191,plain,
( join(complement(X_61),join(X_60,X_61)) != join(X_60,n1)
| join(X_61,join(X_60,complement(X_61))) = join(X_60,n1) ),
inference(resolve,[$cnf( $equal(join(complement(X_61),join(X_60,X_61)),join(X_61,join(X_60,complement(X_61)))) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
join(X_60,n1) = n1,
inference(subst,[],[refute_0_119:[bind(Y,$fot(X_60))]]) ).
cnf(refute_0_193,plain,
( join(X_60,n1) != n1
| join(X_61,join(X_60,complement(X_61))) != join(X_60,n1)
| join(X_61,join(X_60,complement(X_61))) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_61,join(X_60,complement(X_61))),join(X_60,n1)) ),[1],$fot(n1)]]) ).
cnf(refute_0_194,plain,
( join(X_61,join(X_60,complement(X_61))) != join(X_60,n1)
| join(X_61,join(X_60,complement(X_61))) = n1 ),
inference(resolve,[$cnf( $equal(join(X_60,n1),n1) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
( join(complement(X_61),join(X_60,X_61)) != join(X_60,n1)
| join(X_61,join(X_60,complement(X_61))) = n1 ),
inference(resolve,[$cnf( $equal(join(X_61,join(X_60,complement(X_61))),join(X_60,n1)) )],[refute_0_191,refute_0_194]) ).
cnf(refute_0_196,plain,
join(X_61,join(X_60,complement(X_61))) = n1,
inference(resolve,[$cnf( $equal(join(complement(X_61),join(X_60,X_61)),join(X_60,n1)) )],[refute_0_179,refute_0_195]) ).
cnf(refute_0_197,plain,
join(X_77,join(X_105,complement(X_77))) = n1,
inference(subst,[],[refute_0_196:[bind(X_60,$fot(X_105)),bind(X_61,$fot(X_77))]]) ).
cnf(refute_0_198,plain,
( join(X_77,join(X_105,complement(X_77))) != n1
| meet(complement(join(X_105,complement(X_77))),join(X_77,join(X_105,complement(X_77)))) != meet(complement(join(X_105,complement(X_77))),X_77)
| meet(complement(join(X_105,complement(X_77))),n1) = meet(complement(join(X_105,complement(X_77))),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),join(X_77,join(X_105,complement(X_77)))),meet(complement(join(X_105,complement(X_77))),X_77)) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_199,plain,
( meet(complement(join(X_105,complement(X_77))),join(X_77,join(X_105,complement(X_77)))) != meet(complement(join(X_105,complement(X_77))),X_77)
| meet(complement(join(X_105,complement(X_77))),n1) = meet(complement(join(X_105,complement(X_77))),X_77) ),
inference(resolve,[$cnf( $equal(join(X_77,join(X_105,complement(X_77))),n1) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
meet(complement(join(X_105,complement(X_77))),n1) = meet(complement(join(X_105,complement(X_77))),X_77),
inference(resolve,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),join(X_77,join(X_105,complement(X_77)))),meet(complement(join(X_105,complement(X_77))),X_77)) )],[refute_0_169,refute_0_199]) ).
cnf(refute_0_201,plain,
meet(n1,complement(join(X_105,complement(X_77)))) = complement(join(X_105,complement(X_77))),
inference(subst,[],[refute_0_111:[bind(X_5,$fot(complement(join(X_105,complement(X_77)))))]]) ).
cnf(refute_0_202,plain,
join(meet(X_57,Y),meet(Y,meet(X_57,Y))) = meet(X_57,Y),
inference(subst,[],[refute_0_76:[bind(X,$fot(meet(X_57,Y)))]]) ).
cnf(refute_0_203,plain,
( join(X,Y) != join(Y,X)
| meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,Y)),X) ),[0,1],$fot(join(Y,X))]]) ).
cnf(refute_0_204,plain,
( meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_203]) ).
cnf(refute_0_205,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_204]) ).
cnf(refute_0_206,plain,
meet(meet(X_26,Y),join(X_26,meet(X_26,Y))) = meet(X_26,Y),
inference(subst,[],[refute_0_205:[bind(X,$fot(meet(X_26,Y))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_207,plain,
join(X_26,meet(X_26,Y)) = X_26,
inference(subst,[],[absorption2:[bind(X,$fot(X_26))]]) ).
cnf(refute_0_208,plain,
( join(X_26,meet(X_26,Y)) != X_26
| meet(meet(X_26,Y),join(X_26,meet(X_26,Y))) != meet(X_26,Y)
| meet(meet(X_26,Y),X_26) = meet(X_26,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_26,Y),join(X_26,meet(X_26,Y))),meet(X_26,Y)) ),[0,1],$fot(X_26)]]) ).
cnf(refute_0_209,plain,
( meet(meet(X_26,Y),join(X_26,meet(X_26,Y))) != meet(X_26,Y)
| meet(meet(X_26,Y),X_26) = meet(X_26,Y) ),
inference(resolve,[$cnf( $equal(join(X_26,meet(X_26,Y)),X_26) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
meet(meet(X_26,Y),X_26) = meet(X_26,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_26,Y),join(X_26,meet(X_26,Y))),meet(X_26,Y)) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(meet(X_26,Y),X_26) = meet(X_26,meet(Y,X_26)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_26)),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_212,plain,
( meet(meet(X_26,Y),X_26) != meet(X_26,Y)
| meet(meet(X_26,Y),X_26) != meet(X_26,meet(Y,X_26))
| meet(X_26,meet(Y,X_26)) = meet(X_26,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_26,Y),X_26),meet(X_26,Y)) ),[0],$fot(meet(X_26,meet(Y,X_26)))]]) ).
cnf(refute_0_213,plain,
( meet(meet(X_26,Y),X_26) != meet(X_26,Y)
| meet(X_26,meet(Y,X_26)) = meet(X_26,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_26,Y),X_26),meet(X_26,meet(Y,X_26))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
meet(X_26,meet(Y,X_26)) = meet(X_26,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_26,Y),X_26),meet(X_26,Y)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
meet(Y,meet(X_57,Y)) = meet(Y,X_57),
inference(subst,[],[refute_0_214:[bind(Y,$fot(X_57)),bind(X_26,$fot(Y))]]) ).
cnf(refute_0_216,plain,
( join(meet(X_57,Y),meet(Y,meet(X_57,Y))) != meet(X_57,Y)
| meet(Y,meet(X_57,Y)) != meet(Y,X_57)
| join(meet(X_57,Y),meet(Y,X_57)) = meet(X_57,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_57,Y),meet(Y,meet(X_57,Y))),meet(X_57,Y)) ),[0,1],$fot(meet(Y,X_57))]]) ).
cnf(refute_0_217,plain,
( join(meet(X_57,Y),meet(Y,meet(X_57,Y))) != meet(X_57,Y)
| join(meet(X_57,Y),meet(Y,X_57)) = meet(X_57,Y) ),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_57,Y)),meet(Y,X_57)) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
join(meet(X_57,Y),meet(Y,X_57)) = meet(X_57,Y),
inference(resolve,[$cnf( $equal(join(meet(X_57,Y),meet(Y,meet(X_57,Y))),meet(X_57,Y)) )],[refute_0_202,refute_0_217]) ).
cnf(refute_0_219,plain,
join(X_57,X_57) = X_57,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_57))]]) ).
cnf(refute_0_220,plain,
meet(Y,join(X_57,X_57)) = meet(Y,join(X_57,X_57)),
introduced(tautology,[refl,[$fot(meet(Y,join(X_57,X_57)))]]) ).
cnf(refute_0_221,plain,
( join(X_57,X_57) != X_57
| meet(Y,join(X_57,X_57)) != meet(Y,join(X_57,X_57))
| meet(Y,join(X_57,X_57)) = meet(Y,X_57) ),
introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(X_57,X_57)),meet(Y,join(X_57,X_57))) ),[1,1],$fot(X_57)]]) ).
cnf(refute_0_222,plain,
( join(X_57,X_57) != X_57
| meet(Y,join(X_57,X_57)) = meet(Y,X_57) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_57,X_57)),meet(Y,join(X_57,X_57))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
meet(Y,join(X_57,X_57)) = meet(Y,X_57),
inference(resolve,[$cnf( $equal(join(X_57,X_57),X_57) )],[refute_0_219,refute_0_222]) ).
cnf(refute_0_224,plain,
meet(X_71,join(X_72,X_73)) = join(meet(X_71,X_72),meet(X_71,X_73)),
inference(subst,[],[distributivity:[bind(X,$fot(X_71)),bind(Y,$fot(X_72)),bind(Z,$fot(X_73))]]) ).
cnf(refute_0_225,plain,
meet(X_72,X_71) = meet(X_71,X_72),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_72)),bind(Y,$fot(X_71))]]) ).
cnf(refute_0_226,plain,
( meet(X_72,X_71) != meet(X_71,X_72)
| meet(X_71,X_72) = meet(X_72,X_71) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_72,X_71))),bind(Y0,$fot(meet(X_71,X_72)))]]) ).
cnf(refute_0_227,plain,
meet(X_71,X_72) = meet(X_72,X_71),
inference(resolve,[$cnf( $equal(meet(X_72,X_71),meet(X_71,X_72)) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
( meet(X_71,X_72) != meet(X_72,X_71)
| meet(X_71,join(X_72,X_73)) != join(meet(X_71,X_72),meet(X_71,X_73))
| meet(X_71,join(X_72,X_73)) = join(meet(X_72,X_71),meet(X_71,X_73)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_71,join(X_72,X_73)),join(meet(X_71,X_72),meet(X_71,X_73))) ),[1,0],$fot(meet(X_72,X_71))]]) ).
cnf(refute_0_229,plain,
( meet(X_71,join(X_72,X_73)) != join(meet(X_71,X_72),meet(X_71,X_73))
| meet(X_71,join(X_72,X_73)) = join(meet(X_72,X_71),meet(X_71,X_73)) ),
inference(resolve,[$cnf( $equal(meet(X_71,X_72),meet(X_72,X_71)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
meet(X_71,join(X_72,X_73)) = join(meet(X_72,X_71),meet(X_71,X_73)),
inference(resolve,[$cnf( $equal(meet(X_71,join(X_72,X_73)),join(meet(X_71,X_72),meet(X_71,X_73))) )],[refute_0_224,refute_0_229]) ).
cnf(refute_0_231,plain,
( meet(X_71,join(X_72,X_73)) != join(meet(X_72,X_71),meet(X_71,X_73))
| join(meet(X_72,X_71),meet(X_71,X_73)) = meet(X_71,join(X_72,X_73)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_71,join(X_72,X_73)))),bind(Y0,$fot(join(meet(X_72,X_71),meet(X_71,X_73))))]]) ).
cnf(refute_0_232,plain,
join(meet(X_72,X_71),meet(X_71,X_73)) = meet(X_71,join(X_72,X_73)),
inference(resolve,[$cnf( $equal(meet(X_71,join(X_72,X_73)),join(meet(X_72,X_71),meet(X_71,X_73))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
join(meet(X_57,Y),meet(Y,X_57)) = meet(Y,join(X_57,X_57)),
inference(subst,[],[refute_0_232:[bind(X_71,$fot(Y)),bind(X_72,$fot(X_57)),bind(X_73,$fot(X_57))]]) ).
cnf(refute_0_234,plain,
( join(meet(X_57,Y),meet(Y,X_57)) != meet(Y,join(X_57,X_57))
| meet(Y,join(X_57,X_57)) != meet(Y,X_57)
| join(meet(X_57,Y),meet(Y,X_57)) = meet(Y,X_57) ),
inference(subst,[],[refute_0_138:[bind(X0,$fot(join(meet(X_57,Y),meet(Y,X_57)))),bind(Y0,$fot(meet(Y,join(X_57,X_57)))),bind(Z0,$fot(meet(Y,X_57)))]]) ).
cnf(refute_0_235,plain,
( meet(Y,join(X_57,X_57)) != meet(Y,X_57)
| join(meet(X_57,Y),meet(Y,X_57)) = meet(Y,X_57) ),
inference(resolve,[$cnf( $equal(join(meet(X_57,Y),meet(Y,X_57)),meet(Y,join(X_57,X_57))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
join(meet(X_57,Y),meet(Y,X_57)) = meet(Y,X_57),
inference(resolve,[$cnf( $equal(meet(Y,join(X_57,X_57)),meet(Y,X_57)) )],[refute_0_223,refute_0_235]) ).
cnf(refute_0_237,plain,
( join(meet(X_57,Y),meet(Y,X_57)) != meet(Y,X_57)
| join(meet(X_57,Y),meet(Y,X_57)) != meet(X_57,Y)
| meet(Y,X_57) = meet(X_57,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_57,Y),meet(Y,X_57)),meet(X_57,Y)) ),[0],$fot(meet(Y,X_57))]]) ).
cnf(refute_0_238,plain,
( join(meet(X_57,Y),meet(Y,X_57)) != meet(X_57,Y)
| meet(Y,X_57) = meet(X_57,Y) ),
inference(resolve,[$cnf( $equal(join(meet(X_57,Y),meet(Y,X_57)),meet(Y,X_57)) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
meet(Y,X_57) = meet(X_57,Y),
inference(resolve,[$cnf( $equal(join(meet(X_57,Y),meet(Y,X_57)),meet(X_57,Y)) )],[refute_0_218,refute_0_238]) ).
cnf(refute_0_240,plain,
( meet(Y,X_57) != meet(X_57,Y)
| meet(X_57,Y) = meet(Y,X_57) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(Y,X_57))),bind(Y0,$fot(meet(X_57,Y)))]]) ).
cnf(refute_0_241,plain,
meet(X_57,Y) = meet(Y,X_57),
inference(resolve,[$cnf( $equal(meet(Y,X_57),meet(X_57,Y)) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
meet(complement(join(X_105,complement(X_77))),n1) = meet(n1,complement(join(X_105,complement(X_77)))),
inference(subst,[],[refute_0_241:[bind(Y,$fot(n1)),bind(X_57,$fot(complement(join(X_105,complement(X_77)))))]]) ).
cnf(refute_0_243,plain,
( meet(complement(join(X_105,complement(X_77))),n1) != meet(n1,complement(join(X_105,complement(X_77))))
| meet(n1,complement(join(X_105,complement(X_77)))) != complement(join(X_105,complement(X_77)))
| meet(complement(join(X_105,complement(X_77))),n1) = complement(join(X_105,complement(X_77))) ),
inference(subst,[],[refute_0_138:[bind(X0,$fot(meet(complement(join(X_105,complement(X_77))),n1))),bind(Y0,$fot(meet(n1,complement(join(X_105,complement(X_77)))))),bind(Z0,$fot(complement(join(X_105,complement(X_77)))))]]) ).
cnf(refute_0_244,plain,
( meet(n1,complement(join(X_105,complement(X_77)))) != complement(join(X_105,complement(X_77)))
| meet(complement(join(X_105,complement(X_77))),n1) = complement(join(X_105,complement(X_77))) ),
inference(resolve,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),n1),meet(n1,complement(join(X_105,complement(X_77))))) )],[refute_0_242,refute_0_243]) ).
cnf(refute_0_245,plain,
meet(complement(join(X_105,complement(X_77))),n1) = complement(join(X_105,complement(X_77))),
inference(resolve,[$cnf( $equal(meet(n1,complement(join(X_105,complement(X_77)))),complement(join(X_105,complement(X_77)))) )],[refute_0_201,refute_0_244]) ).
cnf(refute_0_246,plain,
( meet(complement(join(X_105,complement(X_77))),n1) != complement(join(X_105,complement(X_77)))
| meet(complement(join(X_105,complement(X_77))),n1) != meet(complement(join(X_105,complement(X_77))),X_77)
| complement(join(X_105,complement(X_77))) = meet(complement(join(X_105,complement(X_77))),X_77) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),n1),meet(complement(join(X_105,complement(X_77))),X_77)) ),[0],$fot(complement(join(X_105,complement(X_77))))]]) ).
cnf(refute_0_247,plain,
( meet(complement(join(X_105,complement(X_77))),n1) != meet(complement(join(X_105,complement(X_77))),X_77)
| complement(join(X_105,complement(X_77))) = meet(complement(join(X_105,complement(X_77))),X_77) ),
inference(resolve,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),n1),complement(join(X_105,complement(X_77)))) )],[refute_0_245,refute_0_246]) ).
cnf(refute_0_248,plain,
meet(complement(join(X_105,complement(X_77))),X_77) = meet(X_77,complement(join(X_105,complement(X_77)))),
inference(subst,[],[refute_0_241:[bind(Y,$fot(X_77)),bind(X_57,$fot(complement(join(X_105,complement(X_77)))))]]) ).
cnf(refute_0_249,plain,
( complement(join(X_105,complement(X_77))) != meet(complement(join(X_105,complement(X_77))),X_77)
| meet(complement(join(X_105,complement(X_77))),X_77) != meet(X_77,complement(join(X_105,complement(X_77))))
| complement(join(X_105,complement(X_77))) = meet(X_77,complement(join(X_105,complement(X_77)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(join(X_105,complement(X_77))),meet(X_77,complement(join(X_105,complement(X_77))))) ),[0],$fot(meet(complement(join(X_105,complement(X_77))),X_77))]]) ).
cnf(refute_0_250,plain,
( complement(join(X_105,complement(X_77))) != meet(complement(join(X_105,complement(X_77))),X_77)
| complement(join(X_105,complement(X_77))) = meet(X_77,complement(join(X_105,complement(X_77)))) ),
inference(resolve,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),X_77),meet(X_77,complement(join(X_105,complement(X_77))))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( meet(complement(join(X_105,complement(X_77))),n1) != meet(complement(join(X_105,complement(X_77))),X_77)
| complement(join(X_105,complement(X_77))) = meet(X_77,complement(join(X_105,complement(X_77)))) ),
inference(resolve,[$cnf( $equal(complement(join(X_105,complement(X_77))),meet(complement(join(X_105,complement(X_77))),X_77)) )],[refute_0_247,refute_0_250]) ).
cnf(refute_0_252,plain,
complement(join(X_105,complement(X_77))) = meet(X_77,complement(join(X_105,complement(X_77)))),
inference(resolve,[$cnf( $equal(meet(complement(join(X_105,complement(X_77))),n1),meet(complement(join(X_105,complement(X_77))),X_77)) )],[refute_0_200,refute_0_251]) ).
cnf(refute_0_253,plain,
complement(join(X_130,complement(X))) = meet(X,complement(join(X_130,complement(X)))),
inference(subst,[],[refute_0_252:[bind(X_105,$fot(X_130)),bind(X_77,$fot(X))]]) ).
cnf(refute_0_254,plain,
( complement(join(X_130,complement(X))) != meet(X,complement(join(X_130,complement(X))))
| meet(X,complement(join(X_130,complement(X)))) = complement(join(X_130,complement(X))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(join(X_130,complement(X))))),bind(Y0,$fot(meet(X,complement(join(X_130,complement(X))))))]]) ).
cnf(refute_0_255,plain,
meet(X,complement(join(X_130,complement(X)))) = complement(join(X_130,complement(X))),
inference(resolve,[$cnf( $equal(complement(join(X_130,complement(X))),meet(X,complement(join(X_130,complement(X))))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( meet(X,complement(join(X_130,complement(X)))) != complement(join(X_130,complement(X)))
| meet(X,join(Y,complement(join(X_130,complement(X))))) != join(meet(X,Y),meet(X,complement(join(X_130,complement(X)))))
| meet(X,join(Y,complement(join(X_130,complement(X))))) = join(meet(X,Y),complement(join(X_130,complement(X)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,complement(join(X_130,complement(X))))),join(meet(X,Y),meet(X,complement(join(X_130,complement(X)))))) ),[1,1],$fot(complement(join(X_130,complement(X))))]]) ).
cnf(refute_0_257,plain,
( meet(X,join(Y,complement(join(X_130,complement(X))))) != join(meet(X,Y),meet(X,complement(join(X_130,complement(X)))))
| meet(X,join(Y,complement(join(X_130,complement(X))))) = join(meet(X,Y),complement(join(X_130,complement(X)))) ),
inference(resolve,[$cnf( $equal(meet(X,complement(join(X_130,complement(X)))),complement(join(X_130,complement(X)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
meet(X,join(Y,complement(join(X_130,complement(X))))) = join(meet(X,Y),complement(join(X_130,complement(X)))),
inference(resolve,[$cnf( $equal(meet(X,join(Y,complement(join(X_130,complement(X))))),join(meet(X,Y),meet(X,complement(join(X_130,complement(X)))))) )],[refute_0_156,refute_0_257]) ).
cnf(refute_0_259,plain,
meet(X_74,join(Y,complement(join(Y,complement(X_74))))) = join(meet(X_74,Y),complement(join(Y,complement(X_74)))),
inference(subst,[],[refute_0_258:[bind(X,$fot(X_74)),bind(X_130,$fot(Y))]]) ).
cnf(refute_0_260,plain,
( X_74 != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| meet(X_74,join(Y,complement(join(Y,complement(X_74))))) != join(meet(X_74,Y),complement(join(Y,complement(X_74))))
| X_74 = join(meet(X_74,Y),complement(join(Y,complement(X_74)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(meet(X_74,Y),complement(join(Y,complement(X_74))))) ),[0],$fot(meet(X_74,join(Y,complement(join(Y,complement(X_74))))))]]) ).
cnf(refute_0_261,plain,
( X_74 != meet(X_74,join(Y,complement(join(Y,complement(X_74)))))
| X_74 = join(meet(X_74,Y),complement(join(Y,complement(X_74)))) ),
inference(resolve,[$cnf( $equal(meet(X_74,join(Y,complement(join(Y,complement(X_74))))),join(meet(X_74,Y),complement(join(Y,complement(X_74))))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
X_74 = join(meet(X_74,Y),complement(join(Y,complement(X_74)))),
inference(resolve,[$cnf( $equal(X_74,meet(X_74,join(Y,complement(join(Y,complement(X_74)))))) )],[refute_0_155,refute_0_261]) ).
cnf(refute_0_263,plain,
X_242 = join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242)))),
inference(subst,[],[refute_0_262:[bind(Y,$fot(complement(X_243))),bind(X_74,$fot(X_242))]]) ).
cnf(refute_0_264,plain,
( X_242 != join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))
| join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242)))) = X_242 ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X_242)),bind(Y0,$fot(join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))))]]) ).
cnf(refute_0_265,plain,
join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242)))) = X_242,
inference(resolve,[$cnf( $equal(X_242,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242)))) != X_242
| meet(X_243,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))) != meet(X_243,complement(join(complement(X_243),complement(X_242))))
| meet(X_243,X_242) = meet(X_243,complement(join(complement(X_243),complement(X_242)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_243,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))),meet(X_243,complement(join(complement(X_243),complement(X_242))))) ),[0,1],$fot(X_242)]]) ).
cnf(refute_0_267,plain,
( meet(X_243,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))) != meet(X_243,complement(join(complement(X_243),complement(X_242))))
| meet(X_243,X_242) = meet(X_243,complement(join(complement(X_243),complement(X_242)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242)))),X_242) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
meet(X_243,X_242) = meet(X_243,complement(join(complement(X_243),complement(X_242)))),
inference(resolve,[$cnf( $equal(meet(X_243,join(meet(X_242,complement(X_243)),complement(join(complement(X_243),complement(X_242))))),meet(X_243,complement(join(complement(X_243),complement(X_242))))) )],[refute_0_64,refute_0_267]) ).
cnf(refute_0_269,plain,
meet(complement(join(complement(X_79),X_39)),join(X_79,join(complement(X_79),X_39))) = meet(complement(join(complement(X_79),X_39)),X_79),
inference(subst,[],[refute_0_168:[bind(X,$fot(join(complement(X_79),X_39))),bind(X_77,$fot(X_79))]]) ).
cnf(refute_0_270,plain,
join(join(X_37,complement(X_37)),X_39) = join(X_37,join(complement(X_37),X_39)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_37)),bind(Y,$fot(complement(X_37))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_271,plain,
join(X_37,complement(X_37)) = n1,
inference(subst,[],[refute_0_92:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_272,plain,
( join(X_37,complement(X_37)) != n1
| join(join(X_37,complement(X_37)),X_39) != join(X_37,join(complement(X_37),X_39))
| join(n1,X_39) = join(X_37,join(complement(X_37),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_37,complement(X_37)),X_39),join(X_37,join(complement(X_37),X_39))) ),[0,0],$fot(n1)]]) ).
cnf(refute_0_273,plain,
( join(join(X_37,complement(X_37)),X_39) != join(X_37,join(complement(X_37),X_39))
| join(n1,X_39) = join(X_37,join(complement(X_37),X_39)) ),
inference(resolve,[$cnf( $equal(join(X_37,complement(X_37)),n1) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
join(n1,X_39) = join(X_37,join(complement(X_37),X_39)),
inference(resolve,[$cnf( $equal(join(join(X_37,complement(X_37)),X_39),join(X_37,join(complement(X_37),X_39))) )],[refute_0_270,refute_0_273]) ).
cnf(refute_0_275,plain,
join(n1,X_39) = n1,
inference(subst,[],[refute_0_115:[bind(Y,$fot(X_39))]]) ).
cnf(refute_0_276,plain,
( join(n1,X_39) != join(X_37,join(complement(X_37),X_39))
| join(n1,X_39) != n1
| n1 = join(X_37,join(complement(X_37),X_39)) ),
introduced(tautology,[equality,[$cnf( $equal(join(n1,X_39),join(X_37,join(complement(X_37),X_39))) ),[0],$fot(n1)]]) ).
cnf(refute_0_277,plain,
( join(n1,X_39) != join(X_37,join(complement(X_37),X_39))
| n1 = join(X_37,join(complement(X_37),X_39)) ),
inference(resolve,[$cnf( $equal(join(n1,X_39),n1) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
n1 = join(X_37,join(complement(X_37),X_39)),
inference(resolve,[$cnf( $equal(join(n1,X_39),join(X_37,join(complement(X_37),X_39))) )],[refute_0_274,refute_0_277]) ).
cnf(refute_0_279,plain,
n1 = join(X_79,join(complement(X_79),X_39)),
inference(subst,[],[refute_0_278:[bind(X_37,$fot(X_79))]]) ).
cnf(refute_0_280,plain,
( n1 != join(X_79,join(complement(X_79),X_39))
| join(X_79,join(complement(X_79),X_39)) = n1 ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(n1)),bind(Y0,$fot(join(X_79,join(complement(X_79),X_39))))]]) ).
cnf(refute_0_281,plain,
join(X_79,join(complement(X_79),X_39)) = n1,
inference(resolve,[$cnf( $equal(n1,join(X_79,join(complement(X_79),X_39))) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
( join(X_79,join(complement(X_79),X_39)) != n1
| meet(complement(join(complement(X_79),X_39)),join(X_79,join(complement(X_79),X_39))) != meet(complement(join(complement(X_79),X_39)),X_79)
| meet(complement(join(complement(X_79),X_39)),n1) = meet(complement(join(complement(X_79),X_39)),X_79) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),join(X_79,join(complement(X_79),X_39))),meet(complement(join(complement(X_79),X_39)),X_79)) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_283,plain,
( meet(complement(join(complement(X_79),X_39)),join(X_79,join(complement(X_79),X_39))) != meet(complement(join(complement(X_79),X_39)),X_79)
| meet(complement(join(complement(X_79),X_39)),n1) = meet(complement(join(complement(X_79),X_39)),X_79) ),
inference(resolve,[$cnf( $equal(join(X_79,join(complement(X_79),X_39)),n1) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
meet(complement(join(complement(X_79),X_39)),n1) = meet(complement(join(complement(X_79),X_39)),X_79),
inference(resolve,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),join(X_79,join(complement(X_79),X_39))),meet(complement(join(complement(X_79),X_39)),X_79)) )],[refute_0_269,refute_0_283]) ).
cnf(refute_0_285,plain,
meet(n1,complement(join(complement(X_79),X_39))) = complement(join(complement(X_79),X_39)),
inference(subst,[],[refute_0_111:[bind(X_5,$fot(complement(join(complement(X_79),X_39))))]]) ).
cnf(refute_0_286,plain,
meet(complement(join(complement(X_79),X_39)),n1) = meet(n1,complement(join(complement(X_79),X_39))),
inference(subst,[],[refute_0_241:[bind(Y,$fot(n1)),bind(X_57,$fot(complement(join(complement(X_79),X_39))))]]) ).
cnf(refute_0_287,plain,
( meet(complement(join(complement(X_79),X_39)),n1) != meet(n1,complement(join(complement(X_79),X_39)))
| meet(n1,complement(join(complement(X_79),X_39))) != complement(join(complement(X_79),X_39))
| meet(complement(join(complement(X_79),X_39)),n1) = complement(join(complement(X_79),X_39)) ),
inference(subst,[],[refute_0_138:[bind(X0,$fot(meet(complement(join(complement(X_79),X_39)),n1))),bind(Y0,$fot(meet(n1,complement(join(complement(X_79),X_39))))),bind(Z0,$fot(complement(join(complement(X_79),X_39))))]]) ).
cnf(refute_0_288,plain,
( meet(n1,complement(join(complement(X_79),X_39))) != complement(join(complement(X_79),X_39))
| meet(complement(join(complement(X_79),X_39)),n1) = complement(join(complement(X_79),X_39)) ),
inference(resolve,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),n1),meet(n1,complement(join(complement(X_79),X_39)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
meet(complement(join(complement(X_79),X_39)),n1) = complement(join(complement(X_79),X_39)),
inference(resolve,[$cnf( $equal(meet(n1,complement(join(complement(X_79),X_39))),complement(join(complement(X_79),X_39))) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
( meet(complement(join(complement(X_79),X_39)),n1) != complement(join(complement(X_79),X_39))
| meet(complement(join(complement(X_79),X_39)),n1) != meet(complement(join(complement(X_79),X_39)),X_79)
| complement(join(complement(X_79),X_39)) = meet(complement(join(complement(X_79),X_39)),X_79) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),n1),meet(complement(join(complement(X_79),X_39)),X_79)) ),[0],$fot(complement(join(complement(X_79),X_39)))]]) ).
cnf(refute_0_291,plain,
( meet(complement(join(complement(X_79),X_39)),n1) != meet(complement(join(complement(X_79),X_39)),X_79)
| complement(join(complement(X_79),X_39)) = meet(complement(join(complement(X_79),X_39)),X_79) ),
inference(resolve,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),n1),complement(join(complement(X_79),X_39))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
meet(complement(join(complement(X_79),X_39)),X_79) = meet(X_79,complement(join(complement(X_79),X_39))),
inference(subst,[],[refute_0_241:[bind(Y,$fot(X_79)),bind(X_57,$fot(complement(join(complement(X_79),X_39))))]]) ).
cnf(refute_0_293,plain,
( complement(join(complement(X_79),X_39)) != meet(complement(join(complement(X_79),X_39)),X_79)
| meet(complement(join(complement(X_79),X_39)),X_79) != meet(X_79,complement(join(complement(X_79),X_39)))
| complement(join(complement(X_79),X_39)) = meet(X_79,complement(join(complement(X_79),X_39))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(join(complement(X_79),X_39)),meet(X_79,complement(join(complement(X_79),X_39)))) ),[0],$fot(meet(complement(join(complement(X_79),X_39)),X_79))]]) ).
cnf(refute_0_294,plain,
( complement(join(complement(X_79),X_39)) != meet(complement(join(complement(X_79),X_39)),X_79)
| complement(join(complement(X_79),X_39)) = meet(X_79,complement(join(complement(X_79),X_39))) ),
inference(resolve,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),X_79),meet(X_79,complement(join(complement(X_79),X_39)))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
( meet(complement(join(complement(X_79),X_39)),n1) != meet(complement(join(complement(X_79),X_39)),X_79)
| complement(join(complement(X_79),X_39)) = meet(X_79,complement(join(complement(X_79),X_39))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_79),X_39)),meet(complement(join(complement(X_79),X_39)),X_79)) )],[refute_0_291,refute_0_294]) ).
cnf(refute_0_296,plain,
complement(join(complement(X_79),X_39)) = meet(X_79,complement(join(complement(X_79),X_39))),
inference(resolve,[$cnf( $equal(meet(complement(join(complement(X_79),X_39)),n1),meet(complement(join(complement(X_79),X_39)),X_79)) )],[refute_0_284,refute_0_295]) ).
cnf(refute_0_297,plain,
( complement(join(complement(X_79),X_39)) != meet(X_79,complement(join(complement(X_79),X_39)))
| meet(X_79,complement(join(complement(X_79),X_39))) = complement(join(complement(X_79),X_39)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(complement(join(complement(X_79),X_39)))),bind(Y0,$fot(meet(X_79,complement(join(complement(X_79),X_39)))))]]) ).
cnf(refute_0_298,plain,
meet(X_79,complement(join(complement(X_79),X_39))) = complement(join(complement(X_79),X_39)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_79),X_39)),meet(X_79,complement(join(complement(X_79),X_39)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
meet(X_243,complement(join(complement(X_243),complement(X_242)))) = complement(join(complement(X_243),complement(X_242))),
inference(subst,[],[refute_0_298:[bind(X_39,$fot(complement(X_242))),bind(X_79,$fot(X_243))]]) ).
cnf(refute_0_300,plain,
( meet(X_243,X_242) != meet(X_243,complement(join(complement(X_243),complement(X_242))))
| meet(X_243,complement(join(complement(X_243),complement(X_242)))) != complement(join(complement(X_243),complement(X_242)))
| meet(X_243,X_242) = complement(join(complement(X_243),complement(X_242))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X_243,X_242),complement(join(complement(X_243),complement(X_242)))) ),[0],$fot(meet(X_243,complement(join(complement(X_243),complement(X_242)))))]]) ).
cnf(refute_0_301,plain,
( meet(X_243,X_242) != meet(X_243,complement(join(complement(X_243),complement(X_242))))
| meet(X_243,X_242) = complement(join(complement(X_243),complement(X_242))) ),
inference(resolve,[$cnf( $equal(meet(X_243,complement(join(complement(X_243),complement(X_242)))),complement(join(complement(X_243),complement(X_242)))) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
meet(X_243,X_242) = complement(join(complement(X_243),complement(X_242))),
inference(resolve,[$cnf( $equal(meet(X_243,X_242),meet(X_243,complement(join(complement(X_243),complement(X_242))))) )],[refute_0_268,refute_0_301]) ).
cnf(refute_0_303,plain,
meet(X_246,complement(X)) = complement(join(complement(X_246),complement(complement(X)))),
inference(subst,[],[refute_0_302:[bind(X_242,$fot(complement(X))),bind(X_243,$fot(X_246))]]) ).
cnf(refute_0_304,plain,
( complement(complement(X)) != X
| meet(X_246,complement(X)) != complement(join(complement(X_246),complement(complement(X))))
| meet(X_246,complement(X)) = complement(join(complement(X_246),X)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_246,complement(X)),complement(join(complement(X_246),complement(complement(X))))) ),[1,0,1],$fot(X)]]) ).
cnf(refute_0_305,plain,
( meet(X_246,complement(X)) != complement(join(complement(X_246),complement(complement(X))))
| meet(X_246,complement(X)) = complement(join(complement(X_246),X)) ),
inference(resolve,[$cnf( $equal(complement(complement(X)),X) )],[invertability3,refute_0_304]) ).
cnf(refute_0_306,plain,
meet(X_246,complement(X)) = complement(join(complement(X_246),X)),
inference(resolve,[$cnf( $equal(meet(X_246,complement(X)),complement(join(complement(X_246),complement(complement(X))))) )],[refute_0_303,refute_0_305]) ).
cnf(refute_0_307,plain,
meet(complement(X),complement(X_249)) = complement(join(complement(complement(X)),X_249)),
inference(subst,[],[refute_0_306:[bind(X,$fot(X_249)),bind(X_246,$fot(complement(X)))]]) ).
cnf(refute_0_308,plain,
( complement(complement(X)) != X
| meet(complement(X),complement(X_249)) != complement(join(complement(complement(X)),X_249))
| meet(complement(X),complement(X_249)) = complement(join(X,X_249)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X),complement(X_249)),complement(join(complement(complement(X)),X_249))) ),[1,0,0],$fot(X)]]) ).
cnf(refute_0_309,plain,
( meet(complement(X),complement(X_249)) != complement(join(complement(complement(X)),X_249))
| meet(complement(X),complement(X_249)) = complement(join(X,X_249)) ),
inference(resolve,[$cnf( $equal(complement(complement(X)),X) )],[invertability3,refute_0_308]) ).
cnf(refute_0_310,plain,
meet(complement(X),complement(X_249)) = complement(join(X,X_249)),
inference(resolve,[$cnf( $equal(meet(complement(X),complement(X_249)),complement(join(complement(complement(X)),X_249))) )],[refute_0_307,refute_0_309]) ).
cnf(refute_0_311,plain,
meet(complement(c),complement(d)) = complement(join(c,d)),
inference(subst,[],[refute_0_310:[bind(X,$fot(c)),bind(X_249,$fot(d))]]) ).
cnf(refute_0_312,plain,
( complement(join(c,d)) != complement(join(c,d))
| meet(complement(c),complement(d)) != complement(join(c,d))
| complement(join(c,d)) = meet(complement(c),complement(d)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(join(c,d)),meet(complement(c),complement(d))) ),[1],$fot(complement(join(c,d)))]]) ).
cnf(refute_0_313,plain,
( complement(join(c,d)) != complement(join(c,d))
| complement(join(c,d)) = meet(complement(c),complement(d)) ),
inference(resolve,[$cnf( $equal(meet(complement(c),complement(d)),complement(join(c,d))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
complement(join(c,d)) != complement(join(c,d)),
inference(resolve,[$cnf( $equal(complement(join(c,d)),meet(complement(c),complement(d))) )],[refute_0_313,prove_compatability_law]) ).
cnf(refute_0_315,plain,
complement(join(c,d)) = complement(join(c,d)),
introduced(tautology,[refl,[$fot(complement(join(c,d)))]]) ).
cnf(refute_0_316,plain,
$false,
inference(resolve,[$cnf( $equal(complement(join(c,d)),complement(join(c,d))) )],[refute_0_315,refute_0_314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT043-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.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 01:40:52 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 8.93/9.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.93/9.11
% 8.93/9.11 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.93/9.14
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