TSTP Solution File: LAT031-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 05:59:00 EDT 2022
% Result : Unsatisfiable 6.88s 7.11s
% Output : CNFRefutation 6.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 60
% Syntax : Number of clauses : 262 ( 141 unt; 0 nHn; 125 RR)
% Number of literals : 434 ( 433 equ; 174 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; 3 con; 0-2 aty)
% Number of variables : 699 ( 16 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(dist_meet,hypothesis,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
cnf(dist_join,negated_conjecture,
join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)) ).
cnf(refute_0_0,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_1,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_0]) ).
cnf(refute_0_2,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_1]) ).
cnf(refute_0_3,plain,
join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,meet(X_152,Y)))) = join(X_154,meet(X_152,Y)),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_154,meet(X_152,Y))))]]) ).
cnf(refute_0_4,plain,
meet(X_31,join(X_32,meet(Y,X_31))) = join(meet(X_31,X_32),meet(X_31,meet(Y,X_31))),
inference(subst,[],[dist_meet:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(meet(Y,X_31)))]]) ).
cnf(refute_0_5,plain,
meet(X_6,join(X_6,X_7)) = X_6,
inference(subst,[],[absorption1:[bind(X,$fot(X_6)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_6,plain,
join(X_7,X_6) = join(X_6,X_7),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).
cnf(refute_0_7,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( join(X_7,X_6) != join(X_6,X_7)
| join(X_6,X_7) = join(X_7,X_6) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_7,X_6))),bind(Y0,$fot(join(X_6,X_7)))]]) ).
cnf(refute_0_11,plain,
join(X_6,X_7) = join(X_7,X_6),
inference(resolve,[$cnf( $equal(join(X_7,X_6),join(X_6,X_7)) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( join(X_6,X_7) != join(X_7,X_6)
| meet(X_6,join(X_6,X_7)) != X_6
| meet(X_6,join(X_7,X_6)) = X_6 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_6,join(X_6,X_7)),X_6) ),[0,1],$fot(join(X_7,X_6))]]) ).
cnf(refute_0_13,plain,
( meet(X_6,join(X_6,X_7)) != X_6
| meet(X_6,join(X_7,X_6)) = X_6 ),
inference(resolve,[$cnf( $equal(join(X_6,X_7),join(X_7,X_6)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
meet(X_6,join(X_7,X_6)) = X_6,
inference(resolve,[$cnf( $equal(meet(X_6,join(X_6,X_7)),X_6) )],[refute_0_5,refute_0_13]) ).
cnf(refute_0_15,plain,
meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) = meet(X_9,Y),
inference(subst,[],[refute_0_14:[bind(X_6,$fot(meet(X_9,Y))),bind(X_7,$fot(X_9))]]) ).
cnf(refute_0_16,plain,
join(X_9,meet(X_9,Y)) = X_9,
inference(subst,[],[absorption2:[bind(X,$fot(X_9))]]) ).
cnf(refute_0_17,plain,
( join(X_9,meet(X_9,Y)) != X_9
| meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) ),[0,1],$fot(X_9)]]) ).
cnf(refute_0_18,plain,
( meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
inference(resolve,[$cnf( $equal(join(X_9,meet(X_9,Y)),X_9) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(meet(X_9,Y),X_9) = meet(X_9,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) )],[refute_0_15,refute_0_18]) ).
cnf(refute_0_20,plain,
meet(meet(X_9,Y),X_9) = meet(X_9,meet(Y,X_9)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_9)),bind(Z,$fot(X_9))]]) ).
cnf(refute_0_21,plain,
( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
| meet(meet(X_9,Y),X_9) != meet(X_9,meet(Y,X_9))
| meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) ),[0],$fot(meet(X_9,meet(Y,X_9)))]]) ).
cnf(refute_0_22,plain,
( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
| meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,meet(Y,X_9))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
meet(X_9,meet(Y,X_9)) = meet(X_9,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
meet(X_31,meet(Y,X_31)) = meet(X_31,Y),
inference(subst,[],[refute_0_23:[bind(X_9,$fot(X_31))]]) ).
cnf(refute_0_25,plain,
( meet(X_31,join(X_32,meet(Y,X_31))) != join(meet(X_31,X_32),meet(X_31,meet(Y,X_31)))
| meet(X_31,meet(Y,X_31)) != meet(X_31,Y)
| meet(X_31,join(X_32,meet(Y,X_31))) = join(meet(X_31,X_32),meet(X_31,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_31,join(X_32,meet(Y,X_31))),join(meet(X_31,X_32),meet(X_31,meet(Y,X_31)))) ),[1,1],$fot(meet(X_31,Y))]]) ).
cnf(refute_0_26,plain,
( meet(X_31,join(X_32,meet(Y,X_31))) != join(meet(X_31,X_32),meet(X_31,meet(Y,X_31)))
| meet(X_31,join(X_32,meet(Y,X_31))) = join(meet(X_31,X_32),meet(X_31,Y)) ),
inference(resolve,[$cnf( $equal(meet(X_31,meet(Y,X_31)),meet(X_31,Y)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
meet(X_31,join(X_32,meet(Y,X_31))) = join(meet(X_31,X_32),meet(X_31,Y)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,meet(Y,X_31))),join(meet(X_31,X_32),meet(X_31,meet(Y,X_31)))) )],[refute_0_4,refute_0_26]) ).
cnf(refute_0_28,plain,
( meet(X,join(Y,Z)) != join(meet(X,Y),meet(X,Z))
| join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X,join(Y,Z)))),bind(Y0,$fot(join(meet(X,Y),meet(X,Z))))]]) ).
cnf(refute_0_29,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
inference(resolve,[$cnf( $equal(meet(X,join(Y,Z)),join(meet(X,Y),meet(X,Z))) )],[dist_meet,refute_0_28]) ).
cnf(refute_0_30,plain,
join(meet(X_31,X_32),meet(X_31,Y)) = meet(X_31,join(X_32,Y)),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_31,plain,
( join(meet(X_31,X_32),meet(X_31,Y)) != meet(X_31,join(X_32,Y))
| meet(X_31,join(X_32,meet(Y,X_31))) != join(meet(X_31,X_32),meet(X_31,Y))
| meet(X_31,join(X_32,meet(Y,X_31))) = meet(X_31,join(X_32,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_31,join(X_32,meet(Y,X_31))),join(meet(X_31,X_32),meet(X_31,Y))) ),[1],$fot(meet(X_31,join(X_32,Y)))]]) ).
cnf(refute_0_32,plain,
( meet(X_31,join(X_32,meet(Y,X_31))) != join(meet(X_31,X_32),meet(X_31,Y))
| meet(X_31,join(X_32,meet(Y,X_31))) = meet(X_31,join(X_32,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,X_32),meet(X_31,Y)),meet(X_31,join(X_32,Y))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
meet(X_31,join(X_32,meet(Y,X_31))) = meet(X_31,join(X_32,Y)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,meet(Y,X_31))),join(meet(X_31,X_32),meet(X_31,Y))) )],[refute_0_27,refute_0_32]) ).
cnf(refute_0_34,plain,
meet(Y,join(X_154,meet(X_152,Y))) = meet(Y,join(X_154,X_152)),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_152)),bind(X_31,$fot(Y)),bind(X_32,$fot(X_154))]]) ).
cnf(refute_0_35,plain,
( join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,meet(X_152,Y)))) != join(X_154,meet(X_152,Y))
| meet(Y,join(X_154,meet(X_152,Y))) != meet(Y,join(X_154,X_152))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(X_152,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,meet(X_152,Y)))),join(X_154,meet(X_152,Y))) ),[0,1],$fot(meet(Y,join(X_154,X_152)))]]) ).
cnf(refute_0_36,plain,
( join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,meet(X_152,Y)))) != join(X_154,meet(X_152,Y))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(X_152,Y)) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_154,meet(X_152,Y))),meet(Y,join(X_154,X_152))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(X_152,Y)),
inference(resolve,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,meet(X_152,Y)))),join(X_154,meet(X_152,Y))) )],[refute_0_3,refute_0_36]) ).
cnf(refute_0_38,plain,
join(X_152,X_152) = X_152,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_152))]]) ).
cnf(refute_0_39,plain,
meet(Y,join(X_152,X_152)) = meet(Y,join(X_152,X_152)),
introduced(tautology,[refl,[$fot(meet(Y,join(X_152,X_152)))]]) ).
cnf(refute_0_40,plain,
( join(X_152,X_152) != X_152
| meet(Y,join(X_152,X_152)) != meet(Y,join(X_152,X_152))
| meet(Y,join(X_152,X_152)) = meet(Y,X_152) ),
introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(X_152,X_152)),meet(Y,join(X_152,X_152))) ),[1,1],$fot(X_152)]]) ).
cnf(refute_0_41,plain,
( join(X_152,X_152) != X_152
| meet(Y,join(X_152,X_152)) = meet(Y,X_152) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_152,X_152)),meet(Y,join(X_152,X_152))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
meet(Y,join(X_152,X_152)) = meet(Y,X_152),
inference(resolve,[$cnf( $equal(join(X_152,X_152),X_152) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
meet(X_31,join(X_32,X_33)) = join(meet(X_31,X_32),meet(X_31,X_33)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_31)),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_44,plain,
meet(X_32,X_31) = meet(X_31,X_32),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_32)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_45,plain,
( meet(X_32,X_31) != meet(X_31,X_32)
| meet(X_31,X_32) = meet(X_32,X_31) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_32,X_31))),bind(Y0,$fot(meet(X_31,X_32)))]]) ).
cnf(refute_0_46,plain,
meet(X_31,X_32) = meet(X_32,X_31),
inference(resolve,[$cnf( $equal(meet(X_32,X_31),meet(X_31,X_32)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( meet(X_31,X_32) != meet(X_32,X_31)
| meet(X_31,join(X_32,X_33)) != join(meet(X_31,X_32),meet(X_31,X_33))
| meet(X_31,join(X_32,X_33)) = join(meet(X_32,X_31),meet(X_31,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_31,X_32),meet(X_31,X_33))) ),[1,0],$fot(meet(X_32,X_31))]]) ).
cnf(refute_0_48,plain,
( meet(X_31,join(X_32,X_33)) != join(meet(X_31,X_32),meet(X_31,X_33))
| meet(X_31,join(X_32,X_33)) = join(meet(X_32,X_31),meet(X_31,X_33)) ),
inference(resolve,[$cnf( $equal(meet(X_31,X_32),meet(X_32,X_31)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
meet(X_31,join(X_32,X_33)) = join(meet(X_32,X_31),meet(X_31,X_33)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_31,X_32),meet(X_31,X_33))) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
( meet(X_31,join(X_32,X_33)) != join(meet(X_32,X_31),meet(X_31,X_33))
| join(meet(X_32,X_31),meet(X_31,X_33)) = meet(X_31,join(X_32,X_33)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_31,join(X_32,X_33)))),bind(Y0,$fot(join(meet(X_32,X_31),meet(X_31,X_33))))]]) ).
cnf(refute_0_51,plain,
join(meet(X_32,X_31),meet(X_31,X_33)) = meet(X_31,join(X_32,X_33)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_32,X_31),meet(X_31,X_33))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
join(meet(X_152,Y),meet(Y,X_152)) = meet(Y,join(X_152,X_152)),
inference(subst,[],[refute_0_51:[bind(X_31,$fot(Y)),bind(X_32,$fot(X_152)),bind(X_33,$fot(X_152))]]) ).
cnf(refute_0_53,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_54,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_53]) ).
cnf(refute_0_55,plain,
( join(meet(X_152,Y),meet(Y,X_152)) != meet(Y,join(X_152,X_152))
| meet(Y,join(X_152,X_152)) != meet(Y,X_152)
| join(meet(X_152,Y),meet(Y,X_152)) = meet(Y,X_152) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(join(meet(X_152,Y),meet(Y,X_152)))),bind(Y0,$fot(meet(Y,join(X_152,X_152)))),bind(Z0,$fot(meet(Y,X_152)))]]) ).
cnf(refute_0_56,plain,
( meet(Y,join(X_152,X_152)) != meet(Y,X_152)
| join(meet(X_152,Y),meet(Y,X_152)) = meet(Y,X_152) ),
inference(resolve,[$cnf( $equal(join(meet(X_152,Y),meet(Y,X_152)),meet(Y,join(X_152,X_152))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
join(meet(X_152,Y),meet(Y,X_152)) = meet(Y,X_152),
inference(resolve,[$cnf( $equal(meet(Y,join(X_152,X_152)),meet(Y,X_152)) )],[refute_0_42,refute_0_56]) ).
cnf(refute_0_58,plain,
join(X_154,join(meet(X_152,Y),meet(Y,X_152))) = join(X_154,join(meet(X_152,Y),meet(Y,X_152))),
introduced(tautology,[refl,[$fot(join(X_154,join(meet(X_152,Y),meet(Y,X_152))))]]) ).
cnf(refute_0_59,plain,
( join(X_154,join(meet(X_152,Y),meet(Y,X_152))) != join(X_154,join(meet(X_152,Y),meet(Y,X_152)))
| join(meet(X_152,Y),meet(Y,X_152)) != meet(Y,X_152)
| join(X_154,join(meet(X_152,Y),meet(Y,X_152))) = join(X_154,meet(Y,X_152)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_154,join(meet(X_152,Y),meet(Y,X_152))),join(X_154,join(meet(X_152,Y),meet(Y,X_152)))) ),[1,1],$fot(meet(Y,X_152))]]) ).
cnf(refute_0_60,plain,
( join(meet(X_152,Y),meet(Y,X_152)) != meet(Y,X_152)
| join(X_154,join(meet(X_152,Y),meet(Y,X_152))) = join(X_154,meet(Y,X_152)) ),
inference(resolve,[$cnf( $equal(join(X_154,join(meet(X_152,Y),meet(Y,X_152))),join(X_154,join(meet(X_152,Y),meet(Y,X_152)))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
join(X_154,join(meet(X_152,Y),meet(Y,X_152))) = join(X_154,meet(Y,X_152)),
inference(resolve,[$cnf( $equal(join(meet(X_152,Y),meet(Y,X_152)),meet(Y,X_152)) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
join(join(X_20,join(Y,X_20)),X_22) = join(X_20,join(join(Y,X_20),X_22)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(join(Y,X_20))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_63,plain,
join(join(X_17,Y),meet(X_17,join(X_17,Y))) = join(X_17,Y),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_17,Y))),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_64,plain,
meet(X_17,join(X_17,Y)) = X_17,
inference(subst,[],[absorption1:[bind(X,$fot(X_17))]]) ).
cnf(refute_0_65,plain,
( join(join(X_17,Y),meet(X_17,join(X_17,Y))) != join(X_17,Y)
| meet(X_17,join(X_17,Y)) != X_17
| join(join(X_17,Y),X_17) = join(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_17,Y),meet(X_17,join(X_17,Y))),join(X_17,Y)) ),[0,1],$fot(X_17)]]) ).
cnf(refute_0_66,plain,
( join(join(X_17,Y),meet(X_17,join(X_17,Y))) != join(X_17,Y)
| join(join(X_17,Y),X_17) = join(X_17,Y) ),
inference(resolve,[$cnf( $equal(meet(X_17,join(X_17,Y)),X_17) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
join(join(X_17,Y),X_17) = join(X_17,Y),
inference(resolve,[$cnf( $equal(join(join(X_17,Y),meet(X_17,join(X_17,Y))),join(X_17,Y)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
join(join(X_17,Y),X_17) = join(X_17,join(Y,X_17)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_17)),bind(Z,$fot(X_17))]]) ).
cnf(refute_0_69,plain,
( join(join(X_17,Y),X_17) != join(X_17,Y)
| join(join(X_17,Y),X_17) != join(X_17,join(Y,X_17))
| join(X_17,join(Y,X_17)) = join(X_17,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_17,Y),X_17),join(X_17,Y)) ),[0],$fot(join(X_17,join(Y,X_17)))]]) ).
cnf(refute_0_70,plain,
( join(join(X_17,Y),X_17) != join(X_17,Y)
| join(X_17,join(Y,X_17)) = join(X_17,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_17,Y),X_17),join(X_17,join(Y,X_17))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
join(X_17,join(Y,X_17)) = join(X_17,Y),
inference(resolve,[$cnf( $equal(join(join(X_17,Y),X_17),join(X_17,Y)) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
join(X_20,join(Y,X_20)) = join(X_20,Y),
inference(subst,[],[refute_0_71:[bind(X_17,$fot(X_20))]]) ).
cnf(refute_0_73,plain,
( join(X_20,join(Y,X_20)) != join(X_20,Y)
| join(join(X_20,join(Y,X_20)),X_22) != join(X_20,join(join(Y,X_20),X_22))
| join(join(X_20,Y),X_22) = join(X_20,join(join(Y,X_20),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,join(Y,X_20)),X_22),join(X_20,join(join(Y,X_20),X_22))) ),[0,0],$fot(join(X_20,Y))]]) ).
cnf(refute_0_74,plain,
( join(join(X_20,join(Y,X_20)),X_22) != join(X_20,join(join(Y,X_20),X_22))
| join(join(X_20,Y),X_22) = join(X_20,join(join(Y,X_20),X_22)) ),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,X_20)),join(X_20,Y)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
join(join(X_20,Y),X_22) = join(X_20,join(join(Y,X_20),X_22)),
inference(resolve,[$cnf( $equal(join(join(X_20,join(Y,X_20)),X_22),join(X_20,join(join(Y,X_20),X_22))) )],[refute_0_62,refute_0_74]) ).
cnf(refute_0_76,plain,
join(join(X_20,Y),X_22) = join(X_20,join(Y,X_22)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_77,plain,
( join(join(X_20,Y),X_22) != join(X_20,join(Y,X_22))
| join(join(X_20,Y),X_22) != join(X_20,join(join(Y,X_20),X_22))
| join(X_20,join(Y,X_22)) = join(X_20,join(join(Y,X_20),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,Y),X_22),join(X_20,join(join(Y,X_20),X_22))) ),[0],$fot(join(X_20,join(Y,X_22)))]]) ).
cnf(refute_0_78,plain,
( join(join(X_20,Y),X_22) != join(X_20,join(join(Y,X_20),X_22))
| join(X_20,join(Y,X_22)) = join(X_20,join(join(Y,X_20),X_22)) ),
inference(resolve,[$cnf( $equal(join(join(X_20,Y),X_22),join(X_20,join(Y,X_22))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
join(join(Y,X_20),X_22) = join(Y,join(X_20,X_22)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(Y)),bind(Y,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_80,plain,
join(X_20,join(join(Y,X_20),X_22)) = join(X_20,join(join(Y,X_20),X_22)),
introduced(tautology,[refl,[$fot(join(X_20,join(join(Y,X_20),X_22)))]]) ).
cnf(refute_0_81,plain,
( join(X_20,join(join(Y,X_20),X_22)) != join(X_20,join(join(Y,X_20),X_22))
| join(join(Y,X_20),X_22) != join(Y,join(X_20,X_22))
| join(X_20,join(join(Y,X_20),X_22)) = join(X_20,join(Y,join(X_20,X_22))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_20,join(join(Y,X_20),X_22)),join(X_20,join(join(Y,X_20),X_22))) ),[1,1],$fot(join(Y,join(X_20,X_22)))]]) ).
cnf(refute_0_82,plain,
( join(join(Y,X_20),X_22) != join(Y,join(X_20,X_22))
| join(X_20,join(join(Y,X_20),X_22)) = join(X_20,join(Y,join(X_20,X_22))) ),
inference(resolve,[$cnf( $equal(join(X_20,join(join(Y,X_20),X_22)),join(X_20,join(join(Y,X_20),X_22))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
join(X_20,join(join(Y,X_20),X_22)) = join(X_20,join(Y,join(X_20,X_22))),
inference(resolve,[$cnf( $equal(join(join(Y,X_20),X_22),join(Y,join(X_20,X_22))) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
( join(X_20,join(Y,X_22)) != join(X_20,join(join(Y,X_20),X_22))
| join(X_20,join(join(Y,X_20),X_22)) != join(X_20,join(Y,join(X_20,X_22)))
| join(X_20,join(Y,X_22)) = join(X_20,join(Y,join(X_20,X_22))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_20,join(Y,X_22)),join(X_20,join(Y,join(X_20,X_22)))) ),[0],$fot(join(X_20,join(join(Y,X_20),X_22)))]]) ).
cnf(refute_0_85,plain,
( join(X_20,join(Y,X_22)) != join(X_20,join(join(Y,X_20),X_22))
| join(X_20,join(Y,X_22)) = join(X_20,join(Y,join(X_20,X_22))) ),
inference(resolve,[$cnf( $equal(join(X_20,join(join(Y,X_20),X_22)),join(X_20,join(Y,join(X_20,X_22)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( join(join(X_20,Y),X_22) != join(X_20,join(join(Y,X_20),X_22))
| join(X_20,join(Y,X_22)) = join(X_20,join(Y,join(X_20,X_22))) ),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,X_22)),join(X_20,join(join(Y,X_20),X_22))) )],[refute_0_78,refute_0_85]) ).
cnf(refute_0_87,plain,
join(X_20,join(Y,X_22)) = join(X_20,join(Y,join(X_20,X_22))),
inference(resolve,[$cnf( $equal(join(join(X_20,Y),X_22),join(X_20,join(join(Y,X_20),X_22))) )],[refute_0_75,refute_0_86]) ).
cnf(refute_0_88,plain,
join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,join(X_20,meet(X_147,join(X_20,X_146))))),
inference(subst,[],[refute_0_87:[bind(X_22,$fot(meet(X_147,join(X_20,X_146))))]]) ).
cnf(refute_0_89,plain,
join(join(X_20,meet(Y,X_20)),X_22) = join(X_20,join(meet(Y,X_20),X_22)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(meet(Y,X_20))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_90,plain,
join(X_20,meet(Y,X_20)) = X_20,
inference(subst,[],[refute_0_2:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_91,plain,
( join(X_20,meet(Y,X_20)) != X_20
| join(join(X_20,meet(Y,X_20)),X_22) != join(X_20,join(meet(Y,X_20),X_22))
| join(X_20,X_22) = join(X_20,join(meet(Y,X_20),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,meet(Y,X_20)),X_22),join(X_20,join(meet(Y,X_20),X_22))) ),[0,0],$fot(X_20)]]) ).
cnf(refute_0_92,plain,
( join(join(X_20,meet(Y,X_20)),X_22) != join(X_20,join(meet(Y,X_20),X_22))
| join(X_20,X_22) = join(X_20,join(meet(Y,X_20),X_22)) ),
inference(resolve,[$cnf( $equal(join(X_20,meet(Y,X_20)),X_20) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
join(X_20,X_22) = join(X_20,join(meet(Y,X_20),X_22)),
inference(resolve,[$cnf( $equal(join(join(X_20,meet(Y,X_20)),X_22),join(X_20,join(meet(Y,X_20),X_22))) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
join(X_48,meet(X_47,Z)) = join(X_48,join(meet(X_47,X_48),meet(X_47,Z))),
inference(subst,[],[refute_0_93:[bind(Y,$fot(X_47)),bind(X_20,$fot(X_48)),bind(X_22,$fot(meet(X_47,Z)))]]) ).
cnf(refute_0_95,plain,
meet(X_47,join(X_48,Z)) = join(meet(X_47,X_48),meet(X_47,Z)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_47)),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_96,plain,
( meet(X_47,join(X_48,Z)) != join(meet(X_47,X_48),meet(X_47,Z))
| join(meet(X_47,X_48),meet(X_47,Z)) = meet(X_47,join(X_48,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_47,join(X_48,Z)))),bind(Y0,$fot(join(meet(X_47,X_48),meet(X_47,Z))))]]) ).
cnf(refute_0_97,plain,
join(meet(X_47,X_48),meet(X_47,Z)) = meet(X_47,join(X_48,Z)),
inference(resolve,[$cnf( $equal(meet(X_47,join(X_48,Z)),join(meet(X_47,X_48),meet(X_47,Z))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
( join(X_48,meet(X_47,Z)) != join(X_48,join(meet(X_47,X_48),meet(X_47,Z)))
| join(meet(X_47,X_48),meet(X_47,Z)) != meet(X_47,join(X_48,Z))
| join(X_48,meet(X_47,Z)) = join(X_48,meet(X_47,join(X_48,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_48,meet(X_47,Z)),join(X_48,join(meet(X_47,X_48),meet(X_47,Z)))) ),[1,1],$fot(meet(X_47,join(X_48,Z)))]]) ).
cnf(refute_0_99,plain,
( join(X_48,meet(X_47,Z)) != join(X_48,join(meet(X_47,X_48),meet(X_47,Z)))
| join(X_48,meet(X_47,Z)) = join(X_48,meet(X_47,join(X_48,Z))) ),
inference(resolve,[$cnf( $equal(join(meet(X_47,X_48),meet(X_47,Z)),meet(X_47,join(X_48,Z))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
join(X_48,meet(X_47,Z)) = join(X_48,meet(X_47,join(X_48,Z))),
inference(resolve,[$cnf( $equal(join(X_48,meet(X_47,Z)),join(X_48,join(meet(X_47,X_48),meet(X_47,Z)))) )],[refute_0_94,refute_0_99]) ).
cnf(refute_0_101,plain,
join(X_20,meet(X_147,X_146)) = join(X_20,meet(X_147,join(X_20,X_146))),
inference(subst,[],[refute_0_100:[bind(Z,$fot(X_146)),bind(X_47,$fot(X_147)),bind(X_48,$fot(X_20))]]) ).
cnf(refute_0_102,plain,
( join(X_20,meet(X_147,X_146)) != join(X_20,meet(X_147,join(X_20,X_146)))
| join(X_20,meet(X_147,join(X_20,X_146))) = join(X_20,meet(X_147,X_146)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_20,meet(X_147,X_146)))),bind(Y0,$fot(join(X_20,meet(X_147,join(X_20,X_146)))))]]) ).
cnf(refute_0_103,plain,
join(X_20,meet(X_147,join(X_20,X_146))) = join(X_20,meet(X_147,X_146)),
inference(resolve,[$cnf( $equal(join(X_20,meet(X_147,X_146)),join(X_20,meet(X_147,join(X_20,X_146)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
( join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) != join(X_20,join(Y,join(X_20,meet(X_147,join(X_20,X_146)))))
| join(X_20,meet(X_147,join(X_20,X_146))) != join(X_20,meet(X_147,X_146))
| join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,join(X_20,meet(X_147,X_146)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_20,join(Y,meet(X_147,join(X_20,X_146)))),join(X_20,join(Y,join(X_20,meet(X_147,join(X_20,X_146)))))) ),[1,1,1],$fot(join(X_20,meet(X_147,X_146)))]]) ).
cnf(refute_0_105,plain,
( join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) != join(X_20,join(Y,join(X_20,meet(X_147,join(X_20,X_146)))))
| join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,join(X_20,meet(X_147,X_146)))) ),
inference(resolve,[$cnf( $equal(join(X_20,meet(X_147,join(X_20,X_146))),join(X_20,meet(X_147,X_146))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,join(X_20,meet(X_147,X_146)))),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,meet(X_147,join(X_20,X_146)))),join(X_20,join(Y,join(X_20,meet(X_147,join(X_20,X_146)))))) )],[refute_0_88,refute_0_105]) ).
cnf(refute_0_107,plain,
( join(X_20,join(Y,X_22)) != join(X_20,join(Y,join(X_20,X_22)))
| join(X_20,join(Y,join(X_20,X_22))) = join(X_20,join(Y,X_22)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_20,join(Y,X_22)))),bind(Y0,$fot(join(X_20,join(Y,join(X_20,X_22)))))]]) ).
cnf(refute_0_108,plain,
join(X_20,join(Y,join(X_20,X_22))) = join(X_20,join(Y,X_22)),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,X_22)),join(X_20,join(Y,join(X_20,X_22)))) )],[refute_0_87,refute_0_107]) ).
cnf(refute_0_109,plain,
join(X_20,join(Y,join(X_20,meet(X_147,X_146)))) = join(X_20,join(Y,meet(X_147,X_146))),
inference(subst,[],[refute_0_108:[bind(X_22,$fot(meet(X_147,X_146)))]]) ).
cnf(refute_0_110,plain,
( join(X_20,join(Y,join(X_20,meet(X_147,X_146)))) != join(X_20,join(Y,meet(X_147,X_146)))
| join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) != join(X_20,join(Y,join(X_20,meet(X_147,X_146))))
| join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,meet(X_147,X_146))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_20,join(Y,meet(X_147,join(X_20,X_146)))),join(X_20,join(Y,join(X_20,meet(X_147,X_146))))) ),[1],$fot(join(X_20,join(Y,meet(X_147,X_146))))]]) ).
cnf(refute_0_111,plain,
( join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) != join(X_20,join(Y,join(X_20,meet(X_147,X_146))))
| join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,meet(X_147,X_146))) ),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,join(X_20,meet(X_147,X_146)))),join(X_20,join(Y,meet(X_147,X_146)))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
join(X_20,join(Y,meet(X_147,join(X_20,X_146)))) = join(X_20,join(Y,meet(X_147,X_146))),
inference(resolve,[$cnf( $equal(join(X_20,join(Y,meet(X_147,join(X_20,X_146)))),join(X_20,join(Y,join(X_20,meet(X_147,X_146))))) )],[refute_0_106,refute_0_111]) ).
cnf(refute_0_113,plain,
join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))) = join(X_154,join(meet(X_152,Y),meet(Y,X_152))),
inference(subst,[],[refute_0_112:[bind(Y,$fot(meet(X_152,Y))),bind(X_146,$fot(X_152)),bind(X_147,$fot(Y)),bind(X_20,$fot(X_154))]]) ).
cnf(refute_0_114,plain,
join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_154)),bind(Y,$fot(meet(X_152,Y))),bind(Z,$fot(meet(Y,join(X_154,X_152))))]]) ).
cnf(refute_0_115,plain,
( join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))) != join(X_154,join(meet(X_152,Y),meet(Y,X_152)))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) != join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152))))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,join(meet(X_152,Y),meet(Y,X_152))) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))))),bind(Y0,$fot(join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))))),bind(Z0,$fot(join(X_154,join(meet(X_152,Y),meet(Y,X_152)))))]]) ).
cnf(refute_0_116,plain,
( join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))) != join(X_154,join(meet(X_152,Y),meet(Y,X_152)))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,join(meet(X_152,Y),meet(Y,X_152))) ),
inference(resolve,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))),join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152))))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,join(meet(X_152,Y),meet(Y,X_152))),
inference(resolve,[$cnf( $equal(join(X_154,join(meet(X_152,Y),meet(Y,join(X_154,X_152)))),join(X_154,join(meet(X_152,Y),meet(Y,X_152)))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( join(X_154,join(meet(X_152,Y),meet(Y,X_152))) != join(X_154,meet(Y,X_152))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) != join(X_154,join(meet(X_152,Y),meet(Y,X_152)))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(Y,X_152)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))))),bind(Y0,$fot(join(X_154,join(meet(X_152,Y),meet(Y,X_152))))),bind(Z0,$fot(join(X_154,meet(Y,X_152))))]]) ).
cnf(refute_0_119,plain,
( join(X_154,join(meet(X_152,Y),meet(Y,X_152))) != join(X_154,meet(Y,X_152))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(Y,X_152)) ),
inference(resolve,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))),join(X_154,join(meet(X_152,Y),meet(Y,X_152)))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) = join(X_154,meet(Y,X_152)),
inference(resolve,[$cnf( $equal(join(X_154,join(meet(X_152,Y),meet(Y,X_152))),join(X_154,meet(Y,X_152))) )],[refute_0_61,refute_0_119]) ).
cnf(refute_0_121,plain,
( join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) != join(X_154,meet(Y,X_152))
| join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) != join(X_154,meet(X_152,Y))
| join(X_154,meet(Y,X_152)) = join(X_154,meet(X_152,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))),join(X_154,meet(X_152,Y))) ),[0],$fot(join(X_154,meet(Y,X_152)))]]) ).
cnf(refute_0_122,plain,
( join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))) != join(X_154,meet(X_152,Y))
| join(X_154,meet(Y,X_152)) = join(X_154,meet(X_152,Y)) ),
inference(resolve,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))),join(X_154,meet(Y,X_152))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
join(X_154,meet(Y,X_152)) = join(X_154,meet(X_152,Y)),
inference(resolve,[$cnf( $equal(join(join(X_154,meet(X_152,Y)),meet(Y,join(X_154,X_152))),join(X_154,meet(X_152,Y))) )],[refute_0_37,refute_0_122]) ).
cnf(refute_0_124,plain,
( join(X_154,meet(Y,X_152)) != join(X_154,meet(X_152,Y))
| join(X_154,meet(X_152,Y)) = join(X_154,meet(Y,X_152)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_154,meet(Y,X_152)))),bind(Y0,$fot(join(X_154,meet(X_152,Y))))]]) ).
cnf(refute_0_125,plain,
join(X_154,meet(X_152,Y)) = join(X_154,meet(Y,X_152)),
inference(resolve,[$cnf( $equal(join(X_154,meet(Y,X_152)),join(X_154,meet(X_152,Y))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
join(xx,meet(zz,yy)) = join(xx,meet(yy,zz)),
inference(subst,[],[refute_0_125:[bind(Y,$fot(yy)),bind(X_152,$fot(zz)),bind(X_154,$fot(xx))]]) ).
cnf(refute_0_127,plain,
meet(join(X_154,Z),join(X_154,meet(X_152,join(X_154,Z)))) = meet(join(X_154,Z),join(X_154,X_152)),
inference(subst,[],[refute_0_33:[bind(Y,$fot(X_152)),bind(X_31,$fot(join(X_154,Z))),bind(X_32,$fot(X_154))]]) ).
cnf(refute_0_128,plain,
join(X_154,meet(X_152,Z)) = join(X_154,meet(X_152,join(X_154,Z))),
inference(subst,[],[refute_0_100:[bind(X_47,$fot(X_152)),bind(X_48,$fot(X_154))]]) ).
cnf(refute_0_129,plain,
( join(X_154,meet(X_152,Z)) != join(X_154,meet(X_152,join(X_154,Z)))
| join(X_154,meet(X_152,join(X_154,Z))) = join(X_154,meet(X_152,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_154,meet(X_152,Z)))),bind(Y0,$fot(join(X_154,meet(X_152,join(X_154,Z)))))]]) ).
cnf(refute_0_130,plain,
join(X_154,meet(X_152,join(X_154,Z))) = join(X_154,meet(X_152,Z)),
inference(resolve,[$cnf( $equal(join(X_154,meet(X_152,Z)),join(X_154,meet(X_152,join(X_154,Z)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( join(X_154,meet(X_152,join(X_154,Z))) != join(X_154,meet(X_152,Z))
| meet(join(X_154,Z),join(X_154,meet(X_152,join(X_154,Z)))) != meet(join(X_154,Z),join(X_154,X_152))
| meet(join(X_154,Z),join(X_154,meet(X_152,Z))) = meet(join(X_154,Z),join(X_154,X_152)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_154,Z),join(X_154,meet(X_152,join(X_154,Z)))),meet(join(X_154,Z),join(X_154,X_152))) ),[0,1],$fot(join(X_154,meet(X_152,Z)))]]) ).
cnf(refute_0_132,plain,
( meet(join(X_154,Z),join(X_154,meet(X_152,join(X_154,Z)))) != meet(join(X_154,Z),join(X_154,X_152))
| meet(join(X_154,Z),join(X_154,meet(X_152,Z))) = meet(join(X_154,Z),join(X_154,X_152)) ),
inference(resolve,[$cnf( $equal(join(X_154,meet(X_152,join(X_154,Z))),join(X_154,meet(X_152,Z))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
meet(join(X_154,Z),join(X_154,meet(X_152,Z))) = meet(join(X_154,Z),join(X_154,X_152)),
inference(resolve,[$cnf( $equal(meet(join(X_154,Z),join(X_154,meet(X_152,join(X_154,Z)))),meet(join(X_154,Z),join(X_154,X_152))) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,join(X_73,meet(join(X_7,X_73),X_71)))) = join(X_73,meet(join(X_7,X_73),X_71)),
inference(subst,[],[refute_0_14:[bind(X_6,$fot(join(X_73,meet(join(X_7,X_73),X_71))))]]) ).
cnf(refute_0_135,plain,
join(join(X_20,X_21),meet(join(X_20,X_21),Y)) = join(X_20,X_21),
inference(subst,[],[absorption2:[bind(X,$fot(join(X_20,X_21)))]]) ).
cnf(refute_0_136,plain,
join(join(X_20,X_21),meet(join(X_20,X_21),Y)) = join(X_20,join(X_21,meet(join(X_20,X_21),Y))),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(meet(join(X_20,X_21),Y)))]]) ).
cnf(refute_0_137,plain,
( join(join(X_20,X_21),meet(join(X_20,X_21),Y)) != join(X_20,X_21)
| join(join(X_20,X_21),meet(join(X_20,X_21),Y)) != join(X_20,join(X_21,meet(join(X_20,X_21),Y)))
| join(X_20,join(X_21,meet(join(X_20,X_21),Y))) = join(X_20,X_21) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,X_21),meet(join(X_20,X_21),Y)),join(X_20,X_21)) ),[0],$fot(join(X_20,join(X_21,meet(join(X_20,X_21),Y))))]]) ).
cnf(refute_0_138,plain,
( join(join(X_20,X_21),meet(join(X_20,X_21),Y)) != join(X_20,X_21)
| join(X_20,join(X_21,meet(join(X_20,X_21),Y))) = join(X_20,X_21) ),
inference(resolve,[$cnf( $equal(join(join(X_20,X_21),meet(join(X_20,X_21),Y)),join(X_20,join(X_21,meet(join(X_20,X_21),Y)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
join(X_20,join(X_21,meet(join(X_20,X_21),Y))) = join(X_20,X_21),
inference(resolve,[$cnf( $equal(join(join(X_20,X_21),meet(join(X_20,X_21),Y)),join(X_20,X_21)) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
join(X_7,join(X_73,meet(join(X_7,X_73),X_71))) = join(X_7,X_73),
inference(subst,[],[refute_0_139:[bind(Y,$fot(X_71)),bind(X_20,$fot(X_7)),bind(X_21,$fot(X_73))]]) ).
cnf(refute_0_141,plain,
( join(X_7,join(X_73,meet(join(X_7,X_73),X_71))) != join(X_7,X_73)
| meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,join(X_73,meet(join(X_7,X_73),X_71)))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) = join(X_73,meet(join(X_7,X_73),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,join(X_73,meet(join(X_7,X_73),X_71)))),join(X_73,meet(join(X_7,X_73),X_71))) ),[0,1],$fot(join(X_7,X_73))]]) ).
cnf(refute_0_142,plain,
( meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,join(X_73,meet(join(X_7,X_73),X_71)))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) = join(X_73,meet(join(X_7,X_73),X_71)) ),
inference(resolve,[$cnf( $equal(join(X_7,join(X_73,meet(join(X_7,X_73),X_71))),join(X_7,X_73)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) = join(X_73,meet(join(X_7,X_73),X_71)),
inference(resolve,[$cnf( $equal(meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,join(X_73,meet(join(X_7,X_73),X_71)))),join(X_73,meet(join(X_7,X_73),X_71))) )],[refute_0_134,refute_0_142]) ).
cnf(refute_0_144,plain,
meet(join(X_70,X_69),Y) = meet(Y,join(X_70,X_69)),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(join(X_70,X_69)))]]) ).
cnf(refute_0_145,plain,
join(meet(X_31,X_33),meet(X_31,X_32)) = join(meet(X_31,X_32),meet(X_31,X_33)),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(meet(X_31,X_33))),bind(Y,$fot(meet(X_31,X_32)))]]) ).
cnf(refute_0_146,plain,
( meet(X_31,join(X_32,X_33)) != join(meet(X_31,X_32),meet(X_31,X_33))
| join(meet(X_31,X_32),meet(X_31,X_33)) = meet(X_31,join(X_32,X_33)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_31,join(X_32,X_33)))),bind(Y0,$fot(join(meet(X_31,X_32),meet(X_31,X_33))))]]) ).
cnf(refute_0_147,plain,
join(meet(X_31,X_32),meet(X_31,X_33)) = meet(X_31,join(X_32,X_33)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_31,X_32),meet(X_31,X_33))) )],[refute_0_43,refute_0_146]) ).
cnf(refute_0_148,plain,
( join(meet(X_31,X_32),meet(X_31,X_33)) != meet(X_31,join(X_32,X_33))
| join(meet(X_31,X_33),meet(X_31,X_32)) != join(meet(X_31,X_32),meet(X_31,X_33))
| join(meet(X_31,X_33),meet(X_31,X_32)) = meet(X_31,join(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_31,X_33),meet(X_31,X_32)),join(meet(X_31,X_32),meet(X_31,X_33))) ),[1],$fot(meet(X_31,join(X_32,X_33)))]]) ).
cnf(refute_0_149,plain,
( join(meet(X_31,X_33),meet(X_31,X_32)) != join(meet(X_31,X_32),meet(X_31,X_33))
| join(meet(X_31,X_33),meet(X_31,X_32)) = meet(X_31,join(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,X_32),meet(X_31,X_33)),meet(X_31,join(X_32,X_33))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
join(meet(X_31,X_33),meet(X_31,X_32)) = meet(X_31,join(X_32,X_33)),
inference(resolve,[$cnf( $equal(join(meet(X_31,X_33),meet(X_31,X_32)),join(meet(X_31,X_32),meet(X_31,X_33))) )],[refute_0_145,refute_0_149]) ).
cnf(refute_0_151,plain,
join(meet(X_31,X_33),meet(X_31,X_32)) = meet(X_31,join(X_33,X_32)),
inference(subst,[],[refute_0_29:[bind(X,$fot(X_31)),bind(Y,$fot(X_33)),bind(Z,$fot(X_32))]]) ).
cnf(refute_0_152,plain,
( join(meet(X_31,X_33),meet(X_31,X_32)) != meet(X_31,join(X_32,X_33))
| join(meet(X_31,X_33),meet(X_31,X_32)) != meet(X_31,join(X_33,X_32))
| meet(X_31,join(X_33,X_32)) = meet(X_31,join(X_32,X_33)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_31,X_33),meet(X_31,X_32)),meet(X_31,join(X_32,X_33))) ),[0],$fot(meet(X_31,join(X_33,X_32)))]]) ).
cnf(refute_0_153,plain,
( join(meet(X_31,X_33),meet(X_31,X_32)) != meet(X_31,join(X_32,X_33))
| meet(X_31,join(X_33,X_32)) = meet(X_31,join(X_32,X_33)) ),
inference(resolve,[$cnf( $equal(join(meet(X_31,X_33),meet(X_31,X_32)),meet(X_31,join(X_33,X_32))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
meet(X_31,join(X_33,X_32)) = meet(X_31,join(X_32,X_33)),
inference(resolve,[$cnf( $equal(join(meet(X_31,X_33),meet(X_31,X_32)),meet(X_31,join(X_32,X_33))) )],[refute_0_150,refute_0_153]) ).
cnf(refute_0_155,plain,
meet(Y,join(X_70,X_69)) = meet(Y,join(X_69,X_70)),
inference(subst,[],[refute_0_154:[bind(X_31,$fot(Y)),bind(X_32,$fot(X_69)),bind(X_33,$fot(X_70))]]) ).
cnf(refute_0_156,plain,
( meet(Y,join(X_70,X_69)) != meet(Y,join(X_69,X_70))
| meet(join(X_70,X_69),Y) != meet(Y,join(X_70,X_69))
| meet(join(X_70,X_69),Y) = meet(Y,join(X_69,X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_70,X_69),Y),meet(Y,join(X_70,X_69))) ),[1],$fot(meet(Y,join(X_69,X_70)))]]) ).
cnf(refute_0_157,plain,
( meet(join(X_70,X_69),Y) != meet(Y,join(X_70,X_69))
| meet(join(X_70,X_69),Y) = meet(Y,join(X_69,X_70)) ),
inference(resolve,[$cnf( $equal(meet(Y,join(X_70,X_69)),meet(Y,join(X_69,X_70))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
meet(join(X_70,X_69),Y) = meet(Y,join(X_69,X_70)),
inference(resolve,[$cnf( $equal(meet(join(X_70,X_69),Y),meet(Y,join(X_70,X_69))) )],[refute_0_144,refute_0_157]) ).
cnf(refute_0_159,plain,
( meet(join(X_70,X_69),Y) != meet(Y,join(X_69,X_70))
| meet(Y,join(X_69,X_70)) = meet(join(X_70,X_69),Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(join(X_70,X_69),Y))),bind(Y0,$fot(meet(Y,join(X_69,X_70))))]]) ).
cnf(refute_0_160,plain,
meet(Y,join(X_69,X_70)) = meet(join(X_70,X_69),Y),
inference(resolve,[$cnf( $equal(meet(join(X_70,X_69),Y),meet(Y,join(X_69,X_70))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) = meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),
inference(subst,[],[refute_0_160:[bind(Y,$fot(join(X_73,meet(join(X_7,X_73),X_71)))),bind(X_69,$fot(X_7)),bind(X_70,$fot(X_73))]]) ).
cnf(refute_0_162,plain,
( meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) != meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71)))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = join(X_73,meet(join(X_7,X_73),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)),join(X_73,meet(join(X_7,X_73),X_71))) ),[0],$fot(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))))]]) ).
cnf(refute_0_163,plain,
( meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = join(X_73,meet(join(X_7,X_73),X_71)) ),
inference(resolve,[$cnf( $equal(meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)),meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71)))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = join(X_73,meet(join(X_7,X_73),X_71)),
inference(resolve,[$cnf( $equal(meet(join(X_73,meet(join(X_7,X_73),X_71)),join(X_7,X_73)),join(X_73,meet(join(X_7,X_73),X_71))) )],[refute_0_143,refute_0_163]) ).
cnf(refute_0_165,plain,
join(X_148,meet(X_147,X_146)) = join(X_148,meet(X_147,join(X_148,X_146))),
inference(subst,[],[refute_0_100:[bind(Z,$fot(X_146)),bind(X_47,$fot(X_147)),bind(X_48,$fot(X_148))]]) ).
cnf(refute_0_166,plain,
join(meet(join(X_76,Y),X_75),meet(Y,meet(join(X_76,Y),X_75))) = meet(join(X_76,Y),X_75),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(join(X_76,Y),X_75)))]]) ).
cnf(refute_0_167,plain,
meet(meet(X_25,join(X_7,X_25)),X_27) = meet(X_25,meet(join(X_7,X_25),X_27)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_25)),bind(Y,$fot(join(X_7,X_25))),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_168,plain,
meet(X_25,join(X_7,X_25)) = X_25,
inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_25))]]) ).
cnf(refute_0_169,plain,
( meet(X_25,join(X_7,X_25)) != X_25
| meet(meet(X_25,join(X_7,X_25)),X_27) != meet(X_25,meet(join(X_7,X_25),X_27))
| meet(X_25,X_27) = meet(X_25,meet(join(X_7,X_25),X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_25,join(X_7,X_25)),X_27),meet(X_25,meet(join(X_7,X_25),X_27))) ),[0,0],$fot(X_25)]]) ).
cnf(refute_0_170,plain,
( meet(meet(X_25,join(X_7,X_25)),X_27) != meet(X_25,meet(join(X_7,X_25),X_27))
| meet(X_25,X_27) = meet(X_25,meet(join(X_7,X_25),X_27)) ),
inference(resolve,[$cnf( $equal(meet(X_25,join(X_7,X_25)),X_25) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
meet(X_25,X_27) = meet(X_25,meet(join(X_7,X_25),X_27)),
inference(resolve,[$cnf( $equal(meet(meet(X_25,join(X_7,X_25)),X_27),meet(X_25,meet(join(X_7,X_25),X_27))) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
meet(Y,X_75) = meet(Y,meet(join(X_76,Y),X_75)),
inference(subst,[],[refute_0_171:[bind(X_25,$fot(Y)),bind(X_27,$fot(X_75)),bind(X_7,$fot(X_76))]]) ).
cnf(refute_0_173,plain,
( meet(Y,X_75) != meet(Y,meet(join(X_76,Y),X_75))
| meet(Y,meet(join(X_76,Y),X_75)) = meet(Y,X_75) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(Y,X_75))),bind(Y0,$fot(meet(Y,meet(join(X_76,Y),X_75))))]]) ).
cnf(refute_0_174,plain,
meet(Y,meet(join(X_76,Y),X_75)) = meet(Y,X_75),
inference(resolve,[$cnf( $equal(meet(Y,X_75),meet(Y,meet(join(X_76,Y),X_75))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,meet(join(X_76,Y),X_75))) != meet(join(X_76,Y),X_75)
| meet(Y,meet(join(X_76,Y),X_75)) != meet(Y,X_75)
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(join(X_76,Y),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,meet(join(X_76,Y),X_75))),meet(join(X_76,Y),X_75)) ),[0,1],$fot(meet(Y,X_75))]]) ).
cnf(refute_0_176,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,meet(join(X_76,Y),X_75))) != meet(join(X_76,Y),X_75)
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(join(X_76,Y),X_75) ),
inference(resolve,[$cnf( $equal(meet(Y,meet(join(X_76,Y),X_75)),meet(Y,X_75)) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(join(X_76,Y),X_75),
inference(resolve,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,meet(join(X_76,Y),X_75))),meet(join(X_76,Y),X_75)) )],[refute_0_166,refute_0_176]) ).
cnf(refute_0_178,plain,
join(Y,join(X_76,Y)) = join(Y,X_76),
inference(subst,[],[refute_0_71:[bind(Y,$fot(X_76)),bind(X_17,$fot(Y))]]) ).
cnf(refute_0_179,plain,
meet(X_75,join(Y,join(X_76,Y))) = meet(X_75,join(Y,join(X_76,Y))),
introduced(tautology,[refl,[$fot(meet(X_75,join(Y,join(X_76,Y))))]]) ).
cnf(refute_0_180,plain,
( join(Y,join(X_76,Y)) != join(Y,X_76)
| meet(X_75,join(Y,join(X_76,Y))) != meet(X_75,join(Y,join(X_76,Y)))
| meet(X_75,join(Y,join(X_76,Y))) = meet(X_75,join(Y,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_75,join(Y,join(X_76,Y))),meet(X_75,join(Y,join(X_76,Y)))) ),[1,1],$fot(join(Y,X_76))]]) ).
cnf(refute_0_181,plain,
( join(Y,join(X_76,Y)) != join(Y,X_76)
| meet(X_75,join(Y,join(X_76,Y))) = meet(X_75,join(Y,X_76)) ),
inference(resolve,[$cnf( $equal(meet(X_75,join(Y,join(X_76,Y))),meet(X_75,join(Y,join(X_76,Y)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
meet(X_75,join(Y,join(X_76,Y))) = meet(X_75,join(Y,X_76)),
inference(resolve,[$cnf( $equal(join(Y,join(X_76,Y)),join(Y,X_76)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
join(meet(X_67,X_65),meet(X_65,X_66)) = join(meet(X_65,X_66),meet(X_67,X_65)),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(meet(X_67,X_65))),bind(Y,$fot(meet(X_65,X_66)))]]) ).
cnf(refute_0_184,plain,
meet(X_33,X_31) = meet(X_31,X_33),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_33)),bind(Y,$fot(X_31))]]) ).
cnf(refute_0_185,plain,
( meet(X_33,X_31) != meet(X_31,X_33)
| meet(X_31,X_33) = meet(X_33,X_31) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_33,X_31))),bind(Y0,$fot(meet(X_31,X_33)))]]) ).
cnf(refute_0_186,plain,
meet(X_31,X_33) = meet(X_33,X_31),
inference(resolve,[$cnf( $equal(meet(X_33,X_31),meet(X_31,X_33)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
( meet(X_31,X_33) != meet(X_33,X_31)
| meet(X_31,join(X_32,X_33)) != join(meet(X_31,X_32),meet(X_31,X_33))
| meet(X_31,join(X_32,X_33)) = join(meet(X_31,X_32),meet(X_33,X_31)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_31,X_32),meet(X_31,X_33))) ),[1,1],$fot(meet(X_33,X_31))]]) ).
cnf(refute_0_188,plain,
( meet(X_31,join(X_32,X_33)) != join(meet(X_31,X_32),meet(X_31,X_33))
| meet(X_31,join(X_32,X_33)) = join(meet(X_31,X_32),meet(X_33,X_31)) ),
inference(resolve,[$cnf( $equal(meet(X_31,X_33),meet(X_33,X_31)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
meet(X_31,join(X_32,X_33)) = join(meet(X_31,X_32),meet(X_33,X_31)),
inference(resolve,[$cnf( $equal(meet(X_31,join(X_32,X_33)),join(meet(X_31,X_32),meet(X_31,X_33))) )],[refute_0_43,refute_0_188]) ).
cnf(refute_0_190,plain,
meet(X_65,join(X_66,X_67)) = join(meet(X_65,X_66),meet(X_67,X_65)),
inference(subst,[],[refute_0_189:[bind(X_31,$fot(X_65)),bind(X_32,$fot(X_66)),bind(X_33,$fot(X_67))]]) ).
cnf(refute_0_191,plain,
( meet(X_65,join(X_66,X_67)) != join(meet(X_65,X_66),meet(X_67,X_65))
| join(meet(X_65,X_66),meet(X_67,X_65)) = meet(X_65,join(X_66,X_67)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_65,join(X_66,X_67)))),bind(Y0,$fot(join(meet(X_65,X_66),meet(X_67,X_65))))]]) ).
cnf(refute_0_192,plain,
join(meet(X_65,X_66),meet(X_67,X_65)) = meet(X_65,join(X_66,X_67)),
inference(resolve,[$cnf( $equal(meet(X_65,join(X_66,X_67)),join(meet(X_65,X_66),meet(X_67,X_65))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
( join(meet(X_65,X_66),meet(X_67,X_65)) != meet(X_65,join(X_66,X_67))
| join(meet(X_67,X_65),meet(X_65,X_66)) != join(meet(X_65,X_66),meet(X_67,X_65))
| join(meet(X_67,X_65),meet(X_65,X_66)) = meet(X_65,join(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_67,X_65),meet(X_65,X_66)),join(meet(X_65,X_66),meet(X_67,X_65))) ),[1],$fot(meet(X_65,join(X_66,X_67)))]]) ).
cnf(refute_0_194,plain,
( join(meet(X_67,X_65),meet(X_65,X_66)) != join(meet(X_65,X_66),meet(X_67,X_65))
| join(meet(X_67,X_65),meet(X_65,X_66)) = meet(X_65,join(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(join(meet(X_65,X_66),meet(X_67,X_65)),meet(X_65,join(X_66,X_67))) )],[refute_0_192,refute_0_193]) ).
cnf(refute_0_195,plain,
join(meet(X_67,X_65),meet(X_65,X_66)) = meet(X_65,join(X_66,X_67)),
inference(resolve,[$cnf( $equal(join(meet(X_67,X_65),meet(X_65,X_66)),join(meet(X_65,X_66),meet(X_67,X_65))) )],[refute_0_183,refute_0_194]) ).
cnf(refute_0_196,plain,
join(meet(X_67,X_65),meet(X_65,X_66)) = meet(X_65,join(X_67,X_66)),
inference(subst,[],[refute_0_51:[bind(X_31,$fot(X_65)),bind(X_32,$fot(X_67)),bind(X_33,$fot(X_66))]]) ).
cnf(refute_0_197,plain,
( join(meet(X_67,X_65),meet(X_65,X_66)) != meet(X_65,join(X_66,X_67))
| join(meet(X_67,X_65),meet(X_65,X_66)) != meet(X_65,join(X_67,X_66))
| meet(X_65,join(X_67,X_66)) = meet(X_65,join(X_66,X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_67,X_65),meet(X_65,X_66)),meet(X_65,join(X_66,X_67))) ),[0],$fot(meet(X_65,join(X_67,X_66)))]]) ).
cnf(refute_0_198,plain,
( join(meet(X_67,X_65),meet(X_65,X_66)) != meet(X_65,join(X_66,X_67))
| meet(X_65,join(X_67,X_66)) = meet(X_65,join(X_66,X_67)) ),
inference(resolve,[$cnf( $equal(join(meet(X_67,X_65),meet(X_65,X_66)),meet(X_65,join(X_67,X_66))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
meet(X_65,join(X_67,X_66)) = meet(X_65,join(X_66,X_67)),
inference(resolve,[$cnf( $equal(join(meet(X_67,X_65),meet(X_65,X_66)),meet(X_65,join(X_66,X_67))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
( meet(X_65,join(X_67,X_66)) != meet(X_65,join(X_66,X_67))
| meet(X_65,join(X_66,X_67)) = meet(X_65,join(X_67,X_66)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_65,join(X_67,X_66)))),bind(Y0,$fot(meet(X_65,join(X_66,X_67))))]]) ).
cnf(refute_0_201,plain,
meet(X_65,join(X_66,X_67)) = meet(X_65,join(X_67,X_66)),
inference(resolve,[$cnf( $equal(meet(X_65,join(X_67,X_66)),meet(X_65,join(X_66,X_67))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
meet(X_75,join(join(X_76,Y),Y)) = meet(X_75,join(Y,join(X_76,Y))),
inference(subst,[],[refute_0_201:[bind(X_65,$fot(X_75)),bind(X_66,$fot(join(X_76,Y))),bind(X_67,$fot(Y))]]) ).
cnf(refute_0_203,plain,
meet(X_66,X_65) = meet(X_65,X_66),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_66)),bind(Y,$fot(X_65))]]) ).
cnf(refute_0_204,plain,
( meet(X_66,X_65) != meet(X_65,X_66)
| meet(X_65,X_66) = meet(X_66,X_65) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_66,X_65))),bind(Y0,$fot(meet(X_65,X_66)))]]) ).
cnf(refute_0_205,plain,
meet(X_65,X_66) = meet(X_66,X_65),
inference(resolve,[$cnf( $equal(meet(X_66,X_65),meet(X_65,X_66)) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
( meet(X_65,X_66) != meet(X_66,X_65)
| meet(X_65,join(X_66,X_67)) != join(meet(X_65,X_66),meet(X_67,X_65))
| meet(X_65,join(X_66,X_67)) = join(meet(X_66,X_65),meet(X_67,X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_65,join(X_66,X_67)),join(meet(X_65,X_66),meet(X_67,X_65))) ),[1,0],$fot(meet(X_66,X_65))]]) ).
cnf(refute_0_207,plain,
( meet(X_65,join(X_66,X_67)) != join(meet(X_65,X_66),meet(X_67,X_65))
| meet(X_65,join(X_66,X_67)) = join(meet(X_66,X_65),meet(X_67,X_65)) ),
inference(resolve,[$cnf( $equal(meet(X_65,X_66),meet(X_66,X_65)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
meet(X_65,join(X_66,X_67)) = join(meet(X_66,X_65),meet(X_67,X_65)),
inference(resolve,[$cnf( $equal(meet(X_65,join(X_66,X_67)),join(meet(X_65,X_66),meet(X_67,X_65))) )],[refute_0_190,refute_0_207]) ).
cnf(refute_0_209,plain,
( meet(X_65,join(X_66,X_67)) != join(meet(X_66,X_65),meet(X_67,X_65))
| join(meet(X_66,X_65),meet(X_67,X_65)) = meet(X_65,join(X_66,X_67)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_65,join(X_66,X_67)))),bind(Y0,$fot(join(meet(X_66,X_65),meet(X_67,X_65))))]]) ).
cnf(refute_0_210,plain,
join(meet(X_66,X_65),meet(X_67,X_65)) = meet(X_65,join(X_66,X_67)),
inference(resolve,[$cnf( $equal(meet(X_65,join(X_66,X_67)),join(meet(X_66,X_65),meet(X_67,X_65))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(join(X_76,Y),Y)),
inference(subst,[],[refute_0_210:[bind(X_65,$fot(X_75)),bind(X_66,$fot(join(X_76,Y))),bind(X_67,$fot(Y))]]) ).
cnf(refute_0_212,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,X_75)) != meet(X_75,join(join(X_76,Y),Y))
| meet(X_75,join(join(X_76,Y),Y)) != meet(X_75,join(Y,join(X_76,Y)))
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,join(X_76,Y))) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(join(meet(join(X_76,Y),X_75),meet(Y,X_75)))),bind(Y0,$fot(meet(X_75,join(join(X_76,Y),Y)))),bind(Z0,$fot(meet(X_75,join(Y,join(X_76,Y)))))]]) ).
cnf(refute_0_213,plain,
( meet(X_75,join(join(X_76,Y),Y)) != meet(X_75,join(Y,join(X_76,Y)))
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,join(X_76,Y))) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,X_75)),meet(X_75,join(join(X_76,Y),Y))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,join(X_76,Y))),
inference(resolve,[$cnf( $equal(meet(X_75,join(join(X_76,Y),Y)),meet(X_75,join(Y,join(X_76,Y)))) )],[refute_0_202,refute_0_213]) ).
cnf(refute_0_215,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,X_75)) != meet(X_75,join(Y,join(X_76,Y)))
| meet(X_75,join(Y,join(X_76,Y))) != meet(X_75,join(Y,X_76))
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,X_76)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(join(meet(join(X_76,Y),X_75),meet(Y,X_75)))),bind(Y0,$fot(meet(X_75,join(Y,join(X_76,Y))))),bind(Z0,$fot(meet(X_75,join(Y,X_76))))]]) ).
cnf(refute_0_216,plain,
( meet(X_75,join(Y,join(X_76,Y))) != meet(X_75,join(Y,X_76))
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,X_76)) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,X_75)),meet(X_75,join(Y,join(X_76,Y)))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
join(meet(join(X_76,Y),X_75),meet(Y,X_75)) = meet(X_75,join(Y,X_76)),
inference(resolve,[$cnf( $equal(meet(X_75,join(Y,join(X_76,Y))),meet(X_75,join(Y,X_76))) )],[refute_0_182,refute_0_216]) ).
cnf(refute_0_218,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,X_75)) != meet(X_75,join(Y,X_76))
| join(meet(join(X_76,Y),X_75),meet(Y,X_75)) != meet(join(X_76,Y),X_75)
| meet(X_75,join(Y,X_76)) = meet(join(X_76,Y),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,X_75)),meet(join(X_76,Y),X_75)) ),[0],$fot(meet(X_75,join(Y,X_76)))]]) ).
cnf(refute_0_219,plain,
( join(meet(join(X_76,Y),X_75),meet(Y,X_75)) != meet(join(X_76,Y),X_75)
| meet(X_75,join(Y,X_76)) = meet(join(X_76,Y),X_75) ),
inference(resolve,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,X_75)),meet(X_75,join(Y,X_76))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
meet(X_75,join(Y,X_76)) = meet(join(X_76,Y),X_75),
inference(resolve,[$cnf( $equal(join(meet(join(X_76,Y),X_75),meet(Y,X_75)),meet(join(X_76,Y),X_75)) )],[refute_0_177,refute_0_219]) ).
cnf(refute_0_221,plain,
meet(X_147,join(X_148,X_146)) = meet(join(X_146,X_148),X_147),
inference(subst,[],[refute_0_220:[bind(Y,$fot(X_148)),bind(X_75,$fot(X_147)),bind(X_76,$fot(X_146))]]) ).
cnf(refute_0_222,plain,
( join(X_148,meet(X_147,X_146)) != join(X_148,meet(X_147,join(X_148,X_146)))
| meet(X_147,join(X_148,X_146)) != meet(join(X_146,X_148),X_147)
| join(X_148,meet(X_147,X_146)) = join(X_148,meet(join(X_146,X_148),X_147)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_148,meet(X_147,X_146)),join(X_148,meet(X_147,join(X_148,X_146)))) ),[1,1],$fot(meet(join(X_146,X_148),X_147))]]) ).
cnf(refute_0_223,plain,
( join(X_148,meet(X_147,X_146)) != join(X_148,meet(X_147,join(X_148,X_146)))
| join(X_148,meet(X_147,X_146)) = join(X_148,meet(join(X_146,X_148),X_147)) ),
inference(resolve,[$cnf( $equal(meet(X_147,join(X_148,X_146)),meet(join(X_146,X_148),X_147)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
join(X_148,meet(X_147,X_146)) = join(X_148,meet(join(X_146,X_148),X_147)),
inference(resolve,[$cnf( $equal(join(X_148,meet(X_147,X_146)),join(X_148,meet(X_147,join(X_148,X_146)))) )],[refute_0_165,refute_0_223]) ).
cnf(refute_0_225,plain,
( join(X_148,meet(X_147,X_146)) != join(X_148,meet(join(X_146,X_148),X_147))
| join(X_148,meet(join(X_146,X_148),X_147)) = join(X_148,meet(X_147,X_146)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_148,meet(X_147,X_146)))),bind(Y0,$fot(join(X_148,meet(join(X_146,X_148),X_147))))]]) ).
cnf(refute_0_226,plain,
join(X_148,meet(join(X_146,X_148),X_147)) = join(X_148,meet(X_147,X_146)),
inference(resolve,[$cnf( $equal(join(X_148,meet(X_147,X_146)),join(X_148,meet(join(X_146,X_148),X_147))) )],[refute_0_224,refute_0_225]) ).
cnf(refute_0_227,plain,
join(X_73,meet(join(X_7,X_73),X_71)) = join(X_73,meet(X_71,X_7)),
inference(subst,[],[refute_0_226:[bind(X_146,$fot(X_7)),bind(X_147,$fot(X_71)),bind(X_148,$fot(X_73))]]) ).
cnf(refute_0_228,plain,
meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),
introduced(tautology,[refl,[$fot(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))))]]) ).
cnf(refute_0_229,plain,
( join(X_73,meet(join(X_7,X_73),X_71)) != join(X_73,meet(X_71,X_7))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) != meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71)))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71)))) ),[1,1],$fot(join(X_73,meet(X_71,X_7)))]]) ).
cnf(refute_0_230,plain,
( join(X_73,meet(join(X_7,X_73),X_71)) != join(X_73,meet(X_71,X_7))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) ),
inference(resolve,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71)))) )],[refute_0_228,refute_0_229]) ).
cnf(refute_0_231,plain,
meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) = meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))),
inference(resolve,[$cnf( $equal(join(X_73,meet(join(X_7,X_73),X_71)),join(X_73,meet(X_71,X_7))) )],[refute_0_227,refute_0_230]) ).
cnf(refute_0_232,plain,
( meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) != meet(join(X_73,X_7),join(X_73,meet(X_71,X_7)))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(join(X_7,X_73),X_71)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),join(X_73,meet(join(X_7,X_73),X_71))) ),[0],$fot(meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))))]]) ).
cnf(refute_0_233,plain,
( meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(join(X_7,X_73),X_71)) ),
inference(resolve,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),meet(join(X_73,X_7),join(X_73,meet(X_71,X_7)))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( join(X_73,meet(join(X_7,X_73),X_71)) != join(X_73,meet(X_71,X_7))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(X_71,X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))),join(X_73,meet(join(X_7,X_73),X_71))) ),[1],$fot(join(X_73,meet(X_71,X_7)))]]) ).
cnf(refute_0_235,plain,
( meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(X_71,X_7)) ),
inference(resolve,[$cnf( $equal(join(X_73,meet(join(X_7,X_73),X_71)),join(X_73,meet(X_71,X_7))) )],[refute_0_227,refute_0_234]) ).
cnf(refute_0_236,plain,
( meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))) != join(X_73,meet(join(X_7,X_73),X_71))
| meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(X_71,X_7)) ),
inference(resolve,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))),join(X_73,meet(join(X_7,X_73),X_71))) )],[refute_0_233,refute_0_235]) ).
cnf(refute_0_237,plain,
meet(join(X_73,X_7),join(X_73,meet(X_71,X_7))) = join(X_73,meet(X_71,X_7)),
inference(resolve,[$cnf( $equal(meet(join(X_73,X_7),join(X_73,meet(join(X_7,X_73),X_71))),join(X_73,meet(join(X_7,X_73),X_71))) )],[refute_0_164,refute_0_236]) ).
cnf(refute_0_238,plain,
meet(join(X_154,Z),join(X_154,meet(X_152,Z))) = join(X_154,meet(X_152,Z)),
inference(subst,[],[refute_0_237:[bind(X_7,$fot(Z)),bind(X_71,$fot(X_152)),bind(X_73,$fot(X_154))]]) ).
cnf(refute_0_239,plain,
( meet(join(X_154,Z),join(X_154,meet(X_152,Z))) != join(X_154,meet(X_152,Z))
| meet(join(X_154,Z),join(X_154,meet(X_152,Z))) != meet(join(X_154,Z),join(X_154,X_152))
| join(X_154,meet(X_152,Z)) = meet(join(X_154,Z),join(X_154,X_152)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_154,Z),join(X_154,meet(X_152,Z))),meet(join(X_154,Z),join(X_154,X_152))) ),[0],$fot(join(X_154,meet(X_152,Z)))]]) ).
cnf(refute_0_240,plain,
( meet(join(X_154,Z),join(X_154,meet(X_152,Z))) != meet(join(X_154,Z),join(X_154,X_152))
| join(X_154,meet(X_152,Z)) = meet(join(X_154,Z),join(X_154,X_152)) ),
inference(resolve,[$cnf( $equal(meet(join(X_154,Z),join(X_154,meet(X_152,Z))),join(X_154,meet(X_152,Z))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
join(X_154,meet(X_152,Z)) = meet(join(X_154,Z),join(X_154,X_152)),
inference(resolve,[$cnf( $equal(meet(join(X_154,Z),join(X_154,meet(X_152,Z))),meet(join(X_154,Z),join(X_154,X_152))) )],[refute_0_133,refute_0_240]) ).
cnf(refute_0_242,plain,
( join(X_154,meet(X_152,Z)) != meet(join(X_154,Z),join(X_154,X_152))
| meet(join(X_154,Z),join(X_154,X_152)) = join(X_154,meet(X_152,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_154,meet(X_152,Z)))),bind(Y0,$fot(meet(join(X_154,Z),join(X_154,X_152))))]]) ).
cnf(refute_0_243,plain,
meet(join(X_154,Z),join(X_154,X_152)) = join(X_154,meet(X_152,Z)),
inference(resolve,[$cnf( $equal(join(X_154,meet(X_152,Z)),meet(join(X_154,Z),join(X_154,X_152))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
meet(join(xx,yy),join(xx,zz)) = join(xx,meet(zz,yy)),
inference(subst,[],[refute_0_243:[bind(Z,$fot(yy)),bind(X_152,$fot(zz)),bind(X_154,$fot(xx))]]) ).
cnf(refute_0_245,plain,
( join(xx,meet(zz,yy)) != join(xx,meet(yy,zz))
| meet(join(xx,yy),join(xx,zz)) != join(xx,meet(zz,yy))
| meet(join(xx,yy),join(xx,zz)) = join(xx,meet(yy,zz)) ),
inference(subst,[],[refute_0_54:[bind(X0,$fot(meet(join(xx,yy),join(xx,zz)))),bind(Y0,$fot(join(xx,meet(zz,yy)))),bind(Z0,$fot(join(xx,meet(yy,zz))))]]) ).
cnf(refute_0_246,plain,
( join(xx,meet(zz,yy)) != join(xx,meet(yy,zz))
| meet(join(xx,yy),join(xx,zz)) = join(xx,meet(yy,zz)) ),
inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(xx,zz)),join(xx,meet(zz,yy))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
meet(join(xx,yy),join(xx,zz)) = join(xx,meet(yy,zz)),
inference(resolve,[$cnf( $equal(join(xx,meet(zz,yy)),join(xx,meet(yy,zz))) )],[refute_0_126,refute_0_246]) ).
cnf(refute_0_248,plain,
( join(xx,meet(yy,zz)) != join(xx,meet(yy,zz))
| meet(join(xx,yy),join(xx,zz)) != join(xx,meet(yy,zz))
| join(xx,meet(yy,zz)) = meet(join(xx,yy),join(xx,zz)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(xx,meet(yy,zz)),meet(join(xx,yy),join(xx,zz))) ),[1],$fot(join(xx,meet(yy,zz)))]]) ).
cnf(refute_0_249,plain,
( join(xx,meet(yy,zz)) != join(xx,meet(yy,zz))
| join(xx,meet(yy,zz)) = meet(join(xx,yy),join(xx,zz)) ),
inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(xx,zz)),join(xx,meet(yy,zz))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
join(xx,meet(yy,zz)) != join(xx,meet(yy,zz)),
inference(resolve,[$cnf( $equal(join(xx,meet(yy,zz)),meet(join(xx,yy),join(xx,zz))) )],[refute_0_249,dist_join]) ).
cnf(refute_0_251,plain,
join(xx,meet(yy,zz)) = join(xx,meet(yy,zz)),
introduced(tautology,[refl,[$fot(join(xx,meet(yy,zz)))]]) ).
cnf(refute_0_252,plain,
$false,
inference(resolve,[$cnf( $equal(join(xx,meet(yy,zz)),join(xx,meet(yy,zz))) )],[refute_0_251,refute_0_250]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT031-1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 29 00:59:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.88/7.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.88/7.11
% 6.88/7.11 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.97/7.13
%------------------------------------------------------------------------------