TSTP Solution File: LAT038-1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT038-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:59:03 EDT 2022
% Result : Unsatisfiable 9.36s 9.59s
% Output : CNFRefutation 9.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 190
% Syntax : Number of clauses : 895 ( 464 unt; 0 nHn; 474 RR)
% Number of literals : 1514 (1513 equ; 621 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 : 1912 ( 65 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_join,hypothesis,
join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).
cnf(dist_meet,hypothesis,
meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
cnf(f_on_left_join,axiom,
f(join(U,V),W) = join(f(U,W),f(V,W)) ).
cnf(f_on_right_join,axiom,
f(W,join(U,V)) = join(f(W,U),f(W,V)) ).
cnf(lhs1,hypothesis,
f(join(aa,bb),dd) = f(join(cc,bb),dd) ).
cnf(lhs2,hypothesis,
meet(f(aa,dd),f(bb,dd)) = meet(f(cc,dd),f(bb,dd)) ).
cnf(rhs,negated_conjecture,
f(aa,dd) != f(cc,dd) ).
cnf(refute_0_0,plain,
join(X,meet(X,meet(X_40,X_38))) = X,
inference(subst,[],[absorption2:[bind(Y,$fot(meet(X_40,X_38)))]]) ).
cnf(refute_0_1,plain,
meet(X,meet(X_20,X_21)) = meet(meet(X_20,X_21),X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(meet(X_20,X_21)))]]) ).
cnf(refute_0_2,plain,
meet(meet(X_20,X_21),X) = meet(X_20,meet(X_21,X)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X))]]) ).
cnf(refute_0_3,plain,
( meet(X,meet(X_20,X_21)) != meet(meet(X_20,X_21),X)
| meet(meet(X_20,X_21),X) != meet(X_20,meet(X_21,X))
| meet(X,meet(X_20,X_21)) = meet(X_20,meet(X_21,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X,meet(X_20,X_21)),meet(X_20,meet(X_21,X))) ),[0],$fot(meet(meet(X_20,X_21),X))]]) ).
cnf(refute_0_4,plain,
( meet(X,meet(X_20,X_21)) != meet(meet(X_20,X_21),X)
| meet(X,meet(X_20,X_21)) = meet(X_20,meet(X_21,X)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_20,X_21),X),meet(X_20,meet(X_21,X))) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
meet(X,meet(X_20,X_21)) = meet(X_20,meet(X_21,X)),
inference(resolve,[$cnf( $equal(meet(X,meet(X_20,X_21)),meet(meet(X_20,X_21),X)) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
meet(X_38,meet(X,X_40)) = meet(X,meet(X_40,X_38)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_38)),bind(X_20,$fot(X)),bind(X_21,$fot(X_40))]]) ).
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( $equal(X0,X0) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( meet(X_38,meet(X,X_40)) != meet(X,meet(X_40,X_38))
| meet(X,meet(X_40,X_38)) = meet(X_38,meet(X,X_40)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_38,meet(X,X_40)))),bind(Y0,$fot(meet(X,meet(X_40,X_38))))]]) ).
cnf(refute_0_11,plain,
meet(X,meet(X_40,X_38)) = meet(X_38,meet(X,X_40)),
inference(resolve,[$cnf( $equal(meet(X_38,meet(X,X_40)),meet(X,meet(X_40,X_38))) )],[refute_0_6,refute_0_10]) ).
cnf(refute_0_12,plain,
( join(X,meet(X,meet(X_40,X_38))) != X
| meet(X,meet(X_40,X_38)) != meet(X_38,meet(X,X_40))
| join(X,meet(X_38,meet(X,X_40))) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,meet(X_40,X_38))),X) ),[0,1],$fot(meet(X_38,meet(X,X_40)))]]) ).
cnf(refute_0_13,plain,
( join(X,meet(X,meet(X_40,X_38))) != X
| join(X,meet(X_38,meet(X,X_40))) = X ),
inference(resolve,[$cnf( $equal(meet(X,meet(X_40,X_38)),meet(X_38,meet(X,X_40))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
join(X,meet(X_38,meet(X,X_40))) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,meet(X_40,X_38))),X) )],[refute_0_0,refute_0_13]) ).
cnf(refute_0_15,plain,
join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))) = f(aa,dd),
inference(subst,[],[refute_0_14:[bind(X,$fot(f(aa,dd))),bind(X_38,$fot(f(cc,dd)))]]) ).
cnf(refute_0_16,plain,
( join(X,Y) != join(Y,X)
| meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,Y)),X) ),[0,1],$fot(join(Y,X))]]) ).
cnf(refute_0_17,plain,
( meet(X,join(X,Y)) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_16]) ).
cnf(refute_0_18,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(X,join(join(X_23,X_24),X)) = X,
inference(subst,[],[refute_0_18:[bind(Y,$fot(join(X_23,X_24)))]]) ).
cnf(refute_0_20,plain,
join(join(X_23,X_24),X) = join(X_23,join(X_24,X)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(Z,$fot(X))]]) ).
cnf(refute_0_21,plain,
( join(join(X_23,X_24),X) != join(X_23,join(X_24,X))
| meet(X,join(join(X_23,X_24),X)) != X
| meet(X,join(X_23,join(X_24,X))) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(join(X_23,X_24),X)),X) ),[0,1],$fot(join(X_23,join(X_24,X)))]]) ).
cnf(refute_0_22,plain,
( meet(X,join(join(X_23,X_24),X)) != X
| meet(X,join(X_23,join(X_24,X))) = X ),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X),join(X_23,join(X_24,X))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
meet(X,join(X_23,join(X_24,X))) = X,
inference(resolve,[$cnf( $equal(meet(X,join(join(X_23,X_24),X)),X) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
meet(f(X_64,X_65),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))) = f(X_64,X_65),
inference(subst,[],[refute_0_23:[bind(X,$fot(f(X_64,X_65))),bind(X_24,$fot(f(X_63,X_65)))]]) ).
cnf(refute_0_25,plain,
f(join(X_63,X_64),X_65) = join(f(X_63,X_65),f(X_64,X_65)),
inference(subst,[],[f_on_left_join:[bind(U,$fot(X_63)),bind(V,$fot(X_64)),bind(W,$fot(X_65))]]) ).
cnf(refute_0_26,plain,
( f(join(X_63,X_64),X_65) != join(f(X_63,X_65),f(X_64,X_65))
| join(f(X_63,X_65),f(X_64,X_65)) = f(join(X_63,X_64),X_65) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(join(X_63,X_64),X_65))),bind(Y0,$fot(join(f(X_63,X_65),f(X_64,X_65))))]]) ).
cnf(refute_0_27,plain,
join(f(X_63,X_65),f(X_64,X_65)) = f(join(X_63,X_64),X_65),
inference(resolve,[$cnf( $equal(f(join(X_63,X_64),X_65),join(f(X_63,X_65),f(X_64,X_65))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( join(f(X_63,X_65),f(X_64,X_65)) != f(join(X_63,X_64),X_65)
| meet(f(X_64,X_65),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))) != f(X_64,X_65)
| meet(f(X_64,X_65),join(X_23,f(join(X_63,X_64),X_65))) = f(X_64,X_65) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(X_64,X_65),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))),f(X_64,X_65)) ),[0,1,1],$fot(f(join(X_63,X_64),X_65))]]) ).
cnf(refute_0_29,plain,
( meet(f(X_64,X_65),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))) != f(X_64,X_65)
| meet(f(X_64,X_65),join(X_23,f(join(X_63,X_64),X_65))) = f(X_64,X_65) ),
inference(resolve,[$cnf( $equal(join(f(X_63,X_65),f(X_64,X_65)),f(join(X_63,X_64),X_65)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
meet(f(X_64,X_65),join(X_23,f(join(X_63,X_64),X_65))) = f(X_64,X_65),
inference(resolve,[$cnf( $equal(meet(f(X_64,X_65),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))),f(X_64,X_65)) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
meet(f(cc,dd),join(X_205,f(join(bb,cc),dd))) = f(cc,dd),
inference(subst,[],[refute_0_30:[bind(X_23,$fot(X_205)),bind(X_63,$fot(bb)),bind(X_64,$fot(cc)),bind(X_65,$fot(dd))]]) ).
cnf(refute_0_32,plain,
( join(X,Y) != join(Y,X)
| join(Y,X) = join(X,Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).
cnf(refute_0_33,plain,
join(Y,X) = join(X,Y),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_32]) ).
cnf(refute_0_34,plain,
join(cc,bb) = join(bb,cc),
inference(subst,[],[refute_0_33:[bind(X,$fot(bb)),bind(Y,$fot(cc))]]) ).
cnf(refute_0_35,plain,
f(join(cc,bb),dd) = f(join(cc,bb),dd),
introduced(tautology,[refl,[$fot(f(join(cc,bb),dd))]]) ).
cnf(refute_0_36,plain,
( f(join(cc,bb),dd) != f(join(cc,bb),dd)
| join(cc,bb) != join(bb,cc)
| f(join(cc,bb),dd) = f(join(bb,cc),dd) ),
introduced(tautology,[equality,[$cnf( $equal(f(join(cc,bb),dd),f(join(cc,bb),dd)) ),[1,0],$fot(join(bb,cc))]]) ).
cnf(refute_0_37,plain,
( join(cc,bb) != join(bb,cc)
| f(join(cc,bb),dd) = f(join(bb,cc),dd) ),
inference(resolve,[$cnf( $equal(f(join(cc,bb),dd),f(join(cc,bb),dd)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
f(join(cc,bb),dd) = f(join(bb,cc),dd),
inference(resolve,[$cnf( $equal(join(cc,bb),join(bb,cc)) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( f(join(aa,bb),dd) != f(join(cc,bb),dd)
| f(join(cc,bb),dd) != f(join(bb,cc),dd)
| f(join(aa,bb),dd) = f(join(bb,cc),dd) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(join(aa,bb),dd),f(join(bb,cc),dd)) ),[0],$fot(f(join(cc,bb),dd))]]) ).
cnf(refute_0_40,plain,
( f(join(aa,bb),dd) != f(join(cc,bb),dd)
| f(join(aa,bb),dd) = f(join(bb,cc),dd) ),
inference(resolve,[$cnf( $equal(f(join(cc,bb),dd),f(join(bb,cc),dd)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
f(join(aa,bb),dd) = f(join(bb,cc),dd),
inference(resolve,[$cnf( $equal(f(join(aa,bb),dd),f(join(cc,bb),dd)) )],[lhs1,refute_0_40]) ).
cnf(refute_0_42,plain,
( f(join(aa,bb),dd) != f(join(bb,cc),dd)
| f(join(bb,cc),dd) = f(join(aa,bb),dd) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(join(aa,bb),dd))),bind(Y0,$fot(f(join(bb,cc),dd)))]]) ).
cnf(refute_0_43,plain,
f(join(bb,cc),dd) = f(join(aa,bb),dd),
inference(resolve,[$cnf( $equal(f(join(aa,bb),dd),f(join(bb,cc),dd)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( f(join(bb,cc),dd) != f(join(aa,bb),dd)
| meet(f(cc,dd),join(X_205,f(join(bb,cc),dd))) != f(cc,dd)
| meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(X_205,f(join(bb,cc),dd))),f(cc,dd)) ),[0,1,1],$fot(f(join(aa,bb),dd))]]) ).
cnf(refute_0_45,plain,
( meet(f(cc,dd),join(X_205,f(join(bb,cc),dd))) != f(cc,dd)
| meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(f(join(bb,cc),dd),f(join(aa,bb),dd)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) = f(cc,dd),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(X_205,f(join(bb,cc),dd))),f(cc,dd)) )],[refute_0_31,refute_0_45]) ).
cnf(refute_0_47,plain,
( join(X,meet(X,Y)) != X
| meet(X,Y) != meet(Y,X)
| join(X,meet(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).
cnf(refute_0_48,plain,
( join(X,meet(X,Y)) != X
| join(X,meet(Y,X)) = X ),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_47]) ).
cnf(refute_0_49,plain,
join(X,meet(Y,X)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_48]) ).
cnf(refute_0_50,plain,
join(meet(f(cc,dd),X_34),meet(f(bb,dd),meet(f(cc,dd),X_34))) = meet(f(cc,dd),X_34),
inference(subst,[],[refute_0_49:[bind(X,$fot(meet(f(cc,dd),X_34))),bind(Y,$fot(f(bb,dd)))]]) ).
cnf(refute_0_51,plain,
meet(meet(f(bb,dd),f(cc,dd)),X_22) = meet(f(bb,dd),meet(f(cc,dd),X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(f(bb,dd))),bind(Y,$fot(f(cc,dd))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_52,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_53,plain,
meet(Y,X) = meet(X,Y),
inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_52]) ).
cnf(refute_0_54,plain,
meet(f(cc,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)),
inference(subst,[],[refute_0_53:[bind(X,$fot(f(bb,dd))),bind(Y,$fot(f(cc,dd)))]]) ).
cnf(refute_0_55,plain,
( meet(f(aa,dd),f(bb,dd)) != meet(f(cc,dd),f(bb,dd))
| meet(f(cc,dd),f(bb,dd)) != meet(f(bb,dd),f(cc,dd))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),f(cc,dd))) ),[0],$fot(meet(f(cc,dd),f(bb,dd)))]]) ).
cnf(refute_0_56,plain,
( meet(f(aa,dd),f(bb,dd)) != meet(f(cc,dd),f(bb,dd))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),f(bb,dd)),meet(f(bb,dd),f(cc,dd))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(cc,dd)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(bb,dd))) )],[lhs2,refute_0_56]) ).
cnf(refute_0_58,plain,
( meet(f(aa,dd),f(bb,dd)) != meet(f(bb,dd),f(cc,dd))
| meet(f(bb,dd),f(cc,dd)) = meet(f(aa,dd),f(bb,dd)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(f(aa,dd),f(bb,dd)))),bind(Y0,$fot(meet(f(bb,dd),f(cc,dd))))]]) ).
cnf(refute_0_59,plain,
meet(f(bb,dd),f(cc,dd)) = meet(f(aa,dd),f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),f(cc,dd))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| meet(meet(f(bb,dd),f(cc,dd)),X_22) != meet(f(bb,dd),meet(f(cc,dd),X_22))
| meet(meet(f(aa,dd),f(bb,dd)),X_22) = meet(f(bb,dd),meet(f(cc,dd),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(f(bb,dd),f(cc,dd)),X_22),meet(f(bb,dd),meet(f(cc,dd),X_22))) ),[0,0],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_61,plain,
( meet(meet(f(bb,dd),f(cc,dd)),X_22) != meet(f(bb,dd),meet(f(cc,dd),X_22))
| meet(meet(f(aa,dd),f(bb,dd)),X_22) = meet(f(bb,dd),meet(f(cc,dd),X_22)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
meet(meet(f(aa,dd),f(bb,dd)),X_22) = meet(f(bb,dd),meet(f(cc,dd),X_22)),
inference(resolve,[$cnf( $equal(meet(meet(f(bb,dd),f(cc,dd)),X_22),meet(f(bb,dd),meet(f(cc,dd),X_22))) )],[refute_0_51,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(meet(f(aa,dd),f(bb,dd)),X_22) = meet(f(aa,dd),meet(f(bb,dd),X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(f(aa,dd))),bind(Y,$fot(f(bb,dd))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_64,plain,
( meet(meet(f(aa,dd),f(bb,dd)),X_22) != meet(f(aa,dd),meet(f(bb,dd),X_22))
| meet(meet(f(aa,dd),f(bb,dd)),X_22) != meet(f(bb,dd),meet(f(cc,dd),X_22))
| meet(f(aa,dd),meet(f(bb,dd),X_22)) = meet(f(bb,dd),meet(f(cc,dd),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(f(aa,dd),f(bb,dd)),X_22),meet(f(bb,dd),meet(f(cc,dd),X_22))) ),[0],$fot(meet(f(aa,dd),meet(f(bb,dd),X_22)))]]) ).
cnf(refute_0_65,plain,
( meet(meet(f(aa,dd),f(bb,dd)),X_22) != meet(f(bb,dd),meet(f(cc,dd),X_22))
| meet(f(aa,dd),meet(f(bb,dd),X_22)) = meet(f(bb,dd),meet(f(cc,dd),X_22)) ),
inference(resolve,[$cnf( $equal(meet(meet(f(aa,dd),f(bb,dd)),X_22),meet(f(aa,dd),meet(f(bb,dd),X_22))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
meet(f(aa,dd),meet(f(bb,dd),X_22)) = meet(f(bb,dd),meet(f(cc,dd),X_22)),
inference(resolve,[$cnf( $equal(meet(meet(f(aa,dd),f(bb,dd)),X_22),meet(f(bb,dd),meet(f(cc,dd),X_22))) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
meet(f(aa,dd),meet(f(bb,dd),X_34)) = meet(f(bb,dd),meet(f(cc,dd),X_34)),
inference(subst,[],[refute_0_66:[bind(X_22,$fot(X_34))]]) ).
cnf(refute_0_68,plain,
( meet(f(aa,dd),meet(f(bb,dd),X_34)) != meet(f(bb,dd),meet(f(cc,dd),X_34))
| meet(f(bb,dd),meet(f(cc,dd),X_34)) = meet(f(aa,dd),meet(f(bb,dd),X_34)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(f(aa,dd),meet(f(bb,dd),X_34)))),bind(Y0,$fot(meet(f(bb,dd),meet(f(cc,dd),X_34))))]]) ).
cnf(refute_0_69,plain,
meet(f(bb,dd),meet(f(cc,dd),X_34)) = meet(f(aa,dd),meet(f(bb,dd),X_34)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),X_34)),meet(f(bb,dd),meet(f(cc,dd),X_34))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( join(meet(f(cc,dd),X_34),meet(f(bb,dd),meet(f(cc,dd),X_34))) != meet(f(cc,dd),X_34)
| meet(f(bb,dd),meet(f(cc,dd),X_34)) != meet(f(aa,dd),meet(f(bb,dd),X_34))
| join(meet(f(cc,dd),X_34),meet(f(aa,dd),meet(f(bb,dd),X_34))) = meet(f(cc,dd),X_34) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),X_34),meet(f(bb,dd),meet(f(cc,dd),X_34))),meet(f(cc,dd),X_34)) ),[0,1],$fot(meet(f(aa,dd),meet(f(bb,dd),X_34)))]]) ).
cnf(refute_0_71,plain,
( join(meet(f(cc,dd),X_34),meet(f(bb,dd),meet(f(cc,dd),X_34))) != meet(f(cc,dd),X_34)
| join(meet(f(cc,dd),X_34),meet(f(aa,dd),meet(f(bb,dd),X_34))) = meet(f(cc,dd),X_34) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),meet(f(cc,dd),X_34)),meet(f(aa,dd),meet(f(bb,dd),X_34))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
join(meet(f(cc,dd),X_34),meet(f(aa,dd),meet(f(bb,dd),X_34))) = meet(f(cc,dd),X_34),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),X_34),meet(f(bb,dd),meet(f(cc,dd),X_34))),meet(f(cc,dd),X_34)) )],[refute_0_50,refute_0_71]) ).
cnf(refute_0_73,plain,
join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(join(f(aa,dd),meet(Y,f(cc,dd)))))]]) ).
cnf(refute_0_74,plain,
meet(f(bb,dd),join(f(cc,dd),X_53)) = join(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),X_53)),
inference(subst,[],[dist_meet:[bind(X,$fot(f(bb,dd))),bind(Y,$fot(f(cc,dd))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_75,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| meet(f(bb,dd),join(f(cc,dd),X_53)) != join(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),X_53))
| meet(f(bb,dd),join(f(cc,dd),X_53)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),X_53)),join(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),X_53))) ),[1,0],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_76,plain,
( meet(f(bb,dd),join(f(cc,dd),X_53)) != join(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),X_53))
| meet(f(bb,dd),join(f(cc,dd),X_53)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_59,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(f(bb,dd),join(f(cc,dd),X_53)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),X_53)),join(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),X_53))) )],[refute_0_74,refute_0_76]) ).
cnf(refute_0_78,plain,
meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_52),meet(X_51,X_53)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_79,plain,
meet(X_52,X_51) = meet(X_51,X_52),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_52)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_80,plain,
( meet(X_52,X_51) != meet(X_51,X_52)
| meet(X_51,X_52) = meet(X_52,X_51) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_52,X_51))),bind(Y0,$fot(meet(X_51,X_52)))]]) ).
cnf(refute_0_81,plain,
meet(X_51,X_52) = meet(X_52,X_51),
inference(resolve,[$cnf( $equal(meet(X_52,X_51),meet(X_51,X_52)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( meet(X_51,X_52) != meet(X_52,X_51)
| meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_51,X_53))
| meet(X_51,join(X_52,X_53)) = join(meet(X_52,X_51),meet(X_51,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_51,X_53))) ),[1,0],$fot(meet(X_52,X_51))]]) ).
cnf(refute_0_83,plain,
( meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_51,X_53))
| meet(X_51,join(X_52,X_53)) = join(meet(X_52,X_51),meet(X_51,X_53)) ),
inference(resolve,[$cnf( $equal(meet(X_51,X_52),meet(X_52,X_51)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
meet(X_51,join(X_52,X_53)) = join(meet(X_52,X_51),meet(X_51,X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_51,X_53))) )],[refute_0_78,refute_0_83]) ).
cnf(refute_0_85,plain,
( meet(X_51,join(X_52,X_53)) != join(meet(X_52,X_51),meet(X_51,X_53))
| join(meet(X_52,X_51),meet(X_51,X_53)) = meet(X_51,join(X_52,X_53)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_51,join(X_52,X_53)))),bind(Y0,$fot(join(meet(X_52,X_51),meet(X_51,X_53))))]]) ).
cnf(refute_0_86,plain,
join(meet(X_52,X_51),meet(X_51,X_53)) = meet(X_51,join(X_52,X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_52,X_51),meet(X_51,X_53))) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)) = meet(f(bb,dd),join(f(aa,dd),X_53)),
inference(subst,[],[refute_0_86:[bind(X_51,$fot(f(bb,dd))),bind(X_52,$fot(f(aa,dd)))]]) ).
cnf(refute_0_88,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)) != meet(f(bb,dd),join(f(aa,dd),X_53))
| meet(f(bb,dd),join(f(cc,dd),X_53)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53))
| meet(f(bb,dd),join(f(cc,dd),X_53)) = meet(f(bb,dd),join(f(aa,dd),X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),X_53)),join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53))) ),[1],$fot(meet(f(bb,dd),join(f(aa,dd),X_53)))]]) ).
cnf(refute_0_89,plain,
( meet(f(bb,dd),join(f(cc,dd),X_53)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53))
| meet(f(bb,dd),join(f(cc,dd),X_53)) = meet(f(bb,dd),join(f(aa,dd),X_53)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53)),meet(f(bb,dd),join(f(aa,dd),X_53))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
meet(f(bb,dd),join(f(cc,dd),X_53)) = meet(f(bb,dd),join(f(aa,dd),X_53)),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),X_53)),join(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),X_53))) )],[refute_0_77,refute_0_89]) ).
cnf(refute_0_91,plain,
meet(f(bb,dd),join(f(cc,dd),meet(Y,f(cc,dd)))) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),
inference(subst,[],[refute_0_90:[bind(X_53,$fot(meet(Y,f(cc,dd))))]]) ).
cnf(refute_0_92,plain,
join(f(cc,dd),meet(Y,f(cc,dd))) = f(cc,dd),
inference(subst,[],[refute_0_49:[bind(X,$fot(f(cc,dd)))]]) ).
cnf(refute_0_93,plain,
( join(f(cc,dd),meet(Y,f(cc,dd))) != f(cc,dd)
| meet(f(bb,dd),join(f(cc,dd),meet(Y,f(cc,dd)))) != meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(bb,dd),f(cc,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),meet(Y,f(cc,dd)))),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),[0,1],$fot(f(cc,dd))]]) ).
cnf(refute_0_94,plain,
( meet(f(bb,dd),join(f(cc,dd),meet(Y,f(cc,dd)))) != meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(bb,dd),f(cc,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
inference(resolve,[$cnf( $equal(join(f(cc,dd),meet(Y,f(cc,dd))),f(cc,dd)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
meet(f(bb,dd),f(cc,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),meet(Y,f(cc,dd)))),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| meet(f(bb,dd),f(cc,dd)) != meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),[0],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_97,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_59,refute_0_96]) ).
cnf(refute_0_98,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_95,refute_0_97]) ).
cnf(refute_0_99,plain,
( meet(f(aa,dd),f(bb,dd)) != meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) = meet(f(aa,dd),f(bb,dd)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(f(aa,dd),f(bb,dd)))),bind(Y0,$fot(meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))]]) ).
cnf(refute_0_100,plain,
meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) = meet(f(aa,dd),f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) != meet(f(aa,dd),f(bb,dd))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),[0,1,1],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_102,plain,
( join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),f(bb,dd))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_73,refute_0_102]) ).
cnf(refute_0_104,plain,
meet(X_51,join(X_52,meet(Y,X_51))) = join(meet(X_51,X_52),meet(X_51,meet(Y,X_51))),
inference(subst,[],[dist_meet:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(meet(Y,X_51)))]]) ).
cnf(refute_0_105,plain,
meet(meet(X_15,Y),join(X_15,meet(X_15,Y))) = meet(X_15,Y),
inference(subst,[],[refute_0_18:[bind(X,$fot(meet(X_15,Y))),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_106,plain,
join(X_15,meet(X_15,Y)) = X_15,
inference(subst,[],[absorption2:[bind(X,$fot(X_15))]]) ).
cnf(refute_0_107,plain,
( join(X_15,meet(X_15,Y)) != X_15
| meet(meet(X_15,Y),join(X_15,meet(X_15,Y))) != meet(X_15,Y)
| meet(meet(X_15,Y),X_15) = meet(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_15,Y),join(X_15,meet(X_15,Y))),meet(X_15,Y)) ),[0,1],$fot(X_15)]]) ).
cnf(refute_0_108,plain,
( meet(meet(X_15,Y),join(X_15,meet(X_15,Y))) != meet(X_15,Y)
| meet(meet(X_15,Y),X_15) = meet(X_15,Y) ),
inference(resolve,[$cnf( $equal(join(X_15,meet(X_15,Y)),X_15) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
meet(meet(X_15,Y),X_15) = meet(X_15,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_15,Y),join(X_15,meet(X_15,Y))),meet(X_15,Y)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
meet(meet(X_15,Y),X_15) = meet(X_15,meet(Y,X_15)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_15)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_111,plain,
( meet(meet(X_15,Y),X_15) != meet(X_15,Y)
| meet(meet(X_15,Y),X_15) != meet(X_15,meet(Y,X_15))
| meet(X_15,meet(Y,X_15)) = meet(X_15,Y) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_15,Y),X_15),meet(X_15,Y)) ),[0],$fot(meet(X_15,meet(Y,X_15)))]]) ).
cnf(refute_0_112,plain,
( meet(meet(X_15,Y),X_15) != meet(X_15,Y)
| meet(X_15,meet(Y,X_15)) = meet(X_15,Y) ),
inference(resolve,[$cnf( $equal(meet(meet(X_15,Y),X_15),meet(X_15,meet(Y,X_15))) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
meet(X_15,meet(Y,X_15)) = meet(X_15,Y),
inference(resolve,[$cnf( $equal(meet(meet(X_15,Y),X_15),meet(X_15,Y)) )],[refute_0_109,refute_0_112]) ).
cnf(refute_0_114,plain,
meet(X_51,meet(Y,X_51)) = meet(X_51,Y),
inference(subst,[],[refute_0_113:[bind(X_15,$fot(X_51))]]) ).
cnf(refute_0_115,plain,
( meet(X_51,join(X_52,meet(Y,X_51))) != join(meet(X_51,X_52),meet(X_51,meet(Y,X_51)))
| meet(X_51,meet(Y,X_51)) != meet(X_51,Y)
| meet(X_51,join(X_52,meet(Y,X_51))) = join(meet(X_51,X_52),meet(X_51,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,meet(Y,X_51))),join(meet(X_51,X_52),meet(X_51,meet(Y,X_51)))) ),[1,1],$fot(meet(X_51,Y))]]) ).
cnf(refute_0_116,plain,
( meet(X_51,join(X_52,meet(Y,X_51))) != join(meet(X_51,X_52),meet(X_51,meet(Y,X_51)))
| meet(X_51,join(X_52,meet(Y,X_51))) = join(meet(X_51,X_52),meet(X_51,Y)) ),
inference(resolve,[$cnf( $equal(meet(X_51,meet(Y,X_51)),meet(X_51,Y)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
meet(X_51,join(X_52,meet(Y,X_51))) = join(meet(X_51,X_52),meet(X_51,Y)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,meet(Y,X_51))),join(meet(X_51,X_52),meet(X_51,meet(Y,X_51)))) )],[refute_0_104,refute_0_116]) ).
cnf(refute_0_118,plain,
( meet(X,join(Y,Z)) != join(meet(X,Y),meet(X,Z))
| join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X,join(Y,Z)))),bind(Y0,$fot(join(meet(X,Y),meet(X,Z))))]]) ).
cnf(refute_0_119,plain,
join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
inference(resolve,[$cnf( $equal(meet(X,join(Y,Z)),join(meet(X,Y),meet(X,Z))) )],[dist_meet,refute_0_118]) ).
cnf(refute_0_120,plain,
join(meet(X_51,X_52),meet(X_51,Y)) = meet(X_51,join(X_52,Y)),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_121,plain,
( join(meet(X_51,X_52),meet(X_51,Y)) != meet(X_51,join(X_52,Y))
| meet(X_51,join(X_52,meet(Y,X_51))) != join(meet(X_51,X_52),meet(X_51,Y))
| meet(X_51,join(X_52,meet(Y,X_51))) = meet(X_51,join(X_52,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,meet(Y,X_51))),join(meet(X_51,X_52),meet(X_51,Y))) ),[1],$fot(meet(X_51,join(X_52,Y)))]]) ).
cnf(refute_0_122,plain,
( meet(X_51,join(X_52,meet(Y,X_51))) != join(meet(X_51,X_52),meet(X_51,Y))
| meet(X_51,join(X_52,meet(Y,X_51))) = meet(X_51,join(X_52,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_51,X_52),meet(X_51,Y)),meet(X_51,join(X_52,Y))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
meet(X_51,join(X_52,meet(Y,X_51))) = meet(X_51,join(X_52,Y)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,meet(Y,X_51))),join(meet(X_51,X_52),meet(X_51,Y))) )],[refute_0_117,refute_0_122]) ).
cnf(refute_0_124,plain,
meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) = meet(f(cc,dd),join(f(aa,dd),Y)),
inference(subst,[],[refute_0_123:[bind(X_51,$fot(f(cc,dd))),bind(X_52,$fot(f(aa,dd)))]]) ).
cnf(refute_0_125,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),
introduced(tautology,[refl,[$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))]]) ).
cnf(refute_0_126,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))
| meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) != meet(f(cc,dd),join(f(aa,dd),Y))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) ),[1,1],$fot(meet(f(cc,dd),join(f(aa,dd),Y)))]]) ).
cnf(refute_0_127,plain,
( meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) != meet(f(cc,dd),join(f(aa,dd),Y))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(cc,dd),join(f(aa,dd),Y))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
meet(X_17,meet(X_16,X_17)) = meet(X_17,X_16),
inference(subst,[],[refute_0_113:[bind(Y,$fot(X_16)),bind(X_15,$fot(X_17))]]) ).
cnf(refute_0_130,plain,
meet(X_17,X_16) = meet(X_16,X_17),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_17)),bind(Y,$fot(X_16))]]) ).
cnf(refute_0_131,plain,
( meet(X_17,X_16) != meet(X_16,X_17)
| meet(X_16,X_17) = meet(X_17,X_16) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_17,X_16))),bind(Y0,$fot(meet(X_16,X_17)))]]) ).
cnf(refute_0_132,plain,
meet(X_16,X_17) = meet(X_17,X_16),
inference(resolve,[$cnf( $equal(meet(X_17,X_16),meet(X_16,X_17)) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( meet(X_16,X_17) != meet(X_17,X_16)
| meet(X_17,meet(X_16,X_17)) != meet(X_17,X_16)
| meet(X_17,meet(X_17,X_16)) = meet(X_17,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_17,meet(X_16,X_17)),meet(X_17,X_16)) ),[0,1],$fot(meet(X_17,X_16))]]) ).
cnf(refute_0_134,plain,
( meet(X_17,meet(X_16,X_17)) != meet(X_17,X_16)
| meet(X_17,meet(X_17,X_16)) = meet(X_17,X_16) ),
inference(resolve,[$cnf( $equal(meet(X_16,X_17),meet(X_17,X_16)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
meet(X_17,meet(X_17,X_16)) = meet(X_17,X_16),
inference(resolve,[$cnf( $equal(meet(X_17,meet(X_16,X_17)),meet(X_17,X_16)) )],[refute_0_129,refute_0_134]) ).
cnf(refute_0_136,plain,
meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),f(bb,dd)),
inference(subst,[],[refute_0_135:[bind(X_16,$fot(f(bb,dd))),bind(X_17,$fot(f(aa,dd)))]]) ).
cnf(refute_0_137,plain,
meet(meet(X_20,join(X_20,Y)),X_22) = meet(X_20,meet(join(X_20,Y),X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_20)),bind(Y,$fot(join(X_20,Y))),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_138,plain,
meet(X_20,join(X_20,Y)) = X_20,
inference(subst,[],[absorption1:[bind(X,$fot(X_20))]]) ).
cnf(refute_0_139,plain,
( meet(X_20,join(X_20,Y)) != X_20
| meet(meet(X_20,join(X_20,Y)),X_22) != meet(X_20,meet(join(X_20,Y),X_22))
| meet(X_20,X_22) = meet(X_20,meet(join(X_20,Y),X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_20,join(X_20,Y)),X_22),meet(X_20,meet(join(X_20,Y),X_22))) ),[0,0],$fot(X_20)]]) ).
cnf(refute_0_140,plain,
( meet(meet(X_20,join(X_20,Y)),X_22) != meet(X_20,meet(join(X_20,Y),X_22))
| meet(X_20,X_22) = meet(X_20,meet(join(X_20,Y),X_22)) ),
inference(resolve,[$cnf( $equal(meet(X_20,join(X_20,Y)),X_20) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
meet(X_20,X_22) = meet(X_20,meet(join(X_20,Y),X_22)),
inference(resolve,[$cnf( $equal(meet(meet(X_20,join(X_20,Y)),X_22),meet(X_20,meet(join(X_20,Y),X_22))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(join(X_20,Y),meet(X_114,X_113))),
inference(subst,[],[refute_0_141:[bind(X_22,$fot(meet(X_114,X_113)))]]) ).
cnf(refute_0_143,plain,
join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,meet(X_103,Y)))) = meet(X_102,meet(X_103,Y)),
inference(subst,[],[refute_0_49:[bind(X,$fot(meet(X_102,meet(X_103,Y))))]]) ).
cnf(refute_0_144,plain,
meet(X_15,meet(meet(X_20,X_21),X_15)) = meet(X_15,meet(X_20,X_21)),
inference(subst,[],[refute_0_113:[bind(Y,$fot(meet(X_20,X_21)))]]) ).
cnf(refute_0_145,plain,
meet(meet(X_20,X_21),X_15) = meet(X_20,meet(X_21,X_15)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_146,plain,
( meet(X_15,meet(meet(X_20,X_21),X_15)) != meet(X_15,meet(X_20,X_21))
| meet(meet(X_20,X_21),X_15) != meet(X_20,meet(X_21,X_15))
| meet(X_15,meet(X_20,meet(X_21,X_15))) = meet(X_15,meet(X_20,X_21)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_15,meet(meet(X_20,X_21),X_15)),meet(X_15,meet(X_20,X_21))) ),[0,1],$fot(meet(X_20,meet(X_21,X_15)))]]) ).
cnf(refute_0_147,plain,
( meet(X_15,meet(meet(X_20,X_21),X_15)) != meet(X_15,meet(X_20,X_21))
| meet(X_15,meet(X_20,meet(X_21,X_15))) = meet(X_15,meet(X_20,X_21)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_20,X_21),X_15),meet(X_20,meet(X_21,X_15))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
meet(X_15,meet(X_20,meet(X_21,X_15))) = meet(X_15,meet(X_20,X_21)),
inference(resolve,[$cnf( $equal(meet(X_15,meet(meet(X_20,X_21),X_15)),meet(X_15,meet(X_20,X_21))) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
meet(Y,meet(X_102,meet(X_103,Y))) = meet(Y,meet(X_102,X_103)),
inference(subst,[],[refute_0_148:[bind(X_15,$fot(Y)),bind(X_20,$fot(X_102)),bind(X_21,$fot(X_103))]]) ).
cnf(refute_0_150,plain,
( join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,meet(X_103,Y)))) != meet(X_102,meet(X_103,Y))
| meet(Y,meet(X_102,meet(X_103,Y))) != meet(Y,meet(X_102,X_103))
| join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(X_102,meet(X_103,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,meet(X_103,Y)))),meet(X_102,meet(X_103,Y))) ),[0,1],$fot(meet(Y,meet(X_102,X_103)))]]) ).
cnf(refute_0_151,plain,
( join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,meet(X_103,Y)))) != meet(X_102,meet(X_103,Y))
| join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(X_102,meet(X_103,Y)) ),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_102,meet(X_103,Y))),meet(Y,meet(X_102,X_103))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(X_102,meet(X_103,Y)),
inference(resolve,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,meet(X_103,Y)))),meet(X_102,meet(X_103,Y))) )],[refute_0_143,refute_0_151]) ).
cnf(refute_0_153,plain,
join(X_102,X_102) = X_102,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_102))]]) ).
cnf(refute_0_154,plain,
meet(X_103,join(X_102,X_102)) = meet(X_103,join(X_102,X_102)),
introduced(tautology,[refl,[$fot(meet(X_103,join(X_102,X_102)))]]) ).
cnf(refute_0_155,plain,
( join(X_102,X_102) != X_102
| meet(X_103,join(X_102,X_102)) != meet(X_103,join(X_102,X_102))
| meet(X_103,join(X_102,X_102)) = meet(X_103,X_102) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_103,join(X_102,X_102)),meet(X_103,join(X_102,X_102))) ),[1,1],$fot(X_102)]]) ).
cnf(refute_0_156,plain,
( join(X_102,X_102) != X_102
| meet(X_103,join(X_102,X_102)) = meet(X_103,X_102) ),
inference(resolve,[$cnf( $equal(meet(X_103,join(X_102,X_102)),meet(X_103,join(X_102,X_102))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
meet(X_103,join(X_102,X_102)) = meet(X_103,X_102),
inference(resolve,[$cnf( $equal(join(X_102,X_102),X_102) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
meet(X_53,X_51) = meet(X_51,X_53),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_53)),bind(Y,$fot(X_51))]]) ).
cnf(refute_0_159,plain,
( meet(X_53,X_51) != meet(X_51,X_53)
| meet(X_51,X_53) = meet(X_53,X_51) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_53,X_51))),bind(Y0,$fot(meet(X_51,X_53)))]]) ).
cnf(refute_0_160,plain,
meet(X_51,X_53) = meet(X_53,X_51),
inference(resolve,[$cnf( $equal(meet(X_53,X_51),meet(X_51,X_53)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
( meet(X_51,X_53) != meet(X_53,X_51)
| meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_51,X_53))
| meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_52),meet(X_53,X_51)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_51,X_53))) ),[1,1],$fot(meet(X_53,X_51))]]) ).
cnf(refute_0_162,plain,
( meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_51,X_53))
| meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_52),meet(X_53,X_51)) ),
inference(resolve,[$cnf( $equal(meet(X_51,X_53),meet(X_53,X_51)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_52),meet(X_53,X_51)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_51,X_53))) )],[refute_0_78,refute_0_162]) ).
cnf(refute_0_164,plain,
meet(X_85,join(X_86,X_87)) = join(meet(X_85,X_86),meet(X_87,X_85)),
inference(subst,[],[refute_0_163:[bind(X_51,$fot(X_85)),bind(X_52,$fot(X_86)),bind(X_53,$fot(X_87))]]) ).
cnf(refute_0_165,plain,
meet(X_86,X_85) = meet(X_85,X_86),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_86)),bind(Y,$fot(X_85))]]) ).
cnf(refute_0_166,plain,
( meet(X_86,X_85) != meet(X_85,X_86)
| meet(X_85,X_86) = meet(X_86,X_85) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_86,X_85))),bind(Y0,$fot(meet(X_85,X_86)))]]) ).
cnf(refute_0_167,plain,
meet(X_85,X_86) = meet(X_86,X_85),
inference(resolve,[$cnf( $equal(meet(X_86,X_85),meet(X_85,X_86)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
( meet(X_85,X_86) != meet(X_86,X_85)
| meet(X_85,join(X_86,X_87)) != join(meet(X_85,X_86),meet(X_87,X_85))
| meet(X_85,join(X_86,X_87)) = join(meet(X_86,X_85),meet(X_87,X_85)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_85,join(X_86,X_87)),join(meet(X_85,X_86),meet(X_87,X_85))) ),[1,0],$fot(meet(X_86,X_85))]]) ).
cnf(refute_0_169,plain,
( meet(X_85,join(X_86,X_87)) != join(meet(X_85,X_86),meet(X_87,X_85))
| meet(X_85,join(X_86,X_87)) = join(meet(X_86,X_85),meet(X_87,X_85)) ),
inference(resolve,[$cnf( $equal(meet(X_85,X_86),meet(X_86,X_85)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
meet(X_85,join(X_86,X_87)) = join(meet(X_86,X_85),meet(X_87,X_85)),
inference(resolve,[$cnf( $equal(meet(X_85,join(X_86,X_87)),join(meet(X_85,X_86),meet(X_87,X_85))) )],[refute_0_164,refute_0_169]) ).
cnf(refute_0_171,plain,
( meet(X_85,join(X_86,X_87)) != join(meet(X_86,X_85),meet(X_87,X_85))
| join(meet(X_86,X_85),meet(X_87,X_85)) = meet(X_85,join(X_86,X_87)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_85,join(X_86,X_87)))),bind(Y0,$fot(join(meet(X_86,X_85),meet(X_87,X_85))))]]) ).
cnf(refute_0_172,plain,
join(meet(X_86,X_85),meet(X_87,X_85)) = meet(X_85,join(X_86,X_87)),
inference(resolve,[$cnf( $equal(meet(X_85,join(X_86,X_87)),join(meet(X_86,X_85),meet(X_87,X_85))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
join(meet(X_102,X_103),meet(X_102,X_103)) = meet(X_103,join(X_102,X_102)),
inference(subst,[],[refute_0_172:[bind(X_85,$fot(X_103)),bind(X_86,$fot(X_102)),bind(X_87,$fot(X_102))]]) ).
cnf(refute_0_174,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_175,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_9,refute_0_174]) ).
cnf(refute_0_176,plain,
( join(meet(X_102,X_103),meet(X_102,X_103)) != meet(X_103,join(X_102,X_102))
| meet(X_103,join(X_102,X_102)) != meet(X_103,X_102)
| join(meet(X_102,X_103),meet(X_102,X_103)) = meet(X_103,X_102) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(X_102,X_103),meet(X_102,X_103)))),bind(Y0,$fot(meet(X_103,join(X_102,X_102)))),bind(Z0,$fot(meet(X_103,X_102)))]]) ).
cnf(refute_0_177,plain,
( meet(X_103,join(X_102,X_102)) != meet(X_103,X_102)
| join(meet(X_102,X_103),meet(X_102,X_103)) = meet(X_103,X_102) ),
inference(resolve,[$cnf( $equal(join(meet(X_102,X_103),meet(X_102,X_103)),meet(X_103,join(X_102,X_102))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
join(meet(X_102,X_103),meet(X_102,X_103)) = meet(X_103,X_102),
inference(resolve,[$cnf( $equal(meet(X_103,join(X_102,X_102)),meet(X_103,X_102)) )],[refute_0_157,refute_0_177]) ).
cnf(refute_0_179,plain,
meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) = meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))),
introduced(tautology,[refl,[$fot(meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))))]]) ).
cnf(refute_0_180,plain,
( join(meet(X_102,X_103),meet(X_102,X_103)) != meet(X_103,X_102)
| meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) != meet(Y,join(meet(X_102,X_103),meet(X_102,X_103)))
| meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))),meet(Y,join(meet(X_102,X_103),meet(X_102,X_103)))) ),[1,1],$fot(meet(X_103,X_102))]]) ).
cnf(refute_0_181,plain,
( join(meet(X_102,X_103),meet(X_102,X_103)) != meet(X_103,X_102)
| meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)) ),
inference(resolve,[$cnf( $equal(meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))),meet(Y,join(meet(X_102,X_103),meet(X_102,X_103)))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)),
inference(resolve,[$cnf( $equal(join(meet(X_102,X_103),meet(X_102,X_103)),meet(X_103,X_102)) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
meet(X_51,join(meet(X_20,X_21),X_53)) = join(meet(X_51,meet(X_20,X_21)),meet(X_51,X_53)),
inference(subst,[],[dist_meet:[bind(X,$fot(X_51)),bind(Y,$fot(meet(X_20,X_21))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_184,plain,
meet(X_51,meet(X_20,X_21)) = meet(X_20,meet(X_21,X_51)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_185,plain,
( meet(X_51,join(meet(X_20,X_21),X_53)) != join(meet(X_51,meet(X_20,X_21)),meet(X_51,X_53))
| meet(X_51,meet(X_20,X_21)) != meet(X_20,meet(X_21,X_51))
| meet(X_51,join(meet(X_20,X_21),X_53)) = join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(meet(X_20,X_21),X_53)),join(meet(X_51,meet(X_20,X_21)),meet(X_51,X_53))) ),[1,0],$fot(meet(X_20,meet(X_21,X_51)))]]) ).
cnf(refute_0_186,plain,
( meet(X_51,join(meet(X_20,X_21),X_53)) != join(meet(X_51,meet(X_20,X_21)),meet(X_51,X_53))
| meet(X_51,join(meet(X_20,X_21),X_53)) = join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53)) ),
inference(resolve,[$cnf( $equal(meet(X_51,meet(X_20,X_21)),meet(X_20,meet(X_21,X_51))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
meet(X_51,join(meet(X_20,X_21),X_53)) = join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(meet(X_20,X_21),X_53)),join(meet(X_51,meet(X_20,X_21)),meet(X_51,X_53))) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( meet(X_51,join(meet(X_20,X_21),X_53)) != join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53))
| join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53)) = meet(X_51,join(meet(X_20,X_21),X_53)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_51,join(meet(X_20,X_21),X_53)))),bind(Y0,$fot(join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53))))]]) ).
cnf(refute_0_189,plain,
join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53)) = meet(X_51,join(meet(X_20,X_21),X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(meet(X_20,X_21),X_53)),join(meet(X_20,meet(X_21,X_51)),meet(X_51,X_53))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))),
inference(subst,[],[refute_0_189:[bind(X_20,$fot(X_102)),bind(X_21,$fot(X_103)),bind(X_51,$fot(Y)),bind(X_53,$fot(meet(X_102,X_103)))]]) ).
cnf(refute_0_191,plain,
( join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) != meet(Y,join(meet(X_102,X_103),meet(X_102,X_103)))
| meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) != meet(Y,meet(X_103,X_102))
| join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))))),bind(Y0,$fot(meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))))),bind(Z0,$fot(meet(Y,meet(X_103,X_102))))]]) ).
cnf(refute_0_192,plain,
( meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))) != meet(Y,meet(X_103,X_102))
| join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)) ),
inference(resolve,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))),meet(Y,join(meet(X_102,X_103),meet(X_102,X_103)))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) = meet(Y,meet(X_103,X_102)),
inference(resolve,[$cnf( $equal(meet(Y,join(meet(X_102,X_103),meet(X_102,X_103))),meet(Y,meet(X_103,X_102))) )],[refute_0_182,refute_0_192]) ).
cnf(refute_0_194,plain,
( join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) != meet(Y,meet(X_103,X_102))
| join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) != meet(X_102,meet(X_103,Y))
| meet(Y,meet(X_103,X_102)) = meet(X_102,meet(X_103,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))),meet(X_102,meet(X_103,Y))) ),[0],$fot(meet(Y,meet(X_103,X_102)))]]) ).
cnf(refute_0_195,plain,
( join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))) != meet(X_102,meet(X_103,Y))
| meet(Y,meet(X_103,X_102)) = meet(X_102,meet(X_103,Y)) ),
inference(resolve,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))),meet(Y,meet(X_103,X_102))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
meet(Y,meet(X_103,X_102)) = meet(X_102,meet(X_103,Y)),
inference(resolve,[$cnf( $equal(join(meet(X_102,meet(X_103,Y)),meet(Y,meet(X_102,X_103))),meet(X_102,meet(X_103,Y))) )],[refute_0_152,refute_0_195]) ).
cnf(refute_0_197,plain,
meet(join(X_20,Y),meet(X_114,X_113)) = meet(X_113,meet(X_114,join(X_20,Y))),
inference(subst,[],[refute_0_196:[bind(Y,$fot(join(X_20,Y))),bind(X_102,$fot(X_113)),bind(X_103,$fot(X_114))]]) ).
cnf(refute_0_198,plain,
( meet(X_20,meet(X_114,X_113)) != meet(X_20,meet(join(X_20,Y),meet(X_114,X_113)))
| meet(join(X_20,Y),meet(X_114,X_113)) != meet(X_113,meet(X_114,join(X_20,Y)))
| meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_20,meet(X_114,X_113)),meet(X_20,meet(join(X_20,Y),meet(X_114,X_113)))) ),[1,1],$fot(meet(X_113,meet(X_114,join(X_20,Y))))]]) ).
cnf(refute_0_199,plain,
( meet(X_20,meet(X_114,X_113)) != meet(X_20,meet(join(X_20,Y),meet(X_114,X_113)))
| meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))) ),
inference(resolve,[$cnf( $equal(meet(join(X_20,Y),meet(X_114,X_113)),meet(X_113,meet(X_114,join(X_20,Y)))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))),
inference(resolve,[$cnf( $equal(meet(X_20,meet(X_114,X_113)),meet(X_20,meet(join(X_20,Y),meet(X_114,X_113)))) )],[refute_0_142,refute_0_199]) ).
cnf(refute_0_201,plain,
meet(X_81,meet(X_20,X_21)) = meet(X_81,meet(join(X_81,X_80),meet(X_20,X_21))),
inference(subst,[],[refute_0_141:[bind(Y,$fot(X_80)),bind(X_20,$fot(X_81)),bind(X_22,$fot(meet(X_20,X_21)))]]) ).
cnf(refute_0_202,plain,
meet(join(X_81,X_80),meet(X_20,X_21)) = meet(X_20,meet(X_21,join(X_81,X_80))),
inference(subst,[],[refute_0_5:[bind(X,$fot(join(X_81,X_80)))]]) ).
cnf(refute_0_203,plain,
( meet(X_81,meet(X_20,X_21)) != meet(X_81,meet(join(X_81,X_80),meet(X_20,X_21)))
| meet(join(X_81,X_80),meet(X_20,X_21)) != meet(X_20,meet(X_21,join(X_81,X_80)))
| meet(X_81,meet(X_20,X_21)) = meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_81,meet(X_20,X_21)),meet(X_81,meet(join(X_81,X_80),meet(X_20,X_21)))) ),[1,1],$fot(meet(X_20,meet(X_21,join(X_81,X_80))))]]) ).
cnf(refute_0_204,plain,
( meet(X_81,meet(X_20,X_21)) != meet(X_81,meet(join(X_81,X_80),meet(X_20,X_21)))
| meet(X_81,meet(X_20,X_21)) = meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80)))) ),
inference(resolve,[$cnf( $equal(meet(join(X_81,X_80),meet(X_20,X_21)),meet(X_20,meet(X_21,join(X_81,X_80)))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
meet(X_81,meet(X_20,X_21)) = meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80)))),
inference(resolve,[$cnf( $equal(meet(X_81,meet(X_20,X_21)),meet(X_81,meet(join(X_81,X_80),meet(X_20,X_21)))) )],[refute_0_201,refute_0_204]) ).
cnf(refute_0_206,plain,
( meet(X_81,meet(X_20,X_21)) != meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80))))
| meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80)))) = meet(X_81,meet(X_20,X_21)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_81,meet(X_20,X_21)))),bind(Y0,$fot(meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80))))))]]) ).
cnf(refute_0_207,plain,
meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80)))) = meet(X_81,meet(X_20,X_21)),
inference(resolve,[$cnf( $equal(meet(X_81,meet(X_20,X_21)),meet(X_81,meet(X_20,meet(X_21,join(X_81,X_80))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))) = meet(X_20,meet(X_113,X_114)),
inference(subst,[],[refute_0_207:[bind(X_20,$fot(X_113)),bind(X_21,$fot(X_114)),bind(X_80,$fot(Y)),bind(X_81,$fot(X_20))]]) ).
cnf(refute_0_209,plain,
( meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))) != meet(X_20,meet(X_113,X_114))
| meet(X_20,meet(X_114,X_113)) != meet(X_20,meet(X_113,meet(X_114,join(X_20,Y))))
| meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,X_114)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_20,meet(X_114,X_113)),meet(X_20,meet(X_113,meet(X_114,join(X_20,Y))))) ),[1],$fot(meet(X_20,meet(X_113,X_114)))]]) ).
cnf(refute_0_210,plain,
( meet(X_20,meet(X_114,X_113)) != meet(X_20,meet(X_113,meet(X_114,join(X_20,Y))))
| meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,X_114)) ),
inference(resolve,[$cnf( $equal(meet(X_20,meet(X_113,meet(X_114,join(X_20,Y)))),meet(X_20,meet(X_113,X_114))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(X_20,meet(X_114,X_113)) = meet(X_20,meet(X_113,X_114)),
inference(resolve,[$cnf( $equal(meet(X_20,meet(X_114,X_113)),meet(X_20,meet(X_113,meet(X_114,join(X_20,Y))))) )],[refute_0_200,refute_0_210]) ).
cnf(refute_0_212,plain,
( meet(X_20,meet(X_114,X_113)) != meet(X_20,meet(X_113,X_114))
| meet(X_20,meet(X_113,X_114)) = meet(X_20,meet(X_114,X_113)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_20,meet(X_114,X_113)))),bind(Y0,$fot(meet(X_20,meet(X_113,X_114))))]]) ).
cnf(refute_0_213,plain,
meet(X_20,meet(X_113,X_114)) = meet(X_20,meet(X_114,X_113)),
inference(resolve,[$cnf( $equal(meet(X_20,meet(X_114,X_113)),meet(X_20,meet(X_113,X_114))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) = meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))),
inference(subst,[],[refute_0_213:[bind(X_113,$fot(f(bb,dd))),bind(X_114,$fot(f(aa,dd))),bind(X_20,$fot(f(aa,dd)))]]) ).
cnf(refute_0_215,plain,
( meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))) != meet(f(aa,dd),f(bb,dd))
| meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) != meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))
| meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) = meet(f(aa,dd),f(bb,dd)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))))),bind(Y0,$fot(meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))))),bind(Z0,$fot(meet(f(aa,dd),f(bb,dd))))]]) ).
cnf(refute_0_216,plain,
( meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))) != meet(f(aa,dd),f(bb,dd))
| meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) = meet(f(aa,dd),f(bb,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) = meet(f(aa,dd),f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(aa,dd),f(bb,dd))),meet(f(aa,dd),f(bb,dd))) )],[refute_0_136,refute_0_216]) ).
cnf(refute_0_218,plain,
join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),
introduced(tautology,[refl,[$fot(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))]]) ).
cnf(refute_0_219,plain,
( join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))
| meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) != meet(f(aa,dd),f(bb,dd))
| join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) ),[1,0],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_220,plain,
( meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) != meet(f(aa,dd),f(bb,dd))
| join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) )],[refute_0_218,refute_0_219]) ).
cnf(refute_0_221,plain,
join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(aa,dd),f(bb,dd))) )],[refute_0_217,refute_0_220]) ).
cnf(refute_0_222,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))
| join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))
| join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))),bind(Y0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))),bind(Z0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))))]]) ).
cnf(refute_0_223,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))
| join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))) )],[refute_0_128,refute_0_223]) ).
cnf(refute_0_225,plain,
meet(join(meet(X_104,Y),X_106),join(Y,join(meet(X_104,Y),X_106))) = join(meet(X_104,Y),X_106),
inference(subst,[],[refute_0_18:[bind(X,$fot(join(meet(X_104,Y),X_106)))]]) ).
cnf(refute_0_226,plain,
join(join(X_23,meet(Y,X_23)),X_25) = join(X_23,join(meet(Y,X_23),X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Y,$fot(meet(Y,X_23))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_227,plain,
join(X_23,meet(Y,X_23)) = X_23,
inference(subst,[],[refute_0_49:[bind(X,$fot(X_23))]]) ).
cnf(refute_0_228,plain,
( join(X_23,meet(Y,X_23)) != X_23
| join(join(X_23,meet(Y,X_23)),X_25) != join(X_23,join(meet(Y,X_23),X_25))
| join(X_23,X_25) = join(X_23,join(meet(Y,X_23),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,meet(Y,X_23)),X_25),join(X_23,join(meet(Y,X_23),X_25))) ),[0,0],$fot(X_23)]]) ).
cnf(refute_0_229,plain,
( join(join(X_23,meet(Y,X_23)),X_25) != join(X_23,join(meet(Y,X_23),X_25))
| join(X_23,X_25) = join(X_23,join(meet(Y,X_23),X_25)) ),
inference(resolve,[$cnf( $equal(join(X_23,meet(Y,X_23)),X_23) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
join(X_23,X_25) = join(X_23,join(meet(Y,X_23),X_25)),
inference(resolve,[$cnf( $equal(join(join(X_23,meet(Y,X_23)),X_25),join(X_23,join(meet(Y,X_23),X_25))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
join(Y,X_106) = join(Y,join(meet(X_104,Y),X_106)),
inference(subst,[],[refute_0_230:[bind(Y,$fot(X_104)),bind(X_23,$fot(Y)),bind(X_25,$fot(X_106))]]) ).
cnf(refute_0_232,plain,
( join(Y,X_106) != join(Y,join(meet(X_104,Y),X_106))
| join(Y,join(meet(X_104,Y),X_106)) = join(Y,X_106) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(Y,X_106))),bind(Y0,$fot(join(Y,join(meet(X_104,Y),X_106))))]]) ).
cnf(refute_0_233,plain,
join(Y,join(meet(X_104,Y),X_106)) = join(Y,X_106),
inference(resolve,[$cnf( $equal(join(Y,X_106),join(Y,join(meet(X_104,Y),X_106))) )],[refute_0_231,refute_0_232]) ).
cnf(refute_0_234,plain,
( join(Y,join(meet(X_104,Y),X_106)) != join(Y,X_106)
| meet(join(meet(X_104,Y),X_106),join(Y,join(meet(X_104,Y),X_106))) != join(meet(X_104,Y),X_106)
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(meet(X_104,Y),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,join(meet(X_104,Y),X_106))),join(meet(X_104,Y),X_106)) ),[0,1],$fot(join(Y,X_106))]]) ).
cnf(refute_0_235,plain,
( meet(join(meet(X_104,Y),X_106),join(Y,join(meet(X_104,Y),X_106))) != join(meet(X_104,Y),X_106)
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(meet(X_104,Y),X_106) ),
inference(resolve,[$cnf( $equal(join(Y,join(meet(X_104,Y),X_106)),join(Y,X_106)) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(meet(X_104,Y),X_106),
inference(resolve,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,join(meet(X_104,Y),X_106))),join(meet(X_104,Y),X_106)) )],[refute_0_225,refute_0_235]) ).
cnf(refute_0_237,plain,
meet(Y,meet(X_104,Y)) = meet(Y,X_104),
inference(subst,[],[refute_0_113:[bind(Y,$fot(X_104)),bind(X_15,$fot(Y))]]) ).
cnf(refute_0_238,plain,
join(X_106,meet(Y,meet(X_104,Y))) = join(X_106,meet(Y,meet(X_104,Y))),
introduced(tautology,[refl,[$fot(join(X_106,meet(Y,meet(X_104,Y))))]]) ).
cnf(refute_0_239,plain,
( join(X_106,meet(Y,meet(X_104,Y))) != join(X_106,meet(Y,meet(X_104,Y)))
| meet(Y,meet(X_104,Y)) != meet(Y,X_104)
| join(X_106,meet(Y,meet(X_104,Y))) = join(X_106,meet(Y,X_104)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_106,meet(Y,meet(X_104,Y))),join(X_106,meet(Y,meet(X_104,Y)))) ),[1,1],$fot(meet(Y,X_104))]]) ).
cnf(refute_0_240,plain,
( meet(Y,meet(X_104,Y)) != meet(Y,X_104)
| join(X_106,meet(Y,meet(X_104,Y))) = join(X_106,meet(Y,X_104)) ),
inference(resolve,[$cnf( $equal(join(X_106,meet(Y,meet(X_104,Y))),join(X_106,meet(Y,meet(X_104,Y)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
join(X_106,meet(Y,meet(X_104,Y))) = join(X_106,meet(Y,X_104)),
inference(resolve,[$cnf( $equal(meet(Y,meet(X_104,Y)),meet(Y,X_104)) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
meet(join(X,Y),join(X,Z)) = meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))),
inference(subst,[],[refute_0_141:[bind(Y,$fot(X_80)),bind(X_20,$fot(join(X,Y))),bind(X_22,$fot(join(X,Z)))]]) ).
cnf(refute_0_243,plain,
( join(X,meet(Y,Z)) != meet(join(X,Y),join(X,Z))
| meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X,meet(Y,Z)))),bind(Y0,$fot(meet(join(X,Y),join(X,Z))))]]) ).
cnf(refute_0_244,plain,
meet(join(X,Y),join(X,Z)) = join(X,meet(Y,Z)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),meet(join(X,Y),join(X,Z))) )],[dist_join,refute_0_243]) ).
cnf(refute_0_245,plain,
( meet(join(X,Y),join(X,Z)) != join(X,meet(Y,Z))
| meet(join(X,Y),join(X,Z)) != meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))
| join(X,meet(Y,Z)) = meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X,Y),join(X,Z)),meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))) ),[0],$fot(join(X,meet(Y,Z)))]]) ).
cnf(refute_0_246,plain,
( meet(join(X,Y),join(X,Z)) != meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))
| join(X,meet(Y,Z)) = meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) ),
inference(resolve,[$cnf( $equal(meet(join(X,Y),join(X,Z)),join(X,meet(Y,Z))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
join(X,meet(Y,Z)) = meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))),
inference(resolve,[$cnf( $equal(meet(join(X,Y),join(X,Z)),meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))) )],[refute_0_242,refute_0_246]) ).
cnf(refute_0_248,plain,
meet(join(X_40,Y),meet(X_39,X_40)) = meet(X_39,meet(X_40,join(X_40,Y))),
inference(subst,[],[refute_0_5:[bind(X,$fot(join(X_40,Y))),bind(X_20,$fot(X_39)),bind(X_21,$fot(X_40))]]) ).
cnf(refute_0_249,plain,
meet(X_40,join(X_40,Y)) = X_40,
inference(subst,[],[absorption1:[bind(X,$fot(X_40))]]) ).
cnf(refute_0_250,plain,
( meet(X_40,join(X_40,Y)) != X_40
| meet(join(X_40,Y),meet(X_39,X_40)) != meet(X_39,meet(X_40,join(X_40,Y)))
| meet(join(X_40,Y),meet(X_39,X_40)) = meet(X_39,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_40,Y),meet(X_39,X_40)),meet(X_39,meet(X_40,join(X_40,Y)))) ),[1,1],$fot(X_40)]]) ).
cnf(refute_0_251,plain,
( meet(join(X_40,Y),meet(X_39,X_40)) != meet(X_39,meet(X_40,join(X_40,Y)))
| meet(join(X_40,Y),meet(X_39,X_40)) = meet(X_39,X_40) ),
inference(resolve,[$cnf( $equal(meet(X_40,join(X_40,Y)),X_40) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
meet(join(X_40,Y),meet(X_39,X_40)) = meet(X_39,X_40),
inference(resolve,[$cnf( $equal(meet(join(X_40,Y),meet(X_39,X_40)),meet(X_39,meet(X_40,join(X_40,Y)))) )],[refute_0_248,refute_0_251]) ).
cnf(refute_0_253,plain,
meet(X_38,meet(X_39,X_40)) = meet(X_39,meet(X_40,X_38)),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_38)),bind(X_20,$fot(X_39)),bind(X_21,$fot(X_40))]]) ).
cnf(refute_0_254,plain,
meet(X_40,X_39) = meet(X_39,X_40),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_40)),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_255,plain,
( meet(X_40,X_39) != meet(X_39,X_40)
| meet(X_39,X_40) = meet(X_40,X_39) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_40,X_39))),bind(Y0,$fot(meet(X_39,X_40)))]]) ).
cnf(refute_0_256,plain,
meet(X_39,X_40) = meet(X_40,X_39),
inference(resolve,[$cnf( $equal(meet(X_40,X_39),meet(X_39,X_40)) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( meet(X_38,meet(X_39,X_40)) != meet(X_39,meet(X_40,X_38))
| meet(X_39,X_40) != meet(X_40,X_39)
| meet(X_38,meet(X_40,X_39)) = meet(X_39,meet(X_40,X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_38,meet(X_39,X_40)),meet(X_39,meet(X_40,X_38))) ),[0,1],$fot(meet(X_40,X_39))]]) ).
cnf(refute_0_258,plain,
( meet(X_38,meet(X_39,X_40)) != meet(X_39,meet(X_40,X_38))
| meet(X_38,meet(X_40,X_39)) = meet(X_39,meet(X_40,X_38)) ),
inference(resolve,[$cnf( $equal(meet(X_39,X_40),meet(X_40,X_39)) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
meet(X_38,meet(X_40,X_39)) = meet(X_39,meet(X_40,X_38)),
inference(resolve,[$cnf( $equal(meet(X_38,meet(X_39,X_40)),meet(X_39,meet(X_40,X_38))) )],[refute_0_253,refute_0_258]) ).
cnf(refute_0_260,plain,
( meet(X_38,meet(X_40,X_39)) != meet(X_39,meet(X_40,X_38))
| meet(X_39,meet(X_40,X_38)) = meet(X_38,meet(X_40,X_39)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_38,meet(X_40,X_39)))),bind(Y0,$fot(meet(X_39,meet(X_40,X_38))))]]) ).
cnf(refute_0_261,plain,
meet(X_39,meet(X_40,X_38)) = meet(X_38,meet(X_40,X_39)),
inference(resolve,[$cnf( $equal(meet(X_38,meet(X_40,X_39)),meet(X_39,meet(X_40,X_38))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
meet(join(X_40,Y),meet(X_39,X_40)) = meet(X_40,meet(X_39,join(X_40,Y))),
inference(subst,[],[refute_0_261:[bind(X_38,$fot(X_40)),bind(X_39,$fot(join(X_40,Y))),bind(X_40,$fot(X_39))]]) ).
cnf(refute_0_263,plain,
( meet(join(X_40,Y),meet(X_39,X_40)) != meet(X_39,X_40)
| meet(join(X_40,Y),meet(X_39,X_40)) != meet(X_40,meet(X_39,join(X_40,Y)))
| meet(X_40,meet(X_39,join(X_40,Y))) = meet(X_39,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_40,Y),meet(X_39,X_40)),meet(X_39,X_40)) ),[0],$fot(meet(X_40,meet(X_39,join(X_40,Y))))]]) ).
cnf(refute_0_264,plain,
( meet(join(X_40,Y),meet(X_39,X_40)) != meet(X_39,X_40)
| meet(X_40,meet(X_39,join(X_40,Y))) = meet(X_39,X_40) ),
inference(resolve,[$cnf( $equal(meet(join(X_40,Y),meet(X_39,X_40)),meet(X_40,meet(X_39,join(X_40,Y)))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
meet(X_40,meet(X_39,join(X_40,Y))) = meet(X_39,X_40),
inference(resolve,[$cnf( $equal(meet(join(X_40,Y),meet(X_39,X_40)),meet(X_39,X_40)) )],[refute_0_252,refute_0_264]) ).
cnf(refute_0_266,plain,
meet(Y,meet(Z,join(Y,X_80))) = meet(Z,Y),
inference(subst,[],[refute_0_265:[bind(Y,$fot(X_80)),bind(X_39,$fot(Z)),bind(X_40,$fot(Y))]]) ).
cnf(refute_0_267,plain,
join(X,meet(Y,meet(Z,join(Y,X_80)))) = join(X,meet(Y,meet(Z,join(Y,X_80)))),
introduced(tautology,[refl,[$fot(join(X,meet(Y,meet(Z,join(Y,X_80)))))]]) ).
cnf(refute_0_268,plain,
( join(X,meet(Y,meet(Z,join(Y,X_80)))) != join(X,meet(Y,meet(Z,join(Y,X_80))))
| meet(Y,meet(Z,join(Y,X_80))) != meet(Z,Y)
| join(X,meet(Y,meet(Z,join(Y,X_80)))) = join(X,meet(Z,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(Y,meet(Z,join(Y,X_80)))),join(X,meet(Y,meet(Z,join(Y,X_80))))) ),[1,1],$fot(meet(Z,Y))]]) ).
cnf(refute_0_269,plain,
( meet(Y,meet(Z,join(Y,X_80))) != meet(Z,Y)
| join(X,meet(Y,meet(Z,join(Y,X_80)))) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(join(X,meet(Y,meet(Z,join(Y,X_80)))),join(X,meet(Y,meet(Z,join(Y,X_80))))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
join(X,meet(Y,meet(Z,join(Y,X_80)))) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(meet(Y,meet(Z,join(Y,X_80))),meet(Z,Y)) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
join(X_46,meet(X_47,meet(X_21,X))) = meet(join(X_46,X_47),join(X_46,meet(X_21,X))),
inference(subst,[],[dist_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(meet(X_21,X)))]]) ).
cnf(refute_0_272,plain,
meet(X,meet(X_47,X_21)) = meet(X_47,meet(X_21,X)),
inference(subst,[],[refute_0_5:[bind(X_20,$fot(X_47))]]) ).
cnf(refute_0_273,plain,
( meet(X,meet(X_47,X_21)) != meet(X_47,meet(X_21,X))
| meet(X_47,meet(X_21,X)) = meet(X,meet(X_47,X_21)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X,meet(X_47,X_21)))),bind(Y0,$fot(meet(X_47,meet(X_21,X))))]]) ).
cnf(refute_0_274,plain,
meet(X_47,meet(X_21,X)) = meet(X,meet(X_47,X_21)),
inference(resolve,[$cnf( $equal(meet(X,meet(X_47,X_21)),meet(X_47,meet(X_21,X))) )],[refute_0_272,refute_0_273]) ).
cnf(refute_0_275,plain,
( join(X_46,meet(X_47,meet(X_21,X))) != meet(join(X_46,X_47),join(X_46,meet(X_21,X)))
| meet(X_47,meet(X_21,X)) != meet(X,meet(X_47,X_21))
| join(X_46,meet(X,meet(X_47,X_21))) = meet(join(X_46,X_47),join(X_46,meet(X_21,X))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(X_47,meet(X_21,X))),meet(join(X_46,X_47),join(X_46,meet(X_21,X)))) ),[0,1],$fot(meet(X,meet(X_47,X_21)))]]) ).
cnf(refute_0_276,plain,
( join(X_46,meet(X_47,meet(X_21,X))) != meet(join(X_46,X_47),join(X_46,meet(X_21,X)))
| join(X_46,meet(X,meet(X_47,X_21))) = meet(join(X_46,X_47),join(X_46,meet(X_21,X))) ),
inference(resolve,[$cnf( $equal(meet(X_47,meet(X_21,X)),meet(X,meet(X_47,X_21))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
join(X_46,meet(X,meet(X_47,X_21))) = meet(join(X_46,X_47),join(X_46,meet(X_21,X))),
inference(resolve,[$cnf( $equal(join(X_46,meet(X_47,meet(X_21,X))),meet(join(X_46,X_47),join(X_46,meet(X_21,X)))) )],[refute_0_271,refute_0_276]) ).
cnf(refute_0_278,plain,
meet(join(X_46,X_47),join(X_46,meet(X_21,X))) = join(X_46,meet(X_47,meet(X_21,X))),
inference(subst,[],[refute_0_244:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(meet(X_21,X)))]]) ).
cnf(refute_0_279,plain,
( join(X_46,meet(X,meet(X_47,X_21))) != meet(join(X_46,X_47),join(X_46,meet(X_21,X)))
| meet(join(X_46,X_47),join(X_46,meet(X_21,X))) != join(X_46,meet(X_47,meet(X_21,X)))
| join(X_46,meet(X,meet(X_47,X_21))) = join(X_46,meet(X_47,meet(X_21,X))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_46,meet(X,meet(X_47,X_21))),join(X_46,meet(X_47,meet(X_21,X)))) ),[0],$fot(meet(join(X_46,X_47),join(X_46,meet(X_21,X))))]]) ).
cnf(refute_0_280,plain,
( join(X_46,meet(X,meet(X_47,X_21))) != meet(join(X_46,X_47),join(X_46,meet(X_21,X)))
| join(X_46,meet(X,meet(X_47,X_21))) = join(X_46,meet(X_47,meet(X_21,X))) ),
inference(resolve,[$cnf( $equal(meet(join(X_46,X_47),join(X_46,meet(X_21,X))),join(X_46,meet(X_47,meet(X_21,X)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
join(X_46,meet(X,meet(X_47,X_21))) = join(X_46,meet(X_47,meet(X_21,X))),
inference(resolve,[$cnf( $equal(join(X_46,meet(X,meet(X_47,X_21))),meet(join(X_46,X_47),join(X_46,meet(X_21,X)))) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
join(X,meet(join(Y,X_80),meet(Y,Z))) = join(X,meet(Y,meet(Z,join(Y,X_80)))),
inference(subst,[],[refute_0_281:[bind(X,$fot(join(Y,X_80))),bind(X_21,$fot(Z)),bind(X_46,$fot(X)),bind(X_47,$fot(Y))]]) ).
cnf(refute_0_283,plain,
( join(X,meet(Y,meet(Z,join(Y,X_80)))) != join(X,meet(Z,Y))
| join(X,meet(join(Y,X_80),meet(Y,Z))) != join(X,meet(Y,meet(Z,join(Y,X_80))))
| join(X,meet(join(Y,X_80),meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(X,meet(join(Y,X_80),meet(Y,Z))))),bind(Y0,$fot(join(X,meet(Y,meet(Z,join(Y,X_80)))))),bind(Z0,$fot(join(X,meet(Z,Y))))]]) ).
cnf(refute_0_284,plain,
( join(X,meet(Y,meet(Z,join(Y,X_80)))) != join(X,meet(Z,Y))
| join(X,meet(join(Y,X_80),meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(join(X,meet(join(Y,X_80),meet(Y,Z))),join(X,meet(Y,meet(Z,join(Y,X_80))))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
join(X,meet(join(Y,X_80),meet(Y,Z))) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,meet(Z,join(Y,X_80)))),join(X,meet(Z,Y))) )],[refute_0_270,refute_0_284]) ).
cnf(refute_0_286,plain,
meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) = join(X,meet(join(Y,X_80),meet(Y,Z))),
inference(subst,[],[refute_0_244:[bind(Y,$fot(join(Y,X_80))),bind(Z,$fot(meet(Y,Z)))]]) ).
cnf(refute_0_287,plain,
( join(X,meet(join(Y,X_80),meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) != join(X,meet(join(Y,X_80),meet(Y,Z)))
| meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))))),bind(Y0,$fot(join(X,meet(join(Y,X_80),meet(Y,Z))))),bind(Z0,$fot(join(X,meet(Z,Y))))]]) ).
cnf(refute_0_288,plain,
( join(X,meet(join(Y,X_80),meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))),join(X,meet(join(Y,X_80),meet(Y,Z)))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(join(X,meet(join(Y,X_80),meet(Y,Z))),join(X,meet(Z,Y))) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
join(join(X,Y),X_80) = join(X,join(Y,X_80)),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_80))]]) ).
cnf(refute_0_291,plain,
meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),
introduced(tautology,[refl,[$fot(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))))]]) ).
cnf(refute_0_292,plain,
( join(join(X,Y),X_80) != join(X,join(Y,X_80))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) != meet(join(join(X,Y),X_80),join(X,meet(Y,Z)))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),meet(join(join(X,Y),X_80),join(X,meet(Y,Z)))) ),[1,0],$fot(join(X,join(Y,X_80)))]]) ).
cnf(refute_0_293,plain,
( join(join(X,Y),X_80) != join(X,join(Y,X_80))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) ),
inference(resolve,[$cnf( $equal(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),meet(join(join(X,Y),X_80),join(X,meet(Y,Z)))) )],[refute_0_291,refute_0_292]) ).
cnf(refute_0_294,plain,
meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))),
inference(resolve,[$cnf( $equal(join(join(X,Y),X_80),join(X,join(Y,X_80))) )],[refute_0_290,refute_0_293]) ).
cnf(refute_0_295,plain,
( meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) != meet(join(X,join(Y,X_80)),join(X,meet(Y,Z)))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))))),bind(Y0,$fot(meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))))),bind(Z0,$fot(join(X,meet(Z,Y))))]]) ).
cnf(refute_0_296,plain,
( meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),meet(join(X,join(Y,X_80)),join(X,meet(Y,Z)))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(meet(join(X,join(Y,X_80)),join(X,meet(Y,Z))),join(X,meet(Z,Y))) )],[refute_0_289,refute_0_296]) ).
cnf(refute_0_298,plain,
meet(meet(X_20,X_21),X_22) = meet(X_20,meet(X_21,X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_20)),bind(Y,$fot(X_21)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_299,plain,
meet(X_21,X_20) = meet(X_20,X_21),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_21)),bind(Y,$fot(X_20))]]) ).
cnf(refute_0_300,plain,
( meet(X_21,X_20) != meet(X_20,X_21)
| meet(X_20,X_21) = meet(X_21,X_20) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_21,X_20))),bind(Y0,$fot(meet(X_20,X_21)))]]) ).
cnf(refute_0_301,plain,
meet(X_20,X_21) = meet(X_21,X_20),
inference(resolve,[$cnf( $equal(meet(X_21,X_20),meet(X_20,X_21)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
( meet(X_20,X_21) != meet(X_21,X_20)
| meet(meet(X_20,X_21),X_22) != meet(X_20,meet(X_21,X_22))
| meet(meet(X_21,X_20),X_22) = meet(X_20,meet(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_20,X_21),X_22),meet(X_20,meet(X_21,X_22))) ),[0,0],$fot(meet(X_21,X_20))]]) ).
cnf(refute_0_303,plain,
( meet(meet(X_20,X_21),X_22) != meet(X_20,meet(X_21,X_22))
| meet(meet(X_21,X_20),X_22) = meet(X_20,meet(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(meet(X_20,X_21),meet(X_21,X_20)) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
meet(meet(X_21,X_20),X_22) = meet(X_20,meet(X_21,X_22)),
inference(resolve,[$cnf( $equal(meet(meet(X_20,X_21),X_22),meet(X_20,meet(X_21,X_22))) )],[refute_0_298,refute_0_303]) ).
cnf(refute_0_305,plain,
meet(meet(X_21,X_20),X_22) = meet(X_21,meet(X_20,X_22)),
inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_21)),bind(Y,$fot(X_20)),bind(Z,$fot(X_22))]]) ).
cnf(refute_0_306,plain,
( meet(meet(X_21,X_20),X_22) != meet(X_20,meet(X_21,X_22))
| meet(meet(X_21,X_20),X_22) != meet(X_21,meet(X_20,X_22))
| meet(X_21,meet(X_20,X_22)) = meet(X_20,meet(X_21,X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_21,X_20),X_22),meet(X_20,meet(X_21,X_22))) ),[0],$fot(meet(X_21,meet(X_20,X_22)))]]) ).
cnf(refute_0_307,plain,
( meet(meet(X_21,X_20),X_22) != meet(X_20,meet(X_21,X_22))
| meet(X_21,meet(X_20,X_22)) = meet(X_20,meet(X_21,X_22)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_21,X_20),X_22),meet(X_21,meet(X_20,X_22))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
meet(X_21,meet(X_20,X_22)) = meet(X_20,meet(X_21,X_22)),
inference(resolve,[$cnf( $equal(meet(meet(X_21,X_20),X_22),meet(X_20,meet(X_21,X_22))) )],[refute_0_304,refute_0_307]) ).
cnf(refute_0_309,plain,
meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) = meet(X_20,meet(join(X_46,X_47),join(X_46,X_48))),
inference(subst,[],[refute_0_308:[bind(X_21,$fot(join(X_46,X_47))),bind(X_22,$fot(join(X_46,X_48)))]]) ).
cnf(refute_0_310,plain,
join(X_46,meet(X_47,X_48)) = meet(join(X_46,X_47),join(X_46,X_48)),
inference(subst,[],[dist_join:[bind(X,$fot(X_46)),bind(Y,$fot(X_47)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_311,plain,
( join(X_46,meet(X_47,X_48)) != meet(join(X_46,X_47),join(X_46,X_48))
| meet(join(X_46,X_47),join(X_46,X_48)) = join(X_46,meet(X_47,X_48)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_46,meet(X_47,X_48)))),bind(Y0,$fot(meet(join(X_46,X_47),join(X_46,X_48))))]]) ).
cnf(refute_0_312,plain,
meet(join(X_46,X_47),join(X_46,X_48)) = join(X_46,meet(X_47,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,meet(X_47,X_48)),meet(join(X_46,X_47),join(X_46,X_48))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
( meet(join(X_46,X_47),join(X_46,X_48)) != join(X_46,meet(X_47,X_48))
| meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) != meet(X_20,meet(join(X_46,X_47),join(X_46,X_48)))
| meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) = meet(X_20,join(X_46,meet(X_47,X_48))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))),meet(X_20,meet(join(X_46,X_47),join(X_46,X_48)))) ),[1,1],$fot(join(X_46,meet(X_47,X_48)))]]) ).
cnf(refute_0_314,plain,
( meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) != meet(X_20,meet(join(X_46,X_47),join(X_46,X_48)))
| meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) = meet(X_20,join(X_46,meet(X_47,X_48))) ),
inference(resolve,[$cnf( $equal(meet(join(X_46,X_47),join(X_46,X_48)),join(X_46,meet(X_47,X_48))) )],[refute_0_312,refute_0_313]) ).
cnf(refute_0_315,plain,
meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))) = meet(X_20,join(X_46,meet(X_47,X_48))),
inference(resolve,[$cnf( $equal(meet(join(X_46,X_47),meet(X_20,join(X_46,X_48))),meet(X_20,meet(join(X_46,X_47),join(X_46,X_48)))) )],[refute_0_309,refute_0_314]) ).
cnf(refute_0_316,plain,
meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) = meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),
inference(subst,[],[refute_0_315:[bind(X_20,$fot(join(join(X,Y),X_80))),bind(X_46,$fot(X)),bind(X_47,$fot(Y)),bind(X_48,$fot(Z))]]) ).
cnf(refute_0_317,plain,
( meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) != meet(join(join(X,Y),X_80),join(X,meet(Y,Z)))
| meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) = join(X,meet(Z,Y)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))))),bind(Y0,$fot(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))))),bind(Z0,$fot(join(X,meet(Z,Y))))]]) ).
cnf(refute_0_318,plain,
( meet(join(join(X,Y),X_80),join(X,meet(Y,Z))) != join(X,meet(Z,Y))
| meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))),meet(join(join(X,Y),X_80),join(X,meet(Y,Z)))) )],[refute_0_316,refute_0_317]) ).
cnf(refute_0_319,plain,
meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(meet(join(join(X,Y),X_80),join(X,meet(Y,Z))),join(X,meet(Z,Y))) )],[refute_0_297,refute_0_318]) ).
cnf(refute_0_320,plain,
( join(X,meet(Y,Z)) != meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))
| meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))) != join(X,meet(Z,Y))
| join(X,meet(Y,Z)) = join(X,meet(Z,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,meet(Y,Z)),join(X,meet(Z,Y))) ),[0],$fot(meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))))]]) ).
cnf(refute_0_321,plain,
( join(X,meet(Y,Z)) != meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))
| join(X,meet(Y,Z)) = join(X,meet(Z,Y)) ),
inference(resolve,[$cnf( $equal(meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z))),join(X,meet(Z,Y))) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
join(X,meet(Y,Z)) = join(X,meet(Z,Y)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),meet(join(X,Y),meet(join(join(X,Y),X_80),join(X,Z)))) )],[refute_0_247,refute_0_321]) ).
cnf(refute_0_323,plain,
( join(X,meet(Y,Z)) != join(X,meet(Z,Y))
| join(X,meet(Z,Y)) = join(X,meet(Y,Z)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X,meet(Y,Z)))),bind(Y0,$fot(join(X,meet(Z,Y))))]]) ).
cnf(refute_0_324,plain,
join(X,meet(Z,Y)) = join(X,meet(Y,Z)),
inference(resolve,[$cnf( $equal(join(X,meet(Y,Z)),join(X,meet(Z,Y))) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
join(X_106,meet(meet(X_104,Y),Y)) = join(X_106,meet(Y,meet(X_104,Y))),
inference(subst,[],[refute_0_324:[bind(X,$fot(X_106)),bind(Z,$fot(meet(X_104,Y)))]]) ).
cnf(refute_0_326,plain,
meet(join(Y,X_87),join(X_86,X_87)) = join(meet(join(Y,X_87),X_86),meet(X_87,join(Y,X_87))),
inference(subst,[],[refute_0_163:[bind(X_51,$fot(join(Y,X_87))),bind(X_52,$fot(X_86)),bind(X_53,$fot(X_87))]]) ).
cnf(refute_0_327,plain,
meet(X_87,join(Y,X_87)) = X_87,
inference(subst,[],[refute_0_18:[bind(X,$fot(X_87))]]) ).
cnf(refute_0_328,plain,
( meet(X_87,join(Y,X_87)) != X_87
| meet(join(Y,X_87),join(X_86,X_87)) != join(meet(join(Y,X_87),X_86),meet(X_87,join(Y,X_87)))
| meet(join(Y,X_87),join(X_86,X_87)) = join(meet(join(Y,X_87),X_86),X_87) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(Y,X_87),join(X_86,X_87)),join(meet(join(Y,X_87),X_86),meet(X_87,join(Y,X_87)))) ),[1,1],$fot(X_87)]]) ).
cnf(refute_0_329,plain,
( meet(join(Y,X_87),join(X_86,X_87)) != join(meet(join(Y,X_87),X_86),meet(X_87,join(Y,X_87)))
| meet(join(Y,X_87),join(X_86,X_87)) = join(meet(join(Y,X_87),X_86),X_87) ),
inference(resolve,[$cnf( $equal(meet(X_87,join(Y,X_87)),X_87) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
meet(join(Y,X_87),join(X_86,X_87)) = join(meet(join(Y,X_87),X_86),X_87),
inference(resolve,[$cnf( $equal(meet(join(Y,X_87),join(X_86,X_87)),join(meet(join(Y,X_87),X_86),meet(X_87,join(Y,X_87)))) )],[refute_0_326,refute_0_329]) ).
cnf(refute_0_331,plain,
join(X_46,meet(join(Y,X_46),X_48)) = meet(join(X_46,join(Y,X_46)),join(X_46,X_48)),
inference(subst,[],[dist_join:[bind(X,$fot(X_46)),bind(Y,$fot(join(Y,X_46))),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_332,plain,
join(join(X_13,Y),meet(X_13,join(X_13,Y))) = join(X_13,Y),
inference(subst,[],[refute_0_49:[bind(X,$fot(join(X_13,Y))),bind(Y,$fot(X_13))]]) ).
cnf(refute_0_333,plain,
meet(X_13,join(X_13,Y)) = X_13,
inference(subst,[],[absorption1:[bind(X,$fot(X_13))]]) ).
cnf(refute_0_334,plain,
( join(join(X_13,Y),meet(X_13,join(X_13,Y))) != join(X_13,Y)
| meet(X_13,join(X_13,Y)) != X_13
| join(join(X_13,Y),X_13) = join(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_13,Y),meet(X_13,join(X_13,Y))),join(X_13,Y)) ),[0,1],$fot(X_13)]]) ).
cnf(refute_0_335,plain,
( join(join(X_13,Y),meet(X_13,join(X_13,Y))) != join(X_13,Y)
| join(join(X_13,Y),X_13) = join(X_13,Y) ),
inference(resolve,[$cnf( $equal(meet(X_13,join(X_13,Y)),X_13) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
join(join(X_13,Y),X_13) = join(X_13,Y),
inference(resolve,[$cnf( $equal(join(join(X_13,Y),meet(X_13,join(X_13,Y))),join(X_13,Y)) )],[refute_0_332,refute_0_335]) ).
cnf(refute_0_337,plain,
join(join(X_13,Y),X_13) = join(X_13,join(Y,X_13)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_338,plain,
( join(join(X_13,Y),X_13) != join(X_13,Y)
| join(join(X_13,Y),X_13) != join(X_13,join(Y,X_13))
| join(X_13,join(Y,X_13)) = join(X_13,Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,Y)) ),[0],$fot(join(X_13,join(Y,X_13)))]]) ).
cnf(refute_0_339,plain,
( join(join(X_13,Y),X_13) != join(X_13,Y)
| join(X_13,join(Y,X_13)) = join(X_13,Y) ),
inference(resolve,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,join(Y,X_13))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
join(X_13,join(Y,X_13)) = join(X_13,Y),
inference(resolve,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,Y)) )],[refute_0_336,refute_0_339]) ).
cnf(refute_0_341,plain,
join(X_46,join(Y,X_46)) = join(X_46,Y),
inference(subst,[],[refute_0_340:[bind(X_13,$fot(X_46))]]) ).
cnf(refute_0_342,plain,
( join(X_46,join(Y,X_46)) != join(X_46,Y)
| join(X_46,meet(join(Y,X_46),X_48)) != meet(join(X_46,join(Y,X_46)),join(X_46,X_48))
| join(X_46,meet(join(Y,X_46),X_48)) = meet(join(X_46,Y),join(X_46,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(join(Y,X_46),X_48)),meet(join(X_46,join(Y,X_46)),join(X_46,X_48))) ),[1,0],$fot(join(X_46,Y))]]) ).
cnf(refute_0_343,plain,
( join(X_46,meet(join(Y,X_46),X_48)) != meet(join(X_46,join(Y,X_46)),join(X_46,X_48))
| join(X_46,meet(join(Y,X_46),X_48)) = meet(join(X_46,Y),join(X_46,X_48)) ),
inference(resolve,[$cnf( $equal(join(X_46,join(Y,X_46)),join(X_46,Y)) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
join(X_46,meet(join(Y,X_46),X_48)) = meet(join(X_46,Y),join(X_46,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(Y,X_46),X_48)),meet(join(X_46,join(Y,X_46)),join(X_46,X_48))) )],[refute_0_331,refute_0_343]) ).
cnf(refute_0_345,plain,
meet(join(X_46,Y),join(X_46,X_48)) = join(X_46,meet(Y,X_48)),
inference(subst,[],[refute_0_244:[bind(X,$fot(X_46)),bind(Z,$fot(X_48))]]) ).
cnf(refute_0_346,plain,
( join(X_46,meet(join(Y,X_46),X_48)) != meet(join(X_46,Y),join(X_46,X_48))
| meet(join(X_46,Y),join(X_46,X_48)) != join(X_46,meet(Y,X_48))
| join(X_46,meet(join(Y,X_46),X_48)) = join(X_46,meet(Y,X_48)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_46,meet(join(Y,X_46),X_48)),join(X_46,meet(Y,X_48))) ),[0],$fot(meet(join(X_46,Y),join(X_46,X_48)))]]) ).
cnf(refute_0_347,plain,
( join(X_46,meet(join(Y,X_46),X_48)) != meet(join(X_46,Y),join(X_46,X_48))
| join(X_46,meet(join(Y,X_46),X_48)) = join(X_46,meet(Y,X_48)) ),
inference(resolve,[$cnf( $equal(meet(join(X_46,Y),join(X_46,X_48)),join(X_46,meet(Y,X_48))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
join(X_46,meet(join(Y,X_46),X_48)) = join(X_46,meet(Y,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,meet(join(Y,X_46),X_48)),meet(join(X_46,Y),join(X_46,X_48))) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
join(X_87,meet(join(Y,X_87),X_86)) = join(X_87,meet(Y,X_86)),
inference(subst,[],[refute_0_348:[bind(X_46,$fot(X_87)),bind(X_48,$fot(X_86))]]) ).
cnf(refute_0_350,plain,
meet(join(X_37,X_35),join(Y,join(X_37,X_35))) = join(X_37,X_35),
inference(subst,[],[refute_0_18:[bind(X,$fot(join(X_37,X_35)))]]) ).
cnf(refute_0_351,plain,
join(X,join(X_23,X_24)) = join(join(X_23,X_24),X),
inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_23,X_24)))]]) ).
cnf(refute_0_352,plain,
( join(X,join(X_23,X_24)) != join(join(X_23,X_24),X)
| join(join(X_23,X_24),X) != join(X_23,join(X_24,X))
| join(X,join(X_23,X_24)) = join(X_23,join(X_24,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_23,X_24)),join(X_23,join(X_24,X))) ),[0],$fot(join(join(X_23,X_24),X))]]) ).
cnf(refute_0_353,plain,
( join(X,join(X_23,X_24)) != join(join(X_23,X_24),X)
| join(X,join(X_23,X_24)) = join(X_23,join(X_24,X)) ),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X),join(X_23,join(X_24,X))) )],[refute_0_20,refute_0_352]) ).
cnf(refute_0_354,plain,
join(X,join(X_23,X_24)) = join(X_23,join(X_24,X)),
inference(resolve,[$cnf( $equal(join(X,join(X_23,X_24)),join(join(X_23,X_24),X)) )],[refute_0_351,refute_0_353]) ).
cnf(refute_0_355,plain,
join(X_35,join(Y,X_37)) = join(Y,join(X_37,X_35)),
inference(subst,[],[refute_0_354:[bind(X,$fot(X_35)),bind(X_23,$fot(Y)),bind(X_24,$fot(X_37))]]) ).
cnf(refute_0_356,plain,
( join(X_35,join(Y,X_37)) != join(Y,join(X_37,X_35))
| join(Y,join(X_37,X_35)) = join(X_35,join(Y,X_37)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_35,join(Y,X_37)))),bind(Y0,$fot(join(Y,join(X_37,X_35))))]]) ).
cnf(refute_0_357,plain,
join(Y,join(X_37,X_35)) = join(X_35,join(Y,X_37)),
inference(resolve,[$cnf( $equal(join(X_35,join(Y,X_37)),join(Y,join(X_37,X_35))) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
( join(Y,join(X_37,X_35)) != join(X_35,join(Y,X_37))
| meet(join(X_37,X_35),join(Y,join(X_37,X_35))) != join(X_37,X_35)
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_37,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_37,X_35),join(Y,join(X_37,X_35))),join(X_37,X_35)) ),[0,1],$fot(join(X_35,join(Y,X_37)))]]) ).
cnf(refute_0_359,plain,
( meet(join(X_37,X_35),join(Y,join(X_37,X_35))) != join(X_37,X_35)
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_37,X_35) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_37,X_35)),join(X_35,join(Y,X_37))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_37,X_35),
inference(resolve,[$cnf( $equal(meet(join(X_37,X_35),join(Y,join(X_37,X_35))),join(X_37,X_35)) )],[refute_0_350,refute_0_359]) ).
cnf(refute_0_361,plain,
meet(X_37,join(Y,X_37)) = X_37,
inference(subst,[],[refute_0_18:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_362,plain,
join(X_35,meet(X_37,join(Y,X_37))) = join(X_35,meet(X_37,join(Y,X_37))),
introduced(tautology,[refl,[$fot(join(X_35,meet(X_37,join(Y,X_37))))]]) ).
cnf(refute_0_363,plain,
( join(X_35,meet(X_37,join(Y,X_37))) != join(X_35,meet(X_37,join(Y,X_37)))
| meet(X_37,join(Y,X_37)) != X_37
| join(X_35,meet(X_37,join(Y,X_37))) = join(X_35,X_37) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_35,meet(X_37,join(Y,X_37))),join(X_35,meet(X_37,join(Y,X_37)))) ),[1,1],$fot(X_37)]]) ).
cnf(refute_0_364,plain,
( meet(X_37,join(Y,X_37)) != X_37
| join(X_35,meet(X_37,join(Y,X_37))) = join(X_35,X_37) ),
inference(resolve,[$cnf( $equal(join(X_35,meet(X_37,join(Y,X_37))),join(X_35,meet(X_37,join(Y,X_37)))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
join(X_35,meet(X_37,join(Y,X_37))) = join(X_35,X_37),
inference(resolve,[$cnf( $equal(meet(X_37,join(Y,X_37)),X_37) )],[refute_0_361,refute_0_364]) ).
cnf(refute_0_366,plain,
join(X_47,X_46) = join(X_46,X_47),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_47)),bind(Y,$fot(X_46))]]) ).
cnf(refute_0_367,plain,
( join(X_47,X_46) != join(X_46,X_47)
| join(X_46,X_47) = join(X_47,X_46) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_47,X_46))),bind(Y0,$fot(join(X_46,X_47)))]]) ).
cnf(refute_0_368,plain,
join(X_46,X_47) = join(X_47,X_46),
inference(resolve,[$cnf( $equal(join(X_47,X_46),join(X_46,X_47)) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
( join(X_46,X_47) != join(X_47,X_46)
| join(X_46,meet(X_47,X_48)) != meet(join(X_46,X_47),join(X_46,X_48))
| join(X_46,meet(X_47,X_48)) = meet(join(X_47,X_46),join(X_46,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_46,meet(X_47,X_48)),meet(join(X_46,X_47),join(X_46,X_48))) ),[1,0],$fot(join(X_47,X_46))]]) ).
cnf(refute_0_370,plain,
( join(X_46,meet(X_47,X_48)) != meet(join(X_46,X_47),join(X_46,X_48))
| join(X_46,meet(X_47,X_48)) = meet(join(X_47,X_46),join(X_46,X_48)) ),
inference(resolve,[$cnf( $equal(join(X_46,X_47),join(X_47,X_46)) )],[refute_0_368,refute_0_369]) ).
cnf(refute_0_371,plain,
join(X_46,meet(X_47,X_48)) = meet(join(X_47,X_46),join(X_46,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,meet(X_47,X_48)),meet(join(X_46,X_47),join(X_46,X_48))) )],[refute_0_310,refute_0_370]) ).
cnf(refute_0_372,plain,
( join(X_46,meet(X_47,X_48)) != meet(join(X_47,X_46),join(X_46,X_48))
| meet(join(X_47,X_46),join(X_46,X_48)) = join(X_46,meet(X_47,X_48)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_46,meet(X_47,X_48)))),bind(Y0,$fot(meet(join(X_47,X_46),join(X_46,X_48))))]]) ).
cnf(refute_0_373,plain,
meet(join(X_47,X_46),join(X_46,X_48)) = join(X_46,meet(X_47,X_48)),
inference(resolve,[$cnf( $equal(join(X_46,meet(X_47,X_48)),meet(join(X_47,X_46),join(X_46,X_48))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_35,meet(X_37,join(Y,X_37))),
inference(subst,[],[refute_0_373:[bind(X_46,$fot(X_35)),bind(X_47,$fot(X_37)),bind(X_48,$fot(join(Y,X_37)))]]) ).
cnf(refute_0_375,plain,
( join(X_35,meet(X_37,join(Y,X_37))) != join(X_35,X_37)
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) != join(X_35,meet(X_37,join(Y,X_37)))
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_35,X_37) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(X_37,X_35),join(X_35,join(Y,X_37))))),bind(Y0,$fot(join(X_35,meet(X_37,join(Y,X_37))))),bind(Z0,$fot(join(X_35,X_37)))]]) ).
cnf(refute_0_376,plain,
( join(X_35,meet(X_37,join(Y,X_37))) != join(X_35,X_37)
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_35,X_37) ),
inference(resolve,[$cnf( $equal(meet(join(X_37,X_35),join(X_35,join(Y,X_37))),join(X_35,meet(X_37,join(Y,X_37)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
meet(join(X_37,X_35),join(X_35,join(Y,X_37))) = join(X_35,X_37),
inference(resolve,[$cnf( $equal(join(X_35,meet(X_37,join(Y,X_37))),join(X_35,X_37)) )],[refute_0_365,refute_0_376]) ).
cnf(refute_0_378,plain,
( meet(join(X_37,X_35),join(X_35,join(Y,X_37))) != join(X_35,X_37)
| meet(join(X_37,X_35),join(X_35,join(Y,X_37))) != join(X_37,X_35)
| join(X_35,X_37) = join(X_37,X_35) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(X_37,X_35),join(X_35,join(Y,X_37))),join(X_37,X_35)) ),[0],$fot(join(X_35,X_37))]]) ).
cnf(refute_0_379,plain,
( meet(join(X_37,X_35),join(X_35,join(Y,X_37))) != join(X_37,X_35)
| join(X_35,X_37) = join(X_37,X_35) ),
inference(resolve,[$cnf( $equal(meet(join(X_37,X_35),join(X_35,join(Y,X_37))),join(X_35,X_37)) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
join(X_35,X_37) = join(X_37,X_35),
inference(resolve,[$cnf( $equal(meet(join(X_37,X_35),join(X_35,join(Y,X_37))),join(X_37,X_35)) )],[refute_0_360,refute_0_379]) ).
cnf(refute_0_381,plain,
( join(X_35,X_37) != join(X_37,X_35)
| join(X_37,X_35) = join(X_35,X_37) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_35,X_37))),bind(Y0,$fot(join(X_37,X_35)))]]) ).
cnf(refute_0_382,plain,
join(X_37,X_35) = join(X_35,X_37),
inference(resolve,[$cnf( $equal(join(X_35,X_37),join(X_37,X_35)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
join(meet(join(Y,X_87),X_86),X_87) = join(X_87,meet(join(Y,X_87),X_86)),
inference(subst,[],[refute_0_382:[bind(X_35,$fot(X_87)),bind(X_37,$fot(meet(join(Y,X_87),X_86)))]]) ).
cnf(refute_0_384,plain,
( join(X_87,meet(join(Y,X_87),X_86)) != join(X_87,meet(Y,X_86))
| join(meet(join(Y,X_87),X_86),X_87) != join(X_87,meet(join(Y,X_87),X_86))
| join(meet(join(Y,X_87),X_86),X_87) = join(X_87,meet(Y,X_86)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(join(Y,X_87),X_86),X_87))),bind(Y0,$fot(join(X_87,meet(join(Y,X_87),X_86)))),bind(Z0,$fot(join(X_87,meet(Y,X_86))))]]) ).
cnf(refute_0_385,plain,
( join(X_87,meet(join(Y,X_87),X_86)) != join(X_87,meet(Y,X_86))
| join(meet(join(Y,X_87),X_86),X_87) = join(X_87,meet(Y,X_86)) ),
inference(resolve,[$cnf( $equal(join(meet(join(Y,X_87),X_86),X_87),join(X_87,meet(join(Y,X_87),X_86))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
join(meet(join(Y,X_87),X_86),X_87) = join(X_87,meet(Y,X_86)),
inference(resolve,[$cnf( $equal(join(X_87,meet(join(Y,X_87),X_86)),join(X_87,meet(Y,X_86))) )],[refute_0_349,refute_0_385]) ).
cnf(refute_0_387,plain,
( join(meet(join(Y,X_87),X_86),X_87) != join(X_87,meet(Y,X_86))
| meet(join(Y,X_87),join(X_86,X_87)) != join(meet(join(Y,X_87),X_86),X_87)
| meet(join(Y,X_87),join(X_86,X_87)) = join(X_87,meet(Y,X_86)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(Y,X_87),join(X_86,X_87)),join(meet(join(Y,X_87),X_86),X_87)) ),[1],$fot(join(X_87,meet(Y,X_86)))]]) ).
cnf(refute_0_388,plain,
( meet(join(Y,X_87),join(X_86,X_87)) != join(meet(join(Y,X_87),X_86),X_87)
| meet(join(Y,X_87),join(X_86,X_87)) = join(X_87,meet(Y,X_86)) ),
inference(resolve,[$cnf( $equal(join(meet(join(Y,X_87),X_86),X_87),join(X_87,meet(Y,X_86))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
meet(join(Y,X_87),join(X_86,X_87)) = join(X_87,meet(Y,X_86)),
inference(resolve,[$cnf( $equal(meet(join(Y,X_87),join(X_86,X_87)),join(meet(join(Y,X_87),X_86),X_87)) )],[refute_0_330,refute_0_388]) ).
cnf(refute_0_390,plain,
meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(meet(X_104,Y),Y)),
inference(subst,[],[refute_0_389:[bind(Y,$fot(meet(X_104,Y))),bind(X_86,$fot(Y)),bind(X_87,$fot(X_106))]]) ).
cnf(refute_0_391,plain,
( join(X_106,meet(meet(X_104,Y),Y)) != join(X_106,meet(Y,meet(X_104,Y)))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) != join(X_106,meet(meet(X_104,Y),Y))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,meet(X_104,Y))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(meet(X_104,Y),X_106),join(Y,X_106)))),bind(Y0,$fot(join(X_106,meet(meet(X_104,Y),Y)))),bind(Z0,$fot(join(X_106,meet(Y,meet(X_104,Y)))))]]) ).
cnf(refute_0_392,plain,
( join(X_106,meet(meet(X_104,Y),Y)) != join(X_106,meet(Y,meet(X_104,Y)))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,meet(X_104,Y))) ),
inference(resolve,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,X_106)),join(X_106,meet(meet(X_104,Y),Y))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,meet(X_104,Y))),
inference(resolve,[$cnf( $equal(join(X_106,meet(meet(X_104,Y),Y)),join(X_106,meet(Y,meet(X_104,Y)))) )],[refute_0_325,refute_0_392]) ).
cnf(refute_0_394,plain,
( join(X_106,meet(Y,meet(X_104,Y))) != join(X_106,meet(Y,X_104))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) != join(X_106,meet(Y,meet(X_104,Y)))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,X_104)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(join(meet(X_104,Y),X_106),join(Y,X_106)))),bind(Y0,$fot(join(X_106,meet(Y,meet(X_104,Y))))),bind(Z0,$fot(join(X_106,meet(Y,X_104))))]]) ).
cnf(refute_0_395,plain,
( join(X_106,meet(Y,meet(X_104,Y))) != join(X_106,meet(Y,X_104))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,X_104)) ),
inference(resolve,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,X_106)),join(X_106,meet(Y,meet(X_104,Y)))) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
meet(join(meet(X_104,Y),X_106),join(Y,X_106)) = join(X_106,meet(Y,X_104)),
inference(resolve,[$cnf( $equal(join(X_106,meet(Y,meet(X_104,Y))),join(X_106,meet(Y,X_104))) )],[refute_0_241,refute_0_395]) ).
cnf(refute_0_397,plain,
( meet(join(meet(X_104,Y),X_106),join(Y,X_106)) != join(X_106,meet(Y,X_104))
| meet(join(meet(X_104,Y),X_106),join(Y,X_106)) != join(meet(X_104,Y),X_106)
| join(X_106,meet(Y,X_104)) = join(meet(X_104,Y),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,X_106)),join(meet(X_104,Y),X_106)) ),[0],$fot(join(X_106,meet(Y,X_104)))]]) ).
cnf(refute_0_398,plain,
( meet(join(meet(X_104,Y),X_106),join(Y,X_106)) != join(meet(X_104,Y),X_106)
| join(X_106,meet(Y,X_104)) = join(meet(X_104,Y),X_106) ),
inference(resolve,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,X_106)),join(X_106,meet(Y,X_104))) )],[refute_0_396,refute_0_397]) ).
cnf(refute_0_399,plain,
join(X_106,meet(Y,X_104)) = join(meet(X_104,Y),X_106),
inference(resolve,[$cnf( $equal(meet(join(meet(X_104,Y),X_106),join(Y,X_106)),join(meet(X_104,Y),X_106)) )],[refute_0_236,refute_0_398]) ).
cnf(refute_0_400,plain,
join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) = join(meet(f(aa,dd),meet(X_149,f(bb,dd))),X_106),
inference(subst,[],[refute_0_399:[bind(Y,$fot(meet(X_149,f(bb,dd)))),bind(X_104,$fot(f(aa,dd)))]]) ).
cnf(refute_0_401,plain,
meet(X_34,f(bb,dd)) = meet(f(bb,dd),X_34),
inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_34)),bind(Y,$fot(f(bb,dd)))]]) ).
cnf(refute_0_402,plain,
( meet(X_34,f(bb,dd)) != meet(f(bb,dd),X_34)
| meet(f(bb,dd),X_34) = meet(X_34,f(bb,dd)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_34,f(bb,dd)))),bind(Y0,$fot(meet(f(bb,dd),X_34)))]]) ).
cnf(refute_0_403,plain,
meet(f(bb,dd),X_34) = meet(X_34,f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(X_34,f(bb,dd)),meet(f(bb,dd),X_34)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
( meet(f(aa,dd),meet(f(bb,dd),X_34)) != meet(f(bb,dd),meet(f(cc,dd),X_34))
| meet(f(bb,dd),X_34) != meet(X_34,f(bb,dd))
| meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(bb,dd),meet(f(cc,dd),X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),X_34)),meet(f(bb,dd),meet(f(cc,dd),X_34))) ),[0,1],$fot(meet(X_34,f(bb,dd)))]]) ).
cnf(refute_0_405,plain,
( meet(f(aa,dd),meet(f(bb,dd),X_34)) != meet(f(bb,dd),meet(f(cc,dd),X_34))
| meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(bb,dd),meet(f(cc,dd),X_34)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),X_34),meet(X_34,f(bb,dd))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(bb,dd),meet(f(cc,dd),X_34)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),X_34)),meet(f(bb,dd),meet(f(cc,dd),X_34))) )],[refute_0_67,refute_0_405]) ).
cnf(refute_0_407,plain,
( meet(f(aa,dd),meet(X_34,f(bb,dd))) != meet(f(bb,dd),meet(f(cc,dd),X_34))
| meet(f(bb,dd),meet(f(cc,dd),X_34)) != meet(f(aa,dd),meet(f(bb,dd),X_34))
| meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(aa,dd),meet(f(bb,dd),X_34)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(f(aa,dd),meet(X_34,f(bb,dd))),meet(f(aa,dd),meet(f(bb,dd),X_34))) ),[0],$fot(meet(f(bb,dd),meet(f(cc,dd),X_34)))]]) ).
cnf(refute_0_408,plain,
( meet(f(aa,dd),meet(X_34,f(bb,dd))) != meet(f(bb,dd),meet(f(cc,dd),X_34))
| meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(aa,dd),meet(f(bb,dd),X_34)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),meet(f(cc,dd),X_34)),meet(f(aa,dd),meet(f(bb,dd),X_34))) )],[refute_0_69,refute_0_407]) ).
cnf(refute_0_409,plain,
meet(f(aa,dd),meet(X_34,f(bb,dd))) = meet(f(aa,dd),meet(f(bb,dd),X_34)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(X_34,f(bb,dd))),meet(f(bb,dd),meet(f(cc,dd),X_34))) )],[refute_0_406,refute_0_408]) ).
cnf(refute_0_410,plain,
meet(f(aa,dd),meet(X_149,f(bb,dd))) = meet(f(aa,dd),meet(f(bb,dd),X_149)),
inference(subst,[],[refute_0_409:[bind(X_34,$fot(X_149))]]) ).
cnf(refute_0_411,plain,
( join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) != join(meet(f(aa,dd),meet(X_149,f(bb,dd))),X_106)
| meet(f(aa,dd),meet(X_149,f(bb,dd))) != meet(f(aa,dd),meet(f(bb,dd),X_149))
| join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))),join(meet(f(aa,dd),meet(X_149,f(bb,dd))),X_106)) ),[1,0],$fot(meet(f(aa,dd),meet(f(bb,dd),X_149)))]]) ).
cnf(refute_0_412,plain,
( join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) != join(meet(f(aa,dd),meet(X_149,f(bb,dd))),X_106)
| join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(X_149,f(bb,dd))),meet(f(aa,dd),meet(f(bb,dd),X_149))) )],[refute_0_410,refute_0_411]) ).
cnf(refute_0_413,plain,
join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106),
inference(resolve,[$cnf( $equal(join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))),join(meet(f(aa,dd),meet(X_149,f(bb,dd))),X_106)) )],[refute_0_400,refute_0_412]) ).
cnf(refute_0_414,plain,
join(X_19,join(X_18,X_19)) = join(X_19,X_18),
inference(subst,[],[refute_0_340:[bind(Y,$fot(X_18)),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_415,plain,
join(X_19,X_18) = join(X_18,X_19),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_19)),bind(Y,$fot(X_18))]]) ).
cnf(refute_0_416,plain,
( join(X_19,X_18) != join(X_18,X_19)
| join(X_18,X_19) = join(X_19,X_18) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_19,X_18))),bind(Y0,$fot(join(X_18,X_19)))]]) ).
cnf(refute_0_417,plain,
join(X_18,X_19) = join(X_19,X_18),
inference(resolve,[$cnf( $equal(join(X_19,X_18),join(X_18,X_19)) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
( join(X_18,X_19) != join(X_19,X_18)
| join(X_19,join(X_18,X_19)) != join(X_19,X_18)
| join(X_19,join(X_19,X_18)) = join(X_19,X_18) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_19,join(X_18,X_19)),join(X_19,X_18)) ),[0,1],$fot(join(X_19,X_18))]]) ).
cnf(refute_0_419,plain,
( join(X_19,join(X_18,X_19)) != join(X_19,X_18)
| join(X_19,join(X_19,X_18)) = join(X_19,X_18) ),
inference(resolve,[$cnf( $equal(join(X_18,X_19),join(X_19,X_18)) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
join(X_19,join(X_19,X_18)) = join(X_19,X_18),
inference(resolve,[$cnf( $equal(join(X_19,join(X_18,X_19)),join(X_19,X_18)) )],[refute_0_414,refute_0_419]) ).
cnf(refute_0_421,plain,
join(X_19,join(X_19,meet(X_129,X_130))) = join(X_19,meet(X_129,X_130)),
inference(subst,[],[refute_0_420:[bind(X_18,$fot(meet(X_129,X_130)))]]) ).
cnf(refute_0_422,plain,
join(X_19,meet(X_129,X_130)) = join(meet(X_130,X_129),X_19),
inference(subst,[],[refute_0_399:[bind(Y,$fot(X_129)),bind(X_104,$fot(X_130)),bind(X_106,$fot(X_19))]]) ).
cnf(refute_0_423,plain,
( join(X_19,join(X_19,meet(X_129,X_130))) != join(X_19,meet(X_129,X_130))
| join(X_19,meet(X_129,X_130)) != join(meet(X_130,X_129),X_19)
| join(X_19,join(meet(X_130,X_129),X_19)) = join(X_19,meet(X_129,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_19,join(X_19,meet(X_129,X_130))),join(X_19,meet(X_129,X_130))) ),[0,1],$fot(join(meet(X_130,X_129),X_19))]]) ).
cnf(refute_0_424,plain,
( join(X_19,join(X_19,meet(X_129,X_130))) != join(X_19,meet(X_129,X_130))
| join(X_19,join(meet(X_130,X_129),X_19)) = join(X_19,meet(X_129,X_130)) ),
inference(resolve,[$cnf( $equal(join(X_19,meet(X_129,X_130)),join(meet(X_130,X_129),X_19)) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
join(X_19,join(meet(X_130,X_129),X_19)) = join(X_19,meet(X_129,X_130)),
inference(resolve,[$cnf( $equal(join(X_19,join(X_19,meet(X_129,X_130))),join(X_19,meet(X_129,X_130))) )],[refute_0_421,refute_0_424]) ).
cnf(refute_0_426,plain,
join(X_19,join(meet(X_130,X_129),X_19)) = join(X_19,meet(X_130,X_129)),
inference(subst,[],[refute_0_340:[bind(Y,$fot(meet(X_130,X_129))),bind(X_13,$fot(X_19))]]) ).
cnf(refute_0_427,plain,
( join(X_19,join(meet(X_130,X_129),X_19)) != join(X_19,meet(X_129,X_130))
| join(X_19,join(meet(X_130,X_129),X_19)) != join(X_19,meet(X_130,X_129))
| join(X_19,meet(X_130,X_129)) = join(X_19,meet(X_129,X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_19,join(meet(X_130,X_129),X_19)),join(X_19,meet(X_129,X_130))) ),[0],$fot(join(X_19,meet(X_130,X_129)))]]) ).
cnf(refute_0_428,plain,
( join(X_19,join(meet(X_130,X_129),X_19)) != join(X_19,meet(X_129,X_130))
| join(X_19,meet(X_130,X_129)) = join(X_19,meet(X_129,X_130)) ),
inference(resolve,[$cnf( $equal(join(X_19,join(meet(X_130,X_129),X_19)),join(X_19,meet(X_130,X_129))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
join(X_19,meet(X_130,X_129)) = join(X_19,meet(X_129,X_130)),
inference(resolve,[$cnf( $equal(join(X_19,join(meet(X_130,X_129),X_19)),join(X_19,meet(X_129,X_130))) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
( join(X_19,meet(X_130,X_129)) != join(X_19,meet(X_129,X_130))
| join(X_19,meet(X_129,X_130)) = join(X_19,meet(X_130,X_129)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_19,meet(X_130,X_129)))),bind(Y0,$fot(join(X_19,meet(X_129,X_130))))]]) ).
cnf(refute_0_431,plain,
join(X_19,meet(X_129,X_130)) = join(X_19,meet(X_130,X_129)),
inference(resolve,[$cnf( $equal(join(X_19,meet(X_130,X_129)),join(X_19,meet(X_129,X_130))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) = join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd)))),
inference(subst,[],[refute_0_431:[bind(X_129,$fot(meet(X_149,f(bb,dd)))),bind(X_130,$fot(f(aa,dd))),bind(X_19,$fot(X_106))]]) ).
cnf(refute_0_433,plain,
( join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) != join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd))))
| join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) != join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106)
| join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd)))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))),join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106)) ),[0],$fot(join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd)))))]]) ).
cnf(refute_0_434,plain,
( join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))) != join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106)
| join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd)))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106) ),
inference(resolve,[$cnf( $equal(join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))),join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd))))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
join(X_106,meet(f(aa,dd),meet(X_149,f(bb,dd)))) = join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106),
inference(resolve,[$cnf( $equal(join(X_106,meet(meet(X_149,f(bb,dd)),f(aa,dd))),join(meet(f(aa,dd),meet(f(bb,dd),X_149)),X_106)) )],[refute_0_413,refute_0_434]) ).
cnf(refute_0_436,plain,
join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),
inference(subst,[],[refute_0_435:[bind(X_106,$fot(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))),bind(X_149,$fot(f(aa,dd)))]]) ).
cnf(refute_0_437,plain,
( join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) != join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))))),bind(Y0,$fot(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))))),bind(Z0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))))]]) ).
cnf(refute_0_438,plain,
( join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))),join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))) )],[refute_0_436,refute_0_437]) ).
cnf(refute_0_439,plain,
join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))) )],[refute_0_224,refute_0_438]) ).
cnf(refute_0_440,plain,
( join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))
| join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) ),[0],$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))))]]) ).
cnf(refute_0_441,plain,
( join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y)))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))) != meet(f(cc,dd),join(f(aa,dd),Y))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),Y))) ),[0],$fot(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))))]]) ).
cnf(refute_0_443,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),Y)) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(cc,dd),join(f(aa,dd),Y))) )],[refute_0_124,refute_0_442]) ).
cnf(refute_0_444,plain,
( join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))) != meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),Y)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_441,refute_0_443]) ).
cnf(refute_0_445,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),Y)),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd)))),meet(f(aa,dd),meet(f(aa,dd),f(bb,dd)))),meet(f(cc,dd),join(f(aa,dd),meet(Y,f(cc,dd))))) )],[refute_0_103,refute_0_444]) ).
cnf(refute_0_446,plain,
join(join(X_28,X_30),join(Y,join(X_28,X_30))) = join(join(X_28,X_30),Y),
inference(subst,[],[refute_0_340:[bind(X_13,$fot(join(X_28,X_30)))]]) ).
cnf(refute_0_447,plain,
join(join(X,Y),join(Y,X_26)) = join(X,join(Y,join(Y,X_26))),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(join(Y,X_26)))]]) ).
cnf(refute_0_448,plain,
join(Y,join(Y,X_26)) = join(Y,X_26),
inference(subst,[],[refute_0_420:[bind(X_18,$fot(X_26)),bind(X_19,$fot(Y))]]) ).
cnf(refute_0_449,plain,
( join(Y,join(Y,X_26)) != join(Y,X_26)
| join(join(X,Y),join(Y,X_26)) != join(X,join(Y,join(Y,X_26)))
| join(join(X,Y),join(Y,X_26)) = join(X,join(Y,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(X,join(Y,join(Y,X_26)))) ),[1,1],$fot(join(Y,X_26))]]) ).
cnf(refute_0_450,plain,
( join(join(X,Y),join(Y,X_26)) != join(X,join(Y,join(Y,X_26)))
| join(join(X,Y),join(Y,X_26)) = join(X,join(Y,X_26)) ),
inference(resolve,[$cnf( $equal(join(Y,join(Y,X_26)),join(Y,X_26)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
join(join(X,Y),join(Y,X_26)) = join(X,join(Y,X_26)),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(X,join(Y,join(Y,X_26)))) )],[refute_0_447,refute_0_450]) ).
cnf(refute_0_452,plain,
join(join(X_23,join(Y,X_23)),X_25) = join(X_23,join(join(Y,X_23),X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Y,$fot(join(Y,X_23))),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_453,plain,
join(X_23,join(Y,X_23)) = join(X_23,Y),
inference(subst,[],[refute_0_340:[bind(X_13,$fot(X_23))]]) ).
cnf(refute_0_454,plain,
( join(X_23,join(Y,X_23)) != join(X_23,Y)
| join(join(X_23,join(Y,X_23)),X_25) != join(X_23,join(join(Y,X_23),X_25))
| join(join(X_23,Y),X_25) = join(X_23,join(join(Y,X_23),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,join(Y,X_23)),X_25),join(X_23,join(join(Y,X_23),X_25))) ),[0,0],$fot(join(X_23,Y))]]) ).
cnf(refute_0_455,plain,
( join(join(X_23,join(Y,X_23)),X_25) != join(X_23,join(join(Y,X_23),X_25))
| join(join(X_23,Y),X_25) = join(X_23,join(join(Y,X_23),X_25)) ),
inference(resolve,[$cnf( $equal(join(X_23,join(Y,X_23)),join(X_23,Y)) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
join(join(X_23,Y),X_25) = join(X_23,join(join(Y,X_23),X_25)),
inference(resolve,[$cnf( $equal(join(join(X_23,join(Y,X_23)),X_25),join(X_23,join(join(Y,X_23),X_25))) )],[refute_0_452,refute_0_455]) ).
cnf(refute_0_457,plain,
join(join(X_23,Y),X_25) = join(X_23,join(Y,X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_458,plain,
( join(join(X_23,Y),X_25) != join(X_23,join(Y,X_25))
| join(join(X_23,Y),X_25) != join(X_23,join(join(Y,X_23),X_25))
| join(X_23,join(Y,X_25)) = join(X_23,join(join(Y,X_23),X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,Y),X_25),join(X_23,join(join(Y,X_23),X_25))) ),[0],$fot(join(X_23,join(Y,X_25)))]]) ).
cnf(refute_0_459,plain,
( join(join(X_23,Y),X_25) != join(X_23,join(join(Y,X_23),X_25))
| join(X_23,join(Y,X_25)) = join(X_23,join(join(Y,X_23),X_25)) ),
inference(resolve,[$cnf( $equal(join(join(X_23,Y),X_25),join(X_23,join(Y,X_25))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
join(join(Y,X_23),X_25) = join(Y,join(X_23,X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(Y)),bind(Y,$fot(X_23)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_461,plain,
join(X_23,join(join(Y,X_23),X_25)) = join(X_23,join(join(Y,X_23),X_25)),
introduced(tautology,[refl,[$fot(join(X_23,join(join(Y,X_23),X_25)))]]) ).
cnf(refute_0_462,plain,
( join(X_23,join(join(Y,X_23),X_25)) != join(X_23,join(join(Y,X_23),X_25))
| join(join(Y,X_23),X_25) != join(Y,join(X_23,X_25))
| join(X_23,join(join(Y,X_23),X_25)) = join(X_23,join(Y,join(X_23,X_25))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_23,join(join(Y,X_23),X_25)),join(X_23,join(join(Y,X_23),X_25))) ),[1,1],$fot(join(Y,join(X_23,X_25)))]]) ).
cnf(refute_0_463,plain,
( join(join(Y,X_23),X_25) != join(Y,join(X_23,X_25))
| join(X_23,join(join(Y,X_23),X_25)) = join(X_23,join(Y,join(X_23,X_25))) ),
inference(resolve,[$cnf( $equal(join(X_23,join(join(Y,X_23),X_25)),join(X_23,join(join(Y,X_23),X_25))) )],[refute_0_461,refute_0_462]) ).
cnf(refute_0_464,plain,
join(X_23,join(join(Y,X_23),X_25)) = join(X_23,join(Y,join(X_23,X_25))),
inference(resolve,[$cnf( $equal(join(join(Y,X_23),X_25),join(Y,join(X_23,X_25))) )],[refute_0_460,refute_0_463]) ).
cnf(refute_0_465,plain,
( join(X_23,join(Y,X_25)) != join(X_23,join(join(Y,X_23),X_25))
| join(X_23,join(join(Y,X_23),X_25)) != join(X_23,join(Y,join(X_23,X_25)))
| join(X_23,join(Y,X_25)) = join(X_23,join(Y,join(X_23,X_25))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_23,join(Y,X_25)),join(X_23,join(Y,join(X_23,X_25)))) ),[0],$fot(join(X_23,join(join(Y,X_23),X_25)))]]) ).
cnf(refute_0_466,plain,
( join(X_23,join(Y,X_25)) != join(X_23,join(join(Y,X_23),X_25))
| join(X_23,join(Y,X_25)) = join(X_23,join(Y,join(X_23,X_25))) ),
inference(resolve,[$cnf( $equal(join(X_23,join(join(Y,X_23),X_25)),join(X_23,join(Y,join(X_23,X_25)))) )],[refute_0_464,refute_0_465]) ).
cnf(refute_0_467,plain,
( join(join(X_23,Y),X_25) != join(X_23,join(join(Y,X_23),X_25))
| join(X_23,join(Y,X_25)) = join(X_23,join(Y,join(X_23,X_25))) ),
inference(resolve,[$cnf( $equal(join(X_23,join(Y,X_25)),join(X_23,join(join(Y,X_23),X_25))) )],[refute_0_459,refute_0_466]) ).
cnf(refute_0_468,plain,
join(X_23,join(Y,X_25)) = join(X_23,join(Y,join(X_23,X_25))),
inference(resolve,[$cnf( $equal(join(join(X_23,Y),X_25),join(X_23,join(join(Y,X_23),X_25))) )],[refute_0_456,refute_0_467]) ).
cnf(refute_0_469,plain,
( join(X_23,join(Y,X_25)) != join(X_23,join(Y,join(X_23,X_25)))
| join(X_23,join(Y,join(X_23,X_25))) = join(X_23,join(Y,X_25)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_23,join(Y,X_25)))),bind(Y0,$fot(join(X_23,join(Y,join(X_23,X_25)))))]]) ).
cnf(refute_0_470,plain,
join(X_23,join(Y,join(X_23,X_25))) = join(X_23,join(Y,X_25)),
inference(resolve,[$cnf( $equal(join(X_23,join(Y,X_25)),join(X_23,join(Y,join(X_23,X_25)))) )],[refute_0_468,refute_0_469]) ).
cnf(refute_0_471,plain,
join(Y,join(X,join(Y,X_26))) = join(Y,join(X,X_26)),
inference(subst,[],[refute_0_470:[bind(Y,$fot(X)),bind(X_23,$fot(Y)),bind(X_25,$fot(X_26))]]) ).
cnf(refute_0_472,plain,
join(join(X,Y),X_26) = join(X,join(Y,X_26)),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_26))]]) ).
cnf(refute_0_473,plain,
join(Y,join(join(X,Y),X_26)) = join(Y,join(join(X,Y),X_26)),
introduced(tautology,[refl,[$fot(join(Y,join(join(X,Y),X_26)))]]) ).
cnf(refute_0_474,plain,
( join(Y,join(join(X,Y),X_26)) != join(Y,join(join(X,Y),X_26))
| join(join(X,Y),X_26) != join(X,join(Y,X_26))
| join(Y,join(join(X,Y),X_26)) = join(Y,join(X,join(Y,X_26))) ),
introduced(tautology,[equality,[$cnf( $equal(join(Y,join(join(X,Y),X_26)),join(Y,join(join(X,Y),X_26))) ),[1,1],$fot(join(X,join(Y,X_26)))]]) ).
cnf(refute_0_475,plain,
( join(join(X,Y),X_26) != join(X,join(Y,X_26))
| join(Y,join(join(X,Y),X_26)) = join(Y,join(X,join(Y,X_26))) ),
inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_26)),join(Y,join(join(X,Y),X_26))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
join(Y,join(join(X,Y),X_26)) = join(Y,join(X,join(Y,X_26))),
inference(resolve,[$cnf( $equal(join(join(X,Y),X_26),join(X,join(Y,X_26))) )],[refute_0_472,refute_0_475]) ).
cnf(refute_0_477,plain,
( join(Y,join(X,join(Y,X_26))) != join(Y,join(X,X_26))
| join(Y,join(join(X,Y),X_26)) != join(Y,join(X,join(Y,X_26)))
| join(Y,join(join(X,Y),X_26)) = join(Y,join(X,X_26)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(Y,join(join(X,Y),X_26)))),bind(Y0,$fot(join(Y,join(X,join(Y,X_26))))),bind(Z0,$fot(join(Y,join(X,X_26))))]]) ).
cnf(refute_0_478,plain,
( join(Y,join(X,join(Y,X_26))) != join(Y,join(X,X_26))
| join(Y,join(join(X,Y),X_26)) = join(Y,join(X,X_26)) ),
inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_26)),join(Y,join(X,join(Y,X_26)))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
join(Y,join(join(X,Y),X_26)) = join(Y,join(X,X_26)),
inference(resolve,[$cnf( $equal(join(Y,join(X,join(Y,X_26))),join(Y,join(X,X_26))) )],[refute_0_471,refute_0_478]) ).
cnf(refute_0_480,plain,
join(join(X_23,X_24),X_25) = join(X_23,join(X_24,X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_481,plain,
join(X_24,X_23) = join(X_23,X_24),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(X_23))]]) ).
cnf(refute_0_482,plain,
( join(X_24,X_23) != join(X_23,X_24)
| join(X_23,X_24) = join(X_24,X_23) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_24,X_23))),bind(Y0,$fot(join(X_23,X_24)))]]) ).
cnf(refute_0_483,plain,
join(X_23,X_24) = join(X_24,X_23),
inference(resolve,[$cnf( $equal(join(X_24,X_23),join(X_23,X_24)) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( join(X_23,X_24) != join(X_24,X_23)
| join(join(X_23,X_24),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_24,X_23),X_25) = join(X_23,join(X_24,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_24,X_25))) ),[0,0],$fot(join(X_24,X_23))]]) ).
cnf(refute_0_485,plain,
( join(join(X_23,X_24),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_24,X_23),X_25) = join(X_23,join(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(join(X_23,X_24),join(X_24,X_23)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
join(join(X_24,X_23),X_25) = join(X_23,join(X_24,X_25)),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_24,X_25))) )],[refute_0_480,refute_0_485]) ).
cnf(refute_0_487,plain,
join(join(X_24,X_23),X_25) = join(X_24,join(X_23,X_25)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(X_23)),bind(Z,$fot(X_25))]]) ).
cnf(refute_0_488,plain,
( join(join(X_24,X_23),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_24,X_23),X_25) != join(X_24,join(X_23,X_25))
| join(X_24,join(X_23,X_25)) = join(X_23,join(X_24,X_25)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_23),X_25),join(X_23,join(X_24,X_25))) ),[0],$fot(join(X_24,join(X_23,X_25)))]]) ).
cnf(refute_0_489,plain,
( join(join(X_24,X_23),X_25) != join(X_23,join(X_24,X_25))
| join(X_24,join(X_23,X_25)) = join(X_23,join(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(join(join(X_24,X_23),X_25),join(X_24,join(X_23,X_25))) )],[refute_0_487,refute_0_488]) ).
cnf(refute_0_490,plain,
join(X_24,join(X_23,X_25)) = join(X_23,join(X_24,X_25)),
inference(resolve,[$cnf( $equal(join(join(X_24,X_23),X_25),join(X_23,join(X_24,X_25))) )],[refute_0_486,refute_0_489]) ).
cnf(refute_0_491,plain,
( join(X_24,join(X_23,X_25)) != join(X_23,join(X_24,X_25))
| join(X_23,join(X_24,X_25)) = join(X_24,join(X_23,X_25)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_24,join(X_23,X_25)))),bind(Y0,$fot(join(X_23,join(X_24,X_25))))]]) ).
cnf(refute_0_492,plain,
join(X_23,join(X_24,X_25)) = join(X_24,join(X_23,X_25)),
inference(resolve,[$cnf( $equal(join(X_24,join(X_23,X_25)),join(X_23,join(X_24,X_25))) )],[refute_0_490,refute_0_491]) ).
cnf(refute_0_493,plain,
join(join(X,Y),join(Y,X_26)) = join(Y,join(join(X,Y),X_26)),
inference(subst,[],[refute_0_492:[bind(X_23,$fot(join(X,Y))),bind(X_24,$fot(Y)),bind(X_25,$fot(X_26))]]) ).
cnf(refute_0_494,plain,
( join(Y,join(join(X,Y),X_26)) != join(Y,join(X,X_26))
| join(join(X,Y),join(Y,X_26)) != join(Y,join(join(X,Y),X_26))
| join(join(X,Y),join(Y,X_26)) = join(Y,join(X,X_26)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(join(X,Y),join(Y,X_26)))),bind(Y0,$fot(join(Y,join(join(X,Y),X_26)))),bind(Z0,$fot(join(Y,join(X,X_26))))]]) ).
cnf(refute_0_495,plain,
( join(Y,join(join(X,Y),X_26)) != join(Y,join(X,X_26))
| join(join(X,Y),join(Y,X_26)) = join(Y,join(X,X_26)) ),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(Y,join(join(X,Y),X_26))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
join(join(X,Y),join(Y,X_26)) = join(Y,join(X,X_26)),
inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_26)),join(Y,join(X,X_26))) )],[refute_0_479,refute_0_495]) ).
cnf(refute_0_497,plain,
( join(join(X,Y),join(Y,X_26)) != join(X,join(Y,X_26))
| join(join(X,Y),join(Y,X_26)) != join(Y,join(X,X_26))
| join(Y,join(X,X_26)) = join(X,join(Y,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(X,join(Y,X_26))) ),[0],$fot(join(Y,join(X,X_26)))]]) ).
cnf(refute_0_498,plain,
( join(join(X,Y),join(Y,X_26)) != join(X,join(Y,X_26))
| join(Y,join(X,X_26)) = join(X,join(Y,X_26)) ),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(Y,join(X,X_26))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
join(Y,join(X,X_26)) = join(X,join(Y,X_26)),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_26)),join(X,join(Y,X_26))) )],[refute_0_451,refute_0_498]) ).
cnf(refute_0_500,plain,
join(Y,join(X_28,X_30)) = join(X_28,join(Y,X_30)),
inference(subst,[],[refute_0_499:[bind(X,$fot(X_28)),bind(X_26,$fot(X_30))]]) ).
cnf(refute_0_501,plain,
( join(Y,join(X_28,X_30)) != join(X_28,join(Y,X_30))
| join(join(X_28,X_30),join(Y,join(X_28,X_30))) != join(join(X_28,X_30),Y)
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(join(X_28,X_30),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_28,X_30),join(Y,join(X_28,X_30))),join(join(X_28,X_30),Y)) ),[0,1],$fot(join(X_28,join(Y,X_30)))]]) ).
cnf(refute_0_502,plain,
( join(join(X_28,X_30),join(Y,join(X_28,X_30))) != join(join(X_28,X_30),Y)
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(join(X_28,X_30),Y) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_28,X_30)),join(X_28,join(Y,X_30))) )],[refute_0_500,refute_0_501]) ).
cnf(refute_0_503,plain,
join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(join(X_28,X_30),Y),
inference(resolve,[$cnf( $equal(join(join(X_28,X_30),join(Y,join(X_28,X_30))),join(join(X_28,X_30),Y)) )],[refute_0_446,refute_0_502]) ).
cnf(refute_0_504,plain,
join(X_13,join(join(X_23,X_24),X_13)) = join(X_13,join(X_23,X_24)),
inference(subst,[],[refute_0_340:[bind(Y,$fot(join(X_23,X_24)))]]) ).
cnf(refute_0_505,plain,
join(join(X_23,X_24),X_13) = join(X_23,join(X_24,X_13)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_23)),bind(Y,$fot(X_24)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_506,plain,
( join(X_13,join(join(X_23,X_24),X_13)) != join(X_13,join(X_23,X_24))
| join(join(X_23,X_24),X_13) != join(X_23,join(X_24,X_13))
| join(X_13,join(X_23,join(X_24,X_13))) = join(X_13,join(X_23,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_13,join(join(X_23,X_24),X_13)),join(X_13,join(X_23,X_24))) ),[0,1],$fot(join(X_23,join(X_24,X_13)))]]) ).
cnf(refute_0_507,plain,
( join(X_13,join(join(X_23,X_24),X_13)) != join(X_13,join(X_23,X_24))
| join(X_13,join(X_23,join(X_24,X_13))) = join(X_13,join(X_23,X_24)) ),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X_13),join(X_23,join(X_24,X_13))) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
join(X_13,join(X_23,join(X_24,X_13))) = join(X_13,join(X_23,X_24)),
inference(resolve,[$cnf( $equal(join(X_13,join(join(X_23,X_24),X_13)),join(X_13,join(X_23,X_24))) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
join(X_28,join(Y,join(X_30,X_28))) = join(X_28,join(Y,X_30)),
inference(subst,[],[refute_0_508:[bind(X_13,$fot(X_28)),bind(X_23,$fot(Y)),bind(X_24,$fot(X_30))]]) ).
cnf(refute_0_510,plain,
join(X_30,join(X_28,X_30)) = join(X_30,X_28),
inference(subst,[],[refute_0_340:[bind(Y,$fot(X_28)),bind(X_13,$fot(X_30))]]) ).
cnf(refute_0_511,plain,
join(Y,join(X_30,join(X_28,X_30))) = join(Y,join(X_30,join(X_28,X_30))),
introduced(tautology,[refl,[$fot(join(Y,join(X_30,join(X_28,X_30))))]]) ).
cnf(refute_0_512,plain,
( join(Y,join(X_30,join(X_28,X_30))) != join(Y,join(X_30,join(X_28,X_30)))
| join(X_30,join(X_28,X_30)) != join(X_30,X_28)
| join(Y,join(X_30,join(X_28,X_30))) = join(Y,join(X_30,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(join(Y,join(X_30,join(X_28,X_30))),join(Y,join(X_30,join(X_28,X_30)))) ),[1,1],$fot(join(X_30,X_28))]]) ).
cnf(refute_0_513,plain,
( join(X_30,join(X_28,X_30)) != join(X_30,X_28)
| join(Y,join(X_30,join(X_28,X_30))) = join(Y,join(X_30,X_28)) ),
inference(resolve,[$cnf( $equal(join(Y,join(X_30,join(X_28,X_30))),join(Y,join(X_30,join(X_28,X_30)))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
join(Y,join(X_30,join(X_28,X_30))) = join(Y,join(X_30,X_28)),
inference(resolve,[$cnf( $equal(join(X_30,join(X_28,X_30)),join(X_30,X_28)) )],[refute_0_510,refute_0_513]) ).
cnf(refute_0_515,plain,
join(X_25,X_24) = join(X_24,X_25),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_24))]]) ).
cnf(refute_0_516,plain,
( join(X_25,X_24) != join(X_24,X_25)
| join(X_24,X_25) = join(X_25,X_24) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_25,X_24))),bind(Y0,$fot(join(X_24,X_25)))]]) ).
cnf(refute_0_517,plain,
join(X_24,X_25) = join(X_25,X_24),
inference(resolve,[$cnf( $equal(join(X_25,X_24),join(X_24,X_25)) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
( join(X_24,X_25) != join(X_25,X_24)
| join(join(X_23,X_24),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_23,X_24),X_25) = join(X_23,join(X_25,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_24,X_25))) ),[1,1],$fot(join(X_25,X_24))]]) ).
cnf(refute_0_519,plain,
( join(join(X_23,X_24),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_23,X_24),X_25) = join(X_23,join(X_25,X_24)) ),
inference(resolve,[$cnf( $equal(join(X_24,X_25),join(X_25,X_24)) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
join(join(X_23,X_24),X_25) = join(X_23,join(X_25,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_24,X_25))) )],[refute_0_480,refute_0_519]) ).
cnf(refute_0_521,plain,
( join(join(X_23,X_24),X_25) != join(X_23,join(X_24,X_25))
| join(join(X_23,X_24),X_25) != join(X_23,join(X_25,X_24))
| join(X_23,join(X_24,X_25)) = join(X_23,join(X_25,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_25,X_24))) ),[0],$fot(join(X_23,join(X_24,X_25)))]]) ).
cnf(refute_0_522,plain,
( join(join(X_23,X_24),X_25) != join(X_23,join(X_25,X_24))
| join(X_23,join(X_24,X_25)) = join(X_23,join(X_25,X_24)) ),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_24,X_25))) )],[refute_0_480,refute_0_521]) ).
cnf(refute_0_523,plain,
join(X_23,join(X_24,X_25)) = join(X_23,join(X_25,X_24)),
inference(resolve,[$cnf( $equal(join(join(X_23,X_24),X_25),join(X_23,join(X_25,X_24))) )],[refute_0_520,refute_0_522]) ).
cnf(refute_0_524,plain,
( join(X_23,join(X_24,X_25)) != join(X_23,join(X_25,X_24))
| join(X_23,join(X_25,X_24)) = join(X_23,join(X_24,X_25)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_23,join(X_24,X_25)))),bind(Y0,$fot(join(X_23,join(X_25,X_24))))]]) ).
cnf(refute_0_525,plain,
join(X_23,join(X_25,X_24)) = join(X_23,join(X_24,X_25)),
inference(resolve,[$cnf( $equal(join(X_23,join(X_24,X_25)),join(X_23,join(X_25,X_24))) )],[refute_0_523,refute_0_524]) ).
cnf(refute_0_526,plain,
join(Y,join(join(X_28,X_30),X_30)) = join(Y,join(X_30,join(X_28,X_30))),
inference(subst,[],[refute_0_525:[bind(X_23,$fot(Y)),bind(X_24,$fot(X_30)),bind(X_25,$fot(join(X_28,X_30)))]]) ).
cnf(refute_0_527,plain,
( join(Y,join(X_30,join(X_28,X_30))) != join(Y,join(X_30,X_28))
| join(Y,join(join(X_28,X_30),X_30)) != join(Y,join(X_30,join(X_28,X_30)))
| join(Y,join(join(X_28,X_30),X_30)) = join(Y,join(X_30,X_28)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(Y,join(join(X_28,X_30),X_30)))),bind(Y0,$fot(join(Y,join(X_30,join(X_28,X_30))))),bind(Z0,$fot(join(Y,join(X_30,X_28))))]]) ).
cnf(refute_0_528,plain,
( join(Y,join(X_30,join(X_28,X_30))) != join(Y,join(X_30,X_28))
| join(Y,join(join(X_28,X_30),X_30)) = join(Y,join(X_30,X_28)) ),
inference(resolve,[$cnf( $equal(join(Y,join(join(X_28,X_30),X_30)),join(Y,join(X_30,join(X_28,X_30)))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
join(Y,join(join(X_28,X_30),X_30)) = join(Y,join(X_30,X_28)),
inference(resolve,[$cnf( $equal(join(Y,join(X_30,join(X_28,X_30))),join(Y,join(X_30,X_28))) )],[refute_0_514,refute_0_528]) ).
cnf(refute_0_530,plain,
join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,join(join(X_28,X_30),X_30))),
introduced(tautology,[refl,[$fot(join(X_28,join(Y,join(join(X_28,X_30),X_30))))]]) ).
cnf(refute_0_531,plain,
( join(Y,join(join(X_28,X_30),X_30)) != join(Y,join(X_30,X_28))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) != join(X_28,join(Y,join(join(X_28,X_30),X_30)))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,join(X_30,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(Y,join(join(X_28,X_30),X_30))),join(X_28,join(Y,join(join(X_28,X_30),X_30)))) ),[1,1],$fot(join(Y,join(X_30,X_28)))]]) ).
cnf(refute_0_532,plain,
( join(Y,join(join(X_28,X_30),X_30)) != join(Y,join(X_30,X_28))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,join(X_30,X_28))) ),
inference(resolve,[$cnf( $equal(join(X_28,join(Y,join(join(X_28,X_30),X_30))),join(X_28,join(Y,join(join(X_28,X_30),X_30)))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,join(X_30,X_28))),
inference(resolve,[$cnf( $equal(join(Y,join(join(X_28,X_30),X_30)),join(Y,join(X_30,X_28))) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
( join(X_28,join(Y,join(X_30,X_28))) != join(X_28,join(Y,X_30))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) != join(X_28,join(Y,join(X_30,X_28)))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,X_30)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(X_28,join(Y,join(join(X_28,X_30),X_30))))),bind(Y0,$fot(join(X_28,join(Y,join(X_30,X_28))))),bind(Z0,$fot(join(X_28,join(Y,X_30))))]]) ).
cnf(refute_0_535,plain,
( join(X_28,join(Y,join(X_30,X_28))) != join(X_28,join(Y,X_30))
| join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,X_30)) ),
inference(resolve,[$cnf( $equal(join(X_28,join(Y,join(join(X_28,X_30),X_30))),join(X_28,join(Y,join(X_30,X_28)))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
join(X_28,join(Y,join(join(X_28,X_30),X_30))) = join(X_28,join(Y,X_30)),
inference(resolve,[$cnf( $equal(join(X_28,join(Y,join(X_30,X_28))),join(X_28,join(Y,X_30))) )],[refute_0_509,refute_0_535]) ).
cnf(refute_0_537,plain,
join(join(X,Y),join(X_28,X_30)) = join(X,join(Y,join(X_28,X_30))),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(join(X_28,X_30)))]]) ).
cnf(refute_0_538,plain,
join(join(X,Y),join(X_28,X_30)) = join(X_28,join(join(X,Y),X_30)),
inference(subst,[],[refute_0_499:[bind(X,$fot(X_28)),bind(Y,$fot(join(X,Y))),bind(X_26,$fot(X_30))]]) ).
cnf(refute_0_539,plain,
( join(join(X,Y),join(X_28,X_30)) != join(X,join(Y,join(X_28,X_30)))
| join(join(X,Y),join(X_28,X_30)) != join(X_28,join(join(X,Y),X_30))
| join(X_28,join(join(X,Y),X_30)) = join(X,join(Y,join(X_28,X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(X_28,X_30)),join(X,join(Y,join(X_28,X_30)))) ),[0],$fot(join(X_28,join(join(X,Y),X_30)))]]) ).
cnf(refute_0_540,plain,
( join(join(X,Y),join(X_28,X_30)) != join(X,join(Y,join(X_28,X_30)))
| join(X_28,join(join(X,Y),X_30)) = join(X,join(Y,join(X_28,X_30))) ),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_28,X_30)),join(X_28,join(join(X,Y),X_30))) )],[refute_0_538,refute_0_539]) ).
cnf(refute_0_541,plain,
join(X_28,join(join(X,Y),X_30)) = join(X,join(Y,join(X_28,X_30))),
inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_28,X_30)),join(X,join(Y,join(X_28,X_30)))) )],[refute_0_537,refute_0_540]) ).
cnf(refute_0_542,plain,
join(join(X,Y),X_30) = join(X,join(Y,X_30)),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_30))]]) ).
cnf(refute_0_543,plain,
join(X_28,join(join(X,Y),X_30)) = join(X_28,join(join(X,Y),X_30)),
introduced(tautology,[refl,[$fot(join(X_28,join(join(X,Y),X_30)))]]) ).
cnf(refute_0_544,plain,
( join(X_28,join(join(X,Y),X_30)) != join(X_28,join(join(X,Y),X_30))
| join(join(X,Y),X_30) != join(X,join(Y,X_30))
| join(X_28,join(join(X,Y),X_30)) = join(X_28,join(X,join(Y,X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(join(X,Y),X_30)),join(X_28,join(join(X,Y),X_30))) ),[1,1],$fot(join(X,join(Y,X_30)))]]) ).
cnf(refute_0_545,plain,
( join(join(X,Y),X_30) != join(X,join(Y,X_30))
| join(X_28,join(join(X,Y),X_30)) = join(X_28,join(X,join(Y,X_30))) ),
inference(resolve,[$cnf( $equal(join(X_28,join(join(X,Y),X_30)),join(X_28,join(join(X,Y),X_30))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
join(X_28,join(join(X,Y),X_30)) = join(X_28,join(X,join(Y,X_30))),
inference(resolve,[$cnf( $equal(join(join(X,Y),X_30),join(X,join(Y,X_30))) )],[refute_0_542,refute_0_545]) ).
cnf(refute_0_547,plain,
( join(X_28,join(join(X,Y),X_30)) != join(X,join(Y,join(X_28,X_30)))
| join(X_28,join(join(X,Y),X_30)) != join(X_28,join(X,join(Y,X_30)))
| join(X_28,join(X,join(Y,X_30))) = join(X,join(Y,join(X_28,X_30))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(join(X,Y),X_30)),join(X,join(Y,join(X_28,X_30)))) ),[0],$fot(join(X_28,join(X,join(Y,X_30))))]]) ).
cnf(refute_0_548,plain,
( join(X_28,join(join(X,Y),X_30)) != join(X,join(Y,join(X_28,X_30)))
| join(X_28,join(X,join(Y,X_30))) = join(X,join(Y,join(X_28,X_30))) ),
inference(resolve,[$cnf( $equal(join(X_28,join(join(X,Y),X_30)),join(X_28,join(X,join(Y,X_30)))) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
join(X_28,join(X,join(Y,X_30))) = join(X,join(Y,join(X_28,X_30))),
inference(resolve,[$cnf( $equal(join(X_28,join(join(X,Y),X_30)),join(X,join(Y,join(X_28,X_30)))) )],[refute_0_541,refute_0_548]) ).
cnf(refute_0_550,plain,
join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(X_28,join(Y,join(join(X_28,X_30),X_30))),
inference(subst,[],[refute_0_549:[bind(X,$fot(X_28)),bind(X_28,$fot(join(X_28,X_30)))]]) ).
cnf(refute_0_551,plain,
( join(X_28,join(Y,join(join(X_28,X_30),X_30))) != join(X_28,join(Y,X_30))
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) != join(X_28,join(Y,join(join(X_28,X_30),X_30)))
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(X_28,join(Y,X_30)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(join(X_28,X_30),join(X_28,join(Y,X_30))))),bind(Y0,$fot(join(X_28,join(Y,join(join(X_28,X_30),X_30))))),bind(Z0,$fot(join(X_28,join(Y,X_30))))]]) ).
cnf(refute_0_552,plain,
( join(X_28,join(Y,join(join(X_28,X_30),X_30))) != join(X_28,join(Y,X_30))
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(X_28,join(Y,X_30)) ),
inference(resolve,[$cnf( $equal(join(join(X_28,X_30),join(X_28,join(Y,X_30))),join(X_28,join(Y,join(join(X_28,X_30),X_30)))) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
join(join(X_28,X_30),join(X_28,join(Y,X_30))) = join(X_28,join(Y,X_30)),
inference(resolve,[$cnf( $equal(join(X_28,join(Y,join(join(X_28,X_30),X_30))),join(X_28,join(Y,X_30))) )],[refute_0_536,refute_0_552]) ).
cnf(refute_0_554,plain,
( join(join(X_28,X_30),join(X_28,join(Y,X_30))) != join(X_28,join(Y,X_30))
| join(join(X_28,X_30),join(X_28,join(Y,X_30))) != join(join(X_28,X_30),Y)
| join(X_28,join(Y,X_30)) = join(join(X_28,X_30),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_28,X_30),join(X_28,join(Y,X_30))),join(join(X_28,X_30),Y)) ),[0],$fot(join(X_28,join(Y,X_30)))]]) ).
cnf(refute_0_555,plain,
( join(join(X_28,X_30),join(X_28,join(Y,X_30))) != join(join(X_28,X_30),Y)
| join(X_28,join(Y,X_30)) = join(join(X_28,X_30),Y) ),
inference(resolve,[$cnf( $equal(join(join(X_28,X_30),join(X_28,join(Y,X_30))),join(X_28,join(Y,X_30))) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
join(join(X_28,X_30),Y) = join(X_28,join(X_30,Y)),
inference(subst,[],[associativity_of_join:[bind(X,$fot(X_28)),bind(Y,$fot(X_30)),bind(Z,$fot(Y))]]) ).
cnf(refute_0_557,plain,
( join(X_28,join(Y,X_30)) != join(join(X_28,X_30),Y)
| join(join(X_28,X_30),Y) != join(X_28,join(X_30,Y))
| join(X_28,join(Y,X_30)) = join(X_28,join(X_30,Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_28,join(Y,X_30)),join(X_28,join(X_30,Y))) ),[0],$fot(join(join(X_28,X_30),Y))]]) ).
cnf(refute_0_558,plain,
( join(X_28,join(Y,X_30)) != join(join(X_28,X_30),Y)
| join(X_28,join(Y,X_30)) = join(X_28,join(X_30,Y)) ),
inference(resolve,[$cnf( $equal(join(join(X_28,X_30),Y),join(X_28,join(X_30,Y))) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
( join(join(X_28,X_30),join(X_28,join(Y,X_30))) != join(join(X_28,X_30),Y)
| join(X_28,join(Y,X_30)) = join(X_28,join(X_30,Y)) ),
inference(resolve,[$cnf( $equal(join(X_28,join(Y,X_30)),join(join(X_28,X_30),Y)) )],[refute_0_555,refute_0_558]) ).
cnf(refute_0_560,plain,
join(X_28,join(Y,X_30)) = join(X_28,join(X_30,Y)),
inference(resolve,[$cnf( $equal(join(join(X_28,X_30),join(X_28,join(Y,X_30))),join(join(X_28,X_30),Y)) )],[refute_0_503,refute_0_559]) ).
cnf(refute_0_561,plain,
join(X_124,join(f(U,W),f(V,W))) = join(X_124,join(f(V,W),f(U,W))),
inference(subst,[],[refute_0_560:[bind(Y,$fot(f(U,W))),bind(X_28,$fot(X_124)),bind(X_30,$fot(f(V,W)))]]) ).
cnf(refute_0_562,plain,
( f(join(U,V),W) != join(f(U,W),f(V,W))
| join(f(U,W),f(V,W)) = f(join(U,V),W) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(join(U,V),W))),bind(Y0,$fot(join(f(U,W),f(V,W))))]]) ).
cnf(refute_0_563,plain,
join(f(U,W),f(V,W)) = f(join(U,V),W),
inference(resolve,[$cnf( $equal(f(join(U,V),W),join(f(U,W),f(V,W))) )],[f_on_left_join,refute_0_562]) ).
cnf(refute_0_564,plain,
( join(X_124,join(f(U,W),f(V,W))) != join(X_124,join(f(V,W),f(U,W)))
| join(f(U,W),f(V,W)) != f(join(U,V),W)
| join(X_124,f(join(U,V),W)) = join(X_124,join(f(V,W),f(U,W))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_124,join(f(U,W),f(V,W))),join(X_124,join(f(V,W),f(U,W)))) ),[0,1],$fot(f(join(U,V),W))]]) ).
cnf(refute_0_565,plain,
( join(X_124,join(f(U,W),f(V,W))) != join(X_124,join(f(V,W),f(U,W)))
| join(X_124,f(join(U,V),W)) = join(X_124,join(f(V,W),f(U,W))) ),
inference(resolve,[$cnf( $equal(join(f(U,W),f(V,W)),f(join(U,V),W)) )],[refute_0_563,refute_0_564]) ).
cnf(refute_0_566,plain,
join(X_124,f(join(U,V),W)) = join(X_124,join(f(V,W),f(U,W))),
inference(resolve,[$cnf( $equal(join(X_124,join(f(U,W),f(V,W))),join(X_124,join(f(V,W),f(U,W)))) )],[refute_0_561,refute_0_565]) ).
cnf(refute_0_567,plain,
join(f(V,W),f(U,W)) = f(join(V,U),W),
inference(subst,[],[refute_0_563:[bind(U,$fot(V)),bind(V,$fot(U))]]) ).
cnf(refute_0_568,plain,
join(X_124,join(f(V,W),f(U,W))) = join(X_124,join(f(V,W),f(U,W))),
introduced(tautology,[refl,[$fot(join(X_124,join(f(V,W),f(U,W))))]]) ).
cnf(refute_0_569,plain,
( join(X_124,join(f(V,W),f(U,W))) != join(X_124,join(f(V,W),f(U,W)))
| join(f(V,W),f(U,W)) != f(join(V,U),W)
| join(X_124,join(f(V,W),f(U,W))) = join(X_124,f(join(V,U),W)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_124,join(f(V,W),f(U,W))),join(X_124,join(f(V,W),f(U,W)))) ),[1,1],$fot(f(join(V,U),W))]]) ).
cnf(refute_0_570,plain,
( join(f(V,W),f(U,W)) != f(join(V,U),W)
| join(X_124,join(f(V,W),f(U,W))) = join(X_124,f(join(V,U),W)) ),
inference(resolve,[$cnf( $equal(join(X_124,join(f(V,W),f(U,W))),join(X_124,join(f(V,W),f(U,W)))) )],[refute_0_568,refute_0_569]) ).
cnf(refute_0_571,plain,
join(X_124,join(f(V,W),f(U,W))) = join(X_124,f(join(V,U),W)),
inference(resolve,[$cnf( $equal(join(f(V,W),f(U,W)),f(join(V,U),W)) )],[refute_0_567,refute_0_570]) ).
cnf(refute_0_572,plain,
( join(X_124,f(join(U,V),W)) != join(X_124,join(f(V,W),f(U,W)))
| join(X_124,join(f(V,W),f(U,W))) != join(X_124,f(join(V,U),W))
| join(X_124,f(join(U,V),W)) = join(X_124,f(join(V,U),W)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_124,f(join(U,V),W)),join(X_124,f(join(V,U),W))) ),[0],$fot(join(X_124,join(f(V,W),f(U,W))))]]) ).
cnf(refute_0_573,plain,
( join(X_124,f(join(U,V),W)) != join(X_124,join(f(V,W),f(U,W)))
| join(X_124,f(join(U,V),W)) = join(X_124,f(join(V,U),W)) ),
inference(resolve,[$cnf( $equal(join(X_124,join(f(V,W),f(U,W))),join(X_124,f(join(V,U),W))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
join(X_124,f(join(U,V),W)) = join(X_124,f(join(V,U),W)),
inference(resolve,[$cnf( $equal(join(X_124,f(join(U,V),W)),join(X_124,join(f(V,W),f(U,W)))) )],[refute_0_566,refute_0_573]) ).
cnf(refute_0_575,plain,
( join(X_124,f(join(U,V),W)) != join(X_124,f(join(V,U),W))
| join(X_124,f(join(V,U),W)) = join(X_124,f(join(U,V),W)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_124,f(join(U,V),W)))),bind(Y0,$fot(join(X_124,f(join(V,U),W))))]]) ).
cnf(refute_0_576,plain,
join(X_124,f(join(V,U),W)) = join(X_124,f(join(U,V),W)),
inference(resolve,[$cnf( $equal(join(X_124,f(join(U,V),W)),join(X_124,f(join(V,U),W))) )],[refute_0_574,refute_0_575]) ).
cnf(refute_0_577,plain,
join(Y,f(join(bb,aa),dd)) = join(Y,f(join(aa,bb),dd)),
inference(subst,[],[refute_0_576:[bind(U,$fot(aa)),bind(V,$fot(bb)),bind(W,$fot(dd)),bind(X_124,$fot(Y))]]) ).
cnf(refute_0_578,plain,
join(f(X_64,X_65),join(X_23,f(X_63,X_65))) = join(X_23,join(f(X_63,X_65),f(X_64,X_65))),
inference(subst,[],[refute_0_354:[bind(X,$fot(f(X_64,X_65))),bind(X_24,$fot(f(X_63,X_65)))]]) ).
cnf(refute_0_579,plain,
( join(f(X_63,X_65),f(X_64,X_65)) != f(join(X_63,X_64),X_65)
| join(f(X_64,X_65),join(X_23,f(X_63,X_65))) != join(X_23,join(f(X_63,X_65),f(X_64,X_65)))
| join(f(X_64,X_65),join(X_23,f(X_63,X_65))) = join(X_23,f(join(X_63,X_64),X_65)) ),
introduced(tautology,[equality,[$cnf( $equal(join(f(X_64,X_65),join(X_23,f(X_63,X_65))),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))) ),[1,1],$fot(f(join(X_63,X_64),X_65))]]) ).
cnf(refute_0_580,plain,
( join(f(X_64,X_65),join(X_23,f(X_63,X_65))) != join(X_23,join(f(X_63,X_65),f(X_64,X_65)))
| join(f(X_64,X_65),join(X_23,f(X_63,X_65))) = join(X_23,f(join(X_63,X_64),X_65)) ),
inference(resolve,[$cnf( $equal(join(f(X_63,X_65),f(X_64,X_65)),f(join(X_63,X_64),X_65)) )],[refute_0_27,refute_0_579]) ).
cnf(refute_0_581,plain,
join(f(X_64,X_65),join(X_23,f(X_63,X_65))) = join(X_23,f(join(X_63,X_64),X_65)),
inference(resolve,[$cnf( $equal(join(f(X_64,X_65),join(X_23,f(X_63,X_65))),join(X_23,join(f(X_63,X_65),f(X_64,X_65)))) )],[refute_0_578,refute_0_580]) ).
cnf(refute_0_582,plain,
join(f(aa,dd),join(Y,f(bb,dd))) = join(Y,f(join(bb,aa),dd)),
inference(subst,[],[refute_0_581:[bind(X_23,$fot(Y)),bind(X_63,$fot(bb)),bind(X_64,$fot(aa)),bind(X_65,$fot(dd))]]) ).
cnf(refute_0_583,plain,
( join(Y,f(join(bb,aa),dd)) != join(Y,f(join(aa,bb),dd))
| join(f(aa,dd),join(Y,f(bb,dd))) != join(Y,f(join(bb,aa),dd))
| join(f(aa,dd),join(Y,f(bb,dd))) = join(Y,f(join(aa,bb),dd)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(f(aa,dd),join(Y,f(bb,dd))))),bind(Y0,$fot(join(Y,f(join(bb,aa),dd)))),bind(Z0,$fot(join(Y,f(join(aa,bb),dd))))]]) ).
cnf(refute_0_584,plain,
( join(Y,f(join(bb,aa),dd)) != join(Y,f(join(aa,bb),dd))
| join(f(aa,dd),join(Y,f(bb,dd))) = join(Y,f(join(aa,bb),dd)) ),
inference(resolve,[$cnf( $equal(join(f(aa,dd),join(Y,f(bb,dd))),join(Y,f(join(bb,aa),dd))) )],[refute_0_582,refute_0_583]) ).
cnf(refute_0_585,plain,
join(f(aa,dd),join(Y,f(bb,dd))) = join(Y,f(join(aa,bb),dd)),
inference(resolve,[$cnf( $equal(join(Y,f(join(bb,aa),dd)),join(Y,f(join(aa,bb),dd))) )],[refute_0_577,refute_0_584]) ).
cnf(refute_0_586,plain,
meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),
introduced(tautology,[refl,[$fot(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))))]]) ).
cnf(refute_0_587,plain,
( join(f(aa,dd),join(Y,f(bb,dd))) != join(Y,f(join(aa,bb),dd))
| meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))) ),[1,1],$fot(join(Y,f(join(aa,bb),dd)))]]) ).
cnf(refute_0_588,plain,
( join(f(aa,dd),join(Y,f(bb,dd))) != join(Y,f(join(aa,bb),dd))
| meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))),
inference(resolve,[$cnf( $equal(join(f(aa,dd),join(Y,f(bb,dd))),join(Y,f(join(aa,bb),dd))) )],[refute_0_585,refute_0_588]) ).
cnf(refute_0_590,plain,
join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(join(X_23,join(X_24,f(bb,dd)))))]]) ).
cnf(refute_0_591,plain,
meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))) = f(bb,dd),
inference(subst,[],[refute_0_23:[bind(X,$fot(f(bb,dd)))]]) ).
cnf(refute_0_592,plain,
( join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))) != f(bb,dd)
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) ),[0,1,1],$fot(f(bb,dd))]]) ).
cnf(refute_0_593,plain,
( join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))),f(bb,dd)) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),meet(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) )],[refute_0_590,refute_0_593]) ).
cnf(refute_0_595,plain,
join(meet(X_129,X_130),Y) = join(Y,meet(X_129,X_130)),
inference(subst,[],[commutativity_of_join:[bind(X,$fot(meet(X_129,X_130)))]]) ).
cnf(refute_0_596,plain,
join(Y,meet(X_129,X_130)) = join(meet(X_130,X_129),Y),
inference(subst,[],[refute_0_399:[bind(Y,$fot(X_129)),bind(X_104,$fot(X_130)),bind(X_106,$fot(Y))]]) ).
cnf(refute_0_597,plain,
( join(Y,meet(X_129,X_130)) != join(meet(X_130,X_129),Y)
| join(meet(X_129,X_130),Y) != join(Y,meet(X_129,X_130))
| join(meet(X_129,X_130),Y) = join(meet(X_130,X_129),Y) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_129,X_130),Y),join(Y,meet(X_129,X_130))) ),[1],$fot(join(meet(X_130,X_129),Y))]]) ).
cnf(refute_0_598,plain,
( join(meet(X_129,X_130),Y) != join(Y,meet(X_129,X_130))
| join(meet(X_129,X_130),Y) = join(meet(X_130,X_129),Y) ),
inference(resolve,[$cnf( $equal(join(Y,meet(X_129,X_130)),join(meet(X_130,X_129),Y)) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
join(meet(X_129,X_130),Y) = join(meet(X_130,X_129),Y),
inference(resolve,[$cnf( $equal(join(meet(X_129,X_130),Y),join(Y,meet(X_129,X_130))) )],[refute_0_595,refute_0_598]) ).
cnf(refute_0_600,plain,
( join(meet(X_129,X_130),Y) != join(meet(X_130,X_129),Y)
| join(meet(X_130,X_129),Y) = join(meet(X_129,X_130),Y) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(meet(X_129,X_130),Y))),bind(Y0,$fot(join(meet(X_130,X_129),Y)))]]) ).
cnf(refute_0_601,plain,
join(meet(X_130,X_129),Y) = join(meet(X_129,X_130),Y),
inference(resolve,[$cnf( $equal(join(meet(X_129,X_130),Y),join(meet(X_130,X_129),Y)) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),
inference(subst,[],[refute_0_601:[bind(Y,$fot(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))),bind(X_129,$fot(f(aa,dd))),bind(X_130,$fot(f(bb,dd)))]]) ).
cnf(refute_0_603,plain,
join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),
inference(subst,[],[refute_0_399:[bind(Y,$fot(f(aa,dd))),bind(X_104,$fot(f(bb,dd))),bind(X_106,$fot(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))))]]) ).
cnf(refute_0_604,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) != join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))))),bind(Z0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))))]]) ).
cnf(refute_0_605,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))),join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),
inference(resolve,[$cnf( $equal(join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_602,refute_0_605]) ).
cnf(refute_0_607,plain,
( join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) ),[0],$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))))]]) ).
cnf(refute_0_608,plain,
( join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) )],[refute_0_594,refute_0_608]) ).
cnf(refute_0_610,plain,
join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))) = join(f(bb,dd),join(X_23,X_24)),
inference(subst,[],[refute_0_508:[bind(X_13,$fot(f(bb,dd)))]]) ).
cnf(refute_0_611,plain,
meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),
introduced(tautology,[refl,[$fot(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))))]]) ).
cnf(refute_0_612,plain,
( join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))) != join(f(bb,dd),join(X_23,X_24))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) ),[1,1],$fot(join(f(bb,dd),join(X_23,X_24)))]]) ).
cnf(refute_0_613,plain,
( join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))) != join(f(bb,dd),join(X_23,X_24))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))),
inference(resolve,[$cnf( $equal(join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))),join(f(bb,dd),join(X_23,X_24))) )],[refute_0_610,refute_0_613]) ).
cnf(refute_0_615,plain,
join(meet(X_51,X_52),meet(X_53,X_51)) = join(meet(X_51,X_53),meet(X_51,X_52)),
inference(subst,[],[refute_0_399:[bind(Y,$fot(X_53)),bind(X_104,$fot(X_51)),bind(X_106,$fot(meet(X_51,X_52)))]]) ).
cnf(refute_0_616,plain,
( join(meet(X_51,X_52),meet(X_53,X_51)) != join(meet(X_51,X_53),meet(X_51,X_52))
| meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_53,X_51))
| meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_53),meet(X_51,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_53,X_51))) ),[1],$fot(join(meet(X_51,X_53),meet(X_51,X_52)))]]) ).
cnf(refute_0_617,plain,
( meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_52),meet(X_53,X_51))
| meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_53),meet(X_51,X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(X_51,X_52),meet(X_53,X_51)),join(meet(X_51,X_53),meet(X_51,X_52))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
meet(X_51,join(X_52,X_53)) = join(meet(X_51,X_53),meet(X_51,X_52)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_52),meet(X_53,X_51))) )],[refute_0_163,refute_0_617]) ).
cnf(refute_0_619,plain,
join(meet(X_51,X_53),meet(X_51,X_52)) = meet(X_51,join(X_53,X_52)),
inference(subst,[],[refute_0_119:[bind(X,$fot(X_51)),bind(Y,$fot(X_53)),bind(Z,$fot(X_52))]]) ).
cnf(refute_0_620,plain,
( join(meet(X_51,X_53),meet(X_51,X_52)) != meet(X_51,join(X_53,X_52))
| meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_53),meet(X_51,X_52))
| meet(X_51,join(X_52,X_53)) = meet(X_51,join(X_53,X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_53),meet(X_51,X_52))) ),[1],$fot(meet(X_51,join(X_53,X_52)))]]) ).
cnf(refute_0_621,plain,
( meet(X_51,join(X_52,X_53)) != join(meet(X_51,X_53),meet(X_51,X_52))
| meet(X_51,join(X_52,X_53)) = meet(X_51,join(X_53,X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(X_51,X_53),meet(X_51,X_52)),meet(X_51,join(X_53,X_52))) )],[refute_0_619,refute_0_620]) ).
cnf(refute_0_622,plain,
meet(X_51,join(X_52,X_53)) = meet(X_51,join(X_53,X_52)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),join(meet(X_51,X_53),meet(X_51,X_52))) )],[refute_0_618,refute_0_621]) ).
cnf(refute_0_623,plain,
( meet(X_51,join(X_52,X_53)) != meet(X_51,join(X_53,X_52))
| meet(X_51,join(X_53,X_52)) = meet(X_51,join(X_52,X_53)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_51,join(X_52,X_53)))),bind(Y0,$fot(meet(X_51,join(X_53,X_52))))]]) ).
cnf(refute_0_624,plain,
meet(X_51,join(X_53,X_52)) = meet(X_51,join(X_52,X_53)),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,X_53)),meet(X_51,join(X_53,X_52))) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),
inference(subst,[],[refute_0_624:[bind(X_51,$fot(f(cc,dd))),bind(X_52,$fot(f(bb,dd))),bind(X_53,$fot(join(X_23,join(X_24,f(bb,dd)))))]]) ).
cnf(refute_0_626,plain,
meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(join(aa,cc),dd),X_52),meet(f(bb,dd),f(join(aa,cc),dd))),
inference(subst,[],[refute_0_163:[bind(X_51,$fot(f(join(aa,cc),dd))),bind(X_53,$fot(f(bb,dd)))]]) ).
cnf(refute_0_627,plain,
meet(f(bb,dd),join(f(cc,dd),f(cc,V))) = meet(f(bb,dd),join(f(aa,dd),f(cc,V))),
inference(subst,[],[refute_0_90:[bind(X_53,$fot(f(cc,V)))]]) ).
cnf(refute_0_628,plain,
f(cc,join(dd,V)) = join(f(cc,dd),f(cc,V)),
inference(subst,[],[f_on_right_join:[bind(U,$fot(dd)),bind(W,$fot(cc))]]) ).
cnf(refute_0_629,plain,
( f(cc,join(dd,V)) != join(f(cc,dd),f(cc,V))
| join(f(cc,dd),f(cc,V)) = f(cc,join(dd,V)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(cc,join(dd,V)))),bind(Y0,$fot(join(f(cc,dd),f(cc,V))))]]) ).
cnf(refute_0_630,plain,
join(f(cc,dd),f(cc,V)) = f(cc,join(dd,V)),
inference(resolve,[$cnf( $equal(f(cc,join(dd,V)),join(f(cc,dd),f(cc,V))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
( join(f(cc,dd),f(cc,V)) != f(cc,join(dd,V))
| meet(f(bb,dd),join(f(cc,dd),f(cc,V))) != meet(f(bb,dd),join(f(aa,dd),f(cc,V)))
| meet(f(bb,dd),f(cc,join(dd,V))) = meet(f(bb,dd),join(f(aa,dd),f(cc,V))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),f(cc,V))),meet(f(bb,dd),join(f(aa,dd),f(cc,V)))) ),[0,1],$fot(f(cc,join(dd,V)))]]) ).
cnf(refute_0_632,plain,
( meet(f(bb,dd),join(f(cc,dd),f(cc,V))) != meet(f(bb,dd),join(f(aa,dd),f(cc,V)))
| meet(f(bb,dd),f(cc,join(dd,V))) = meet(f(bb,dd),join(f(aa,dd),f(cc,V))) ),
inference(resolve,[$cnf( $equal(join(f(cc,dd),f(cc,V)),f(cc,join(dd,V))) )],[refute_0_630,refute_0_631]) ).
cnf(refute_0_633,plain,
meet(f(bb,dd),f(cc,join(dd,V))) = meet(f(bb,dd),join(f(aa,dd),f(cc,V))),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(cc,dd),f(cc,V))),meet(f(bb,dd),join(f(aa,dd),f(cc,V)))) )],[refute_0_627,refute_0_632]) ).
cnf(refute_0_634,plain,
meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),join(f(aa,dd),f(cc,dd))),
inference(subst,[],[refute_0_633:[bind(V,$fot(dd))]]) ).
cnf(refute_0_635,plain,
f(join(aa,cc),dd) = join(f(aa,dd),f(cc,dd)),
inference(subst,[],[f_on_left_join:[bind(U,$fot(aa)),bind(V,$fot(cc)),bind(W,$fot(dd))]]) ).
cnf(refute_0_636,plain,
( f(join(aa,cc),dd) != join(f(aa,dd),f(cc,dd))
| join(f(aa,dd),f(cc,dd)) = f(join(aa,cc),dd) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(join(aa,cc),dd))),bind(Y0,$fot(join(f(aa,dd),f(cc,dd))))]]) ).
cnf(refute_0_637,plain,
join(f(aa,dd),f(cc,dd)) = f(join(aa,cc),dd),
inference(resolve,[$cnf( $equal(f(join(aa,cc),dd),join(f(aa,dd),f(cc,dd))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
( join(f(aa,dd),f(cc,dd)) != f(join(aa,cc),dd)
| meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),join(f(aa,dd),f(cc,dd)))
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(join(aa,cc),dd)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),join(f(aa,dd),f(cc,dd)))) ),[1,1],$fot(f(join(aa,cc),dd))]]) ).
cnf(refute_0_639,plain,
( meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),join(f(aa,dd),f(cc,dd)))
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(join(aa,cc),dd)) ),
inference(resolve,[$cnf( $equal(join(f(aa,dd),f(cc,dd)),f(join(aa,cc),dd)) )],[refute_0_637,refute_0_638]) ).
cnf(refute_0_640,plain,
meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(join(aa,cc),dd)),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),join(f(aa,dd),f(cc,dd)))) )],[refute_0_634,refute_0_639]) ).
cnf(refute_0_641,plain,
join(dd,dd) = dd,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(dd))]]) ).
cnf(refute_0_642,plain,
f(cc,join(dd,dd)) = f(cc,join(dd,dd)),
introduced(tautology,[refl,[$fot(f(cc,join(dd,dd)))]]) ).
cnf(refute_0_643,plain,
( f(cc,join(dd,dd)) != f(cc,join(dd,dd))
| join(dd,dd) != dd
| f(cc,join(dd,dd)) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(f(cc,join(dd,dd)),f(cc,join(dd,dd))) ),[1,1],$fot(dd)]]) ).
cnf(refute_0_644,plain,
( join(dd,dd) != dd
| f(cc,join(dd,dd)) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(f(cc,join(dd,dd)),f(cc,join(dd,dd))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
f(cc,join(dd,dd)) = f(cc,dd),
inference(resolve,[$cnf( $equal(join(dd,dd),dd) )],[refute_0_641,refute_0_644]) ).
cnf(refute_0_646,plain,
meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(cc,join(dd,dd))),
introduced(tautology,[refl,[$fot(meet(f(bb,dd),f(cc,join(dd,dd))))]]) ).
cnf(refute_0_647,plain,
( f(cc,join(dd,dd)) != f(cc,dd)
| meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),f(cc,join(dd,dd)))
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(cc,dd)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),f(cc,join(dd,dd)))) ),[1,1],$fot(f(cc,dd))]]) ).
cnf(refute_0_648,plain,
( f(cc,join(dd,dd)) != f(cc,dd)
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(cc,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),f(cc,join(dd,dd)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(bb,dd),f(cc,dd)),
inference(resolve,[$cnf( $equal(f(cc,join(dd,dd)),f(cc,dd)) )],[refute_0_645,refute_0_648]) ).
cnf(refute_0_650,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),f(cc,dd))
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(aa,dd),f(bb,dd)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(f(bb,dd),f(cc,join(dd,dd))))),bind(Y0,$fot(meet(f(bb,dd),f(cc,dd)))),bind(Z0,$fot(meet(f(aa,dd),f(bb,dd))))]]) ).
cnf(refute_0_651,plain,
( meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(aa,dd),f(bb,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),f(cc,dd))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
meet(f(bb,dd),f(cc,join(dd,dd))) = meet(f(aa,dd),f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_59,refute_0_651]) ).
cnf(refute_0_653,plain,
( meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(aa,dd),f(bb,dd))
| meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),f(join(aa,cc),dd))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(join(aa,cc),dd)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),f(join(aa,cc),dd))) ),[0],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_654,plain,
( meet(f(bb,dd),f(cc,join(dd,dd))) != meet(f(bb,dd),f(join(aa,cc),dd))
| meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(join(aa,cc),dd)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(aa,dd),f(bb,dd))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
meet(f(aa,dd),f(bb,dd)) = meet(f(bb,dd),f(join(aa,cc),dd)),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,join(dd,dd))),meet(f(bb,dd),f(join(aa,cc),dd))) )],[refute_0_640,refute_0_654]) ).
cnf(refute_0_656,plain,
( meet(f(aa,dd),f(bb,dd)) != meet(f(bb,dd),f(join(aa,cc),dd))
| meet(f(bb,dd),f(join(aa,cc),dd)) = meet(f(aa,dd),f(bb,dd)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(f(aa,dd),f(bb,dd)))),bind(Y0,$fot(meet(f(bb,dd),f(join(aa,cc),dd))))]]) ).
cnf(refute_0_657,plain,
meet(f(bb,dd),f(join(aa,cc),dd)) = meet(f(aa,dd),f(bb,dd)),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(bb,dd)),meet(f(bb,dd),f(join(aa,cc),dd))) )],[refute_0_655,refute_0_656]) ).
cnf(refute_0_658,plain,
( meet(f(bb,dd),f(join(aa,cc),dd)) != meet(f(aa,dd),f(bb,dd))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(join(aa,cc),dd),X_52),meet(f(bb,dd),f(join(aa,cc),dd)))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(join(aa,cc),dd),X_52),meet(f(bb,dd),f(join(aa,cc),dd)))) ),[1,1],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_659,plain,
( meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(join(aa,cc),dd),X_52),meet(f(bb,dd),f(join(aa,cc),dd)))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(join(aa,cc),dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(join(aa,cc),dd),X_52),meet(f(bb,dd),f(join(aa,cc),dd)))) )],[refute_0_626,refute_0_659]) ).
cnf(refute_0_661,plain,
join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),
inference(subst,[],[refute_0_601:[bind(Y,$fot(meet(f(join(aa,cc),dd),X_52))),bind(X_129,$fot(f(aa,dd))),bind(X_130,$fot(f(bb,dd)))]]) ).
cnf(refute_0_662,plain,
join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) = join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)),
inference(subst,[],[refute_0_399:[bind(Y,$fot(f(aa,dd))),bind(X_104,$fot(f(bb,dd))),bind(X_106,$fot(meet(f(join(aa,cc),dd),X_52)))]]) ).
cnf(refute_0_663,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) != join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52))
| join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)))),bind(Z0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))))]]) ).
cnf(refute_0_664,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))),join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_662,refute_0_663]) ).
cnf(refute_0_665,plain,
join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),
inference(resolve,[$cnf( $equal(join(meet(f(bb,dd),f(aa,dd)),meet(f(join(aa,cc),dd),X_52)),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_661,refute_0_664]) ).
cnf(refute_0_666,plain,
( join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd)))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd)))) ),[1],$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)))]]) ).
cnf(refute_0_667,plain,
( meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd)))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_665,refute_0_666]) ).
cnf(refute_0_668,plain,
meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(join(aa,cc),dd),X_52),meet(f(aa,dd),f(bb,dd)))) )],[refute_0_660,refute_0_667]) ).
cnf(refute_0_669,plain,
join(f(cc,dd),meet(f(aa,dd),f(cc,dd))) = f(cc,dd),
inference(subst,[],[refute_0_49:[bind(X,$fot(f(cc,dd))),bind(Y,$fot(f(aa,dd)))]]) ).
cnf(refute_0_670,plain,
join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),meet(f(bb,dd),f(aa,dd)))) = meet(f(cc,dd),f(aa,dd)),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(f(aa,dd)))]]) ).
cnf(refute_0_671,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),meet(f(bb,dd),f(aa,dd)))) != meet(f(cc,dd),f(aa,dd))
| meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))) != meet(f(aa,dd),f(bb,dd))
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),f(aa,dd)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),meet(f(bb,dd),f(aa,dd)))),meet(f(cc,dd),f(aa,dd))) ),[0,1],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_672,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),meet(f(bb,dd),f(aa,dd)))) != meet(f(cc,dd),f(aa,dd))
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),f(aa,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),meet(f(bb,dd),f(aa,dd))),meet(f(aa,dd),f(bb,dd))) )],[refute_0_217,refute_0_671]) ).
cnf(refute_0_673,plain,
join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),f(aa,dd)),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),meet(f(bb,dd),f(aa,dd)))),meet(f(cc,dd),f(aa,dd))) )],[refute_0_670,refute_0_672]) ).
cnf(refute_0_674,plain,
meet(f(X_63,X_65),join(f(X_63,X_65),f(X_64,X_65))) = f(X_63,X_65),
inference(subst,[],[absorption1:[bind(X,$fot(f(X_63,X_65))),bind(Y,$fot(f(X_64,X_65)))]]) ).
cnf(refute_0_675,plain,
( join(f(X_63,X_65),f(X_64,X_65)) != f(join(X_63,X_64),X_65)
| meet(f(X_63,X_65),join(f(X_63,X_65),f(X_64,X_65))) != f(X_63,X_65)
| meet(f(X_63,X_65),f(join(X_63,X_64),X_65)) = f(X_63,X_65) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(X_63,X_65),join(f(X_63,X_65),f(X_64,X_65))),f(X_63,X_65)) ),[0,1],$fot(f(join(X_63,X_64),X_65))]]) ).
cnf(refute_0_676,plain,
( meet(f(X_63,X_65),join(f(X_63,X_65),f(X_64,X_65))) != f(X_63,X_65)
| meet(f(X_63,X_65),f(join(X_63,X_64),X_65)) = f(X_63,X_65) ),
inference(resolve,[$cnf( $equal(join(f(X_63,X_65),f(X_64,X_65)),f(join(X_63,X_64),X_65)) )],[refute_0_27,refute_0_675]) ).
cnf(refute_0_677,plain,
meet(f(X_63,X_65),f(join(X_63,X_64),X_65)) = f(X_63,X_65),
inference(resolve,[$cnf( $equal(meet(f(X_63,X_65),join(f(X_63,X_65),f(X_64,X_65))),f(X_63,X_65)) )],[refute_0_674,refute_0_676]) ).
cnf(refute_0_678,plain,
meet(f(aa,dd),f(join(aa,bb),dd)) = f(aa,dd),
inference(subst,[],[refute_0_677:[bind(X_63,$fot(aa)),bind(X_64,$fot(bb)),bind(X_65,$fot(dd))]]) ).
cnf(refute_0_679,plain,
join(f(bb,dd),f(cc,dd)) = f(join(bb,cc),dd),
inference(subst,[],[refute_0_563:[bind(U,$fot(bb)),bind(V,$fot(cc)),bind(W,$fot(dd))]]) ).
cnf(refute_0_680,plain,
( f(join(bb,cc),dd) != f(join(aa,bb),dd)
| join(f(bb,dd),f(cc,dd)) != f(join(bb,cc),dd)
| join(f(bb,dd),f(cc,dd)) = f(join(aa,bb),dd) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(f(bb,dd),f(cc,dd)))),bind(Y0,$fot(f(join(bb,cc),dd))),bind(Z0,$fot(f(join(aa,bb),dd)))]]) ).
cnf(refute_0_681,plain,
( f(join(bb,cc),dd) != f(join(aa,bb),dd)
| join(f(bb,dd),f(cc,dd)) = f(join(aa,bb),dd) ),
inference(resolve,[$cnf( $equal(join(f(bb,dd),f(cc,dd)),f(join(bb,cc),dd)) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
join(f(bb,dd),f(cc,dd)) = f(join(aa,bb),dd),
inference(resolve,[$cnf( $equal(f(join(bb,cc),dd),f(join(aa,bb),dd)) )],[refute_0_43,refute_0_681]) ).
cnf(refute_0_683,plain,
meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),
introduced(tautology,[refl,[$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))))]]) ).
cnf(refute_0_684,plain,
( join(f(bb,dd),f(cc,dd)) != f(join(aa,bb),dd)
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = meet(f(aa,dd),f(join(aa,bb),dd)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) ),[1,1],$fot(f(join(aa,bb),dd))]]) ).
cnf(refute_0_685,plain,
( join(f(bb,dd),f(cc,dd)) != f(join(aa,bb),dd)
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = meet(f(aa,dd),f(join(aa,bb),dd)) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) )],[refute_0_683,refute_0_684]) ).
cnf(refute_0_686,plain,
meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = meet(f(aa,dd),f(join(aa,bb),dd)),
inference(resolve,[$cnf( $equal(join(f(bb,dd),f(cc,dd)),f(join(aa,bb),dd)) )],[refute_0_682,refute_0_685]) ).
cnf(refute_0_687,plain,
( meet(f(aa,dd),f(join(aa,bb),dd)) != f(aa,dd)
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) != meet(f(aa,dd),f(join(aa,bb),dd))
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = f(aa,dd) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))))),bind(Y0,$fot(meet(f(aa,dd),f(join(aa,bb),dd)))),bind(Z0,$fot(f(aa,dd)))]]) ).
cnf(refute_0_688,plain,
( meet(f(aa,dd),f(join(aa,bb),dd)) != f(aa,dd)
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = f(aa,dd) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),meet(f(aa,dd),f(join(aa,bb),dd))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) = f(aa,dd),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(join(aa,bb),dd)),f(aa,dd)) )],[refute_0_678,refute_0_688]) ).
cnf(refute_0_690,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),
inference(subst,[],[refute_0_119:[bind(X,$fot(f(aa,dd))),bind(Y,$fot(f(bb,dd))),bind(Z,$fot(f(cc,dd)))]]) ).
cnf(refute_0_691,plain,
join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150)))),
inference(subst,[],[refute_0_560:[bind(Y,$fot(meet(f(aa,dd),meet(f(bb,dd),X_150)))),bind(X_30,$fot(meet(f(cc,dd),X_150)))]]) ).
cnf(refute_0_692,plain,
join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))) = meet(f(cc,dd),X_150),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(X_150))]]) ).
cnf(refute_0_693,plain,
( join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))))
| join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))) != meet(f(cc,dd),X_150)
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(f(cc,dd),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))))) ),[1,1],$fot(meet(f(cc,dd),X_150))]]) ).
cnf(refute_0_694,plain,
( join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))))
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(f(cc,dd),X_150)) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))),meet(f(cc,dd),X_150)) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(f(cc,dd),X_150)),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,join(meet(f(cc,dd),X_150),meet(f(aa,dd),meet(f(bb,dd),X_150))))) )],[refute_0_691,refute_0_694]) ).
cnf(refute_0_696,plain,
join(f(cc,dd),meet(f(bb,dd),f(cc,dd))) = f(cc,dd),
inference(subst,[],[refute_0_49:[bind(X,$fot(f(cc,dd))),bind(Y,$fot(f(bb,dd)))]]) ).
cnf(refute_0_697,plain,
( join(f(cc,dd),meet(f(bb,dd),f(cc,dd))) != f(cc,dd)
| meet(f(bb,dd),f(cc,dd)) != meet(f(aa,dd),f(bb,dd))
| join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(join(f(cc,dd),meet(f(bb,dd),f(cc,dd))),f(cc,dd)) ),[0,1],$fot(meet(f(aa,dd),f(bb,dd)))]]) ).
cnf(refute_0_698,plain,
( join(f(cc,dd),meet(f(bb,dd),f(cc,dd))) != f(cc,dd)
| join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) )],[refute_0_59,refute_0_697]) ).
cnf(refute_0_699,plain,
join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) = f(cc,dd),
inference(resolve,[$cnf( $equal(join(f(cc,dd),meet(f(bb,dd),f(cc,dd))),f(cc,dd)) )],[refute_0_696,refute_0_698]) ).
cnf(refute_0_700,plain,
meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) = meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))),
introduced(tautology,[refl,[$fot(meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))))]]) ).
cnf(refute_0_701,plain,
( join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) != f(cc,dd)
| meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) != meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd))))
| meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) = meet(X_150,f(cc,dd)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))),meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd))))) ),[1,1],$fot(f(cc,dd))]]) ).
cnf(refute_0_702,plain,
( join(f(cc,dd),meet(f(aa,dd),f(bb,dd))) != f(cc,dd)
| meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) = meet(X_150,f(cc,dd)) ),
inference(resolve,[$cnf( $equal(meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))),meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd))))) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) = meet(X_150,f(cc,dd)),
inference(resolve,[$cnf( $equal(join(f(cc,dd),meet(f(aa,dd),f(bb,dd))),f(cc,dd)) )],[refute_0_699,refute_0_702]) ).
cnf(refute_0_704,plain,
meet(X_51,join(X_52,meet(X_20,X_21))) = join(meet(X_51,X_52),meet(X_51,meet(X_20,X_21))),
inference(subst,[],[dist_meet:[bind(X,$fot(X_51)),bind(Y,$fot(X_52)),bind(Z,$fot(meet(X_20,X_21)))]]) ).
cnf(refute_0_705,plain,
( meet(X_51,join(X_52,meet(X_20,X_21))) != join(meet(X_51,X_52),meet(X_51,meet(X_20,X_21)))
| meet(X_51,meet(X_20,X_21)) != meet(X_20,meet(X_21,X_51))
| meet(X_51,join(X_52,meet(X_20,X_21))) = join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_51,join(X_52,meet(X_20,X_21))),join(meet(X_51,X_52),meet(X_51,meet(X_20,X_21)))) ),[1,1],$fot(meet(X_20,meet(X_21,X_51)))]]) ).
cnf(refute_0_706,plain,
( meet(X_51,join(X_52,meet(X_20,X_21))) != join(meet(X_51,X_52),meet(X_51,meet(X_20,X_21)))
| meet(X_51,join(X_52,meet(X_20,X_21))) = join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51))) ),
inference(resolve,[$cnf( $equal(meet(X_51,meet(X_20,X_21)),meet(X_20,meet(X_21,X_51))) )],[refute_0_184,refute_0_705]) ).
cnf(refute_0_707,plain,
meet(X_51,join(X_52,meet(X_20,X_21))) = join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51))),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,meet(X_20,X_21))),join(meet(X_51,X_52),meet(X_51,meet(X_20,X_21)))) )],[refute_0_704,refute_0_706]) ).
cnf(refute_0_708,plain,
( meet(X_51,join(X_52,meet(X_20,X_21))) != join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51)))
| join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51))) = meet(X_51,join(X_52,meet(X_20,X_21))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(X_51,join(X_52,meet(X_20,X_21))))),bind(Y0,$fot(join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51)))))]]) ).
cnf(refute_0_709,plain,
join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51))) = meet(X_51,join(X_52,meet(X_20,X_21))),
inference(resolve,[$cnf( $equal(meet(X_51,join(X_52,meet(X_20,X_21))),join(meet(X_51,X_52),meet(X_20,meet(X_21,X_51)))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) = meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))),
inference(subst,[],[refute_0_709:[bind(X_20,$fot(f(aa,dd))),bind(X_21,$fot(f(bb,dd))),bind(X_51,$fot(X_150)),bind(X_52,$fot(f(cc,dd)))]]) ).
cnf(refute_0_711,plain,
( join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) != meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd))))
| meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) != meet(X_150,f(cc,dd))
| join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) = meet(X_150,f(cc,dd)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))),bind(Y0,$fot(meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))))),bind(Z0,$fot(meet(X_150,f(cc,dd))))]]) ).
cnf(refute_0_712,plain,
( meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))) != meet(X_150,f(cc,dd))
| join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) = meet(X_150,f(cc,dd)) ),
inference(resolve,[$cnf( $equal(join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))),meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd))))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) = meet(X_150,f(cc,dd)),
inference(resolve,[$cnf( $equal(meet(X_150,join(f(cc,dd),meet(f(aa,dd),f(bb,dd)))),meet(X_150,f(cc,dd))) )],[refute_0_703,refute_0_712]) ).
cnf(refute_0_714,plain,
join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) = join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))),
introduced(tautology,[refl,[$fot(join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))))]]) ).
cnf(refute_0_715,plain,
( join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) != join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))
| join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) != meet(X_150,f(cc,dd))
| join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) = join(X_28,meet(X_150,f(cc,dd))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))),join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))) ),[1,1],$fot(meet(X_150,f(cc,dd)))]]) ).
cnf(refute_0_716,plain,
( join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))) != meet(X_150,f(cc,dd))
| join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) = join(X_28,meet(X_150,f(cc,dd))) ),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))),join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) = join(X_28,meet(X_150,f(cc,dd))),
inference(resolve,[$cnf( $equal(join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))),meet(X_150,f(cc,dd))) )],[refute_0_713,refute_0_716]) ).
cnf(refute_0_718,plain,
join(join(X,Y),meet(X_129,X_130)) = join(X,join(Y,meet(X_129,X_130))),
inference(subst,[],[associativity_of_join:[bind(Z,$fot(meet(X_129,X_130)))]]) ).
cnf(refute_0_719,plain,
( join(Y,meet(X_129,X_130)) != join(meet(X_130,X_129),Y)
| join(join(X,Y),meet(X_129,X_130)) != join(X,join(Y,meet(X_129,X_130)))
| join(join(X,Y),meet(X_129,X_130)) = join(X,join(meet(X_130,X_129),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),meet(X_129,X_130)),join(X,join(Y,meet(X_129,X_130)))) ),[1,1],$fot(join(meet(X_130,X_129),Y))]]) ).
cnf(refute_0_720,plain,
( join(join(X,Y),meet(X_129,X_130)) != join(X,join(Y,meet(X_129,X_130)))
| join(join(X,Y),meet(X_129,X_130)) = join(X,join(meet(X_130,X_129),Y)) ),
inference(resolve,[$cnf( $equal(join(Y,meet(X_129,X_130)),join(meet(X_130,X_129),Y)) )],[refute_0_596,refute_0_719]) ).
cnf(refute_0_721,plain,
join(join(X,Y),meet(X_129,X_130)) = join(X,join(meet(X_130,X_129),Y)),
inference(resolve,[$cnf( $equal(join(join(X,Y),meet(X_129,X_130)),join(X,join(Y,meet(X_129,X_130)))) )],[refute_0_718,refute_0_720]) ).
cnf(refute_0_722,plain,
( join(join(X,Y),meet(X_129,X_130)) != join(X,join(Y,meet(X_129,X_130)))
| join(join(X,Y),meet(X_129,X_130)) != join(X,join(meet(X_130,X_129),Y))
| join(X,join(Y,meet(X_129,X_130))) = join(X,join(meet(X_130,X_129),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),meet(X_129,X_130)),join(X,join(meet(X_130,X_129),Y))) ),[0],$fot(join(X,join(Y,meet(X_129,X_130))))]]) ).
cnf(refute_0_723,plain,
( join(join(X,Y),meet(X_129,X_130)) != join(X,join(meet(X_130,X_129),Y))
| join(X,join(Y,meet(X_129,X_130))) = join(X,join(meet(X_130,X_129),Y)) ),
inference(resolve,[$cnf( $equal(join(join(X,Y),meet(X_129,X_130)),join(X,join(Y,meet(X_129,X_130)))) )],[refute_0_718,refute_0_722]) ).
cnf(refute_0_724,plain,
join(X,join(Y,meet(X_129,X_130))) = join(X,join(meet(X_130,X_129),Y)),
inference(resolve,[$cnf( $equal(join(join(X,Y),meet(X_129,X_130)),join(X,join(meet(X_130,X_129),Y))) )],[refute_0_721,refute_0_723]) ).
cnf(refute_0_725,plain,
join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))),
inference(subst,[],[refute_0_724:[bind(X,$fot(X_28)),bind(Y,$fot(meet(f(aa,dd),meet(f(bb,dd),X_150)))),bind(X_129,$fot(f(cc,dd))),bind(X_130,$fot(X_150))]]) ).
cnf(refute_0_726,plain,
( join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) != join(X_28,meet(X_150,f(cc,dd)))
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(X_150,f(cc,dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))))),bind(Y0,$fot(join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))))),bind(Z0,$fot(join(X_28,meet(X_150,f(cc,dd)))))]]) ).
cnf(refute_0_727,plain,
( join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))) != join(X_28,meet(X_150,f(cc,dd)))
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(X_150,f(cc,dd))) ),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150))))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) = join(X_28,meet(X_150,f(cc,dd))),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(X_150,f(cc,dd)),meet(f(aa,dd),meet(f(bb,dd),X_150)))),join(X_28,meet(X_150,f(cc,dd)))) )],[refute_0_717,refute_0_727]) ).
cnf(refute_0_729,plain,
( join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,meet(X_150,f(cc,dd)))
| join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,meet(f(cc,dd),X_150))
| join(X_28,meet(X_150,f(cc,dd))) = join(X_28,meet(f(cc,dd),X_150)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,meet(f(cc,dd),X_150))) ),[0],$fot(join(X_28,meet(X_150,f(cc,dd))))]]) ).
cnf(refute_0_730,plain,
( join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))) != join(X_28,meet(f(cc,dd),X_150))
| join(X_28,meet(X_150,f(cc,dd))) = join(X_28,meet(f(cc,dd),X_150)) ),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,meet(X_150,f(cc,dd)))) )],[refute_0_728,refute_0_729]) ).
cnf(refute_0_731,plain,
join(X_28,meet(X_150,f(cc,dd))) = join(X_28,meet(f(cc,dd),X_150)),
inference(resolve,[$cnf( $equal(join(X_28,join(meet(f(aa,dd),meet(f(bb,dd),X_150)),meet(f(cc,dd),X_150))),join(X_28,meet(f(cc,dd),X_150))) )],[refute_0_695,refute_0_730]) ).
cnf(refute_0_732,plain,
( join(X_28,meet(X_150,f(cc,dd))) != join(X_28,meet(f(cc,dd),X_150))
| join(X_28,meet(f(cc,dd),X_150)) = join(X_28,meet(X_150,f(cc,dd))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_28,meet(X_150,f(cc,dd))))),bind(Y0,$fot(join(X_28,meet(f(cc,dd),X_150))))]]) ).
cnf(refute_0_733,plain,
join(X_28,meet(f(cc,dd),X_150)) = join(X_28,meet(X_150,f(cc,dd))),
inference(resolve,[$cnf( $equal(join(X_28,meet(X_150,f(cc,dd))),join(X_28,meet(f(cc,dd),X_150))) )],[refute_0_731,refute_0_732]) ).
cnf(refute_0_734,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))),
inference(subst,[],[refute_0_733:[bind(X_150,$fot(f(aa,dd))),bind(X_28,$fot(meet(f(aa,dd),f(bb,dd))))]]) ).
cnf(refute_0_735,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))))),bind(Y0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))))),bind(Z0,$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))))]]) ).
cnf(refute_0_736,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd)))) )],[refute_0_734,refute_0_735]) ).
cnf(refute_0_737,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(aa,dd),f(cc,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) )],[refute_0_690,refute_0_736]) ).
cnf(refute_0_738,plain,
( join(X_106,meet(Y,X_104)) != join(meet(X_104,Y),X_106)
| join(meet(X_104,Y),X_106) = join(X_106,meet(Y,X_104)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X_106,meet(Y,X_104)))),bind(Y0,$fot(join(meet(X_104,Y),X_106)))]]) ).
cnf(refute_0_739,plain,
join(meet(X_104,Y),X_106) = join(X_106,meet(Y,X_104)),
inference(resolve,[$cnf( $equal(join(X_106,meet(Y,X_104)),join(meet(X_104,Y),X_106)) )],[refute_0_399,refute_0_738]) ).
cnf(refute_0_740,plain,
join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),
inference(subst,[],[refute_0_739:[bind(Y,$fot(f(cc,dd))),bind(X_104,$fot(f(aa,dd))),bind(X_106,$fot(meet(f(aa,dd),f(bb,dd))))]]) ).
cnf(refute_0_741,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd)))
| join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))))),bind(Z0,$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))))]]) ).
cnf(refute_0_742,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd)))) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),f(aa,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) )],[refute_0_737,refute_0_742]) ).
cnf(refute_0_744,plain,
join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))),
inference(subst,[],[refute_0_601:[bind(Y,$fot(meet(f(aa,dd),f(bb,dd)))),bind(X_129,$fot(f(aa,dd))),bind(X_130,$fot(f(cc,dd)))]]) ).
cnf(refute_0_745,plain,
( join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd)))
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))))),bind(Z0,$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))))]]) ).
cnf(refute_0_746,plain,
( join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))),join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd)))) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(cc,dd)),meet(f(aa,dd),f(bb,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) )],[refute_0_743,refute_0_746]) ).
cnf(refute_0_748,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))
| meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) != f(aa,dd)
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = f(aa,dd) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))))),bind(Z0,$fot(f(aa,dd)))]]) ).
cnf(refute_0_749,plain,
( meet(f(aa,dd),join(f(bb,dd),f(cc,dd))) != f(aa,dd)
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = f(aa,dd) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))),meet(f(aa,dd),join(f(bb,dd),f(cc,dd)))) )],[refute_0_747,refute_0_748]) ).
cnf(refute_0_750,plain,
join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) = f(aa,dd),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),join(f(bb,dd),f(cc,dd))),f(aa,dd)) )],[refute_0_689,refute_0_749]) ).
cnf(refute_0_751,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != f(aa,dd)
| join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),f(aa,dd))
| f(aa,dd) = meet(f(cc,dd),f(aa,dd)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),f(aa,dd))) ),[0],$fot(f(aa,dd))]]) ).
cnf(refute_0_752,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),f(aa,dd))
| f(aa,dd) = meet(f(cc,dd),f(aa,dd)) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))),f(aa,dd)) )],[refute_0_750,refute_0_751]) ).
cnf(refute_0_753,plain,
meet(f(cc,dd),f(aa,dd)) = meet(f(aa,dd),f(cc,dd)),
inference(subst,[],[refute_0_53:[bind(X,$fot(f(aa,dd))),bind(Y,$fot(f(cc,dd)))]]) ).
cnf(refute_0_754,plain,
( f(aa,dd) != meet(f(cc,dd),f(aa,dd))
| meet(f(cc,dd),f(aa,dd)) != meet(f(aa,dd),f(cc,dd))
| f(aa,dd) = meet(f(aa,dd),f(cc,dd)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(f(aa,dd),meet(f(aa,dd),f(cc,dd))) ),[0],$fot(meet(f(cc,dd),f(aa,dd)))]]) ).
cnf(refute_0_755,plain,
( f(aa,dd) != meet(f(cc,dd),f(aa,dd))
| f(aa,dd) = meet(f(aa,dd),f(cc,dd)) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(cc,dd))) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
( join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),f(aa,dd))
| f(aa,dd) = meet(f(aa,dd),f(cc,dd)) ),
inference(resolve,[$cnf( $equal(f(aa,dd),meet(f(cc,dd),f(aa,dd))) )],[refute_0_752,refute_0_755]) ).
cnf(refute_0_757,plain,
f(aa,dd) = meet(f(aa,dd),f(cc,dd)),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),f(aa,dd)),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),f(aa,dd))) )],[refute_0_673,refute_0_756]) ).
cnf(refute_0_758,plain,
( f(aa,dd) != meet(f(aa,dd),f(cc,dd))
| meet(f(aa,dd),f(cc,dd)) = f(aa,dd) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(aa,dd))),bind(Y0,$fot(meet(f(aa,dd),f(cc,dd))))]]) ).
cnf(refute_0_759,plain,
meet(f(aa,dd),f(cc,dd)) = f(aa,dd),
inference(resolve,[$cnf( $equal(f(aa,dd),meet(f(aa,dd),f(cc,dd))) )],[refute_0_757,refute_0_758]) ).
cnf(refute_0_760,plain,
( join(f(cc,dd),meet(f(aa,dd),f(cc,dd))) != f(cc,dd)
| meet(f(aa,dd),f(cc,dd)) != f(aa,dd)
| join(f(cc,dd),f(aa,dd)) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(join(f(cc,dd),meet(f(aa,dd),f(cc,dd))),f(cc,dd)) ),[0,1],$fot(f(aa,dd))]]) ).
cnf(refute_0_761,plain,
( join(f(cc,dd),meet(f(aa,dd),f(cc,dd))) != f(cc,dd)
| join(f(cc,dd),f(aa,dd)) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(cc,dd)),f(aa,dd)) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
join(f(cc,dd),f(aa,dd)) = f(cc,dd),
inference(resolve,[$cnf( $equal(join(f(cc,dd),meet(f(aa,dd),f(cc,dd))),f(cc,dd)) )],[refute_0_669,refute_0_761]) ).
cnf(refute_0_763,plain,
join(f(cc,dd),f(aa,dd)) = join(f(aa,dd),f(cc,dd)),
inference(subst,[],[refute_0_382:[bind(X_35,$fot(f(aa,dd))),bind(X_37,$fot(f(cc,dd)))]]) ).
cnf(refute_0_764,plain,
( join(f(aa,dd),f(cc,dd)) != f(join(aa,cc),dd)
| join(f(cc,dd),f(aa,dd)) != join(f(aa,dd),f(cc,dd))
| join(f(cc,dd),f(aa,dd)) = f(join(aa,cc),dd) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(f(cc,dd),f(aa,dd)))),bind(Y0,$fot(join(f(aa,dd),f(cc,dd)))),bind(Z0,$fot(f(join(aa,cc),dd)))]]) ).
cnf(refute_0_765,plain,
( join(f(aa,dd),f(cc,dd)) != f(join(aa,cc),dd)
| join(f(cc,dd),f(aa,dd)) = f(join(aa,cc),dd) ),
inference(resolve,[$cnf( $equal(join(f(cc,dd),f(aa,dd)),join(f(aa,dd),f(cc,dd))) )],[refute_0_763,refute_0_764]) ).
cnf(refute_0_766,plain,
join(f(cc,dd),f(aa,dd)) = f(join(aa,cc),dd),
inference(resolve,[$cnf( $equal(join(f(aa,dd),f(cc,dd)),f(join(aa,cc),dd)) )],[refute_0_637,refute_0_765]) ).
cnf(refute_0_767,plain,
( join(f(cc,dd),f(aa,dd)) != f(cc,dd)
| join(f(cc,dd),f(aa,dd)) != f(join(aa,cc),dd)
| f(join(aa,cc),dd) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(join(f(cc,dd),f(aa,dd)),f(cc,dd)) ),[0],$fot(f(join(aa,cc),dd))]]) ).
cnf(refute_0_768,plain,
( join(f(cc,dd),f(aa,dd)) != f(cc,dd)
| f(join(aa,cc),dd) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(join(f(cc,dd),f(aa,dd)),f(join(aa,cc),dd)) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
f(join(aa,cc),dd) = f(cc,dd),
inference(resolve,[$cnf( $equal(join(f(cc,dd),f(aa,dd)),f(cc,dd)) )],[refute_0_762,refute_0_768]) ).
cnf(refute_0_770,plain,
meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),
introduced(tautology,[refl,[$fot(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))))]]) ).
cnf(refute_0_771,plain,
( f(join(aa,cc),dd) != f(cc,dd)
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != meet(f(join(aa,cc),dd),join(X_52,f(bb,dd)))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = meet(f(cc,dd),join(X_52,f(bb,dd))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),meet(f(join(aa,cc),dd),join(X_52,f(bb,dd)))) ),[1,0],$fot(f(cc,dd))]]) ).
cnf(refute_0_772,plain,
( f(join(aa,cc),dd) != f(cc,dd)
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = meet(f(cc,dd),join(X_52,f(bb,dd))) ),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),meet(f(join(aa,cc),dd),join(X_52,f(bb,dd)))) )],[refute_0_770,refute_0_771]) ).
cnf(refute_0_773,plain,
meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) = meet(f(cc,dd),join(X_52,f(bb,dd))),
inference(resolve,[$cnf( $equal(f(join(aa,cc),dd),f(cc,dd)) )],[refute_0_769,refute_0_772]) ).
cnf(refute_0_774,plain,
( meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != meet(f(cc,dd),join(X_52,f(bb,dd)))
| meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) ),[0],$fot(meet(f(cc,dd),join(X_52,f(bb,dd))))]]) ).
cnf(refute_0_775,plain,
( meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) ),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),meet(f(cc,dd),join(X_52,f(bb,dd)))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
meet(f(join(aa,cc),dd),X_52) = meet(f(join(aa,cc),dd),X_52),
introduced(tautology,[refl,[$fot(meet(f(join(aa,cc),dd),X_52))]]) ).
cnf(refute_0_777,plain,
( f(join(aa,cc),dd) != f(cc,dd)
| meet(f(join(aa,cc),dd),X_52) != meet(f(join(aa,cc),dd),X_52)
| meet(f(join(aa,cc),dd),X_52) = meet(f(cc,dd),X_52) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(join(aa,cc),dd),X_52),meet(f(join(aa,cc),dd),X_52)) ),[1,0],$fot(f(cc,dd))]]) ).
cnf(refute_0_778,plain,
( f(join(aa,cc),dd) != f(cc,dd)
| meet(f(join(aa,cc),dd),X_52) = meet(f(cc,dd),X_52) ),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),X_52),meet(f(join(aa,cc),dd),X_52)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
meet(f(join(aa,cc),dd),X_52) = meet(f(cc,dd),X_52),
inference(resolve,[$cnf( $equal(f(join(aa,cc),dd),f(cc,dd)) )],[refute_0_769,refute_0_778]) ).
cnf(refute_0_780,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),
introduced(tautology,[refl,[$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)))]]) ).
cnf(refute_0_781,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(join(aa,cc),dd),X_52) != meet(f(cc,dd),X_52)
| join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) ),[1,1],$fot(meet(f(cc,dd),X_52))]]) ).
cnf(refute_0_782,plain,
( meet(f(join(aa,cc),dd),X_52) != meet(f(cc,dd),X_52)
| join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),X_52),meet(f(cc,dd),X_52)) )],[refute_0_779,refute_0_782]) ).
cnf(refute_0_784,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52))
| meet(f(cc,dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(X_52,f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) ),[1],$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)))]]) ).
cnf(refute_0_785,plain,
( meet(f(cc,dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52)),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
( meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))
| meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(X_52,f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_775,refute_0_785]) ).
cnf(refute_0_787,plain,
meet(f(cc,dd),join(X_52,f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)),
inference(resolve,[$cnf( $equal(meet(f(join(aa,cc),dd),join(X_52,f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(join(aa,cc),dd),X_52))) )],[refute_0_668,refute_0_786]) ).
cnf(refute_0_788,plain,
( meet(f(cc,dd),join(X_52,f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) = meet(f(cc,dd),join(X_52,f(bb,dd))) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(meet(f(cc,dd),join(X_52,f(bb,dd))))),bind(Y0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52))))]]) ).
cnf(refute_0_789,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52)) = meet(f(cc,dd),join(X_52,f(bb,dd))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(X_52,f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),X_52))) )],[refute_0_787,refute_0_788]) ).
cnf(refute_0_790,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))),
inference(subst,[],[refute_0_789:[bind(X_52,$fot(join(X_23,join(X_24,f(bb,dd)))))]]) ).
cnf(refute_0_791,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd)))
| meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))))),bind(Y0,$fot(meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))))),bind(Z0,$fot(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))))]]) ).
cnf(refute_0_792,plain,
( meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd)))) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(join(X_23,join(X_24,f(bb,dd))),f(bb,dd))),meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_625,refute_0_792]) ).
cnf(refute_0_794,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))))),bind(Y0,$fot(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))))),bind(Z0,$fot(meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))))]]) ).
cnf(refute_0_795,plain,
( meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd)))))) )],[refute_0_793,refute_0_794]) ).
cnf(refute_0_796,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) = meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))) )],[refute_0_614,refute_0_795]) ).
cnf(refute_0_797,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) ),[0],$fot(meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))))]]) ).
cnf(refute_0_798,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) != meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))
| meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24)))) )],[refute_0_796,refute_0_797]) ).
cnf(refute_0_799,plain,
meet(f(cc,dd),join(f(bb,dd),join(X_23,X_24))) = meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd)))),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))),meet(f(cc,dd),join(X_23,join(X_24,f(bb,dd))))) )],[refute_0_609,refute_0_798]) ).
cnf(refute_0_800,plain,
meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),
inference(subst,[],[refute_0_799:[bind(X_23,$fot(f(aa,dd))),bind(X_24,$fot(Y))]]) ).
cnf(refute_0_801,plain,
join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),meet(f(bb,dd),join(f(bb,dd),Y)))) = meet(f(cc,dd),join(f(bb,dd),Y)),
inference(subst,[],[refute_0_72:[bind(X_34,$fot(join(f(bb,dd),Y)))]]) ).
cnf(refute_0_802,plain,
meet(f(bb,dd),join(f(bb,dd),Y)) = f(bb,dd),
inference(subst,[],[absorption1:[bind(X,$fot(f(bb,dd)))]]) ).
cnf(refute_0_803,plain,
( join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),meet(f(bb,dd),join(f(bb,dd),Y)))) != meet(f(cc,dd),join(f(bb,dd),Y))
| meet(f(bb,dd),join(f(bb,dd),Y)) != f(bb,dd)
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),meet(f(bb,dd),join(f(bb,dd),Y)))),meet(f(cc,dd),join(f(bb,dd),Y))) ),[0,1,1],$fot(f(bb,dd))]]) ).
cnf(refute_0_804,plain,
( join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),meet(f(bb,dd),join(f(bb,dd),Y)))) != meet(f(cc,dd),join(f(bb,dd),Y))
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
inference(resolve,[$cnf( $equal(meet(f(bb,dd),join(f(bb,dd),Y)),f(bb,dd)) )],[refute_0_802,refute_0_803]) ).
cnf(refute_0_805,plain,
join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),meet(f(bb,dd),join(f(bb,dd),Y)))),meet(f(cc,dd),join(f(bb,dd),Y))) )],[refute_0_801,refute_0_804]) ).
cnf(refute_0_806,plain,
join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),
inference(subst,[],[refute_0_601:[bind(Y,$fot(meet(f(cc,dd),join(f(bb,dd),Y)))),bind(X_129,$fot(f(aa,dd))),bind(X_130,$fot(f(bb,dd)))]]) ).
cnf(refute_0_807,plain,
join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),
inference(subst,[],[refute_0_399:[bind(Y,$fot(f(aa,dd))),bind(X_104,$fot(f(bb,dd))),bind(X_106,$fot(meet(f(cc,dd),join(f(bb,dd),Y))))]]) ).
cnf(refute_0_808,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) != join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))))),bind(Y0,$fot(join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))))),bind(Z0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))))]]) ).
cnf(refute_0_809,plain,
( join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))),join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))) )],[refute_0_807,refute_0_808]) ).
cnf(refute_0_810,plain,
join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) = join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),
inference(resolve,[$cnf( $equal(join(meet(f(bb,dd),f(aa,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))) )],[refute_0_806,refute_0_809]) ).
cnf(refute_0_811,plain,
( join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) != join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))
| join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),Y))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),join(f(bb,dd),Y))) ),[0],$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))))]]) ).
cnf(refute_0_812,plain,
( join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),Y))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))),join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y)))) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),Y)),
inference(resolve,[$cnf( $equal(join(meet(f(cc,dd),join(f(bb,dd),Y)),meet(f(aa,dd),f(bb,dd))),meet(f(cc,dd),join(f(bb,dd),Y))) )],[refute_0_805,refute_0_812]) ).
cnf(refute_0_814,plain,
join(bb,bb) = bb,
inference(subst,[],[idempotence_of_join:[bind(X,$fot(bb))]]) ).
cnf(refute_0_815,plain,
f(join(bb,bb),dd) = f(join(bb,bb),dd),
introduced(tautology,[refl,[$fot(f(join(bb,bb),dd))]]) ).
cnf(refute_0_816,plain,
( f(join(bb,bb),dd) != f(join(bb,bb),dd)
| join(bb,bb) != bb
| f(join(bb,bb),dd) = f(bb,dd) ),
introduced(tautology,[equality,[$cnf( $equal(f(join(bb,bb),dd),f(join(bb,bb),dd)) ),[1,0],$fot(bb)]]) ).
cnf(refute_0_817,plain,
( join(bb,bb) != bb
| f(join(bb,bb),dd) = f(bb,dd) ),
inference(resolve,[$cnf( $equal(f(join(bb,bb),dd),f(join(bb,bb),dd)) )],[refute_0_815,refute_0_816]) ).
cnf(refute_0_818,plain,
f(join(bb,bb),dd) = f(bb,dd),
inference(resolve,[$cnf( $equal(join(bb,bb),bb) )],[refute_0_814,refute_0_817]) ).
cnf(refute_0_819,plain,
join(Y,f(join(bb,bb),dd)) = join(Y,f(join(bb,bb),dd)),
introduced(tautology,[refl,[$fot(join(Y,f(join(bb,bb),dd)))]]) ).
cnf(refute_0_820,plain,
( f(join(bb,bb),dd) != f(bb,dd)
| join(Y,f(join(bb,bb),dd)) != join(Y,f(join(bb,bb),dd))
| join(Y,f(join(bb,bb),dd)) = join(Y,f(bb,dd)) ),
introduced(tautology,[equality,[$cnf( $equal(join(Y,f(join(bb,bb),dd)),join(Y,f(join(bb,bb),dd))) ),[1,1],$fot(f(bb,dd))]]) ).
cnf(refute_0_821,plain,
( f(join(bb,bb),dd) != f(bb,dd)
| join(Y,f(join(bb,bb),dd)) = join(Y,f(bb,dd)) ),
inference(resolve,[$cnf( $equal(join(Y,f(join(bb,bb),dd)),join(Y,f(join(bb,bb),dd))) )],[refute_0_819,refute_0_820]) ).
cnf(refute_0_822,plain,
join(Y,f(join(bb,bb),dd)) = join(Y,f(bb,dd)),
inference(resolve,[$cnf( $equal(f(join(bb,bb),dd),f(bb,dd)) )],[refute_0_818,refute_0_821]) ).
cnf(refute_0_823,plain,
join(X,join(f(X_63,X_65),f(X_64,X_65))) = join(f(X_63,X_65),join(f(X_64,X_65),X)),
inference(subst,[],[refute_0_354:[bind(X_23,$fot(f(X_63,X_65))),bind(X_24,$fot(f(X_64,X_65)))]]) ).
cnf(refute_0_824,plain,
( join(X,join(f(X_63,X_65),f(X_64,X_65))) != join(f(X_63,X_65),join(f(X_64,X_65),X))
| join(f(X_63,X_65),f(X_64,X_65)) != f(join(X_63,X_64),X_65)
| join(X,f(join(X_63,X_64),X_65)) = join(f(X_63,X_65),join(f(X_64,X_65),X)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X,join(f(X_63,X_65),f(X_64,X_65))),join(f(X_63,X_65),join(f(X_64,X_65),X))) ),[0,1],$fot(f(join(X_63,X_64),X_65))]]) ).
cnf(refute_0_825,plain,
( join(X,join(f(X_63,X_65),f(X_64,X_65))) != join(f(X_63,X_65),join(f(X_64,X_65),X))
| join(X,f(join(X_63,X_64),X_65)) = join(f(X_63,X_65),join(f(X_64,X_65),X)) ),
inference(resolve,[$cnf( $equal(join(f(X_63,X_65),f(X_64,X_65)),f(join(X_63,X_64),X_65)) )],[refute_0_27,refute_0_824]) ).
cnf(refute_0_826,plain,
join(X,f(join(X_63,X_64),X_65)) = join(f(X_63,X_65),join(f(X_64,X_65),X)),
inference(resolve,[$cnf( $equal(join(X,join(f(X_63,X_65),f(X_64,X_65))),join(f(X_63,X_65),join(f(X_64,X_65),X))) )],[refute_0_823,refute_0_825]) ).
cnf(refute_0_827,plain,
( join(X,f(join(X_63,X_64),X_65)) != join(f(X_63,X_65),join(f(X_64,X_65),X))
| join(f(X_63,X_65),join(f(X_64,X_65),X)) = join(X,f(join(X_63,X_64),X_65)) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(join(X,f(join(X_63,X_64),X_65)))),bind(Y0,$fot(join(f(X_63,X_65),join(f(X_64,X_65),X))))]]) ).
cnf(refute_0_828,plain,
join(f(X_63,X_65),join(f(X_64,X_65),X)) = join(X,f(join(X_63,X_64),X_65)),
inference(resolve,[$cnf( $equal(join(X,f(join(X_63,X_64),X_65)),join(f(X_63,X_65),join(f(X_64,X_65),X))) )],[refute_0_826,refute_0_827]) ).
cnf(refute_0_829,plain,
join(f(bb,dd),join(f(bb,dd),Y)) = join(Y,f(join(bb,bb),dd)),
inference(subst,[],[refute_0_828:[bind(X,$fot(Y)),bind(X_63,$fot(bb)),bind(X_64,$fot(bb)),bind(X_65,$fot(dd))]]) ).
cnf(refute_0_830,plain,
( join(Y,f(join(bb,bb),dd)) != join(Y,f(bb,dd))
| join(f(bb,dd),join(f(bb,dd),Y)) != join(Y,f(join(bb,bb),dd))
| join(f(bb,dd),join(f(bb,dd),Y)) = join(Y,f(bb,dd)) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(f(bb,dd),join(f(bb,dd),Y)))),bind(Y0,$fot(join(Y,f(join(bb,bb),dd)))),bind(Z0,$fot(join(Y,f(bb,dd))))]]) ).
cnf(refute_0_831,plain,
( join(Y,f(join(bb,bb),dd)) != join(Y,f(bb,dd))
| join(f(bb,dd),join(f(bb,dd),Y)) = join(Y,f(bb,dd)) ),
inference(resolve,[$cnf( $equal(join(f(bb,dd),join(f(bb,dd),Y)),join(Y,f(join(bb,bb),dd))) )],[refute_0_829,refute_0_830]) ).
cnf(refute_0_832,plain,
join(f(bb,dd),join(f(bb,dd),Y)) = join(Y,f(bb,dd)),
inference(resolve,[$cnf( $equal(join(Y,f(join(bb,bb),dd)),join(Y,f(bb,dd))) )],[refute_0_822,refute_0_831]) ).
cnf(refute_0_833,plain,
meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),
introduced(tautology,[refl,[$fot(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))))]]) ).
cnf(refute_0_834,plain,
( join(f(bb,dd),join(f(bb,dd),Y)) != join(Y,f(bb,dd))
| meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))
| meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))) ),[1,1],$fot(join(Y,f(bb,dd)))]]) ).
cnf(refute_0_835,plain,
( join(f(bb,dd),join(f(bb,dd),Y)) != join(Y,f(bb,dd))
| meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))) )],[refute_0_833,refute_0_834]) ).
cnf(refute_0_836,plain,
meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))),
inference(resolve,[$cnf( $equal(join(f(bb,dd),join(f(bb,dd),Y)),join(Y,f(bb,dd))) )],[refute_0_832,refute_0_835]) ).
cnf(refute_0_837,plain,
meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),
inference(subst,[],[refute_0_624:[bind(X_51,$fot(f(cc,dd))),bind(X_52,$fot(f(bb,dd))),bind(X_53,$fot(join(f(bb,dd),Y)))]]) ).
cnf(refute_0_838,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))),
inference(subst,[],[refute_0_789:[bind(X_52,$fot(join(f(bb,dd),Y)))]]) ).
cnf(refute_0_839,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd)))
| meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))))),bind(Y0,$fot(meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))))),bind(Z0,$fot(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))))]]) ).
cnf(refute_0_840,plain,
( meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd)))) )],[refute_0_838,refute_0_839]) ).
cnf(refute_0_841,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(join(f(bb,dd),Y),f(bb,dd))),meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))) )],[refute_0_837,refute_0_840]) ).
cnf(refute_0_842,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))
| meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(Y,f(bb,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))))),bind(Y0,$fot(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))))),bind(Z0,$fot(meet(f(cc,dd),join(Y,f(bb,dd)))))]]) ).
cnf(refute_0_843,plain,
( meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(Y,f(bb,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y)))) )],[refute_0_841,refute_0_842]) ).
cnf(refute_0_844,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) = meet(f(cc,dd),join(Y,f(bb,dd))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(Y,f(bb,dd)))) )],[refute_0_836,refute_0_843]) ).
cnf(refute_0_845,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(Y,f(bb,dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(f(bb,dd),Y))
| meet(f(cc,dd),join(Y,f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(f(bb,dd),Y))) ),[0],$fot(meet(f(cc,dd),join(Y,f(bb,dd))))]]) ).
cnf(refute_0_846,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))) != meet(f(cc,dd),join(f(bb,dd),Y))
| meet(f(cc,dd),join(Y,f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(Y,f(bb,dd)))) )],[refute_0_844,refute_0_845]) ).
cnf(refute_0_847,plain,
meet(f(cc,dd),join(Y,f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),Y)),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(bb,dd),Y))),meet(f(cc,dd),join(f(bb,dd),Y))) )],[refute_0_813,refute_0_846]) ).
cnf(refute_0_848,plain,
meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) = meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))),
inference(subst,[],[refute_0_847:[bind(Y,$fot(join(f(aa,dd),Y)))]]) ).
cnf(refute_0_849,plain,
( meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) != meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y)))
| meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))))),bind(Y0,$fot(meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))))),bind(Z0,$fot(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))))]]) ).
cnf(refute_0_850,plain,
( meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))),meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y)))) )],[refute_0_848,refute_0_849]) ).
cnf(refute_0_851,plain,
meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(bb,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))) )],[refute_0_800,refute_0_850]) ).
cnf(refute_0_852,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))),
inference(subst,[],[refute_0_789:[bind(X_52,$fot(join(f(aa,dd),Y)))]]) ).
cnf(refute_0_853,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd)))
| meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))))),bind(Y0,$fot(meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))))),bind(Z0,$fot(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))))]]) ).
cnf(refute_0_854,plain,
( meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd)))) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(join(f(aa,dd),Y),f(bb,dd))),meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))) )],[refute_0_851,refute_0_854]) ).
cnf(refute_0_856,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))
| meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) != meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) ),
inference(subst,[],[refute_0_175:[bind(X0,$fot(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))))),bind(Y0,$fot(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))))),bind(Z0,$fot(meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))))]]) ).
cnf(refute_0_857,plain,
( meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))) != meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd))))) )],[refute_0_855,refute_0_856]) ).
cnf(refute_0_858,plain,
join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) = meet(f(cc,dd),join(Y,f(join(aa,bb),dd))),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),join(Y,f(bb,dd)))),meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))) )],[refute_0_589,refute_0_857]) ).
cnf(refute_0_859,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))
| join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),Y))
| meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = meet(f(cc,dd),join(f(aa,dd),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),Y))) ),[0],$fot(meet(f(cc,dd),join(Y,f(join(aa,bb),dd))))]]) ).
cnf(refute_0_860,plain,
( join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))) != meet(f(cc,dd),join(f(aa,dd),Y))
| meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = meet(f(cc,dd),join(f(aa,dd),Y)) ),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(Y,f(join(aa,bb),dd)))) )],[refute_0_858,refute_0_859]) ).
cnf(refute_0_861,plain,
meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = meet(f(cc,dd),join(f(aa,dd),Y)),
inference(resolve,[$cnf( $equal(join(meet(f(aa,dd),f(bb,dd)),meet(f(cc,dd),join(f(aa,dd),Y))),meet(f(cc,dd),join(f(aa,dd),Y))) )],[refute_0_445,refute_0_860]) ).
cnf(refute_0_862,plain,
meet(f(cc,dd),join(f(aa,dd),X_156)) = join(meet(f(aa,dd),f(cc,dd)),meet(f(cc,dd),X_156)),
inference(subst,[],[refute_0_84:[bind(X_51,$fot(f(cc,dd))),bind(X_52,$fot(f(aa,dd))),bind(X_53,$fot(X_156))]]) ).
cnf(refute_0_863,plain,
( meet(f(aa,dd),f(cc,dd)) != f(aa,dd)
| meet(f(cc,dd),join(f(aa,dd),X_156)) != join(meet(f(aa,dd),f(cc,dd)),meet(f(cc,dd),X_156))
| meet(f(cc,dd),join(f(aa,dd),X_156)) = join(f(aa,dd),meet(f(cc,dd),X_156)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),X_156)),join(meet(f(aa,dd),f(cc,dd)),meet(f(cc,dd),X_156))) ),[1,0],$fot(f(aa,dd))]]) ).
cnf(refute_0_864,plain,
( meet(f(cc,dd),join(f(aa,dd),X_156)) != join(meet(f(aa,dd),f(cc,dd)),meet(f(cc,dd),X_156))
| meet(f(cc,dd),join(f(aa,dd),X_156)) = join(f(aa,dd),meet(f(cc,dd),X_156)) ),
inference(resolve,[$cnf( $equal(meet(f(aa,dd),f(cc,dd)),f(aa,dd)) )],[refute_0_759,refute_0_863]) ).
cnf(refute_0_865,plain,
meet(f(cc,dd),join(f(aa,dd),X_156)) = join(f(aa,dd),meet(f(cc,dd),X_156)),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),X_156)),join(meet(f(aa,dd),f(cc,dd)),meet(f(cc,dd),X_156))) )],[refute_0_862,refute_0_864]) ).
cnf(refute_0_866,plain,
meet(f(cc,dd),join(f(aa,dd),Y)) = join(f(aa,dd),meet(f(cc,dd),Y)),
inference(subst,[],[refute_0_865:[bind(X_156,$fot(Y))]]) ).
cnf(refute_0_867,plain,
( meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) != meet(f(cc,dd),join(f(aa,dd),Y))
| meet(f(cc,dd),join(f(aa,dd),Y)) != join(f(aa,dd),meet(f(cc,dd),Y))
| meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = join(f(aa,dd),meet(f(cc,dd),Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(f(cc,dd),join(Y,f(join(aa,bb),dd))),join(f(aa,dd),meet(f(cc,dd),Y))) ),[0],$fot(meet(f(cc,dd),join(f(aa,dd),Y)))]]) ).
cnf(refute_0_868,plain,
( meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) != meet(f(cc,dd),join(f(aa,dd),Y))
| meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = join(f(aa,dd),meet(f(cc,dd),Y)) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(f(aa,dd),Y)),join(f(aa,dd),meet(f(cc,dd),Y))) )],[refute_0_866,refute_0_867]) ).
cnf(refute_0_869,plain,
meet(f(cc,dd),join(Y,f(join(aa,bb),dd))) = join(f(aa,dd),meet(f(cc,dd),Y)),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(Y,f(join(aa,bb),dd))),meet(f(cc,dd),join(f(aa,dd),Y))) )],[refute_0_861,refute_0_868]) ).
cnf(refute_0_870,plain,
meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) = join(f(aa,dd),meet(f(cc,dd),X_205)),
inference(subst,[],[refute_0_869:[bind(Y,$fot(X_205))]]) ).
cnf(refute_0_871,plain,
( meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) != f(cc,dd)
| meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) != join(f(aa,dd),meet(f(cc,dd),X_205))
| join(f(aa,dd),meet(f(cc,dd),X_205)) = f(cc,dd) ),
introduced(tautology,[equality,[$cnf( $equal(meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))),f(cc,dd)) ),[0],$fot(join(f(aa,dd),meet(f(cc,dd),X_205)))]]) ).
cnf(refute_0_872,plain,
( meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))) != f(cc,dd)
| join(f(aa,dd),meet(f(cc,dd),X_205)) = f(cc,dd) ),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))),join(f(aa,dd),meet(f(cc,dd),X_205))) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
join(f(aa,dd),meet(f(cc,dd),X_205)) = f(cc,dd),
inference(resolve,[$cnf( $equal(meet(f(cc,dd),join(X_205,f(join(aa,bb),dd))),f(cc,dd)) )],[refute_0_46,refute_0_872]) ).
cnf(refute_0_874,plain,
join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))) = f(cc,dd),
inference(subst,[],[refute_0_873:[bind(X_205,$fot(meet(f(aa,dd),X_40)))]]) ).
cnf(refute_0_875,plain,
( join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))) != f(aa,dd)
| join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))) != f(cc,dd)
| f(cc,dd) = f(aa,dd) ),
introduced(tautology,[equality,[$cnf( $equal(join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))),f(aa,dd)) ),[0],$fot(f(cc,dd))]]) ).
cnf(refute_0_876,plain,
( join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))) != f(aa,dd)
| f(cc,dd) = f(aa,dd) ),
inference(resolve,[$cnf( $equal(join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))),f(cc,dd)) )],[refute_0_874,refute_0_875]) ).
cnf(refute_0_877,plain,
f(cc,dd) = f(aa,dd),
inference(resolve,[$cnf( $equal(join(f(aa,dd),meet(f(cc,dd),meet(f(aa,dd),X_40))),f(aa,dd)) )],[refute_0_15,refute_0_876]) ).
cnf(refute_0_878,plain,
( f(cc,dd) != f(aa,dd)
| f(aa,dd) = f(cc,dd) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(f(cc,dd))),bind(Y0,$fot(f(aa,dd)))]]) ).
cnf(refute_0_879,plain,
f(cc,dd) != f(aa,dd),
inference(resolve,[$cnf( $equal(f(aa,dd),f(cc,dd)) )],[refute_0_878,rhs]) ).
cnf(refute_0_880,plain,
$false,
inference(resolve,[$cnf( $equal(f(cc,dd),f(aa,dd)) )],[refute_0_877,refute_0_879]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT038-1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n006.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 15:24:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 9.36/9.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.36/9.59
% 9.36/9.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.52/9.69
%------------------------------------------------------------------------------