%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL042-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 : Mon Jul 18 19:45:44 EDT 2022
% Result : Unsatisfiable 16.53s 16.74s
% Output : CNFRefutation 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 119
% Number of leaves : 462
% Syntax : Number of clauses : 1921 ( 957 unt; 0 nHn;1177 RR)
% Number of literals : 3306 (3305 equ;1388 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 2553 ( 21 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_associativity_5,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
meet(composition(sk1,A),composition(sk1,complement(A))) = zero ).
cnf(goals_15,negated_conjecture,
join(composition(converse(sk1),sk1),one) != one ).
cnf(refute_0_0,plain,
converse(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))]]) ).
cnf(refute_0_1,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_2,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_3,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_5,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_4]) ).
cnf(refute_0_6,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_7,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) ),[0],$fot(join(complement(B),composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_8,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_8]) ).
cnf(refute_0_10,plain,
join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))))) = complement(complement(one)),
inference(subst,[],[refute_0_9:[bind(A,$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),bind(B,$fot(complement(one)))]]) ).
cnf(refute_0_11,plain,
join(complement(one),composition(converse(X_23),complement(composition(X_23,one)))) = complement(one),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_23)),bind(B,$fot(one))]]) ).
cnf(refute_0_12,plain,
composition(X_23,one) = X_23,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_23))]]) ).
cnf(refute_0_13,plain,
( composition(X_23,one) != X_23
| join(complement(one),composition(converse(X_23),complement(composition(X_23,one)))) != complement(one)
| join(complement(one),composition(converse(X_23),complement(X_23))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_23),complement(composition(X_23,one)))),complement(one)) ),[0,1,1,0],$fot(X_23)]]) ).
cnf(refute_0_14,plain,
( join(complement(one),composition(converse(X_23),complement(composition(X_23,one)))) != complement(one)
| join(complement(one),composition(converse(X_23),complement(X_23))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_23,one),X_23) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(complement(one),composition(converse(X_23),complement(X_23))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_23),complement(composition(X_23,one)))),complement(one)) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
join(complement(one),composition(converse(join(X_47,X_48)),complement(join(X_47,X_48)))) = complement(one),
inference(subst,[],[refute_0_15:[bind(X_23,$fot(join(X_47,X_48)))]]) ).
cnf(refute_0_17,plain,
join(converse(X_10),converse(X_9)) = join(converse(X_9),converse(X_10)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_10))),bind(B,$fot(converse(X_9)))]]) ).
cnf(refute_0_18,plain,
converse(join(X_9,X_10)) = join(converse(X_9),converse(X_10)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_9)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_19,plain,
( converse(join(X_9,X_10)) != join(converse(X_9),converse(X_10))
| join(converse(X_9),converse(X_10)) = converse(join(X_9,X_10)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(join(X_9,X_10)))),bind(Y,$fot(join(converse(X_9),converse(X_10))))]]) ).
cnf(refute_0_20,plain,
join(converse(X_9),converse(X_10)) = converse(join(X_9,X_10)),
inference(resolve,[$cnf( $equal(converse(join(X_9,X_10)),join(converse(X_9),converse(X_10))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( join(converse(X_10),converse(X_9)) != join(converse(X_9),converse(X_10))
| join(converse(X_9),converse(X_10)) != converse(join(X_9,X_10))
| join(converse(X_10),converse(X_9)) = converse(join(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(converse(X_10),converse(X_9)),converse(join(X_9,X_10))) ),[0],$fot(join(converse(X_9),converse(X_10)))]]) ).
cnf(refute_0_22,plain,
( join(converse(X_10),converse(X_9)) != join(converse(X_9),converse(X_10))
| join(converse(X_10),converse(X_9)) = converse(join(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(join(converse(X_9),converse(X_10)),converse(join(X_9,X_10))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
join(converse(X_10),converse(X_9)) = converse(join(X_9,X_10)),
inference(resolve,[$cnf( $equal(join(converse(X_10),converse(X_9)),join(converse(X_9),converse(X_10))) )],[refute_0_17,refute_0_22]) ).
cnf(refute_0_24,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_25,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_24]) ).
cnf(refute_0_26,plain,
join(converse(X_10),converse(X_9)) = converse(join(X_10,X_9)),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_10)),bind(B,$fot(X_9))]]) ).
cnf(refute_0_27,plain,
( join(converse(X_10),converse(X_9)) != converse(join(X_10,X_9))
| join(converse(X_10),converse(X_9)) != converse(join(X_9,X_10))
| converse(join(X_10,X_9)) = converse(join(X_9,X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_10),converse(X_9)),converse(join(X_9,X_10))) ),[0],$fot(converse(join(X_10,X_9)))]]) ).
cnf(refute_0_28,plain,
( join(converse(X_10),converse(X_9)) != converse(join(X_9,X_10))
| converse(join(X_10,X_9)) = converse(join(X_9,X_10)) ),
inference(resolve,[$cnf( $equal(join(converse(X_10),converse(X_9)),converse(join(X_10,X_9))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
converse(join(X_10,X_9)) = converse(join(X_9,X_10)),
inference(resolve,[$cnf( $equal(join(converse(X_10),converse(X_9)),converse(join(X_9,X_10))) )],[refute_0_23,refute_0_28]) ).
cnf(refute_0_30,plain,
converse(join(X_47,X_48)) = converse(join(X_48,X_47)),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(X_47)),bind(X_9,$fot(X_48))]]) ).
cnf(refute_0_31,plain,
( converse(join(X_47,X_48)) != converse(join(X_48,X_47))
| join(complement(one),composition(converse(join(X_47,X_48)),complement(join(X_47,X_48)))) != complement(one)
| join(complement(one),composition(converse(join(X_48,X_47)),complement(join(X_47,X_48)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(X_47,X_48)),complement(join(X_47,X_48)))),complement(one)) ),[0,1,0],$fot(converse(join(X_48,X_47)))]]) ).
cnf(refute_0_32,plain,
( join(complement(one),composition(converse(join(X_47,X_48)),complement(join(X_47,X_48)))) != complement(one)
| join(complement(one),composition(converse(join(X_48,X_47)),complement(join(X_47,X_48)))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(X_47,X_48)),converse(join(X_48,X_47))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
join(complement(one),composition(converse(join(X_48,X_47)),complement(join(X_47,X_48)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(X_47,X_48)),complement(join(X_47,X_48)))),complement(one)) )],[refute_0_16,refute_0_32]) ).
cnf(refute_0_34,plain,
join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))) = complement(one),
inference(subst,[],[refute_0_33:[bind(X_47,$fot(complement(composition(sk1,complement(one))))),bind(X_48,$fot(composition(complement(composition(complement(sk1),top)),top)))]]) ).
cnf(refute_0_35,plain,
join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))) = complement(composition(sk1,complement(one))),
inference(subst,[],[refute_0_9:[bind(A,$fot(converse(complement(composition(complement(sk1),top))))),bind(B,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_36,plain,
converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(composition(sk1,complement(one))))),bind(B,$fot(complement(composition(complement(sk1),top))))]]) ).
cnf(refute_0_37,plain,
join(complement(top),composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(subst,[],[refute_0_9:[bind(B,$fot(top))]]) ).
cnf(refute_0_38,plain,
zero = meet(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_27),complement(X_28))))]]) ).
cnf(refute_0_39,plain,
meet(X_27,X_28) = complement(join(complement(X_27),complement(X_28))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_27)),bind(B,$fot(X_28))]]) ).
cnf(refute_0_40,plain,
( meet(X_27,X_28) != complement(join(complement(X_27),complement(X_28)))
| complement(join(complement(X_27),complement(X_28))) = meet(X_27,X_28) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_27,X_28))),bind(Y,$fot(complement(join(complement(X_27),complement(X_28)))))]]) ).
cnf(refute_0_41,plain,
complement(join(complement(X_27),complement(X_28))) = meet(X_27,X_28),
inference(resolve,[$cnf( $equal(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| zero != meet(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))
| zero = meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))) ),[1,1],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_43,plain,
( zero != meet(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))
| zero = meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
zero = meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))) )],[refute_0_38,refute_0_43]) ).
cnf(refute_0_45,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_46,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_45]) ).
cnf(refute_0_47,plain,
join(meet(X_27,X_28),complement(meet(X_27,X_28))) = top,
inference(subst,[],[refute_0_46:[bind(A,$fot(meet(X_27,X_28)))]]) ).
cnf(refute_0_48,plain,
complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) = complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))))]]) ).
cnf(refute_0_49,plain,
( complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) != complement(join(meet(X_27,X_28),complement(meet(X_27,X_28))))
| join(meet(X_27,X_28),complement(meet(X_27,X_28))) != top
| complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))),complement(join(meet(X_27,X_28),complement(meet(X_27,X_28))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_50,plain,
( join(meet(X_27,X_28),complement(meet(X_27,X_28))) != top
| complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))),complement(join(meet(X_27,X_28),complement(meet(X_27,X_28))))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_27,X_28),complement(meet(X_27,X_28))),top) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
meet(join(complement(X_27),complement(X_28)),B) = complement(join(complement(join(complement(X_27),complement(X_28))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_27),complement(X_28))))]]) ).
cnf(refute_0_53,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| meet(join(complement(X_27),complement(X_28)),B) != complement(join(complement(join(complement(X_27),complement(X_28))),complement(B)))
| meet(join(complement(X_27),complement(X_28)),B) = complement(join(meet(X_27,X_28),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_27),complement(X_28)),B),complement(join(complement(join(complement(X_27),complement(X_28))),complement(B)))) ),[1,0,0],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_54,plain,
( meet(join(complement(X_27),complement(X_28)),B) != complement(join(complement(join(complement(X_27),complement(X_28))),complement(B)))
| meet(join(complement(X_27),complement(X_28)),B) = complement(join(meet(X_27,X_28),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_53]) ).
cnf(refute_0_55,plain,
meet(join(complement(X_27),complement(X_28)),B) = complement(join(meet(X_27,X_28),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_27),complement(X_28)),B),complement(join(complement(join(complement(X_27),complement(X_28))),complement(B)))) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) = complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))),
inference(subst,[],[refute_0_55:[bind(B,$fot(meet(X_27,X_28)))]]) ).
cnf(refute_0_57,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_58,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_57]) ).
cnf(refute_0_59,plain,
( complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) != complement(top)
| meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) != complement(join(meet(X_27,X_28),complement(meet(X_27,X_28))))
| meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) = complement(top) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)))),bind(Y,$fot(complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_60,plain,
( complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))) != complement(top)
| meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)),complement(join(meet(X_27,X_28),complement(meet(X_27,X_28))))) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_27,X_28),complement(meet(X_27,X_28)))),complement(top)) )],[refute_0_51,refute_0_60]) ).
cnf(refute_0_62,plain,
( meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) != complement(top)
| zero != meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_63,plain,
( zero != meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28)),complement(top)) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_27),complement(X_28)),meet(X_27,X_28))) )],[refute_0_44,refute_0_63]) ).
cnf(refute_0_65,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_66,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( complement(top) != zero
| join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_68,plain,
( join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_37,refute_0_68]) ).
cnf(refute_0_70,plain,
( complement(top) != zero
| join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_71,plain,
( join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
join(zero,composition(converse(join(X_47,X_48)),complement(composition(join(X_47,X_48),top)))) = zero,
inference(subst,[],[refute_0_72:[bind(A,$fot(join(X_47,X_48)))]]) ).
cnf(refute_0_74,plain,
( converse(join(X_47,X_48)) != converse(join(X_48,X_47))
| join(zero,composition(converse(join(X_47,X_48)),complement(composition(join(X_47,X_48),top)))) != zero
| join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(join(X_47,X_48)),complement(composition(join(X_47,X_48),top)))),zero) ),[0,1,0],$fot(converse(join(X_48,X_47)))]]) ).
cnf(refute_0_75,plain,
( join(zero,composition(converse(join(X_47,X_48)),complement(composition(join(X_47,X_48),top)))) != zero
| join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(join(X_47,X_48)),converse(join(X_48,X_47))) )],[refute_0_30,refute_0_74]) ).
cnf(refute_0_76,plain,
join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(join(X_47,X_48)),complement(composition(join(X_47,X_48),top)))),zero) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
join(zero,join(zero,X_51)) = join(join(zero,zero),X_51),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero)),bind(C,$fot(X_51))]]) ).
cnf(refute_0_78,plain,
join(complement(X_24),composition(converse(one),complement(composition(one,X_24)))) = complement(X_24),
inference(subst,[],[refute_0_9:[bind(A,$fot(one)),bind(B,$fot(X_24))]]) ).
cnf(refute_0_79,plain,
converse(composition(converse(A),X_6)) = composition(converse(X_6),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_6))]]) ).
cnf(refute_0_80,plain,
( converse(composition(converse(A),X_6)) != composition(converse(X_6),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_6)) = composition(converse(X_6),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_6)),composition(converse(X_6),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_81,plain,
( converse(composition(converse(A),X_6)) != composition(converse(X_6),converse(converse(A)))
| converse(composition(converse(A),X_6)) = composition(converse(X_6),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_80]) ).
cnf(refute_0_82,plain,
converse(composition(converse(A),X_6)) = composition(converse(X_6),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_6)),composition(converse(X_6),converse(converse(A)))) )],[refute_0_79,refute_0_81]) ).
cnf(refute_0_83,plain,
converse(composition(converse(X_16),one)) = composition(converse(one),X_16),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_16)),bind(X_6,$fot(one))]]) ).
cnf(refute_0_84,plain,
composition(converse(X_16),one) = converse(X_16),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_16)))]]) ).
cnf(refute_0_85,plain,
( composition(converse(X_16),one) != converse(X_16)
| converse(composition(converse(X_16),one)) != composition(converse(one),X_16)
| converse(converse(X_16)) = composition(converse(one),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_16),one)),composition(converse(one),X_16)) ),[0,0],$fot(converse(X_16))]]) ).
cnf(refute_0_86,plain,
( converse(composition(converse(X_16),one)) != composition(converse(one),X_16)
| converse(converse(X_16)) = composition(converse(one),X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(X_16),one),converse(X_16)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
converse(converse(X_16)) = composition(converse(one),X_16),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_16),one)),composition(converse(one),X_16)) )],[refute_0_83,refute_0_86]) ).
cnf(refute_0_88,plain,
converse(converse(X_16)) = X_16,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_16))]]) ).
cnf(refute_0_89,plain,
( converse(converse(X_16)) != X_16
| converse(converse(X_16)) != composition(converse(one),X_16)
| X_16 = composition(converse(one),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_16)),composition(converse(one),X_16)) ),[0],$fot(X_16)]]) ).
cnf(refute_0_90,plain,
( converse(converse(X_16)) != composition(converse(one),X_16)
| X_16 = composition(converse(one),X_16) ),
inference(resolve,[$cnf( $equal(converse(converse(X_16)),X_16) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
X_16 = composition(converse(one),X_16),
inference(resolve,[$cnf( $equal(converse(converse(X_16)),composition(converse(one),X_16)) )],[refute_0_87,refute_0_90]) ).
cnf(refute_0_92,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_93,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_91:[bind(X_16,$fot(one))]]) ).
cnf(refute_0_94,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_3:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_95,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_97,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_92,refute_0_97]) ).
cnf(refute_0_99,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_3:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_100,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
composition(converse(one),X_16) = composition(converse(one),X_16),
introduced(tautology,[refl,[$fot(composition(converse(one),X_16))]]) ).
cnf(refute_0_102,plain,
( composition(converse(one),X_16) != composition(converse(one),X_16)
| converse(one) != one
| composition(converse(one),X_16) = composition(one,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_16),composition(converse(one),X_16)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_103,plain,
( converse(one) != one
| composition(converse(one),X_16) = composition(one,X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_16),composition(converse(one),X_16)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
composition(converse(one),X_16) = composition(one,X_16),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( X_16 != composition(converse(one),X_16)
| composition(converse(one),X_16) != composition(one,X_16)
| X_16 = composition(one,X_16) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_16,composition(one,X_16)) ),[0],$fot(composition(converse(one),X_16))]]) ).
cnf(refute_0_106,plain,
( X_16 != composition(converse(one),X_16)
| X_16 = composition(one,X_16) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_16),composition(one,X_16)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
X_16 = composition(one,X_16),
inference(resolve,[$cnf( $equal(X_16,composition(converse(one),X_16)) )],[refute_0_91,refute_0_106]) ).
cnf(refute_0_108,plain,
X_24 = composition(one,X_24),
inference(subst,[],[refute_0_107:[bind(X_16,$fot(X_24))]]) ).
cnf(refute_0_109,plain,
( X_24 != composition(one,X_24)
| composition(one,X_24) = X_24 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_24)),bind(Y,$fot(composition(one,X_24)))]]) ).
cnf(refute_0_110,plain,
composition(one,X_24) = X_24,
inference(resolve,[$cnf( $equal(X_24,composition(one,X_24)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( composition(one,X_24) != X_24
| join(complement(X_24),composition(converse(one),complement(composition(one,X_24)))) != complement(X_24)
| join(complement(X_24),composition(converse(one),complement(X_24))) = complement(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(composition(one,X_24)))),complement(X_24)) ),[0,1,1,0],$fot(X_24)]]) ).
cnf(refute_0_112,plain,
( join(complement(X_24),composition(converse(one),complement(composition(one,X_24)))) != complement(X_24)
| join(complement(X_24),composition(converse(one),complement(X_24))) = complement(X_24) ),
inference(resolve,[$cnf( $equal(composition(one,X_24),X_24) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
join(complement(X_24),composition(converse(one),complement(X_24))) = complement(X_24),
inference(resolve,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(composition(one,X_24)))),complement(X_24)) )],[refute_0_78,refute_0_112]) ).
cnf(refute_0_114,plain,
( X_16 != composition(one,X_16)
| composition(one,X_16) = X_16 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_16)),bind(Y,$fot(composition(one,X_16)))]]) ).
cnf(refute_0_115,plain,
composition(one,X_16) = X_16,
inference(resolve,[$cnf( $equal(X_16,composition(one,X_16)) )],[refute_0_107,refute_0_114]) ).
cnf(refute_0_116,plain,
composition(one,complement(X_24)) = complement(X_24),
inference(subst,[],[refute_0_115:[bind(X_16,$fot(complement(X_24)))]]) ).
cnf(refute_0_117,plain,
composition(converse(one),complement(X_24)) = composition(converse(one),complement(X_24)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_24)))]]) ).
cnf(refute_0_118,plain,
( composition(converse(one),complement(X_24)) != composition(converse(one),complement(X_24))
| converse(one) != one
| composition(converse(one),complement(X_24)) = composition(one,complement(X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_24)),composition(converse(one),complement(X_24))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_119,plain,
( converse(one) != one
| composition(converse(one),complement(X_24)) = composition(one,complement(X_24)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_24)),composition(converse(one),complement(X_24))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
composition(converse(one),complement(X_24)) = composition(one,complement(X_24)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_119]) ).
cnf(refute_0_121,plain,
( composition(converse(one),complement(X_24)) != composition(one,complement(X_24))
| composition(one,complement(X_24)) != complement(X_24)
| composition(converse(one),complement(X_24)) = complement(X_24) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(one),complement(X_24)))),bind(Y,$fot(composition(one,complement(X_24)))),bind(Z,$fot(complement(X_24)))]]) ).
cnf(refute_0_122,plain,
( composition(one,complement(X_24)) != complement(X_24)
| composition(converse(one),complement(X_24)) = complement(X_24) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_24)),composition(one,complement(X_24))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
composition(converse(one),complement(X_24)) = complement(X_24),
inference(resolve,[$cnf( $equal(composition(one,complement(X_24)),complement(X_24)) )],[refute_0_116,refute_0_122]) ).
cnf(refute_0_124,plain,
join(complement(X_24),composition(converse(one),complement(X_24))) = join(complement(X_24),composition(converse(one),complement(X_24))),
introduced(tautology,[refl,[$fot(join(complement(X_24),composition(converse(one),complement(X_24))))]]) ).
cnf(refute_0_125,plain,
( composition(converse(one),complement(X_24)) != complement(X_24)
| join(complement(X_24),composition(converse(one),complement(X_24))) != join(complement(X_24),composition(converse(one),complement(X_24)))
| join(complement(X_24),composition(converse(one),complement(X_24))) = join(complement(X_24),complement(X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(X_24))),join(complement(X_24),composition(converse(one),complement(X_24)))) ),[1,1],$fot(complement(X_24))]]) ).
cnf(refute_0_126,plain,
( composition(converse(one),complement(X_24)) != complement(X_24)
| join(complement(X_24),composition(converse(one),complement(X_24))) = join(complement(X_24),complement(X_24)) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(X_24))),join(complement(X_24),composition(converse(one),complement(X_24)))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
join(complement(X_24),composition(converse(one),complement(X_24))) = join(complement(X_24),complement(X_24)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_24)),complement(X_24)) )],[refute_0_123,refute_0_126]) ).
cnf(refute_0_128,plain,
( join(complement(X_24),composition(converse(one),complement(X_24))) != complement(X_24)
| join(complement(X_24),composition(converse(one),complement(X_24))) != join(complement(X_24),complement(X_24))
| join(complement(X_24),complement(X_24)) = complement(X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(X_24))),complement(X_24)) ),[0],$fot(join(complement(X_24),complement(X_24)))]]) ).
cnf(refute_0_129,plain,
( join(complement(X_24),composition(converse(one),complement(X_24))) != complement(X_24)
| join(complement(X_24),complement(X_24)) = complement(X_24) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(X_24))),join(complement(X_24),complement(X_24))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
join(complement(X_24),complement(X_24)) = complement(X_24),
inference(resolve,[$cnf( $equal(join(complement(X_24),composition(converse(one),complement(X_24))),complement(X_24)) )],[refute_0_113,refute_0_129]) ).
cnf(refute_0_131,plain,
join(complement(top),complement(top)) = complement(top),
inference(subst,[],[refute_0_130:[bind(X_24,$fot(top))]]) ).
cnf(refute_0_132,plain,
( complement(top) != zero
| join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_133,plain,
( join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_132]) ).
cnf(refute_0_134,plain,
join(zero,complement(top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) )],[refute_0_131,refute_0_133]) ).
cnf(refute_0_135,plain,
join(zero,complement(top)) = join(zero,complement(top)),
introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).
cnf(refute_0_136,plain,
( complement(top) != zero
| join(zero,complement(top)) != join(zero,complement(top))
| join(zero,complement(top)) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_137,plain,
( complement(top) != zero
| join(zero,complement(top)) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
join(zero,complement(top)) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_137]) ).
cnf(refute_0_139,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,complement(top)) != join(zero,zero)
| join(zero,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),complement(top)) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_140,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
( complement(top) != zero
| join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_142,plain,
( join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_141]) ).
cnf(refute_0_143,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_140,refute_0_142]) ).
cnf(refute_0_144,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,complement(top)),complement(top)) )],[refute_0_134,refute_0_143]) ).
cnf(refute_0_145,plain,
( join(zero,join(zero,X_51)) != join(join(zero,zero),X_51)
| join(zero,zero) != zero
| join(zero,join(zero,X_51)) = join(zero,X_51) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_51)),join(join(zero,zero),X_51)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_146,plain,
( join(zero,join(zero,X_51)) != join(join(zero,zero),X_51)
| join(zero,join(zero,X_51)) = join(zero,X_51) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
join(zero,join(zero,X_51)) = join(zero,X_51),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_51)),join(join(zero,zero),X_51)) )],[refute_0_77,refute_0_146]) ).
cnf(refute_0_148,plain,
join(zero,join(zero,meet(X_76,top))) = join(zero,meet(X_76,top)),
inference(subst,[],[refute_0_147:[bind(X_51,$fot(meet(X_76,top)))]]) ).
cnf(refute_0_149,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_150,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[0],$fot(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))))]]) ).
cnf(refute_0_151,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_151]) ).
cnf(refute_0_153,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_5:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_154,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_155,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_154]) ).
cnf(refute_0_156,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_157,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) ),[1,1],$fot(meet(A,B))]]) ).
cnf(refute_0_158,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_155,refute_0_158]) ).
cnf(refute_0_160,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))),bind(Y,$fot(join(complement(join(complement(A),B)),meet(A,B)))),bind(Z,$fot(join(meet(A,B),complement(join(complement(A),B)))))]]) ).
cnf(refute_0_161,plain,
( join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_153,refute_0_161]) ).
cnf(refute_0_163,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(A,join(meet(A,B),complement(join(complement(A),B)))) ),[0],$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_164,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_152,refute_0_164]) ).
cnf(refute_0_166,plain,
X_74 = join(meet(X_74,top),complement(join(complement(X_74),top))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(top))]]) ).
cnf(refute_0_167,plain,
top = join(join(X_49,X_50),complement(join(X_49,X_50))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_49,X_50)))]]) ).
cnf(refute_0_168,plain,
join(X_49,join(X_50,complement(join(X_49,X_50)))) = join(join(X_49,X_50),complement(join(X_49,X_50))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(X_50)),bind(C,$fot(complement(join(X_49,X_50))))]]) ).
cnf(refute_0_169,plain,
( join(X_49,join(X_50,complement(join(X_49,X_50)))) != join(join(X_49,X_50),complement(join(X_49,X_50)))
| join(join(X_49,X_50),complement(join(X_49,X_50))) = join(X_49,join(X_50,complement(join(X_49,X_50)))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_49,join(X_50,complement(join(X_49,X_50)))))),bind(Y,$fot(join(join(X_49,X_50),complement(join(X_49,X_50)))))]]) ).
cnf(refute_0_170,plain,
join(join(X_49,X_50),complement(join(X_49,X_50))) = join(X_49,join(X_50,complement(join(X_49,X_50)))),
inference(resolve,[$cnf( $equal(join(X_49,join(X_50,complement(join(X_49,X_50)))),join(join(X_49,X_50),complement(join(X_49,X_50)))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
( join(join(X_49,X_50),complement(join(X_49,X_50))) != join(X_49,join(X_50,complement(join(X_49,X_50))))
| top != join(join(X_49,X_50),complement(join(X_49,X_50)))
| top = join(X_49,join(X_50,complement(join(X_49,X_50)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_49,X_50),complement(join(X_49,X_50)))) ),[1],$fot(join(X_49,join(X_50,complement(join(X_49,X_50)))))]]) ).
cnf(refute_0_172,plain,
( top != join(join(X_49,X_50),complement(join(X_49,X_50)))
| top = join(X_49,join(X_50,complement(join(X_49,X_50)))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,X_50),complement(join(X_49,X_50))),join(X_49,join(X_50,complement(join(X_49,X_50))))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
top = join(X_49,join(X_50,complement(join(X_49,X_50)))),
inference(resolve,[$cnf( $equal(top,join(join(X_49,X_50),complement(join(X_49,X_50)))) )],[refute_0_167,refute_0_172]) ).
cnf(refute_0_174,plain,
top = join(X_54,join(top,complement(join(X_54,top)))),
inference(subst,[],[refute_0_173:[bind(X_49,$fot(X_54)),bind(X_50,$fot(top))]]) ).
cnf(refute_0_175,plain,
top = join(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_27),complement(X_28))))]]) ).
cnf(refute_0_176,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| top != join(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))
| top = join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))) ),[1,1],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_177,plain,
( top != join(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))
| top = join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_176]) ).
cnf(refute_0_178,plain,
top = join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_27),complement(X_28)),complement(join(complement(X_27),complement(X_28))))) )],[refute_0_175,refute_0_177]) ).
cnf(refute_0_179,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_180,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_179]) ).
cnf(refute_0_181,plain,
join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) = join(complement(X_27),join(complement(X_28),meet(X_27,X_28))),
inference(subst,[],[refute_0_180:[bind(A,$fot(complement(X_27))),bind(B,$fot(complement(X_28))),bind(C,$fot(meet(X_27,X_28)))]]) ).
cnf(refute_0_182,plain,
( join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)) != join(complement(X_27),join(complement(X_28),meet(X_27,X_28)))
| top != join(join(complement(X_27),complement(X_28)),meet(X_27,X_28))
| top = join(complement(X_27),join(complement(X_28),meet(X_27,X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_27),complement(X_28)),meet(X_27,X_28))) ),[1],$fot(join(complement(X_27),join(complement(X_28),meet(X_27,X_28))))]]) ).
cnf(refute_0_183,plain,
( top != join(join(complement(X_27),complement(X_28)),meet(X_27,X_28))
| top = join(complement(X_27),join(complement(X_28),meet(X_27,X_28))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_27),complement(X_28)),meet(X_27,X_28)),join(complement(X_27),join(complement(X_28),meet(X_27,X_28)))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
top = join(complement(X_27),join(complement(X_28),meet(X_27,X_28))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_27),complement(X_28)),meet(X_27,X_28))) )],[refute_0_178,refute_0_183]) ).
cnf(refute_0_185,plain,
top = join(complement(X_36),join(complement(X_36),meet(X_36,X_36))),
inference(subst,[],[refute_0_184:[bind(X_27,$fot(X_36)),bind(X_28,$fot(X_36))]]) ).
cnf(refute_0_186,plain,
meet(X_28,X_28) = complement(join(complement(X_28),complement(X_28))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_28)),bind(B,$fot(X_28))]]) ).
cnf(refute_0_187,plain,
join(complement(X_28),complement(X_28)) = complement(X_28),
inference(subst,[],[refute_0_130:[bind(X_24,$fot(X_28))]]) ).
cnf(refute_0_188,plain,
( join(complement(X_28),complement(X_28)) != complement(X_28)
| meet(X_28,X_28) != complement(join(complement(X_28),complement(X_28)))
| meet(X_28,X_28) = complement(complement(X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_28,X_28),complement(join(complement(X_28),complement(X_28)))) ),[1,0],$fot(complement(X_28))]]) ).
cnf(refute_0_189,plain,
( meet(X_28,X_28) != complement(join(complement(X_28),complement(X_28)))
| meet(X_28,X_28) = complement(complement(X_28)) ),
inference(resolve,[$cnf( $equal(join(complement(X_28),complement(X_28)),complement(X_28)) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
meet(X_28,X_28) = complement(complement(X_28)),
inference(resolve,[$cnf( $equal(meet(X_28,X_28),complement(join(complement(X_28),complement(X_28)))) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
meet(X_36,X_36) = complement(complement(X_36)),
inference(subst,[],[refute_0_190:[bind(X_28,$fot(X_36))]]) ).
cnf(refute_0_192,plain,
( meet(X_36,X_36) != complement(complement(X_36))
| top != join(complement(X_36),join(complement(X_36),meet(X_36,X_36)))
| top = join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_36),join(complement(X_36),meet(X_36,X_36)))) ),[1,1,1],$fot(complement(complement(X_36)))]]) ).
cnf(refute_0_193,plain,
( top != join(complement(X_36),join(complement(X_36),meet(X_36,X_36)))
| top = join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) ),
inference(resolve,[$cnf( $equal(meet(X_36,X_36),complement(complement(X_36))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
top = join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_36),join(complement(X_36),meet(X_36,X_36)))) )],[refute_0_185,refute_0_193]) ).
cnf(refute_0_195,plain,
join(complement(X_36),top) = join(top,complement(X_36)),
inference(subst,[],[refute_0_5:[bind(A,$fot(top)),bind(B,$fot(complement(X_36)))]]) ).
cnf(refute_0_196,plain,
join(complement(X_36),complement(complement(X_36))) = top,
inference(subst,[],[refute_0_46:[bind(A,$fot(complement(X_36)))]]) ).
cnf(refute_0_197,plain,
join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),
introduced(tautology,[refl,[$fot(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))))]]) ).
cnf(refute_0_198,plain,
( join(complement(X_36),complement(complement(X_36))) != top
| join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) != join(complement(X_36),join(complement(X_36),complement(complement(X_36))))
| join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(complement(X_36),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),join(complement(X_36),join(complement(X_36),complement(complement(X_36))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_199,plain,
( join(complement(X_36),complement(complement(X_36))) != top
| join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(complement(X_36),top) ),
inference(resolve,[$cnf( $equal(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),join(complement(X_36),join(complement(X_36),complement(complement(X_36))))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(complement(X_36),top),
inference(resolve,[$cnf( $equal(join(complement(X_36),complement(complement(X_36))),top) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) != join(complement(X_36),top)
| join(complement(X_36),top) != join(top,complement(X_36))
| join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(top,complement(X_36)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))))),bind(Y,$fot(join(complement(X_36),top))),bind(Z,$fot(join(top,complement(X_36))))]]) ).
cnf(refute_0_202,plain,
( join(complement(X_36),top) != join(top,complement(X_36))
| join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(top,complement(X_36)) ),
inference(resolve,[$cnf( $equal(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),join(complement(X_36),top)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) = join(top,complement(X_36)),
inference(resolve,[$cnf( $equal(join(complement(X_36),top),join(top,complement(X_36))) )],[refute_0_195,refute_0_202]) ).
cnf(refute_0_204,plain,
( join(complement(X_36),join(complement(X_36),complement(complement(X_36)))) != join(top,complement(X_36))
| top != join(complement(X_36),join(complement(X_36),complement(complement(X_36))))
| top = join(top,complement(X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_36),join(complement(X_36),complement(complement(X_36))))) ),[1],$fot(join(top,complement(X_36)))]]) ).
cnf(refute_0_205,plain,
( top != join(complement(X_36),join(complement(X_36),complement(complement(X_36))))
| top = join(top,complement(X_36)) ),
inference(resolve,[$cnf( $equal(join(complement(X_36),join(complement(X_36),complement(complement(X_36)))),join(top,complement(X_36))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
top = join(top,complement(X_36)),
inference(resolve,[$cnf( $equal(top,join(complement(X_36),join(complement(X_36),complement(complement(X_36))))) )],[refute_0_194,refute_0_205]) ).
cnf(refute_0_207,plain,
top = join(top,complement(join(X_54,top))),
inference(subst,[],[refute_0_206:[bind(X_36,$fot(join(X_54,top)))]]) ).
cnf(refute_0_208,plain,
( top != join(top,complement(join(X_54,top)))
| join(top,complement(join(X_54,top))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(join(X_54,top)))))]]) ).
cnf(refute_0_209,plain,
join(top,complement(join(X_54,top))) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(join(X_54,top)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
( join(top,complement(join(X_54,top))) != top
| top != join(X_54,join(top,complement(join(X_54,top))))
| top = join(X_54,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(X_54,join(top,complement(join(X_54,top))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_211,plain,
( top != join(X_54,join(top,complement(join(X_54,top))))
| top = join(X_54,top) ),
inference(resolve,[$cnf( $equal(join(top,complement(join(X_54,top))),top) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
top = join(X_54,top),
inference(resolve,[$cnf( $equal(top,join(X_54,join(top,complement(join(X_54,top))))) )],[refute_0_174,refute_0_211]) ).
cnf(refute_0_213,plain,
top = join(complement(X_74),top),
inference(subst,[],[refute_0_212:[bind(X_54,$fot(complement(X_74)))]]) ).
cnf(refute_0_214,plain,
( top != join(complement(X_74),top)
| join(complement(X_74),top) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_74),top)))]]) ).
cnf(refute_0_215,plain,
join(complement(X_74),top) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_74),top)) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
( X_74 != join(meet(X_74,top),complement(join(complement(X_74),top)))
| join(complement(X_74),top) != top
| X_74 = join(meet(X_74,top),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,top),complement(join(complement(X_74),top)))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_217,plain,
( X_74 != join(meet(X_74,top),complement(join(complement(X_74),top)))
| X_74 = join(meet(X_74,top),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_74),top),top) )],[refute_0_215,refute_0_216]) ).
cnf(refute_0_218,plain,
X_74 = join(meet(X_74,top),complement(top)),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,top),complement(join(complement(X_74),top)))) )],[refute_0_166,refute_0_217]) ).
cnf(refute_0_219,plain,
join(complement(top),meet(X_74,top)) = join(complement(top),meet(X_74,top)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_74,top)))]]) ).
cnf(refute_0_220,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,top)) != join(complement(top),meet(X_74,top))
| join(complement(top),meet(X_74,top)) = join(zero,meet(X_74,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_74,top)),join(complement(top),meet(X_74,top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_221,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,top)) = join(zero,meet(X_74,top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,top)),join(complement(top),meet(X_74,top))) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
join(complement(top),meet(X_74,top)) = join(zero,meet(X_74,top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_221]) ).
cnf(refute_0_223,plain,
join(meet(X_74,top),complement(top)) = join(complement(top),meet(X_74,top)),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_74,top)))]]) ).
cnf(refute_0_224,plain,
( join(complement(top),meet(X_74,top)) != join(zero,meet(X_74,top))
| join(meet(X_74,top),complement(top)) != join(complement(top),meet(X_74,top))
| join(meet(X_74,top),complement(top)) = join(zero,meet(X_74,top)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(X_74,top),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_74,top)))),bind(Z,$fot(join(zero,meet(X_74,top))))]]) ).
cnf(refute_0_225,plain,
( join(complement(top),meet(X_74,top)) != join(zero,meet(X_74,top))
| join(meet(X_74,top),complement(top)) = join(zero,meet(X_74,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,top),complement(top)),join(complement(top),meet(X_74,top))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
join(meet(X_74,top),complement(top)) = join(zero,meet(X_74,top)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,top)),join(zero,meet(X_74,top))) )],[refute_0_222,refute_0_225]) ).
cnf(refute_0_227,plain,
( X_74 != join(meet(X_74,top),complement(top))
| join(meet(X_74,top),complement(top)) != join(zero,meet(X_74,top))
| X_74 = join(zero,meet(X_74,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(zero,meet(X_74,top))) ),[0],$fot(join(meet(X_74,top),complement(top)))]]) ).
cnf(refute_0_228,plain,
( X_74 != join(meet(X_74,top),complement(top))
| X_74 = join(zero,meet(X_74,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,top),complement(top)),join(zero,meet(X_74,top))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
X_74 = join(zero,meet(X_74,top)),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,top),complement(top))) )],[refute_0_218,refute_0_228]) ).
cnf(refute_0_230,plain,
X_76 = join(zero,meet(X_76,top)),
inference(subst,[],[refute_0_229:[bind(X_74,$fot(X_76))]]) ).
cnf(refute_0_231,plain,
( X_76 != join(zero,meet(X_76,top))
| join(zero,meet(X_76,top)) = X_76 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_76)),bind(Y,$fot(join(zero,meet(X_76,top))))]]) ).
cnf(refute_0_232,plain,
join(zero,meet(X_76,top)) = X_76,
inference(resolve,[$cnf( $equal(X_76,join(zero,meet(X_76,top))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( join(zero,join(zero,meet(X_76,top))) != join(zero,meet(X_76,top))
| join(zero,meet(X_76,top)) != X_76
| join(zero,X_76) = join(zero,meet(X_76,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_76,top))),join(zero,meet(X_76,top))) ),[0,1],$fot(X_76)]]) ).
cnf(refute_0_234,plain,
( join(zero,join(zero,meet(X_76,top))) != join(zero,meet(X_76,top))
| join(zero,X_76) = join(zero,meet(X_76,top)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_76,top)),X_76) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
join(zero,X_76) = join(zero,meet(X_76,top)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_76,top))),join(zero,meet(X_76,top))) )],[refute_0_148,refute_0_234]) ).
cnf(refute_0_236,plain,
( join(zero,X_76) != join(zero,meet(X_76,top))
| join(zero,meet(X_76,top)) != X_76
| join(zero,X_76) = X_76 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_76),X_76) ),[0],$fot(join(zero,meet(X_76,top)))]]) ).
cnf(refute_0_237,plain,
( join(zero,X_76) != join(zero,meet(X_76,top))
| join(zero,X_76) = X_76 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_76,top)),X_76) )],[refute_0_232,refute_0_236]) ).
cnf(refute_0_238,plain,
join(zero,X_76) = X_76,
inference(resolve,[$cnf( $equal(join(zero,X_76),join(zero,meet(X_76,top))) )],[refute_0_235,refute_0_237]) ).
cnf(refute_0_239,plain,
join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) = composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))))]]) ).
cnf(refute_0_240,plain,
( join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) != composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))
| join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) != zero
| composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))),zero) ),[0],$fot(composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top))))]]) ).
cnf(refute_0_241,plain,
( join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) != zero
| composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))),composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(join(X_48,X_47)),complement(composition(join(X_47,X_48),top)))),zero) )],[refute_0_76,refute_0_241]) ).
cnf(refute_0_243,plain,
composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(join(complement(sk1),composition(sk1,complement(one))),top))) = zero,
inference(subst,[],[refute_0_242:[bind(X_47,$fot(complement(sk1))),bind(X_48,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_244,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_245,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_246,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_245]) ).
cnf(refute_0_247,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_244,refute_0_246]) ).
cnf(refute_0_248,plain,
meet(top,join(complement(sk1),composition(sk1,complement(one)))) = complement(join(zero,complement(join(complement(sk1),composition(sk1,complement(one)))))),
inference(subst,[],[refute_0_247:[bind(B,$fot(join(complement(sk1),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_249,plain,
sk1 = join(meet(sk1,composition(sk1,complement(one))),complement(join(complement(sk1),composition(sk1,complement(one))))),
inference(subst,[],[refute_0_165:[bind(A,$fot(sk1)),bind(B,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_250,plain,
meet(composition(sk1,one),composition(sk1,complement(one))) = zero,
inference(subst,[],[goals_14:[bind(A,$fot(one))]]) ).
cnf(refute_0_251,plain,
composition(sk1,one) = sk1,
inference(subst,[],[composition_identity_6:[bind(A,$fot(sk1))]]) ).
cnf(refute_0_252,plain,
( composition(sk1,one) != sk1
| meet(composition(sk1,one),composition(sk1,complement(one))) != zero
| meet(sk1,composition(sk1,complement(one))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(composition(sk1,one),composition(sk1,complement(one))),zero) ),[0,0],$fot(sk1)]]) ).
cnf(refute_0_253,plain,
( meet(composition(sk1,one),composition(sk1,complement(one))) != zero
| meet(sk1,composition(sk1,complement(one))) = zero ),
inference(resolve,[$cnf( $equal(composition(sk1,one),sk1) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
meet(sk1,composition(sk1,complement(one))) = zero,
inference(resolve,[$cnf( $equal(meet(composition(sk1,one),composition(sk1,complement(one))),zero) )],[refute_0_250,refute_0_253]) ).
cnf(refute_0_255,plain,
( meet(sk1,composition(sk1,complement(one))) != zero
| sk1 != join(meet(sk1,composition(sk1,complement(one))),complement(join(complement(sk1),composition(sk1,complement(one)))))
| sk1 = join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(sk1,join(meet(sk1,composition(sk1,complement(one))),complement(join(complement(sk1),composition(sk1,complement(one)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_256,plain,
( sk1 != join(meet(sk1,composition(sk1,complement(one))),complement(join(complement(sk1),composition(sk1,complement(one)))))
| sk1 = join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(meet(sk1,composition(sk1,complement(one))),zero) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
sk1 = join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(sk1,join(meet(sk1,composition(sk1,complement(one))),complement(join(complement(sk1),composition(sk1,complement(one)))))) )],[refute_0_249,refute_0_256]) ).
cnf(refute_0_258,plain,
( sk1 != join(zero,complement(join(complement(sk1),composition(sk1,complement(one)))))
| join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))) = sk1 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(sk1)),bind(Y,$fot(join(zero,complement(join(complement(sk1),composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_259,plain,
join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))) = sk1,
inference(resolve,[$cnf( $equal(sk1,join(zero,complement(join(complement(sk1),composition(sk1,complement(one)))))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
( join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))) != sk1
| meet(top,join(complement(sk1),composition(sk1,complement(one)))) != complement(join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))))
| meet(top,join(complement(sk1),composition(sk1,complement(one)))) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(sk1),composition(sk1,complement(one)))),complement(join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_261,plain,
( meet(top,join(complement(sk1),composition(sk1,complement(one)))) != complement(join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))))
| meet(top,join(complement(sk1),composition(sk1,complement(one)))) = complement(sk1) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))),sk1) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
meet(top,join(complement(sk1),composition(sk1,complement(one)))) = complement(sk1),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),composition(sk1,complement(one)))),complement(join(zero,complement(join(complement(sk1),composition(sk1,complement(one))))))) )],[refute_0_248,refute_0_261]) ).
cnf(refute_0_263,plain,
join(complement(X_28),complement(X_27)) = join(complement(X_27),complement(X_28)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_28))),bind(B,$fot(complement(X_27)))]]) ).
cnf(refute_0_264,plain,
( join(complement(X_28),complement(X_27)) != join(complement(X_27),complement(X_28))
| join(complement(X_27),complement(X_28)) = join(complement(X_28),complement(X_27)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(complement(X_28),complement(X_27)))),bind(Y,$fot(join(complement(X_27),complement(X_28))))]]) ).
cnf(refute_0_265,plain,
join(complement(X_27),complement(X_28)) = join(complement(X_28),complement(X_27)),
inference(resolve,[$cnf( $equal(join(complement(X_28),complement(X_27)),join(complement(X_27),complement(X_28))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( join(complement(X_27),complement(X_28)) != join(complement(X_28),complement(X_27))
| meet(X_27,X_28) != complement(join(complement(X_27),complement(X_28)))
| meet(X_27,X_28) = complement(join(complement(X_28),complement(X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) ),[1,0],$fot(join(complement(X_28),complement(X_27)))]]) ).
cnf(refute_0_267,plain,
( meet(X_27,X_28) != complement(join(complement(X_27),complement(X_28)))
| meet(X_27,X_28) = complement(join(complement(X_28),complement(X_27))) ),
inference(resolve,[$cnf( $equal(join(complement(X_27),complement(X_28)),join(complement(X_28),complement(X_27))) )],[refute_0_265,refute_0_266]) ).
cnf(refute_0_268,plain,
meet(X_27,X_28) = complement(join(complement(X_28),complement(X_27))),
inference(resolve,[$cnf( $equal(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) )],[refute_0_39,refute_0_267]) ).
cnf(refute_0_269,plain,
complement(join(complement(X_28),complement(X_27))) = meet(X_28,X_27),
inference(subst,[],[refute_0_155:[bind(A,$fot(X_28)),bind(B,$fot(X_27))]]) ).
cnf(refute_0_270,plain,
( complement(join(complement(X_28),complement(X_27))) != meet(X_28,X_27)
| meet(X_27,X_28) != complement(join(complement(X_28),complement(X_27)))
| meet(X_27,X_28) = meet(X_28,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_27,X_28),complement(join(complement(X_28),complement(X_27)))) ),[1],$fot(meet(X_28,X_27))]]) ).
cnf(refute_0_271,plain,
( meet(X_27,X_28) != complement(join(complement(X_28),complement(X_27)))
| meet(X_27,X_28) = meet(X_28,X_27) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_28),complement(X_27))),meet(X_28,X_27)) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
meet(X_27,X_28) = meet(X_28,X_27),
inference(resolve,[$cnf( $equal(meet(X_27,X_28),complement(join(complement(X_28),complement(X_27)))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
meet(top,X_76) = meet(X_76,top),
inference(subst,[],[refute_0_272:[bind(X_27,$fot(top)),bind(X_28,$fot(X_76))]]) ).
cnf(refute_0_274,plain,
( meet(top,X_76) != meet(X_76,top)
| meet(X_76,top) = meet(top,X_76) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(top,X_76))),bind(Y,$fot(meet(X_76,top)))]]) ).
cnf(refute_0_275,plain,
meet(X_76,top) = meet(top,X_76),
inference(resolve,[$cnf( $equal(meet(top,X_76),meet(X_76,top)) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
( X_76 != join(zero,meet(X_76,top))
| meet(X_76,top) != meet(top,X_76)
| X_76 = join(zero,meet(top,X_76)) ),
introduced(tautology,[equality,[$cnf( $equal(X_76,join(zero,meet(X_76,top))) ),[1,1],$fot(meet(top,X_76))]]) ).
cnf(refute_0_277,plain,
( X_76 != join(zero,meet(X_76,top))
| X_76 = join(zero,meet(top,X_76)) ),
inference(resolve,[$cnf( $equal(meet(X_76,top),meet(top,X_76)) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
X_76 = join(zero,meet(top,X_76)),
inference(resolve,[$cnf( $equal(X_76,join(zero,meet(X_76,top))) )],[refute_0_230,refute_0_277]) ).
cnf(refute_0_279,plain,
join(zero,meet(top,X_76)) = meet(top,X_76),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(top,X_76)))]]) ).
cnf(refute_0_280,plain,
( X_76 != join(zero,meet(top,X_76))
| join(zero,meet(top,X_76)) != meet(top,X_76)
| X_76 = meet(top,X_76) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_76,meet(top,X_76)) ),[0],$fot(join(zero,meet(top,X_76)))]]) ).
cnf(refute_0_281,plain,
( X_76 != join(zero,meet(top,X_76))
| X_76 = meet(top,X_76) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_76)),meet(top,X_76)) )],[refute_0_279,refute_0_280]) ).
cnf(refute_0_282,plain,
X_76 = meet(top,X_76),
inference(resolve,[$cnf( $equal(X_76,join(zero,meet(top,X_76))) )],[refute_0_278,refute_0_281]) ).
cnf(refute_0_283,plain,
( X_76 != meet(top,X_76)
| meet(top,X_76) = X_76 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_76)),bind(Y,$fot(meet(top,X_76)))]]) ).
cnf(refute_0_284,plain,
meet(top,X_76) = X_76,
inference(resolve,[$cnf( $equal(X_76,meet(top,X_76)) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
meet(top,join(complement(sk1),composition(sk1,complement(one)))) = join(complement(sk1),composition(sk1,complement(one))),
inference(subst,[],[refute_0_284:[bind(X_76,$fot(join(complement(sk1),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_286,plain,
( meet(top,join(complement(sk1),composition(sk1,complement(one)))) != complement(sk1)
| meet(top,join(complement(sk1),composition(sk1,complement(one)))) != join(complement(sk1),composition(sk1,complement(one)))
| join(complement(sk1),composition(sk1,complement(one))) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(sk1),composition(sk1,complement(one)))),complement(sk1)) ),[0],$fot(join(complement(sk1),composition(sk1,complement(one))))]]) ).
cnf(refute_0_287,plain,
( meet(top,join(complement(sk1),composition(sk1,complement(one)))) != complement(sk1)
| join(complement(sk1),composition(sk1,complement(one))) = complement(sk1) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),composition(sk1,complement(one)))),join(complement(sk1),composition(sk1,complement(one)))) )],[refute_0_285,refute_0_286]) ).
cnf(refute_0_288,plain,
join(complement(sk1),composition(sk1,complement(one))) = complement(sk1),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),composition(sk1,complement(one)))),complement(sk1)) )],[refute_0_262,refute_0_287]) ).
cnf(refute_0_289,plain,
( composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(join(complement(sk1),composition(sk1,complement(one))),top))) != zero
| join(complement(sk1),composition(sk1,complement(one))) != complement(sk1)
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(join(complement(sk1),composition(sk1,complement(one))),top))),zero) ),[0,1,0,0],$fot(complement(sk1))]]) ).
cnf(refute_0_290,plain,
( composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(join(complement(sk1),composition(sk1,complement(one))),top))) != zero
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = zero ),
inference(resolve,[$cnf( $equal(join(complement(sk1),composition(sk1,complement(one))),complement(sk1)) )],[refute_0_288,refute_0_289]) ).
cnf(refute_0_291,plain,
composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(join(complement(sk1),composition(sk1,complement(one))),top))),zero) )],[refute_0_243,refute_0_290]) ).
cnf(refute_0_292,plain,
composition(join(converse(A),X_123),complement(composition(A,top))) = join(composition(converse(A),complement(composition(A,top))),composition(X_123,complement(composition(A,top)))),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(converse(A))),bind(B,$fot(X_123)),bind(C,$fot(complement(composition(A,top))))]]) ).
cnf(refute_0_293,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = composition(converse(A),complement(composition(A,top))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(composition(converse(A),complement(composition(A,top)))))]]) ).
cnf(refute_0_294,plain,
( join(zero,composition(converse(A),complement(composition(A,top)))) != composition(converse(A),complement(composition(A,top)))
| join(zero,composition(converse(A),complement(composition(A,top)))) != zero
| composition(converse(A),complement(composition(A,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),zero) ),[0],$fot(composition(converse(A),complement(composition(A,top))))]]) ).
cnf(refute_0_295,plain,
( join(zero,composition(converse(A),complement(composition(A,top)))) != zero
| composition(converse(A),complement(composition(A,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),composition(converse(A),complement(composition(A,top)))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),zero) )],[refute_0_72,refute_0_295]) ).
cnf(refute_0_297,plain,
( composition(converse(A),complement(composition(A,top))) != zero
| composition(join(converse(A),X_123),complement(composition(A,top))) != join(composition(converse(A),complement(composition(A,top))),composition(X_123,complement(composition(A,top))))
| composition(join(converse(A),X_123),complement(composition(A,top))) = join(zero,composition(X_123,complement(composition(A,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(A),X_123),complement(composition(A,top))),join(composition(converse(A),complement(composition(A,top))),composition(X_123,complement(composition(A,top))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_298,plain,
( composition(join(converse(A),X_123),complement(composition(A,top))) != join(composition(converse(A),complement(composition(A,top))),composition(X_123,complement(composition(A,top))))
| composition(join(converse(A),X_123),complement(composition(A,top))) = join(zero,composition(X_123,complement(composition(A,top)))) ),
inference(resolve,[$cnf( $equal(composition(converse(A),complement(composition(A,top))),zero) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
composition(join(converse(A),X_123),complement(composition(A,top))) = join(zero,composition(X_123,complement(composition(A,top)))),
inference(resolve,[$cnf( $equal(composition(join(converse(A),X_123),complement(composition(A,top))),join(composition(converse(A),complement(composition(A,top))),composition(X_123,complement(composition(A,top))))) )],[refute_0_292,refute_0_298]) ).
cnf(refute_0_300,plain,
join(zero,composition(X_123,complement(composition(A,top)))) = composition(X_123,complement(composition(A,top))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(composition(X_123,complement(composition(A,top)))))]]) ).
cnf(refute_0_301,plain,
( composition(join(converse(A),X_123),complement(composition(A,top))) != join(zero,composition(X_123,complement(composition(A,top))))
| join(zero,composition(X_123,complement(composition(A,top)))) != composition(X_123,complement(composition(A,top)))
| composition(join(converse(A),X_123),complement(composition(A,top))) = composition(X_123,complement(composition(A,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(converse(A),X_123),complement(composition(A,top))),composition(X_123,complement(composition(A,top)))) ),[0],$fot(join(zero,composition(X_123,complement(composition(A,top)))))]]) ).
cnf(refute_0_302,plain,
( composition(join(converse(A),X_123),complement(composition(A,top))) != join(zero,composition(X_123,complement(composition(A,top))))
| composition(join(converse(A),X_123),complement(composition(A,top))) = composition(X_123,complement(composition(A,top))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_123,complement(composition(A,top)))),composition(X_123,complement(composition(A,top)))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
composition(join(converse(A),X_123),complement(composition(A,top))) = composition(X_123,complement(composition(A,top))),
inference(resolve,[$cnf( $equal(composition(join(converse(A),X_123),complement(composition(A,top))),join(zero,composition(X_123,complement(composition(A,top))))) )],[refute_0_299,refute_0_302]) ).
cnf(refute_0_304,plain,
composition(join(converse(X_203),converse(B)),complement(composition(X_203,top))) = composition(converse(B),complement(composition(X_203,top))),
inference(subst,[],[refute_0_303:[bind(A,$fot(X_203)),bind(X_123,$fot(converse(B)))]]) ).
cnf(refute_0_305,plain,
converse(join(X_203,B)) = join(converse(X_203),converse(B)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_203))]]) ).
cnf(refute_0_306,plain,
( converse(join(X_203,B)) != join(converse(X_203),converse(B))
| join(converse(X_203),converse(B)) = converse(join(X_203,B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(join(X_203,B)))),bind(Y,$fot(join(converse(X_203),converse(B))))]]) ).
cnf(refute_0_307,plain,
join(converse(X_203),converse(B)) = converse(join(X_203,B)),
inference(resolve,[$cnf( $equal(converse(join(X_203,B)),join(converse(X_203),converse(B))) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
( composition(join(converse(X_203),converse(B)),complement(composition(X_203,top))) != composition(converse(B),complement(composition(X_203,top)))
| join(converse(X_203),converse(B)) != converse(join(X_203,B))
| composition(converse(join(X_203,B)),complement(composition(X_203,top))) = composition(converse(B),complement(composition(X_203,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(X_203),converse(B)),complement(composition(X_203,top))),composition(converse(B),complement(composition(X_203,top)))) ),[0,0],$fot(converse(join(X_203,B)))]]) ).
cnf(refute_0_309,plain,
( composition(join(converse(X_203),converse(B)),complement(composition(X_203,top))) != composition(converse(B),complement(composition(X_203,top)))
| composition(converse(join(X_203,B)),complement(composition(X_203,top))) = composition(converse(B),complement(composition(X_203,top))) ),
inference(resolve,[$cnf( $equal(join(converse(X_203),converse(B)),converse(join(X_203,B))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
composition(converse(join(X_203,B)),complement(composition(X_203,top))) = composition(converse(B),complement(composition(X_203,top))),
inference(resolve,[$cnf( $equal(composition(join(converse(X_203),converse(B)),complement(composition(X_203,top))),composition(converse(B),complement(composition(X_203,top)))) )],[refute_0_304,refute_0_309]) ).
cnf(refute_0_311,plain,
composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))) = composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))),
inference(subst,[],[refute_0_310:[bind(B,$fot(composition(sk1,complement(one)))),bind(X_203,$fot(complement(sk1)))]]) ).
cnf(refute_0_312,plain,
converse(composition(converse(A),join(X_47,X_48))) = composition(converse(join(X_47,X_48)),A),
inference(subst,[],[refute_0_82:[bind(X_6,$fot(join(X_47,X_48)))]]) ).
cnf(refute_0_313,plain,
( converse(composition(converse(A),join(X_47,X_48))) != composition(converse(join(X_47,X_48)),A)
| converse(join(X_47,X_48)) != converse(join(X_48,X_47))
| converse(composition(converse(A),join(X_47,X_48))) = composition(converse(join(X_48,X_47)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),join(X_47,X_48))),composition(converse(join(X_47,X_48)),A)) ),[1,0],$fot(converse(join(X_48,X_47)))]]) ).
cnf(refute_0_314,plain,
( converse(composition(converse(A),join(X_47,X_48))) != composition(converse(join(X_47,X_48)),A)
| converse(composition(converse(A),join(X_47,X_48))) = composition(converse(join(X_48,X_47)),A) ),
inference(resolve,[$cnf( $equal(converse(join(X_47,X_48)),converse(join(X_48,X_47))) )],[refute_0_30,refute_0_313]) ).
cnf(refute_0_315,plain,
converse(composition(converse(A),join(X_47,X_48))) = composition(converse(join(X_48,X_47)),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),join(X_47,X_48))),composition(converse(join(X_47,X_48)),A)) )],[refute_0_312,refute_0_314]) ).
cnf(refute_0_316,plain,
( converse(composition(converse(A),join(X_47,X_48))) != composition(converse(join(X_47,X_48)),A)
| converse(composition(converse(A),join(X_47,X_48))) != composition(converse(join(X_48,X_47)),A)
| composition(converse(join(X_47,X_48)),A) = composition(converse(join(X_48,X_47)),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),join(X_47,X_48))),composition(converse(join(X_48,X_47)),A)) ),[0],$fot(composition(converse(join(X_47,X_48)),A))]]) ).
cnf(refute_0_317,plain,
( converse(composition(converse(A),join(X_47,X_48))) != composition(converse(join(X_48,X_47)),A)
| composition(converse(join(X_47,X_48)),A) = composition(converse(join(X_48,X_47)),A) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),join(X_47,X_48))),composition(converse(join(X_47,X_48)),A)) )],[refute_0_312,refute_0_316]) ).
cnf(refute_0_318,plain,
composition(converse(join(X_47,X_48)),A) = composition(converse(join(X_48,X_47)),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),join(X_47,X_48))),composition(converse(join(X_48,X_47)),A)) )],[refute_0_315,refute_0_317]) ).
cnf(refute_0_319,plain,
( composition(converse(join(X_47,X_48)),A) != composition(converse(join(X_48,X_47)),A)
| composition(converse(join(X_48,X_47)),A) = composition(converse(join(X_47,X_48)),A) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(converse(join(X_47,X_48)),A))),bind(Y,$fot(composition(converse(join(X_48,X_47)),A)))]]) ).
cnf(refute_0_320,plain,
composition(converse(join(X_48,X_47)),A) = composition(converse(join(X_47,X_48)),A),
inference(resolve,[$cnf( $equal(composition(converse(join(X_47,X_48)),A),composition(converse(join(X_48,X_47)),A)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))),
inference(subst,[],[refute_0_320:[bind(A,$fot(complement(composition(complement(sk1),top)))),bind(X_47,$fot(complement(sk1))),bind(X_48,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_322,plain,
( composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))) != composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) != composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top)))
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))))),bind(Y,$fot(composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))))),bind(Z,$fot(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))))]]) ).
cnf(refute_0_323,plain,
( composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))) != composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))),composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top)))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) = composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))),
inference(resolve,[$cnf( $equal(composition(converse(join(complement(sk1),composition(sk1,complement(one)))),complement(composition(complement(sk1),top))),composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) )],[refute_0_311,refute_0_323]) ).
cnf(refute_0_325,plain,
( composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) != composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))
| composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) != zero
| composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))),zero) ),[0],$fot(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))))]]) ).
cnf(refute_0_326,plain,
( composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))) != zero
| composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))),composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) = zero,
inference(resolve,[$cnf( $equal(composition(converse(join(composition(sk1,complement(one)),complement(sk1))),complement(composition(complement(sk1),top))),zero) )],[refute_0_291,refute_0_326]) ).
cnf(refute_0_328,plain,
( composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))) != zero
| converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| converse(zero) = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))),composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_329,plain,
( converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| converse(zero) = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))),zero) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
converse(zero) = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))),composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) )],[refute_0_36,refute_0_329]) ).
cnf(refute_0_331,plain,
zero = meet(converse(zero),complement(converse(zero))),
inference(subst,[],[def_zero_13:[bind(A,$fot(converse(zero)))]]) ).
cnf(refute_0_332,plain,
converse(join(converse(A),X_10)) = join(converse(converse(A)),converse(X_10)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_10))]]) ).
cnf(refute_0_333,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_10)) != join(converse(converse(A)),converse(X_10))
| converse(join(converse(A),X_10)) = join(A,converse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_10)),join(converse(converse(A)),converse(X_10))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_334,plain,
( converse(join(converse(A),X_10)) != join(converse(converse(A)),converse(X_10))
| converse(join(converse(A),X_10)) = join(A,converse(X_10)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_333]) ).
cnf(refute_0_335,plain,
converse(join(converse(A),X_10)) = join(A,converse(X_10)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_10)),join(converse(converse(A)),converse(X_10))) )],[refute_0_332,refute_0_334]) ).
cnf(refute_0_336,plain,
converse(join(converse(X_13),complement(converse(X_13)))) = join(X_13,converse(complement(converse(X_13)))),
inference(subst,[],[refute_0_335:[bind(A,$fot(X_13)),bind(X_10,$fot(complement(converse(X_13))))]]) ).
cnf(refute_0_337,plain,
top = join(converse(X_13),complement(converse(X_13))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_13)))]]) ).
cnf(refute_0_338,plain,
( top != join(converse(X_13),complement(converse(X_13)))
| join(converse(X_13),complement(converse(X_13))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_13),complement(converse(X_13)))))]]) ).
cnf(refute_0_339,plain,
join(converse(X_13),complement(converse(X_13))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_13),complement(converse(X_13)))) )],[refute_0_337,refute_0_338]) ).
cnf(refute_0_340,plain,
( converse(join(converse(X_13),complement(converse(X_13)))) != join(X_13,converse(complement(converse(X_13))))
| join(converse(X_13),complement(converse(X_13))) != top
| converse(top) = join(X_13,converse(complement(converse(X_13)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_13),complement(converse(X_13)))),join(X_13,converse(complement(converse(X_13))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_341,plain,
( converse(join(converse(X_13),complement(converse(X_13)))) != join(X_13,converse(complement(converse(X_13))))
| converse(top) = join(X_13,converse(complement(converse(X_13)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_13),complement(converse(X_13))),top) )],[refute_0_339,refute_0_340]) ).
cnf(refute_0_342,plain,
converse(top) = join(X_13,converse(complement(converse(X_13)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_13),complement(converse(X_13)))),join(X_13,converse(complement(converse(X_13))))) )],[refute_0_336,refute_0_341]) ).
cnf(refute_0_343,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(join(converse(top),complement(converse(zero)))),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(complement(converse(zero)))),bind(X_9,$fot(converse(top)))]]) ).
cnf(refute_0_344,plain,
converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(converse(complement(converse(zero))))),bind(X_9,$fot(top))]]) ).
cnf(refute_0_345,plain,
join(top,join(zero,X_51)) = join(join(top,zero),X_51),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_51))]]) ).
cnf(refute_0_346,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_347,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_348,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_347]) ).
cnf(refute_0_349,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_346,refute_0_348]) ).
cnf(refute_0_350,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_351,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
( join(top,join(zero,X_51)) != join(join(top,zero),X_51)
| join(top,zero) != top
| join(top,join(zero,X_51)) = join(top,X_51) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_51)),join(join(top,zero),X_51)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_353,plain,
( join(top,join(zero,X_51)) != join(join(top,zero),X_51)
| join(top,join(zero,X_51)) = join(top,X_51) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
join(top,join(zero,X_51)) = join(top,X_51),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_51)),join(join(top,zero),X_51)) )],[refute_0_345,refute_0_353]) ).
cnf(refute_0_355,plain,
join(top,join(zero,converse(complement(converse(zero))))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_354:[bind(X_51,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_356,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_342:[bind(X_13,$fot(zero))]]) ).
cnf(refute_0_357,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_358,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) != converse(top)
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_360,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_358,refute_0_359]) ).
cnf(refute_0_361,plain,
join(top,converse(top)) = join(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) )],[refute_0_355,refute_0_360]) ).
cnf(refute_0_362,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(top,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_363,plain,
join(top,converse(complement(converse(zero)))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(zero))))) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(complement(converse(zero)))))
| join(top,converse(complement(converse(zero)))) != join(top,converse(top))
| converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(complement(converse(zero)))))) ),[1,0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_365,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(complement(converse(zero)))))
| converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),join(top,converse(top))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
converse(join(converse(complement(converse(zero))),top)) = converse(join(top,converse(top))),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_344,refute_0_365]) ).
cnf(refute_0_367,plain,
converse(join(X_9,converse(A))) = join(converse(X_9),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_9)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_368,plain,
( converse(converse(A)) != A
| converse(join(X_9,converse(A))) != join(converse(X_9),converse(converse(A)))
| converse(join(X_9,converse(A))) = join(converse(X_9),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_9,converse(A))),join(converse(X_9),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_369,plain,
( converse(join(X_9,converse(A))) != join(converse(X_9),converse(converse(A)))
| converse(join(X_9,converse(A))) = join(converse(X_9),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_368]) ).
cnf(refute_0_370,plain,
converse(join(X_9,converse(A))) = join(converse(X_9),A),
inference(resolve,[$cnf( $equal(converse(join(X_9,converse(A))),join(converse(X_9),converse(converse(A)))) )],[refute_0_367,refute_0_369]) ).
cnf(refute_0_371,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(subst,[],[refute_0_370:[bind(A,$fot(complement(converse(zero)))),bind(X_9,$fot(top))]]) ).
cnf(refute_0_372,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(complement(converse(zero)))))
| converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(join(converse(complement(converse(zero))),top)))),bind(Y,$fot(converse(join(top,converse(complement(converse(zero))))))),bind(Z,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_373,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_344,refute_0_372]) ).
cnf(refute_0_374,plain,
converse(join(converse(complement(converse(zero))),top)) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_371,refute_0_373]) ).
cnf(refute_0_375,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| converse(join(converse(complement(converse(zero))),top)) != join(converse(top),complement(converse(zero)))
| join(converse(top),complement(converse(zero))) = converse(join(top,converse(top))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(top)))) ),[0],$fot(join(converse(top),complement(converse(zero))))]]) ).
cnf(refute_0_376,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = converse(join(top,converse(top))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),join(converse(top),complement(converse(zero)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(X_49,join(complement(X_35),join(zero,complement(complement(X_35))))) = join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(complement(X_35))),bind(C,$fot(join(zero,complement(complement(X_35)))))]]) ).
cnf(refute_0_378,plain,
top = join(complement(X_35),join(complement(complement(X_35)),meet(X_35,complement(X_35)))),
inference(subst,[],[refute_0_184:[bind(X_27,$fot(X_35)),bind(X_28,$fot(complement(X_35)))]]) ).
cnf(refute_0_379,plain,
zero = meet(X_35,complement(X_35)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_35))]]) ).
cnf(refute_0_380,plain,
( zero != meet(X_35,complement(X_35))
| meet(X_35,complement(X_35)) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_35,complement(X_35))))]]) ).
cnf(refute_0_381,plain,
meet(X_35,complement(X_35)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_35,complement(X_35))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
( meet(X_35,complement(X_35)) != zero
| top != join(complement(X_35),join(complement(complement(X_35)),meet(X_35,complement(X_35))))
| top = join(complement(X_35),join(complement(complement(X_35)),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_35),join(complement(complement(X_35)),meet(X_35,complement(X_35))))) ),[1,1,1],$fot(zero)]]) ).
cnf(refute_0_383,plain,
( top != join(complement(X_35),join(complement(complement(X_35)),meet(X_35,complement(X_35))))
| top = join(complement(X_35),join(complement(complement(X_35)),zero)) ),
inference(resolve,[$cnf( $equal(meet(X_35,complement(X_35)),zero) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
top = join(complement(X_35),join(complement(complement(X_35)),zero)),
inference(resolve,[$cnf( $equal(top,join(complement(X_35),join(complement(complement(X_35)),meet(X_35,complement(X_35))))) )],[refute_0_378,refute_0_383]) ).
cnf(refute_0_385,plain,
join(complement(complement(X_35)),zero) = join(zero,complement(complement(X_35))),
inference(subst,[],[refute_0_5:[bind(A,$fot(zero)),bind(B,$fot(complement(complement(X_35))))]]) ).
cnf(refute_0_386,plain,
join(complement(X_35),join(complement(complement(X_35)),zero)) = join(complement(X_35),join(complement(complement(X_35)),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_35),join(complement(complement(X_35)),zero)))]]) ).
cnf(refute_0_387,plain,
( join(complement(X_35),join(complement(complement(X_35)),zero)) != join(complement(X_35),join(complement(complement(X_35)),zero))
| join(complement(complement(X_35)),zero) != join(zero,complement(complement(X_35)))
| join(complement(X_35),join(complement(complement(X_35)),zero)) = join(complement(X_35),join(zero,complement(complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_35),join(complement(complement(X_35)),zero)),join(complement(X_35),join(complement(complement(X_35)),zero))) ),[1,1],$fot(join(zero,complement(complement(X_35))))]]) ).
cnf(refute_0_388,plain,
( join(complement(complement(X_35)),zero) != join(zero,complement(complement(X_35)))
| join(complement(X_35),join(complement(complement(X_35)),zero)) = join(complement(X_35),join(zero,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),join(complement(complement(X_35)),zero)),join(complement(X_35),join(complement(complement(X_35)),zero))) )],[refute_0_386,refute_0_387]) ).
cnf(refute_0_389,plain,
join(complement(X_35),join(complement(complement(X_35)),zero)) = join(complement(X_35),join(zero,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),zero),join(zero,complement(complement(X_35)))) )],[refute_0_385,refute_0_388]) ).
cnf(refute_0_390,plain,
( join(complement(X_35),join(complement(complement(X_35)),zero)) != join(complement(X_35),join(zero,complement(complement(X_35))))
| top != join(complement(X_35),join(complement(complement(X_35)),zero))
| top = join(complement(X_35),join(zero,complement(complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_35),join(complement(complement(X_35)),zero))) ),[1],$fot(join(complement(X_35),join(zero,complement(complement(X_35)))))]]) ).
cnf(refute_0_391,plain,
( top != join(complement(X_35),join(complement(complement(X_35)),zero))
| top = join(complement(X_35),join(zero,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),join(complement(complement(X_35)),zero)),join(complement(X_35),join(zero,complement(complement(X_35))))) )],[refute_0_389,refute_0_390]) ).
cnf(refute_0_392,plain,
top = join(complement(X_35),join(zero,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_35),join(complement(complement(X_35)),zero))) )],[refute_0_384,refute_0_391]) ).
cnf(refute_0_393,plain,
( top != join(complement(X_35),join(zero,complement(complement(X_35))))
| join(complement(X_35),join(zero,complement(complement(X_35)))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_35),join(zero,complement(complement(X_35))))))]]) ).
cnf(refute_0_394,plain,
join(complement(X_35),join(zero,complement(complement(X_35)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_35),join(zero,complement(complement(X_35))))) )],[refute_0_392,refute_0_393]) ).
cnf(refute_0_395,plain,
( join(X_49,join(complement(X_35),join(zero,complement(complement(X_35))))) != join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))
| join(complement(X_35),join(zero,complement(complement(X_35)))) != top
| join(X_49,top) = join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,join(complement(X_35),join(zero,complement(complement(X_35))))),join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_396,plain,
( join(X_49,join(complement(X_35),join(zero,complement(complement(X_35))))) != join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))
| join(X_49,top) = join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_35),join(zero,complement(complement(X_35)))),top) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
join(X_49,top) = join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))),
inference(resolve,[$cnf( $equal(join(X_49,join(complement(X_35),join(zero,complement(complement(X_35))))),join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))) )],[refute_0_377,refute_0_396]) ).
cnf(refute_0_398,plain,
join(A,join(X_49,X_50)) = join(join(X_49,X_50),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_49,X_50)))]]) ).
cnf(refute_0_399,plain,
join(X_49,join(X_50,A)) = join(join(X_49,X_50),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(X_50)),bind(C,$fot(A))]]) ).
cnf(refute_0_400,plain,
( join(X_49,join(X_50,A)) != join(join(X_49,X_50),A)
| join(join(X_49,X_50),A) = join(X_49,join(X_50,A)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_49,join(X_50,A)))),bind(Y,$fot(join(join(X_49,X_50),A)))]]) ).
cnf(refute_0_401,plain,
join(join(X_49,X_50),A) = join(X_49,join(X_50,A)),
inference(resolve,[$cnf( $equal(join(X_49,join(X_50,A)),join(join(X_49,X_50),A)) )],[refute_0_399,refute_0_400]) ).
cnf(refute_0_402,plain,
( join(A,join(X_49,X_50)) != join(join(X_49,X_50),A)
| join(join(X_49,X_50),A) != join(X_49,join(X_50,A))
| join(A,join(X_49,X_50)) = join(X_49,join(X_50,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_49,X_50)),join(X_49,join(X_50,A))) ),[0],$fot(join(join(X_49,X_50),A))]]) ).
cnf(refute_0_403,plain,
( join(A,join(X_49,X_50)) != join(join(X_49,X_50),A)
| join(A,join(X_49,X_50)) = join(X_49,join(X_50,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_49,X_50),A),join(X_49,join(X_50,A))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
join(A,join(X_49,X_50)) = join(X_49,join(X_50,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_49,X_50)),join(join(X_49,X_50),A)) )],[refute_0_398,refute_0_403]) ).
cnf(refute_0_405,plain,
( join(A,join(X_49,X_50)) != join(X_49,join(X_50,A))
| join(X_49,join(X_50,A)) = join(A,join(X_49,X_50)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,join(X_49,X_50)))),bind(Y,$fot(join(X_49,join(X_50,A))))]]) ).
cnf(refute_0_406,plain,
join(X_49,join(X_50,A)) = join(A,join(X_49,X_50)),
inference(resolve,[$cnf( $equal(join(A,join(X_49,X_50)),join(X_49,join(X_50,A))) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
join(complement(complement(X_35)),join(X_49,complement(X_35))) = join(complement(X_35),join(complement(complement(X_35)),X_49)),
inference(subst,[],[refute_0_406:[bind(A,$fot(complement(X_35))),bind(X_49,$fot(complement(complement(X_35)))),bind(X_50,$fot(X_49))]]) ).
cnf(refute_0_408,plain,
join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) = join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))))]]) ).
cnf(refute_0_409,plain,
( join(complement(complement(X_35)),join(X_49,complement(X_35))) != join(complement(X_35),join(complement(complement(X_35)),X_49))
| join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) != join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))
| join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))) ),[1,1],$fot(join(complement(X_35),join(complement(complement(X_35)),X_49)))]]) ).
cnf(refute_0_410,plain,
( join(complement(complement(X_35)),join(X_49,complement(X_35))) != join(complement(X_35),join(complement(complement(X_35)),X_49))
| join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),join(X_49,complement(X_35))),join(complement(X_35),join(complement(complement(X_35)),X_49))) )],[refute_0_407,refute_0_410]) ).
cnf(refute_0_412,plain,
join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)) = join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),
inference(subst,[],[refute_0_406:[bind(A,$fot(zero)),bind(X_49,$fot(complement(complement(X_35)))),bind(X_50,$fot(join(X_49,complement(X_35))))]]) ).
cnf(refute_0_413,plain,
join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)),
inference(subst,[],[refute_0_406:[bind(A,$fot(complement(complement(X_35)))),bind(X_49,$fot(join(X_49,complement(X_35)))),bind(X_50,$fot(zero))]]) ).
cnf(refute_0_414,plain,
( join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)) != join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) != join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))))),bind(Y,$fot(join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)))),bind(Z,$fot(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))))]]) ).
cnf(refute_0_415,plain,
( join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)) != join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))),join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero))) )],[refute_0_413,refute_0_414]) ).
cnf(refute_0_416,plain,
join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_35)),join(join(X_49,complement(X_35)),zero)),join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))) )],[refute_0_412,refute_0_415]) ).
cnf(refute_0_417,plain,
( join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) != join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))
| join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))))),bind(Y,$fot(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))))),bind(Z,$fot(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))))]]) ).
cnf(refute_0_418,plain,
( join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))),join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35))))) )],[refute_0_416,refute_0_417]) ).
cnf(refute_0_419,plain,
join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(complement(X_35)),join(X_49,complement(X_35)))),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) )],[refute_0_411,refute_0_418]) ).
cnf(refute_0_420,plain,
( join(X_49,top) != join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))
| join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(X_49,top) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_49,top),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) ),[0],$fot(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))))]]) ).
cnf(refute_0_421,plain,
( join(X_49,top) != join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))
| join(X_49,top) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35)))),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) )],[refute_0_419,refute_0_420]) ).
cnf(refute_0_422,plain,
join(X_49,top) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),
inference(resolve,[$cnf( $equal(join(X_49,top),join(join(X_49,complement(X_35)),join(zero,complement(complement(X_35))))) )],[refute_0_397,refute_0_421]) ).
cnf(refute_0_423,plain,
join(top,join(zero,X_49)) = join(top,X_49),
inference(subst,[],[refute_0_354:[bind(X_51,$fot(X_49))]]) ).
cnf(refute_0_424,plain,
join(X_49,join(X_50,X_51)) = join(join(X_49,X_50),X_51),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(X_50)),bind(C,$fot(X_51))]]) ).
cnf(refute_0_425,plain,
join(X_50,X_49) = join(X_49,X_50),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_50)),bind(B,$fot(X_49))]]) ).
cnf(refute_0_426,plain,
( join(X_50,X_49) != join(X_49,X_50)
| join(X_49,X_50) = join(X_50,X_49) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_50,X_49))),bind(Y,$fot(join(X_49,X_50)))]]) ).
cnf(refute_0_427,plain,
join(X_49,X_50) = join(X_50,X_49),
inference(resolve,[$cnf( $equal(join(X_50,X_49),join(X_49,X_50)) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
( join(X_49,X_50) != join(X_50,X_49)
| join(X_49,join(X_50,X_51)) != join(join(X_49,X_50),X_51)
| join(X_49,join(X_50,X_51)) = join(join(X_50,X_49),X_51) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,join(X_50,X_51)),join(join(X_49,X_50),X_51)) ),[1,0],$fot(join(X_50,X_49))]]) ).
cnf(refute_0_429,plain,
( join(X_49,join(X_50,X_51)) != join(join(X_49,X_50),X_51)
| join(X_49,join(X_50,X_51)) = join(join(X_50,X_49),X_51) ),
inference(resolve,[$cnf( $equal(join(X_49,X_50),join(X_50,X_49)) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
join(X_49,join(X_50,X_51)) = join(join(X_50,X_49),X_51),
inference(resolve,[$cnf( $equal(join(X_49,join(X_50,X_51)),join(join(X_49,X_50),X_51)) )],[refute_0_424,refute_0_429]) ).
cnf(refute_0_431,plain,
join(join(X_50,X_49),X_51) = join(X_50,join(X_49,X_51)),
inference(subst,[],[refute_0_180:[bind(A,$fot(X_50)),bind(B,$fot(X_49)),bind(C,$fot(X_51))]]) ).
cnf(refute_0_432,plain,
( join(X_49,join(X_50,X_51)) != join(join(X_50,X_49),X_51)
| join(join(X_50,X_49),X_51) != join(X_50,join(X_49,X_51))
| join(X_49,join(X_50,X_51)) = join(X_50,join(X_49,X_51)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_49,join(X_50,X_51)),join(X_50,join(X_49,X_51))) ),[0],$fot(join(join(X_50,X_49),X_51))]]) ).
cnf(refute_0_433,plain,
( join(X_49,join(X_50,X_51)) != join(join(X_50,X_49),X_51)
| join(X_49,join(X_50,X_51)) = join(X_50,join(X_49,X_51)) ),
inference(resolve,[$cnf( $equal(join(join(X_50,X_49),X_51),join(X_50,join(X_49,X_51))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
join(X_49,join(X_50,X_51)) = join(X_50,join(X_49,X_51)),
inference(resolve,[$cnf( $equal(join(X_49,join(X_50,X_51)),join(join(X_50,X_49),X_51)) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
( join(X_49,join(X_50,X_51)) != join(X_50,join(X_49,X_51))
| join(X_50,join(X_49,X_51)) = join(X_49,join(X_50,X_51)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_49,join(X_50,X_51)))),bind(Y,$fot(join(X_50,join(X_49,X_51))))]]) ).
cnf(refute_0_436,plain,
join(X_50,join(X_49,X_51)) = join(X_49,join(X_50,X_51)),
inference(resolve,[$cnf( $equal(join(X_49,join(X_50,X_51)),join(X_50,join(X_49,X_51))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
join(zero,join(top,X_49)) = join(top,join(zero,X_49)),
inference(subst,[],[refute_0_436:[bind(X_49,$fot(top)),bind(X_50,$fot(zero)),bind(X_51,$fot(X_49))]]) ).
cnf(refute_0_438,plain,
( join(top,join(zero,X_49)) != join(top,X_49)
| join(zero,join(top,X_49)) != join(top,join(zero,X_49))
| join(zero,join(top,X_49)) = join(top,X_49) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(zero,join(top,X_49)))),bind(Y,$fot(join(top,join(zero,X_49)))),bind(Z,$fot(join(top,X_49)))]]) ).
cnf(refute_0_439,plain,
( join(top,join(zero,X_49)) != join(top,X_49)
| join(zero,join(top,X_49)) = join(top,X_49) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_49)),join(top,join(zero,X_49))) )],[refute_0_437,refute_0_438]) ).
cnf(refute_0_440,plain,
join(zero,join(top,X_49)) = join(top,X_49),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_49)),join(top,X_49)) )],[refute_0_423,refute_0_439]) ).
cnf(refute_0_441,plain,
join(X_49,join(complement(X_49),X_51)) = join(join(X_49,complement(X_49)),X_51),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(complement(X_49))),bind(C,$fot(X_51))]]) ).
cnf(refute_0_442,plain,
top = join(X_49,complement(X_49)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_49))]]) ).
cnf(refute_0_443,plain,
( top != join(X_49,complement(X_49))
| join(X_49,complement(X_49)) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(X_49,complement(X_49))))]]) ).
cnf(refute_0_444,plain,
join(X_49,complement(X_49)) = top,
inference(resolve,[$cnf( $equal(top,join(X_49,complement(X_49))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
( join(X_49,complement(X_49)) != top
| join(X_49,join(complement(X_49),X_51)) != join(join(X_49,complement(X_49)),X_51)
| join(X_49,join(complement(X_49),X_51)) = join(top,X_51) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,join(complement(X_49),X_51)),join(join(X_49,complement(X_49)),X_51)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_446,plain,
( join(X_49,join(complement(X_49),X_51)) != join(join(X_49,complement(X_49)),X_51)
| join(X_49,join(complement(X_49),X_51)) = join(top,X_51) ),
inference(resolve,[$cnf( $equal(join(X_49,complement(X_49)),top) )],[refute_0_444,refute_0_445]) ).
cnf(refute_0_447,plain,
join(X_49,join(complement(X_49),X_51)) = join(top,X_51),
inference(resolve,[$cnf( $equal(join(X_49,join(complement(X_49),X_51)),join(join(X_49,complement(X_49)),X_51)) )],[refute_0_441,refute_0_446]) ).
cnf(refute_0_448,plain,
join(complement(X_35),join(complement(complement(X_35)),X_49)) = join(top,X_49),
inference(subst,[],[refute_0_447:[bind(X_49,$fot(complement(X_35))),bind(X_51,$fot(X_49))]]) ).
cnf(refute_0_449,plain,
join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),
introduced(tautology,[refl,[$fot(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))))]]) ).
cnf(refute_0_450,plain,
( join(complement(X_35),join(complement(complement(X_35)),X_49)) != join(top,X_49)
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(zero,join(top,X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) ),[1,1],$fot(join(top,X_49))]]) ).
cnf(refute_0_451,plain,
( join(complement(X_35),join(complement(complement(X_35)),X_49)) != join(top,X_49)
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(zero,join(top,X_49)) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(zero,join(top,X_49)),
inference(resolve,[$cnf( $equal(join(complement(X_35),join(complement(complement(X_35)),X_49)),join(top,X_49)) )],[refute_0_448,refute_0_451]) ).
cnf(refute_0_453,plain,
( join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) != join(zero,join(top,X_49))
| join(zero,join(top,X_49)) != join(top,X_49)
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(top,X_49) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))))),bind(Y,$fot(join(zero,join(top,X_49)))),bind(Z,$fot(join(top,X_49)))]]) ).
cnf(refute_0_454,plain,
( join(zero,join(top,X_49)) != join(top,X_49)
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(top,X_49) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),join(zero,join(top,X_49))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) = join(top,X_49),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_49)),join(top,X_49)) )],[refute_0_440,refute_0_454]) ).
cnf(refute_0_456,plain,
( join(X_49,top) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))) != join(top,X_49)
| join(X_49,top) = join(top,X_49) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_49,top),join(top,X_49)) ),[0],$fot(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))))]]) ).
cnf(refute_0_457,plain,
( join(X_49,top) != join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))
| join(X_49,top) = join(top,X_49) ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49))),join(top,X_49)) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
join(X_49,top) = join(top,X_49),
inference(resolve,[$cnf( $equal(join(X_49,top),join(zero,join(complement(X_35),join(complement(complement(X_35)),X_49)))) )],[refute_0_422,refute_0_457]) ).
cnf(refute_0_459,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_458:[bind(X_49,$fot(converse(top)))]]) ).
cnf(refute_0_460,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_370:[bind(A,$fot(top)),bind(X_9,$fot(top))]]) ).
cnf(refute_0_461,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(join(top,converse(top))))]]) ).
cnf(refute_0_462,plain,
( join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
converse(join(top,converse(top))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_459,refute_0_462]) ).
cnf(refute_0_464,plain,
( converse(join(top,converse(top))) != join(top,converse(top))
| join(converse(top),complement(converse(zero))) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(top),complement(converse(zero))),converse(join(top,converse(top)))) ),[1],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_465,plain,
( join(converse(top),complement(converse(zero))) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(top,converse(top))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
( converse(join(converse(complement(converse(zero))),top)) != converse(join(top,converse(top)))
| join(converse(top),complement(converse(zero))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),converse(join(top,converse(top)))) )],[refute_0_376,refute_0_465]) ).
cnf(refute_0_467,plain,
join(converse(top),complement(converse(zero))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(zero))),top)),converse(join(top,converse(top)))) )],[refute_0_366,refute_0_466]) ).
cnf(refute_0_468,plain,
join(X_49,join(one,join(one,complement(join(one,one))))) = join(join(X_49,one),join(one,complement(join(one,one)))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_49)),bind(B,$fot(one)),bind(C,$fot(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_469,plain,
converse(converse(join(one,join(one,complement(join(one,one)))))) = join(one,join(one,complement(join(one,one)))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(one,join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_470,plain,
converse(top) = join(join(one,one),converse(complement(converse(join(one,one))))),
inference(subst,[],[refute_0_342:[bind(X_13,$fot(join(one,one)))]]) ).
cnf(refute_0_471,plain,
converse(join(converse(one),X_10)) = join(one,converse(X_10)),
inference(subst,[],[refute_0_335:[bind(A,$fot(one))]]) ).
cnf(refute_0_472,plain,
( converse(join(converse(one),X_10)) != join(one,converse(X_10))
| converse(one) != one
| converse(join(one,X_10)) = join(one,converse(X_10)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(one),X_10)),join(one,converse(X_10))) ),[0,0,0],$fot(one)]]) ).
cnf(refute_0_473,plain,
( converse(join(converse(one),X_10)) != join(one,converse(X_10))
| converse(join(one,X_10)) = join(one,converse(X_10)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_472]) ).
cnf(refute_0_474,plain,
converse(join(one,X_10)) = join(one,converse(X_10)),
inference(resolve,[$cnf( $equal(converse(join(converse(one),X_10)),join(one,converse(X_10))) )],[refute_0_471,refute_0_473]) ).
cnf(refute_0_475,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_474:[bind(X_10,$fot(one))]]) ).
cnf(refute_0_476,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(one) != one
| converse(join(one,one)) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_477,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_476]) ).
cnf(refute_0_478,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_475,refute_0_477]) ).
cnf(refute_0_479,plain,
( converse(join(one,one)) != join(one,one)
| converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) ),[1,1,0,0],$fot(join(one,one))]]) ).
cnf(refute_0_480,plain,
( converse(top) != join(join(one,one),converse(complement(converse(join(one,one)))))
| converse(top) = join(join(one,one),converse(complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
converse(top) = join(join(one,one),converse(complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(converse(join(one,one)))))) )],[refute_0_470,refute_0_480]) ).
cnf(refute_0_482,plain,
( converse(join(one,X_10)) != join(one,converse(X_10))
| join(one,converse(X_10)) = converse(join(one,X_10)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(join(one,X_10)))),bind(Y,$fot(join(one,converse(X_10))))]]) ).
cnf(refute_0_483,plain,
join(one,converse(X_10)) = converse(join(one,X_10)),
inference(resolve,[$cnf( $equal(converse(join(one,X_10)),join(one,converse(X_10))) )],[refute_0_474,refute_0_482]) ).
cnf(refute_0_484,plain,
join(one,converse(join(one,complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(subst,[],[refute_0_483:[bind(X_10,$fot(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_485,plain,
join(one,converse(complement(join(one,one)))) = converse(join(one,complement(join(one,one)))),
inference(subst,[],[refute_0_483:[bind(X_10,$fot(complement(join(one,one))))]]) ).
cnf(refute_0_486,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,join(one,converse(complement(join(one,one))))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(complement(join(one,one))))))]]) ).
cnf(refute_0_487,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) ),[1,1],$fot(converse(join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_488,plain,
( join(one,converse(complement(join(one,one)))) != converse(join(one,complement(join(one,one))))
| join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
join(one,join(one,converse(complement(join(one,one))))) = join(one,converse(join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(complement(join(one,one)))),converse(join(one,complement(join(one,one))))) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != join(one,converse(join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Y,$fot(join(one,converse(join(one,complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_491,plain,
( join(one,converse(join(one,complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),join(one,converse(join(one,complement(join(one,one)))))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
join(one,join(one,converse(complement(join(one,one))))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_484,refute_0_491]) ).
cnf(refute_0_493,plain,
join(join(one,one),converse(complement(join(one,one)))) = join(one,join(one,converse(complement(join(one,one))))),
inference(subst,[],[refute_0_180:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(converse(complement(join(one,one)))))]]) ).
cnf(refute_0_494,plain,
( join(join(one,one),converse(complement(join(one,one)))) != join(one,join(one,converse(complement(join(one,one)))))
| join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(join(one,one),converse(complement(join(one,one)))))),bind(Y,$fot(join(one,join(one,converse(complement(join(one,one))))))),bind(Z,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_495,plain,
( join(one,join(one,converse(complement(join(one,one))))) != converse(join(one,join(one,complement(join(one,one)))))
| join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),join(one,join(one,converse(complement(join(one,one)))))) )],[refute_0_493,refute_0_494]) ).
cnf(refute_0_496,plain,
join(join(one,one),converse(complement(join(one,one)))) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(complement(join(one,one))))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_492,refute_0_495]) ).
cnf(refute_0_497,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| join(join(one,one),converse(complement(join(one,one)))) != converse(join(one,join(one,complement(join(one,one)))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) ),[0],$fot(join(join(one,one),converse(complement(join(one,one)))))]]) ).
cnf(refute_0_498,plain,
( converse(top) != join(join(one,one),converse(complement(join(one,one))))
| converse(top) = converse(join(one,join(one,complement(join(one,one))))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(complement(join(one,one)))),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_496,refute_0_497]) ).
cnf(refute_0_499,plain,
converse(top) = converse(join(one,join(one,complement(join(one,one))))),
inference(resolve,[$cnf( $equal(converse(top),join(join(one,one),converse(complement(join(one,one))))) )],[refute_0_481,refute_0_498]) ).
cnf(refute_0_500,plain,
( converse(top) != converse(join(one,join(one,complement(join(one,one)))))
| converse(join(one,join(one,complement(join(one,one))))) = converse(top) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(top))),bind(Y,$fot(converse(join(one,join(one,complement(join(one,one)))))))]]) ).
cnf(refute_0_501,plain,
converse(join(one,join(one,complement(join(one,one))))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),converse(join(one,join(one,complement(join(one,one)))))) )],[refute_0_499,refute_0_500]) ).
cnf(refute_0_502,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(join(one,join(one,complement(join(one,one))))) != converse(top)
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) ),[0,0],$fot(converse(top))]]) ).
cnf(refute_0_503,plain,
( converse(converse(join(one,join(one,complement(join(one,one)))))) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,complement(join(one,one))))),converse(top)) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
converse(converse(top)) = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(join(one,join(one,complement(join(one,one)))))),join(one,join(one,complement(join(one,one))))) )],[refute_0_469,refute_0_503]) ).
cnf(refute_0_505,plain,
converse(converse(top)) = top,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(top))]]) ).
cnf(refute_0_506,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| converse(converse(top)) != top
| top = join(one,join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) ),[0],$fot(top)]]) ).
cnf(refute_0_507,plain,
( converse(converse(top)) != join(one,join(one,complement(join(one,one))))
| top = join(one,join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(converse(converse(top)),top) )],[refute_0_505,refute_0_506]) ).
cnf(refute_0_508,plain,
top = join(one,join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(converse(converse(top)),join(one,join(one,complement(join(one,one))))) )],[refute_0_504,refute_0_507]) ).
cnf(refute_0_509,plain,
( top != join(one,join(one,complement(join(one,one))))
| join(one,join(one,complement(join(one,one)))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(one,join(one,complement(join(one,one))))))]]) ).
cnf(refute_0_510,plain,
join(one,join(one,complement(join(one,one)))) = top,
inference(resolve,[$cnf( $equal(top,join(one,join(one,complement(join(one,one))))) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
( join(X_49,join(one,join(one,complement(join(one,one))))) != join(join(X_49,one),join(one,complement(join(one,one))))
| join(one,join(one,complement(join(one,one)))) != top
| join(X_49,top) = join(join(X_49,one),join(one,complement(join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,join(one,join(one,complement(join(one,one))))),join(join(X_49,one),join(one,complement(join(one,one))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_512,plain,
( join(X_49,join(one,join(one,complement(join(one,one))))) != join(join(X_49,one),join(one,complement(join(one,one))))
| join(X_49,top) = join(join(X_49,one),join(one,complement(join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,complement(join(one,one)))),top) )],[refute_0_510,refute_0_511]) ).
cnf(refute_0_513,plain,
join(X_49,top) = join(join(X_49,one),join(one,complement(join(one,one)))),
inference(resolve,[$cnf( $equal(join(X_49,join(one,join(one,complement(join(one,one))))),join(join(X_49,one),join(one,complement(join(one,one))))) )],[refute_0_468,refute_0_512]) ).
cnf(refute_0_514,plain,
join(complement(join(one,one)),join(X_49,one)) = join(one,join(complement(join(one,one)),X_49)),
inference(subst,[],[refute_0_406:[bind(A,$fot(one)),bind(X_49,$fot(complement(join(one,one)))),bind(X_50,$fot(X_49))]]) ).
cnf(refute_0_515,plain,
join(one,join(complement(join(one,one)),join(X_49,one))) = join(one,join(complement(join(one,one)),join(X_49,one))),
introduced(tautology,[refl,[$fot(join(one,join(complement(join(one,one)),join(X_49,one))))]]) ).
cnf(refute_0_516,plain,
( join(complement(join(one,one)),join(X_49,one)) != join(one,join(complement(join(one,one)),X_49))
| join(one,join(complement(join(one,one)),join(X_49,one))) != join(one,join(complement(join(one,one)),join(X_49,one)))
| join(one,join(complement(join(one,one)),join(X_49,one))) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_49,one))),join(one,join(complement(join(one,one)),join(X_49,one)))) ),[1,1],$fot(join(one,join(complement(join(one,one)),X_49)))]]) ).
cnf(refute_0_517,plain,
( join(complement(join(one,one)),join(X_49,one)) != join(one,join(complement(join(one,one)),X_49))
| join(one,join(complement(join(one,one)),join(X_49,one))) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
inference(resolve,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_49,one))),join(one,join(complement(join(one,one)),join(X_49,one)))) )],[refute_0_515,refute_0_516]) ).
cnf(refute_0_518,plain,
join(one,join(complement(join(one,one)),join(X_49,one))) = join(one,join(one,join(complement(join(one,one)),X_49))),
inference(resolve,[$cnf( $equal(join(complement(join(one,one)),join(X_49,one)),join(one,join(complement(join(one,one)),X_49))) )],[refute_0_514,refute_0_517]) ).
cnf(refute_0_519,plain,
join(join(X_49,one),join(one,complement(join(one,one)))) = join(one,join(complement(join(one,one)),join(X_49,one))),
inference(subst,[],[refute_0_404:[bind(A,$fot(join(X_49,one))),bind(X_49,$fot(one)),bind(X_50,$fot(complement(join(one,one))))]]) ).
cnf(refute_0_520,plain,
( join(join(X_49,one),join(one,complement(join(one,one)))) != join(one,join(complement(join(one,one)),join(X_49,one)))
| join(one,join(complement(join(one,one)),join(X_49,one))) != join(one,join(one,join(complement(join(one,one)),X_49)))
| join(join(X_49,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(join(X_49,one),join(one,complement(join(one,one)))))),bind(Y,$fot(join(one,join(complement(join(one,one)),join(X_49,one))))),bind(Z,$fot(join(one,join(one,join(complement(join(one,one)),X_49)))))]]) ).
cnf(refute_0_521,plain,
( join(one,join(complement(join(one,one)),join(X_49,one))) != join(one,join(one,join(complement(join(one,one)),X_49)))
| join(join(X_49,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,one),join(one,complement(join(one,one)))),join(one,join(complement(join(one,one)),join(X_49,one)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
join(join(X_49,one),join(one,complement(join(one,one)))) = join(one,join(one,join(complement(join(one,one)),X_49))),
inference(resolve,[$cnf( $equal(join(one,join(complement(join(one,one)),join(X_49,one))),join(one,join(one,join(complement(join(one,one)),X_49)))) )],[refute_0_518,refute_0_521]) ).
cnf(refute_0_523,plain,
( join(X_49,top) != join(join(X_49,one),join(one,complement(join(one,one))))
| join(join(X_49,one),join(one,complement(join(one,one)))) != join(one,join(one,join(complement(join(one,one)),X_49)))
| join(X_49,top) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_49,top),join(one,join(one,join(complement(join(one,one)),X_49)))) ),[0],$fot(join(join(X_49,one),join(one,complement(join(one,one)))))]]) ).
cnf(refute_0_524,plain,
( join(X_49,top) != join(join(X_49,one),join(one,complement(join(one,one))))
| join(X_49,top) = join(one,join(one,join(complement(join(one,one)),X_49))) ),
inference(resolve,[$cnf( $equal(join(join(X_49,one),join(one,complement(join(one,one)))),join(one,join(one,join(complement(join(one,one)),X_49)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
join(X_49,top) = join(one,join(one,join(complement(join(one,one)),X_49))),
inference(resolve,[$cnf( $equal(join(X_49,top),join(join(X_49,one),join(one,complement(join(one,one))))) )],[refute_0_513,refute_0_524]) ).
cnf(refute_0_526,plain,
( top != join(X_54,top)
| join(X_54,top) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(X_54,top)))]]) ).
cnf(refute_0_527,plain,
join(X_54,top) = top,
inference(resolve,[$cnf( $equal(top,join(X_54,top)) )],[refute_0_212,refute_0_526]) ).
cnf(refute_0_528,plain,
join(X_49,top) = top,
inference(subst,[],[refute_0_527:[bind(X_54,$fot(X_49))]]) ).
cnf(refute_0_529,plain,
( join(X_49,top) != join(one,join(one,join(complement(join(one,one)),X_49)))
| join(X_49,top) != top
| top = join(one,join(one,join(complement(join(one,one)),X_49))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,top),join(one,join(one,join(complement(join(one,one)),X_49)))) ),[0],$fot(top)]]) ).
cnf(refute_0_530,plain,
( join(X_49,top) != join(one,join(one,join(complement(join(one,one)),X_49)))
| top = join(one,join(one,join(complement(join(one,one)),X_49))) ),
inference(resolve,[$cnf( $equal(join(X_49,top),top) )],[refute_0_528,refute_0_529]) ).
cnf(refute_0_531,plain,
join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(join(A,join(X_55,complement(join(A,X_55)))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(B,$fot(join(X_55,complement(join(A,X_55)))))]]) ).
cnf(refute_0_532,plain,
top = join(A,join(X_55,complement(join(A,X_55)))),
inference(subst,[],[refute_0_173:[bind(X_49,$fot(A)),bind(X_50,$fot(X_55))]]) ).
cnf(refute_0_533,plain,
( top != join(A,join(X_55,complement(join(A,X_55))))
| join(A,join(X_55,complement(join(A,X_55)))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(A,join(X_55,complement(join(A,X_55))))))]]) ).
cnf(refute_0_534,plain,
join(A,join(X_55,complement(join(A,X_55)))) = top,
inference(resolve,[$cnf( $equal(top,join(A,join(X_55,complement(join(A,X_55))))) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
( join(A,join(X_55,complement(join(A,X_55)))) != top
| join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(join(A,join(X_55,complement(join(A,X_55)))),C)
| join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(join(A,join(X_55,complement(join(A,X_55)))),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_536,plain,
( join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(join(A,join(X_55,complement(join(A,X_55)))),C)
| join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(A,join(X_55,complement(join(A,X_55)))),top) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(join(A,join(X_55,complement(join(A,X_55)))),C)) )],[refute_0_531,refute_0_536]) ).
cnf(refute_0_538,plain,
join(join(X_55,complement(join(A,X_55))),C) = join(X_55,join(complement(join(A,X_55)),C)),
inference(subst,[],[refute_0_180:[bind(A,$fot(X_55)),bind(B,$fot(complement(join(A,X_55))))]]) ).
cnf(refute_0_539,plain,
join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(A,join(join(X_55,complement(join(A,X_55))),C)),
introduced(tautology,[refl,[$fot(join(A,join(join(X_55,complement(join(A,X_55))),C)))]]) ).
cnf(refute_0_540,plain,
( join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(A,join(join(X_55,complement(join(A,X_55))),C))
| join(join(X_55,complement(join(A,X_55))),C) != join(X_55,join(complement(join(A,X_55)),C))
| join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(A,join(X_55,join(complement(join(A,X_55)),C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(A,join(join(X_55,complement(join(A,X_55))),C))) ),[1,1],$fot(join(X_55,join(complement(join(A,X_55)),C)))]]) ).
cnf(refute_0_541,plain,
( join(join(X_55,complement(join(A,X_55))),C) != join(X_55,join(complement(join(A,X_55)),C))
| join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(A,join(X_55,join(complement(join(A,X_55)),C))) ),
inference(resolve,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(A,join(join(X_55,complement(join(A,X_55))),C))) )],[refute_0_539,refute_0_540]) ).
cnf(refute_0_542,plain,
join(A,join(join(X_55,complement(join(A,X_55))),C)) = join(A,join(X_55,join(complement(join(A,X_55)),C))),
inference(resolve,[$cnf( $equal(join(join(X_55,complement(join(A,X_55))),C),join(X_55,join(complement(join(A,X_55)),C))) )],[refute_0_538,refute_0_541]) ).
cnf(refute_0_543,plain,
( join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(A,join(X_55,join(complement(join(A,X_55)),C)))
| join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(top,C)
| join(A,join(X_55,join(complement(join(A,X_55)),C))) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(top,C)) ),[0],$fot(join(A,join(X_55,join(complement(join(A,X_55)),C))))]]) ).
cnf(refute_0_544,plain,
( join(A,join(join(X_55,complement(join(A,X_55))),C)) != join(top,C)
| join(A,join(X_55,join(complement(join(A,X_55)),C))) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(A,join(X_55,join(complement(join(A,X_55)),C)))) )],[refute_0_542,refute_0_543]) ).
cnf(refute_0_545,plain,
join(A,join(X_55,join(complement(join(A,X_55)),C))) = join(top,C),
inference(resolve,[$cnf( $equal(join(A,join(join(X_55,complement(join(A,X_55))),C)),join(top,C)) )],[refute_0_537,refute_0_544]) ).
cnf(refute_0_546,plain,
join(one,join(one,join(complement(join(one,one)),X_49))) = join(top,X_49),
inference(subst,[],[refute_0_545:[bind(A,$fot(one)),bind(C,$fot(X_49)),bind(X_55,$fot(one))]]) ).
cnf(refute_0_547,plain,
( join(one,join(one,join(complement(join(one,one)),X_49))) != join(top,X_49)
| top != join(one,join(one,join(complement(join(one,one)),X_49)))
| top = join(top,X_49) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(one,join(one,join(complement(join(one,one)),X_49)))) ),[1],$fot(join(top,X_49))]]) ).
cnf(refute_0_548,plain,
( top != join(one,join(one,join(complement(join(one,one)),X_49)))
| top = join(top,X_49) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(complement(join(one,one)),X_49))),join(top,X_49)) )],[refute_0_546,refute_0_547]) ).
cnf(refute_0_549,plain,
( join(X_49,top) != join(one,join(one,join(complement(join(one,one)),X_49)))
| top = join(top,X_49) ),
inference(resolve,[$cnf( $equal(top,join(one,join(one,join(complement(join(one,one)),X_49)))) )],[refute_0_530,refute_0_548]) ).
cnf(refute_0_550,plain,
top = join(top,X_49),
inference(resolve,[$cnf( $equal(join(X_49,top),join(one,join(one,join(complement(join(one,one)),X_49)))) )],[refute_0_525,refute_0_549]) ).
cnf(refute_0_551,plain,
( top != join(top,X_49)
| join(top,X_49) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_49)))]]) ).
cnf(refute_0_552,plain,
join(top,X_49) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_49)) )],[refute_0_550,refute_0_551]) ).
cnf(refute_0_553,plain,
join(top,converse(top)) = top,
inference(subst,[],[refute_0_552:[bind(X_49,$fot(converse(top)))]]) ).
cnf(refute_0_554,plain,
( join(converse(top),complement(converse(zero))) != join(top,converse(top))
| join(top,converse(top)) != top
| join(converse(top),complement(converse(zero))) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(converse(top),complement(converse(zero))),top) ),[0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_555,plain,
( join(converse(top),complement(converse(zero))) != join(top,converse(top))
| join(converse(top),complement(converse(zero))) = top ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_553,refute_0_554]) ).
cnf(refute_0_556,plain,
join(converse(top),complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),join(top,converse(top))) )],[refute_0_467,refute_0_555]) ).
cnf(refute_0_557,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| join(converse(top),complement(converse(zero))) != top
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_558,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(join(converse(top),complement(converse(zero))))
| converse(join(complement(converse(zero)),converse(top))) = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),top) )],[refute_0_556,refute_0_557]) ).
cnf(refute_0_559,plain,
converse(join(complement(converse(zero)),converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(join(converse(top),complement(converse(zero))))) )],[refute_0_343,refute_0_558]) ).
cnf(refute_0_560,plain,
join(converse(complement(converse(zero))),top) = top,
inference(subst,[],[refute_0_527:[bind(X_54,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_561,plain,
converse(join(complement(converse(zero)),converse(top))) = join(converse(complement(converse(zero))),top),
inference(subst,[],[refute_0_370:[bind(A,$fot(top)),bind(X_9,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_562,plain,
( converse(join(complement(converse(zero)),converse(top))) != join(converse(complement(converse(zero))),top)
| join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(join(complement(converse(zero)),converse(top))))),bind(Y,$fot(join(converse(complement(converse(zero))),top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_563,plain,
( join(converse(complement(converse(zero))),top) != top
| converse(join(complement(converse(zero)),converse(top))) = top ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),join(converse(complement(converse(zero))),top)) )],[refute_0_561,refute_0_562]) ).
cnf(refute_0_564,plain,
converse(join(complement(converse(zero)),converse(top))) = top,
inference(resolve,[$cnf( $equal(join(converse(complement(converse(zero))),top),top) )],[refute_0_560,refute_0_563]) ).
cnf(refute_0_565,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| converse(join(complement(converse(zero)),converse(top))) != top
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) ),[0],$fot(top)]]) ).
cnf(refute_0_566,plain,
( converse(join(complement(converse(zero)),converse(top))) != converse(top)
| top = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),top) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(converse(join(complement(converse(zero)),converse(top))),converse(top)) )],[refute_0_559,refute_0_566]) ).
cnf(refute_0_568,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_0_569,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
( converse(top) != join(X_13,converse(complement(converse(X_13))))
| converse(top) != top
| top = join(X_13,converse(complement(converse(X_13)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_13,converse(complement(converse(X_13))))) ),[0],$fot(top)]]) ).
cnf(refute_0_571,plain,
( converse(top) != join(X_13,converse(complement(converse(X_13))))
| top = join(X_13,converse(complement(converse(X_13)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
top = join(X_13,converse(complement(converse(X_13)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_13,converse(complement(converse(X_13))))) )],[refute_0_342,refute_0_571]) ).
cnf(refute_0_573,plain,
top = join(complement(converse(zero)),converse(complement(converse(complement(converse(zero)))))),
inference(subst,[],[refute_0_572:[bind(X_13,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_574,plain,
top = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_572:[bind(X_13,$fot(zero))]]) ).
cnf(refute_0_575,plain,
join(zero,converse(complement(converse(zero)))) = converse(complement(converse(zero))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_576,plain,
( join(zero,converse(complement(converse(zero)))) != converse(complement(converse(zero)))
| top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) ),[1],$fot(converse(complement(converse(zero))))]]) ).
cnf(refute_0_577,plain,
( top != join(zero,converse(complement(converse(zero))))
| top = converse(complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(zero,converse(complement(converse(zero)))),converse(complement(converse(zero)))) )],[refute_0_575,refute_0_576]) ).
cnf(refute_0_578,plain,
top = converse(complement(converse(zero))),
inference(resolve,[$cnf( $equal(top,join(zero,converse(complement(converse(zero))))) )],[refute_0_574,refute_0_577]) ).
cnf(refute_0_579,plain,
( top != converse(complement(converse(zero)))
| converse(complement(converse(zero))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_580,plain,
converse(complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,converse(complement(converse(zero)))) )],[refute_0_578,refute_0_579]) ).
cnf(refute_0_581,plain,
( converse(complement(converse(zero))) != top
| top != join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))
| top = join(complement(converse(zero)),converse(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))) ),[1,1,0,0],$fot(top)]]) ).
cnf(refute_0_582,plain,
( top != join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))
| top = join(complement(converse(zero)),converse(complement(top))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(zero))),top) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
top = join(complement(converse(zero)),converse(complement(top))),
inference(resolve,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(converse(complement(converse(zero))))))) )],[refute_0_573,refute_0_582]) ).
cnf(refute_0_584,plain,
converse(join(zero,converse(A))) = join(converse(zero),A),
inference(subst,[],[refute_0_370:[bind(X_9,$fot(zero))]]) ).
cnf(refute_0_585,plain,
join(zero,converse(A)) = converse(A),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(converse(A)))]]) ).
cnf(refute_0_586,plain,
( converse(join(zero,converse(A))) != join(converse(zero),A)
| join(zero,converse(A)) != converse(A)
| converse(converse(A)) = join(converse(zero),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(zero,converse(A))),join(converse(zero),A)) ),[0,0],$fot(converse(A))]]) ).
cnf(refute_0_587,plain,
( converse(join(zero,converse(A))) != join(converse(zero),A)
| converse(converse(A)) = join(converse(zero),A) ),
inference(resolve,[$cnf( $equal(join(zero,converse(A)),converse(A)) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
converse(converse(A)) = join(converse(zero),A),
inference(resolve,[$cnf( $equal(converse(join(zero,converse(A))),join(converse(zero),A)) )],[refute_0_584,refute_0_587]) ).
cnf(refute_0_589,plain,
( converse(converse(A)) != A
| converse(converse(A)) != join(converse(zero),A)
| A = join(converse(zero),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(A)),join(converse(zero),A)) ),[0],$fot(A)]]) ).
cnf(refute_0_590,plain,
( converse(converse(A)) != join(converse(zero),A)
| A = join(converse(zero),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_589]) ).
cnf(refute_0_591,plain,
A = join(converse(zero),A),
inference(resolve,[$cnf( $equal(converse(converse(A)),join(converse(zero),A)) )],[refute_0_588,refute_0_590]) ).
cnf(refute_0_592,plain,
( A != join(converse(zero),A)
| join(converse(zero),A) = A ),
inference(subst,[],[refute_0_3:[bind(X,$fot(A)),bind(Y,$fot(join(converse(zero),A)))]]) ).
cnf(refute_0_593,plain,
join(converse(zero),A) = A,
inference(resolve,[$cnf( $equal(A,join(converse(zero),A)) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
join(converse(zero),complement(converse(zero))) = complement(converse(zero)),
inference(subst,[],[refute_0_593:[bind(A,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_595,plain,
join(complement(converse(zero)),converse(zero)) = join(converse(zero),complement(converse(zero))),
inference(subst,[],[refute_0_5:[bind(A,$fot(converse(zero))),bind(B,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_596,plain,
( join(complement(converse(zero)),converse(zero)) != join(converse(zero),complement(converse(zero)))
| join(converse(zero),complement(converse(zero))) != complement(converse(zero))
| join(complement(converse(zero)),converse(zero)) = complement(converse(zero)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(converse(zero)),converse(zero)))),bind(Y,$fot(join(converse(zero),complement(converse(zero))))),bind(Z,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_597,plain,
( join(converse(zero),complement(converse(zero))) != complement(converse(zero))
| join(complement(converse(zero)),converse(zero)) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(zero)),join(converse(zero),complement(converse(zero)))) )],[refute_0_595,refute_0_596]) ).
cnf(refute_0_598,plain,
join(complement(converse(zero)),converse(zero)) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(join(converse(zero),complement(converse(zero))),complement(converse(zero))) )],[refute_0_594,refute_0_597]) ).
cnf(refute_0_599,plain,
converse(complement(top)) = converse(complement(top)),
introduced(tautology,[refl,[$fot(converse(complement(top)))]]) ).
cnf(refute_0_600,plain,
( complement(top) != zero
| converse(complement(top)) != converse(complement(top))
| converse(complement(top)) = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(top)),converse(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_601,plain,
( complement(top) != zero
| converse(complement(top)) = converse(zero) ),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(complement(top))) )],[refute_0_599,refute_0_600]) ).
cnf(refute_0_602,plain,
converse(complement(top)) = converse(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_601]) ).
cnf(refute_0_603,plain,
join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(complement(top))),
introduced(tautology,[refl,[$fot(join(complement(converse(zero)),converse(complement(top))))]]) ).
cnf(refute_0_604,plain,
( converse(complement(top)) != converse(zero)
| join(complement(converse(zero)),converse(complement(top))) != join(complement(converse(zero)),converse(complement(top)))
| join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(complement(top)))) ),[1,1],$fot(converse(zero))]]) ).
cnf(refute_0_605,plain,
( converse(complement(top)) != converse(zero)
| join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(complement(top)))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
join(complement(converse(zero)),converse(complement(top))) = join(complement(converse(zero)),converse(zero)),
inference(resolve,[$cnf( $equal(converse(complement(top)),converse(zero)) )],[refute_0_602,refute_0_605]) ).
cnf(refute_0_607,plain,
( join(complement(converse(zero)),converse(complement(top))) != join(complement(converse(zero)),converse(zero))
| join(complement(converse(zero)),converse(zero)) != complement(converse(zero))
| join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(converse(zero)),converse(complement(top))))),bind(Y,$fot(join(complement(converse(zero)),converse(zero)))),bind(Z,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_608,plain,
( join(complement(converse(zero)),converse(zero)) != complement(converse(zero))
| join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),join(complement(converse(zero)),converse(zero))) )],[refute_0_606,refute_0_607]) ).
cnf(refute_0_609,plain,
join(complement(converse(zero)),converse(complement(top))) = complement(converse(zero)),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(zero)),complement(converse(zero))) )],[refute_0_598,refute_0_608]) ).
cnf(refute_0_610,plain,
( join(complement(converse(zero)),converse(complement(top))) != complement(converse(zero))
| top != join(complement(converse(zero)),converse(complement(top)))
| top = complement(converse(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(top)))) ),[1],$fot(complement(converse(zero)))]]) ).
cnf(refute_0_611,plain,
( top != join(complement(converse(zero)),converse(complement(top)))
| top = complement(converse(zero)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(zero)),converse(complement(top))),complement(converse(zero))) )],[refute_0_609,refute_0_610]) ).
cnf(refute_0_612,plain,
top = complement(converse(zero)),
inference(resolve,[$cnf( $equal(top,join(complement(converse(zero)),converse(complement(top)))) )],[refute_0_583,refute_0_611]) ).
cnf(refute_0_613,plain,
( top != complement(converse(zero))
| complement(converse(zero)) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_614,plain,
complement(converse(zero)) = top,
inference(resolve,[$cnf( $equal(top,complement(converse(zero))) )],[refute_0_612,refute_0_613]) ).
cnf(refute_0_615,plain,
( complement(converse(zero)) != top
| zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_616,plain,
( zero != meet(converse(zero),complement(converse(zero)))
| zero = meet(converse(zero),top) ),
inference(resolve,[$cnf( $equal(complement(converse(zero)),top) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
zero = meet(converse(zero),top),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),complement(converse(zero)))) )],[refute_0_331,refute_0_616]) ).
cnf(refute_0_618,plain,
join(zero,meet(X_74,top)) = meet(X_74,top),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(X_74,top)))]]) ).
cnf(refute_0_619,plain,
( X_74 != join(zero,meet(X_74,top))
| join(zero,meet(X_74,top)) != meet(X_74,top)
| X_74 = meet(X_74,top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,meet(X_74,top)) ),[0],$fot(join(zero,meet(X_74,top)))]]) ).
cnf(refute_0_620,plain,
( X_74 != join(zero,meet(X_74,top))
| X_74 = meet(X_74,top) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_74,top)),meet(X_74,top)) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
X_74 = meet(X_74,top),
inference(resolve,[$cnf( $equal(X_74,join(zero,meet(X_74,top))) )],[refute_0_229,refute_0_620]) ).
cnf(refute_0_622,plain,
( X_74 != meet(X_74,top)
| meet(X_74,top) = X_74 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_74)),bind(Y,$fot(meet(X_74,top)))]]) ).
cnf(refute_0_623,plain,
meet(X_74,top) = X_74,
inference(resolve,[$cnf( $equal(X_74,meet(X_74,top)) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
meet(converse(zero),top) = converse(zero),
inference(subst,[],[refute_0_623:[bind(X_74,$fot(converse(zero)))]]) ).
cnf(refute_0_625,plain,
( meet(converse(zero),top) != converse(zero)
| zero != meet(converse(zero),top)
| zero = converse(zero) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(converse(zero),top)) ),[1],$fot(converse(zero))]]) ).
cnf(refute_0_626,plain,
( zero != meet(converse(zero),top)
| zero = converse(zero) ),
inference(resolve,[$cnf( $equal(meet(converse(zero),top),converse(zero)) )],[refute_0_624,refute_0_625]) ).
cnf(refute_0_627,plain,
zero = converse(zero),
inference(resolve,[$cnf( $equal(zero,meet(converse(zero),top)) )],[refute_0_617,refute_0_626]) ).
cnf(refute_0_628,plain,
( zero != converse(zero)
| converse(zero) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).
cnf(refute_0_629,plain,
converse(zero) = zero,
inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_627,refute_0_628]) ).
cnf(refute_0_630,plain,
( converse(zero) != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| converse(zero) != zero
| zero = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) ),[0],$fot(zero)]]) ).
cnf(refute_0_631,plain,
( converse(zero) != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| zero = composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))),
inference(subst,[],[refute_0_82:[bind(A,$fot(composition(sk1,complement(one)))),bind(X_6,$fot(complement(composition(complement(sk1),top))))]]) ).
cnf(refute_0_633,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_634,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_633]) ).
cnf(refute_0_635,plain,
composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) = converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))),
inference(subst,[],[refute_0_634:[bind(A,$fot(converse(composition(sk1,complement(one))))),bind(B,$fot(complement(composition(complement(sk1),top))))]]) ).
cnf(refute_0_636,plain,
( composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) != converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))))
| converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) != composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))
| composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))))),bind(Y,$fot(converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))))),bind(Z,$fot(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_637,plain,
( converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))) != composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))
| composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))),converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top))))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(converse(composition(converse(composition(sk1,complement(one))),complement(composition(complement(sk1),top)))),composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))) )],[refute_0_632,refute_0_637]) ).
cnf(refute_0_639,plain,
( composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))) != composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))
| zero != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| zero = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) ),[1],$fot(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))))]]) ).
cnf(refute_0_640,plain,
( zero != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| zero = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one))))),composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
( converse(zero) != composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))
| zero = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) )],[refute_0_631,refute_0_640]) ).
cnf(refute_0_642,plain,
zero = composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(composition(complement(sk1),top))),converse(converse(composition(sk1,complement(one)))))) )],[refute_0_330,refute_0_641]) ).
cnf(refute_0_643,plain,
( zero != composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))
| composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_644,plain,
composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))) )],[refute_0_642,refute_0_643]) ).
cnf(refute_0_645,plain,
( composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))) != zero
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))) != complement(composition(sk1,complement(one)))
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = complement(composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))),complement(composition(sk1,complement(one)))) ),[0,1,1,0],$fot(zero)]]) ).
cnf(refute_0_646,plain,
( join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))) != complement(composition(sk1,complement(one)))
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = complement(composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one))),zero) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = complement(composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(converse(complement(composition(complement(sk1),top))),composition(sk1,complement(one)))))),complement(composition(sk1,complement(one)))) )],[refute_0_35,refute_0_646]) ).
cnf(refute_0_648,plain,
top = join(zero,meet(top,top)),
inference(subst,[],[refute_0_229:[bind(X_74,$fot(top))]]) ).
cnf(refute_0_649,plain,
meet(top,top) = complement(complement(top)),
inference(subst,[],[refute_0_190:[bind(X_28,$fot(top))]]) ).
cnf(refute_0_650,plain,
( meet(top,top) != complement(complement(top))
| top != join(zero,meet(top,top))
| top = join(zero,complement(complement(top))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,meet(top,top))) ),[1,1],$fot(complement(complement(top)))]]) ).
cnf(refute_0_651,plain,
( top != join(zero,meet(top,top))
| top = join(zero,complement(complement(top))) ),
inference(resolve,[$cnf( $equal(meet(top,top),complement(complement(top))) )],[refute_0_649,refute_0_650]) ).
cnf(refute_0_652,plain,
top = join(zero,complement(complement(top))),
inference(resolve,[$cnf( $equal(top,join(zero,meet(top,top))) )],[refute_0_648,refute_0_651]) ).
cnf(refute_0_653,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_654,plain,
( complement(complement(top)) != complement(complement(top))
| complement(top) != zero
| complement(complement(top)) = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(top)),complement(complement(top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_655,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_653,refute_0_654]) ).
cnf(refute_0_656,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_655]) ).
cnf(refute_0_657,plain,
join(zero,complement(complement(top))) = complement(complement(top)),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(complement(complement(top))))]]) ).
cnf(refute_0_658,plain,
( complement(complement(top)) != complement(zero)
| join(zero,complement(complement(top))) != complement(complement(top))
| join(zero,complement(complement(top))) = complement(zero) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(zero,complement(complement(top))))),bind(Y,$fot(complement(complement(top)))),bind(Z,$fot(complement(zero)))]]) ).
cnf(refute_0_659,plain,
( complement(complement(top)) != complement(zero)
| join(zero,complement(complement(top))) = complement(zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(top))),complement(complement(top))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
join(zero,complement(complement(top))) = complement(zero),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_656,refute_0_659]) ).
cnf(refute_0_661,plain,
( join(zero,complement(complement(top))) != complement(zero)
| top != join(zero,complement(complement(top)))
| top = complement(zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,complement(complement(top)))) ),[1],$fot(complement(zero))]]) ).
cnf(refute_0_662,plain,
( top != join(zero,complement(complement(top)))
| top = complement(zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(top))),complement(zero)) )],[refute_0_660,refute_0_661]) ).
cnf(refute_0_663,plain,
top = complement(zero),
inference(resolve,[$cnf( $equal(top,join(zero,complement(complement(top)))) )],[refute_0_652,refute_0_662]) ).
cnf(refute_0_664,plain,
( top != complement(zero)
| complement(zero) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(complement(zero)))]]) ).
cnf(refute_0_665,plain,
complement(zero) = top,
inference(resolve,[$cnf( $equal(top,complement(zero)) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
composition(complement(composition(complement(sk1),top)),complement(zero)) = composition(complement(composition(complement(sk1),top)),complement(zero)),
introduced(tautology,[refl,[$fot(composition(complement(composition(complement(sk1),top)),complement(zero)))]]) ).
cnf(refute_0_667,plain,
( complement(zero) != top
| composition(complement(composition(complement(sk1),top)),complement(zero)) != composition(complement(composition(complement(sk1),top)),complement(zero))
| composition(complement(composition(complement(sk1),top)),complement(zero)) = composition(complement(composition(complement(sk1),top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(complement(sk1),top)),complement(zero)),composition(complement(composition(complement(sk1),top)),complement(zero))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_668,plain,
( complement(zero) != top
| composition(complement(composition(complement(sk1),top)),complement(zero)) = composition(complement(composition(complement(sk1),top)),top) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(complement(sk1),top)),complement(zero)),composition(complement(composition(complement(sk1),top)),complement(zero))) )],[refute_0_666,refute_0_667]) ).
cnf(refute_0_669,plain,
composition(complement(composition(complement(sk1),top)),complement(zero)) = composition(complement(composition(complement(sk1),top)),top),
inference(resolve,[$cnf( $equal(complement(zero),top) )],[refute_0_665,refute_0_668]) ).
cnf(refute_0_670,plain,
converse(converse(complement(composition(complement(sk1),top)))) = complement(composition(complement(sk1),top)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(composition(complement(sk1),top))))]]) ).
cnf(refute_0_671,plain,
composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)),
introduced(tautology,[refl,[$fot(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)))]]) ).
cnf(refute_0_672,plain,
( composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) != composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))
| converse(converse(complement(composition(complement(sk1),top)))) != complement(composition(complement(sk1),top))
| composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) ),[1,0],$fot(complement(composition(complement(sk1),top)))]]) ).
cnf(refute_0_673,plain,
( converse(converse(complement(composition(complement(sk1),top)))) != complement(composition(complement(sk1),top))
| composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),complement(zero)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),complement(zero)),
inference(resolve,[$cnf( $equal(converse(converse(complement(composition(complement(sk1),top)))),complement(composition(complement(sk1),top))) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
( composition(complement(composition(complement(sk1),top)),complement(zero)) != composition(complement(composition(complement(sk1),top)),top)
| composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) != composition(complement(composition(complement(sk1),top)),complement(zero))
| composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),top) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)))),bind(Y,$fot(composition(complement(composition(complement(sk1),top)),complement(zero)))),bind(Z,$fot(composition(complement(composition(complement(sk1),top)),top)))]]) ).
cnf(refute_0_676,plain,
( composition(complement(composition(complement(sk1),top)),complement(zero)) != composition(complement(composition(complement(sk1),top)),top)
| composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),top) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)),composition(complement(composition(complement(sk1),top)),complement(zero))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) = composition(complement(composition(complement(sk1),top)),top),
inference(resolve,[$cnf( $equal(composition(complement(composition(complement(sk1),top)),complement(zero)),composition(complement(composition(complement(sk1),top)),top)) )],[refute_0_669,refute_0_676]) ).
cnf(refute_0_678,plain,
join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),
introduced(tautology,[refl,[$fot(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))))]]) ).
cnf(refute_0_679,plain,
( composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) != composition(complement(composition(complement(sk1),top)),top)
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) != join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)))
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)))) ),[1,1],$fot(composition(complement(composition(complement(sk1),top)),top))]]) ).
cnf(refute_0_680,plain,
( composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)) != composition(complement(composition(complement(sk1),top)),top)
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)))) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) = join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)),
inference(resolve,[$cnf( $equal(composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero)),composition(complement(composition(complement(sk1),top)),top)) )],[refute_0_677,refute_0_680]) ).
cnf(refute_0_682,plain,
( join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) != complement(composition(sk1,complement(one)))
| join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) != join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))
| join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) = complement(composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),complement(composition(sk1,complement(one)))) ),[0],$fot(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)))]]) ).
cnf(refute_0_683,plain,
( join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))) != complement(composition(sk1,complement(one)))
| join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) = complement(composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) = complement(composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(converse(converse(complement(composition(complement(sk1),top)))),complement(zero))),complement(composition(sk1,complement(one)))) )],[refute_0_647,refute_0_683]) ).
cnf(refute_0_685,plain,
( join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) != complement(composition(sk1,complement(one)))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))) != complement(one)
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))),complement(one)) ),[0,1,1,0],$fot(complement(composition(sk1,complement(one))))]]) ).
cnf(refute_0_686,plain,
( join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))) != complement(one)
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)),complement(composition(sk1,complement(one)))) )],[refute_0_684,refute_0_685]) ).
cnf(refute_0_687,plain,
join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))),complement(one)) )],[refute_0_34,refute_0_686]) ).
cnf(refute_0_688,plain,
composition(join(X_122,one),X_124) = join(composition(X_122,X_124),composition(one,X_124)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_122)),bind(B,$fot(one)),bind(C,$fot(X_124))]]) ).
cnf(refute_0_689,plain,
X_124 = composition(one,X_124),
inference(subst,[],[refute_0_107:[bind(X_16,$fot(X_124))]]) ).
cnf(refute_0_690,plain,
( X_124 != composition(one,X_124)
| composition(one,X_124) = X_124 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_124)),bind(Y,$fot(composition(one,X_124)))]]) ).
cnf(refute_0_691,plain,
composition(one,X_124) = X_124,
inference(resolve,[$cnf( $equal(X_124,composition(one,X_124)) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
( composition(join(X_122,one),X_124) != join(composition(X_122,X_124),composition(one,X_124))
| composition(one,X_124) != X_124
| composition(join(X_122,one),X_124) = join(composition(X_122,X_124),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_122,one),X_124),join(composition(X_122,X_124),composition(one,X_124))) ),[1,1],$fot(X_124)]]) ).
cnf(refute_0_693,plain,
( composition(join(X_122,one),X_124) != join(composition(X_122,X_124),composition(one,X_124))
| composition(join(X_122,one),X_124) = join(composition(X_122,X_124),X_124) ),
inference(resolve,[$cnf( $equal(composition(one,X_124),X_124) )],[refute_0_691,refute_0_692]) ).
cnf(refute_0_694,plain,
composition(join(X_122,one),X_124) = join(composition(X_122,X_124),X_124),
inference(resolve,[$cnf( $equal(composition(join(X_122,one),X_124),join(composition(X_122,X_124),composition(one,X_124))) )],[refute_0_688,refute_0_693]) ).
cnf(refute_0_695,plain,
join(composition(X_122,X_124),X_124) = join(X_124,composition(X_122,X_124)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_124)),bind(B,$fot(composition(X_122,X_124)))]]) ).
cnf(refute_0_696,plain,
( composition(join(X_122,one),X_124) != join(composition(X_122,X_124),X_124)
| join(composition(X_122,X_124),X_124) != join(X_124,composition(X_122,X_124))
| composition(join(X_122,one),X_124) = join(X_124,composition(X_122,X_124)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_122,one),X_124),join(X_124,composition(X_122,X_124))) ),[0],$fot(join(composition(X_122,X_124),X_124))]]) ).
cnf(refute_0_697,plain,
( composition(join(X_122,one),X_124) != join(composition(X_122,X_124),X_124)
| composition(join(X_122,one),X_124) = join(X_124,composition(X_122,X_124)) ),
inference(resolve,[$cnf( $equal(join(composition(X_122,X_124),X_124),join(X_124,composition(X_122,X_124))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
composition(join(X_122,one),X_124) = join(X_124,composition(X_122,X_124)),
inference(resolve,[$cnf( $equal(composition(join(X_122,one),X_124),join(composition(X_122,X_124),X_124)) )],[refute_0_694,refute_0_697]) ).
cnf(refute_0_699,plain,
composition(join(composition(A,B),one),X_221) = join(X_221,composition(composition(A,B),X_221)),
inference(subst,[],[refute_0_698:[bind(X_122,$fot(composition(A,B))),bind(X_124,$fot(X_221))]]) ).
cnf(refute_0_700,plain,
composition(A,composition(B,X_221)) = composition(composition(A,B),X_221),
inference(subst,[],[composition_associativity_5:[bind(C,$fot(X_221))]]) ).
cnf(refute_0_701,plain,
( composition(A,composition(B,X_221)) != composition(composition(A,B),X_221)
| composition(composition(A,B),X_221) = composition(A,composition(B,X_221)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(A,composition(B,X_221)))),bind(Y,$fot(composition(composition(A,B),X_221)))]]) ).
cnf(refute_0_702,plain,
composition(composition(A,B),X_221) = composition(A,composition(B,X_221)),
inference(resolve,[$cnf( $equal(composition(A,composition(B,X_221)),composition(composition(A,B),X_221)) )],[refute_0_700,refute_0_701]) ).
cnf(refute_0_703,plain,
( composition(composition(A,B),X_221) != composition(A,composition(B,X_221))
| composition(join(composition(A,B),one),X_221) != join(X_221,composition(composition(A,B),X_221))
| composition(join(composition(A,B),one),X_221) = join(X_221,composition(A,composition(B,X_221))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(composition(A,B),one),X_221),join(X_221,composition(composition(A,B),X_221))) ),[1,1],$fot(composition(A,composition(B,X_221)))]]) ).
cnf(refute_0_704,plain,
( composition(join(composition(A,B),one),X_221) != join(X_221,composition(composition(A,B),X_221))
| composition(join(composition(A,B),one),X_221) = join(X_221,composition(A,composition(B,X_221))) ),
inference(resolve,[$cnf( $equal(composition(composition(A,B),X_221),composition(A,composition(B,X_221))) )],[refute_0_702,refute_0_703]) ).
cnf(refute_0_705,plain,
composition(join(composition(A,B),one),X_221) = join(X_221,composition(A,composition(B,X_221))),
inference(resolve,[$cnf( $equal(composition(join(composition(A,B),one),X_221),join(X_221,composition(composition(A,B),X_221))) )],[refute_0_699,refute_0_704]) ).
cnf(refute_0_706,plain,
join(B,join(B,C)) = join(join(B,B),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(B))]]) ).
cnf(refute_0_707,plain,
join(complement(join(complement(X_27),complement(X_28))),complement(join(complement(X_27),complement(X_28)))) = complement(join(complement(X_27),complement(X_28))),
inference(subst,[],[refute_0_130:[bind(X_24,$fot(join(complement(X_27),complement(X_28))))]]) ).
cnf(refute_0_708,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| join(complement(join(complement(X_27),complement(X_28))),complement(join(complement(X_27),complement(X_28)))) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = complement(join(complement(X_27),complement(X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X_27),complement(X_28))),complement(join(complement(X_27),complement(X_28)))),complement(join(complement(X_27),complement(X_28)))) ),[0,0],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_709,plain,
( join(complement(join(complement(X_27),complement(X_28))),complement(join(complement(X_27),complement(X_28)))) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = complement(join(complement(X_27),complement(X_28))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_708]) ).
cnf(refute_0_710,plain,
join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = complement(join(complement(X_27),complement(X_28))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X_27),complement(X_28))),complement(join(complement(X_27),complement(X_28)))),complement(join(complement(X_27),complement(X_28)))) )],[refute_0_707,refute_0_709]) ).
cnf(refute_0_711,plain,
join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),
introduced(tautology,[refl,[$fot(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))))]]) ).
cnf(refute_0_712,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) != join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28))))
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = join(meet(X_27,X_28),meet(X_27,X_28)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28))))) ),[1,1],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_713,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = join(meet(X_27,X_28),meet(X_27,X_28)) ),
inference(resolve,[$cnf( $equal(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28))))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) = join(meet(X_27,X_28),meet(X_27,X_28)),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_713]) ).
cnf(refute_0_715,plain,
( join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) != join(meet(X_27,X_28),meet(X_27,X_28))
| join(meet(X_27,X_28),meet(X_27,X_28)) = complement(join(complement(X_27),complement(X_28))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),complement(join(complement(X_27),complement(X_28)))) ),[0],$fot(join(meet(X_27,X_28),meet(X_27,X_28)))]]) ).
cnf(refute_0_716,plain,
( join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),meet(X_27,X_28)) = complement(join(complement(X_27),complement(X_28))) ),
inference(resolve,[$cnf( $equal(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),join(meet(X_27,X_28),meet(X_27,X_28))) )],[refute_0_714,refute_0_715]) ).
cnf(refute_0_717,plain,
( complement(join(complement(X_27),complement(X_28))) != meet(X_27,X_28)
| join(meet(X_27,X_28),meet(X_27,X_28)) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),meet(X_27,X_28)) = meet(X_27,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_27,X_28),meet(X_27,X_28)),complement(join(complement(X_27),complement(X_28)))) ),[1],$fot(meet(X_27,X_28))]]) ).
cnf(refute_0_718,plain,
( join(meet(X_27,X_28),meet(X_27,X_28)) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),meet(X_27,X_28)) = meet(X_27,X_28) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_27),complement(X_28))),meet(X_27,X_28)) )],[refute_0_41,refute_0_717]) ).
cnf(refute_0_719,plain,
( join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))) != complement(join(complement(X_27),complement(X_28)))
| join(meet(X_27,X_28),meet(X_27,X_28)) = meet(X_27,X_28) ),
inference(resolve,[$cnf( $equal(join(meet(X_27,X_28),meet(X_27,X_28)),complement(join(complement(X_27),complement(X_28)))) )],[refute_0_716,refute_0_718]) ).
cnf(refute_0_720,plain,
join(meet(X_27,X_28),meet(X_27,X_28)) = meet(X_27,X_28),
inference(resolve,[$cnf( $equal(join(meet(X_27,X_28),complement(join(complement(X_27),complement(X_28)))),complement(join(complement(X_27),complement(X_28)))) )],[refute_0_710,refute_0_719]) ).
cnf(refute_0_721,plain,
join(meet(X_28,X_28),meet(X_28,X_28)) = meet(X_28,X_28),
inference(subst,[],[refute_0_720:[bind(X_27,$fot(X_28))]]) ).
cnf(refute_0_722,plain,
meet(top,B) = B,
inference(subst,[],[refute_0_284:[bind(X_76,$fot(B))]]) ).
cnf(refute_0_723,plain,
( meet(top,B) != B
| meet(top,B) != complement(join(zero,complement(B)))
| B = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) ),[0],$fot(B)]]) ).
cnf(refute_0_724,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| B = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(meet(top,B),B) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
join(zero,complement(B)) = complement(B),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(complement(B)))]]) ).
cnf(refute_0_726,plain,
complement(join(zero,complement(B))) = complement(join(zero,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_727,plain,
( complement(join(zero,complement(B))) != complement(join(zero,complement(B)))
| join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_728,plain,
( join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
complement(join(zero,complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_725,refute_0_728]) ).
cnf(refute_0_730,plain,
( B != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) != complement(complement(B))
| B = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(B,complement(complement(B))) ),[0],$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_731,plain,
( B != complement(join(zero,complement(B)))
| B = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(complement(B))) )],[refute_0_729,refute_0_730]) ).
cnf(refute_0_732,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| B = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(B,complement(join(zero,complement(B)))) )],[refute_0_724,refute_0_731]) ).
cnf(refute_0_733,plain,
B = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_247,refute_0_732]) ).
cnf(refute_0_734,plain,
( B != complement(complement(B))
| complement(complement(B)) = B ),
inference(subst,[],[refute_0_3:[bind(X,$fot(B)),bind(Y,$fot(complement(complement(B))))]]) ).
cnf(refute_0_735,plain,
complement(complement(B)) = B,
inference(resolve,[$cnf( $equal(B,complement(complement(B))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
complement(complement(X_28)) = X_28,
inference(subst,[],[refute_0_735:[bind(B,$fot(X_28))]]) ).
cnf(refute_0_737,plain,
( complement(complement(X_28)) != X_28
| meet(X_28,X_28) != complement(complement(X_28))
| meet(X_28,X_28) = X_28 ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_28,X_28),complement(complement(X_28))) ),[1],$fot(X_28)]]) ).
cnf(refute_0_738,plain,
( meet(X_28,X_28) != complement(complement(X_28))
| meet(X_28,X_28) = X_28 ),
inference(resolve,[$cnf( $equal(complement(complement(X_28)),X_28) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
meet(X_28,X_28) = X_28,
inference(resolve,[$cnf( $equal(meet(X_28,X_28),complement(complement(X_28))) )],[refute_0_190,refute_0_738]) ).
cnf(refute_0_740,plain,
( join(meet(X_28,X_28),meet(X_28,X_28)) != meet(X_28,X_28)
| meet(X_28,X_28) != X_28
| join(X_28,meet(X_28,X_28)) = meet(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_28,X_28),meet(X_28,X_28)),meet(X_28,X_28)) ),[0,0],$fot(X_28)]]) ).
cnf(refute_0_741,plain,
( join(meet(X_28,X_28),meet(X_28,X_28)) != meet(X_28,X_28)
| join(X_28,meet(X_28,X_28)) = meet(X_28,X_28) ),
inference(resolve,[$cnf( $equal(meet(X_28,X_28),X_28) )],[refute_0_739,refute_0_740]) ).
cnf(refute_0_742,plain,
join(X_28,meet(X_28,X_28)) = meet(X_28,X_28),
inference(resolve,[$cnf( $equal(join(meet(X_28,X_28),meet(X_28,X_28)),meet(X_28,X_28)) )],[refute_0_721,refute_0_741]) ).
cnf(refute_0_743,plain,
join(X_28,meet(X_28,X_28)) = join(X_28,meet(X_28,X_28)),
introduced(tautology,[refl,[$fot(join(X_28,meet(X_28,X_28)))]]) ).
cnf(refute_0_744,plain,
( join(X_28,meet(X_28,X_28)) != join(X_28,meet(X_28,X_28))
| meet(X_28,X_28) != X_28
| join(X_28,meet(X_28,X_28)) = join(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,meet(X_28,X_28)),join(X_28,meet(X_28,X_28))) ),[1,1],$fot(X_28)]]) ).
cnf(refute_0_745,plain,
( meet(X_28,X_28) != X_28
| join(X_28,meet(X_28,X_28)) = join(X_28,X_28) ),
inference(resolve,[$cnf( $equal(join(X_28,meet(X_28,X_28)),join(X_28,meet(X_28,X_28))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
join(X_28,meet(X_28,X_28)) = join(X_28,X_28),
inference(resolve,[$cnf( $equal(meet(X_28,X_28),X_28) )],[refute_0_739,refute_0_745]) ).
cnf(refute_0_747,plain,
( join(X_28,meet(X_28,X_28)) != join(X_28,X_28)
| join(X_28,meet(X_28,X_28)) != meet(X_28,X_28)
| join(X_28,X_28) = meet(X_28,X_28) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_28,meet(X_28,X_28)),meet(X_28,X_28)) ),[0],$fot(join(X_28,X_28))]]) ).
cnf(refute_0_748,plain,
( join(X_28,meet(X_28,X_28)) != meet(X_28,X_28)
| join(X_28,X_28) = meet(X_28,X_28) ),
inference(resolve,[$cnf( $equal(join(X_28,meet(X_28,X_28)),join(X_28,X_28)) )],[refute_0_746,refute_0_747]) ).
cnf(refute_0_749,plain,
( join(X_28,X_28) != meet(X_28,X_28)
| meet(X_28,X_28) != X_28
| join(X_28,X_28) = X_28 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_28,X_28),X_28) ),[0],$fot(meet(X_28,X_28))]]) ).
cnf(refute_0_750,plain,
( join(X_28,X_28) != meet(X_28,X_28)
| join(X_28,X_28) = X_28 ),
inference(resolve,[$cnf( $equal(meet(X_28,X_28),X_28) )],[refute_0_739,refute_0_749]) ).
cnf(refute_0_751,plain,
( join(X_28,meet(X_28,X_28)) != meet(X_28,X_28)
| join(X_28,X_28) = X_28 ),
inference(resolve,[$cnf( $equal(join(X_28,X_28),meet(X_28,X_28)) )],[refute_0_748,refute_0_750]) ).
cnf(refute_0_752,plain,
join(X_28,X_28) = X_28,
inference(resolve,[$cnf( $equal(join(X_28,meet(X_28,X_28)),meet(X_28,X_28)) )],[refute_0_742,refute_0_751]) ).
cnf(refute_0_753,plain,
join(B,B) = B,
inference(subst,[],[refute_0_752:[bind(X_28,$fot(B))]]) ).
cnf(refute_0_754,plain,
( join(B,B) != B
| join(B,join(B,C)) != join(join(B,B),C)
| join(B,join(B,C)) = join(B,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,C)),join(join(B,B),C)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_755,plain,
( join(B,join(B,C)) != join(join(B,B),C)
| join(B,join(B,C)) = join(B,C) ),
inference(resolve,[$cnf( $equal(join(B,B),B) )],[refute_0_753,refute_0_754]) ).
cnf(refute_0_756,plain,
join(B,join(B,C)) = join(B,C),
inference(resolve,[$cnf( $equal(join(B,join(B,C)),join(join(B,B),C)) )],[refute_0_706,refute_0_755]) ).
cnf(refute_0_757,plain,
join(B,join(B,composition(X_220,B))) = join(B,composition(X_220,B)),
inference(subst,[],[refute_0_756:[bind(C,$fot(composition(X_220,B)))]]) ).
cnf(refute_0_758,plain,
composition(join(X_220,one),B) = join(B,composition(X_220,B)),
inference(subst,[],[refute_0_698:[bind(X_122,$fot(X_220)),bind(X_124,$fot(B))]]) ).
cnf(refute_0_759,plain,
( composition(join(X_220,one),B) != join(B,composition(X_220,B))
| join(B,composition(X_220,B)) = composition(join(X_220,one),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(X_220,one),B))),bind(Y,$fot(join(B,composition(X_220,B))))]]) ).
cnf(refute_0_760,plain,
join(B,composition(X_220,B)) = composition(join(X_220,one),B),
inference(resolve,[$cnf( $equal(composition(join(X_220,one),B),join(B,composition(X_220,B))) )],[refute_0_758,refute_0_759]) ).
cnf(refute_0_761,plain,
( join(B,composition(X_220,B)) != composition(join(X_220,one),B)
| join(B,join(B,composition(X_220,B))) != join(B,composition(X_220,B))
| join(B,join(B,composition(X_220,B))) = composition(join(X_220,one),B) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,composition(X_220,B))),join(B,composition(X_220,B))) ),[1],$fot(composition(join(X_220,one),B))]]) ).
cnf(refute_0_762,plain,
( join(B,join(B,composition(X_220,B))) != join(B,composition(X_220,B))
| join(B,join(B,composition(X_220,B))) = composition(join(X_220,one),B) ),
inference(resolve,[$cnf( $equal(join(B,composition(X_220,B)),composition(join(X_220,one),B)) )],[refute_0_760,refute_0_761]) ).
cnf(refute_0_763,plain,
join(B,join(B,composition(X_220,B))) = composition(join(X_220,one),B),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(X_220,B))),join(B,composition(X_220,B))) )],[refute_0_757,refute_0_762]) ).
cnf(refute_0_764,plain,
join(join(complement(X_72),X_73),complement(X_72)) = join(complement(X_72),join(complement(X_72),X_73)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_72),X_73))),bind(B,$fot(complement(X_72)))]]) ).
cnf(refute_0_765,plain,
join(complement(X_24),join(complement(X_24),X_51)) = join(join(complement(X_24),complement(X_24)),X_51),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(complement(X_24))),bind(B,$fot(complement(X_24))),bind(C,$fot(X_51))]]) ).
cnf(refute_0_766,plain,
( join(complement(X_24),complement(X_24)) != complement(X_24)
| join(complement(X_24),join(complement(X_24),X_51)) != join(join(complement(X_24),complement(X_24)),X_51)
| join(complement(X_24),join(complement(X_24),X_51)) = join(complement(X_24),X_51) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_24),join(complement(X_24),X_51)),join(join(complement(X_24),complement(X_24)),X_51)) ),[1,0],$fot(complement(X_24))]]) ).
cnf(refute_0_767,plain,
( join(complement(X_24),join(complement(X_24),X_51)) != join(join(complement(X_24),complement(X_24)),X_51)
| join(complement(X_24),join(complement(X_24),X_51)) = join(complement(X_24),X_51) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),complement(X_24)),complement(X_24)) )],[refute_0_130,refute_0_766]) ).
cnf(refute_0_768,plain,
join(complement(X_24),join(complement(X_24),X_51)) = join(complement(X_24),X_51),
inference(resolve,[$cnf( $equal(join(complement(X_24),join(complement(X_24),X_51)),join(join(complement(X_24),complement(X_24)),X_51)) )],[refute_0_765,refute_0_767]) ).
cnf(refute_0_769,plain,
join(complement(X_72),join(complement(X_72),X_73)) = join(complement(X_72),X_73),
inference(subst,[],[refute_0_768:[bind(X_24,$fot(X_72)),bind(X_51,$fot(X_73))]]) ).
cnf(refute_0_770,plain,
( join(complement(X_72),join(complement(X_72),X_73)) != join(complement(X_72),X_73)
| join(join(complement(X_72),X_73),complement(X_72)) != join(complement(X_72),join(complement(X_72),X_73))
| join(join(complement(X_72),X_73),complement(X_72)) = join(complement(X_72),X_73) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_72),X_73),complement(X_72)),join(complement(X_72),join(complement(X_72),X_73))) ),[1],$fot(join(complement(X_72),X_73))]]) ).
cnf(refute_0_771,plain,
( join(join(complement(X_72),X_73),complement(X_72)) != join(complement(X_72),join(complement(X_72),X_73))
| join(join(complement(X_72),X_73),complement(X_72)) = join(complement(X_72),X_73) ),
inference(resolve,[$cnf( $equal(join(complement(X_72),join(complement(X_72),X_73)),join(complement(X_72),X_73)) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
join(join(complement(X_72),X_73),complement(X_72)) = join(complement(X_72),X_73),
inference(resolve,[$cnf( $equal(join(join(complement(X_72),X_73),complement(X_72)),join(complement(X_72),join(complement(X_72),X_73))) )],[refute_0_764,refute_0_771]) ).
cnf(refute_0_773,plain,
join(join(complement(X_72),X_73),complement(X_72)) = join(complement(X_72),join(X_73,complement(X_72))),
inference(subst,[],[refute_0_180:[bind(A,$fot(complement(X_72))),bind(B,$fot(X_73)),bind(C,$fot(complement(X_72)))]]) ).
cnf(refute_0_774,plain,
( join(join(complement(X_72),X_73),complement(X_72)) != join(complement(X_72),X_73)
| join(join(complement(X_72),X_73),complement(X_72)) != join(complement(X_72),join(X_73,complement(X_72)))
| join(complement(X_72),join(X_73,complement(X_72))) = join(complement(X_72),X_73) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_72),X_73),complement(X_72)),join(complement(X_72),X_73)) ),[0],$fot(join(complement(X_72),join(X_73,complement(X_72))))]]) ).
cnf(refute_0_775,plain,
( join(join(complement(X_72),X_73),complement(X_72)) != join(complement(X_72),X_73)
| join(complement(X_72),join(X_73,complement(X_72))) = join(complement(X_72),X_73) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_72),X_73),complement(X_72)),join(complement(X_72),join(X_73,complement(X_72)))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
join(complement(X_72),join(X_73,complement(X_72))) = join(complement(X_72),X_73),
inference(resolve,[$cnf( $equal(join(join(complement(X_72),X_73),complement(X_72)),join(complement(X_72),X_73)) )],[refute_0_772,refute_0_775]) ).
cnf(refute_0_777,plain,
join(complement(complement(B)),join(X_148,complement(complement(B)))) = join(complement(complement(B)),X_148),
inference(subst,[],[refute_0_776:[bind(X_72,$fot(complement(B))),bind(X_73,$fot(X_148))]]) ).
cnf(refute_0_778,plain,
( complement(complement(B)) != B
| join(complement(complement(B)),join(X_148,complement(complement(B)))) != join(complement(complement(B)),X_148)
| join(B,join(X_148,complement(complement(B)))) = join(complement(complement(B)),X_148) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(B)),join(X_148,complement(complement(B)))),join(complement(complement(B)),X_148)) ),[0,0],$fot(B)]]) ).
cnf(refute_0_779,plain,
( join(complement(complement(B)),join(X_148,complement(complement(B)))) != join(complement(complement(B)),X_148)
| join(B,join(X_148,complement(complement(B)))) = join(complement(complement(B)),X_148) ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_735,refute_0_778]) ).
cnf(refute_0_780,plain,
join(B,join(X_148,complement(complement(B)))) = join(complement(complement(B)),X_148),
inference(resolve,[$cnf( $equal(join(complement(complement(B)),join(X_148,complement(complement(B)))),join(complement(complement(B)),X_148)) )],[refute_0_777,refute_0_779]) ).
cnf(refute_0_781,plain,
join(X_148,complement(complement(B))) = join(X_148,complement(complement(B))),
introduced(tautology,[refl,[$fot(join(X_148,complement(complement(B))))]]) ).
cnf(refute_0_782,plain,
( complement(complement(B)) != B
| join(X_148,complement(complement(B))) != join(X_148,complement(complement(B)))
| join(X_148,complement(complement(B))) = join(X_148,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_148,complement(complement(B))),join(X_148,complement(complement(B)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_783,plain,
( complement(complement(B)) != B
| join(X_148,complement(complement(B))) = join(X_148,B) ),
inference(resolve,[$cnf( $equal(join(X_148,complement(complement(B))),join(X_148,complement(complement(B)))) )],[refute_0_781,refute_0_782]) ).
cnf(refute_0_784,plain,
join(X_148,complement(complement(B))) = join(X_148,B),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_735,refute_0_783]) ).
cnf(refute_0_785,plain,
join(B,join(X_148,complement(complement(B)))) = join(B,join(X_148,complement(complement(B)))),
introduced(tautology,[refl,[$fot(join(B,join(X_148,complement(complement(B)))))]]) ).
cnf(refute_0_786,plain,
( join(B,join(X_148,complement(complement(B)))) != join(B,join(X_148,complement(complement(B))))
| join(X_148,complement(complement(B))) != join(X_148,B)
| join(B,join(X_148,complement(complement(B)))) = join(B,join(X_148,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(X_148,complement(complement(B)))),join(B,join(X_148,complement(complement(B))))) ),[1,1],$fot(join(X_148,B))]]) ).
cnf(refute_0_787,plain,
( join(X_148,complement(complement(B))) != join(X_148,B)
| join(B,join(X_148,complement(complement(B)))) = join(B,join(X_148,B)) ),
inference(resolve,[$cnf( $equal(join(B,join(X_148,complement(complement(B)))),join(B,join(X_148,complement(complement(B))))) )],[refute_0_785,refute_0_786]) ).
cnf(refute_0_788,plain,
join(B,join(X_148,complement(complement(B)))) = join(B,join(X_148,B)),
inference(resolve,[$cnf( $equal(join(X_148,complement(complement(B))),join(X_148,B)) )],[refute_0_784,refute_0_787]) ).
cnf(refute_0_789,plain,
( join(B,join(X_148,complement(complement(B)))) != join(B,join(X_148,B))
| join(B,join(X_148,complement(complement(B)))) != join(complement(complement(B)),X_148)
| join(B,join(X_148,B)) = join(complement(complement(B)),X_148) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(X_148,complement(complement(B)))),join(complement(complement(B)),X_148)) ),[0],$fot(join(B,join(X_148,B)))]]) ).
cnf(refute_0_790,plain,
( join(B,join(X_148,complement(complement(B)))) != join(complement(complement(B)),X_148)
| join(B,join(X_148,B)) = join(complement(complement(B)),X_148) ),
inference(resolve,[$cnf( $equal(join(B,join(X_148,complement(complement(B)))),join(B,join(X_148,B))) )],[refute_0_788,refute_0_789]) ).
cnf(refute_0_791,plain,
join(complement(complement(B)),X_148) = join(complement(complement(B)),X_148),
introduced(tautology,[refl,[$fot(join(complement(complement(B)),X_148))]]) ).
cnf(refute_0_792,plain,
( complement(complement(B)) != B
| join(complement(complement(B)),X_148) != join(complement(complement(B)),X_148)
| join(complement(complement(B)),X_148) = join(B,X_148) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(B)),X_148),join(complement(complement(B)),X_148)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_793,plain,
( complement(complement(B)) != B
| join(complement(complement(B)),X_148) = join(B,X_148) ),
inference(resolve,[$cnf( $equal(join(complement(complement(B)),X_148),join(complement(complement(B)),X_148)) )],[refute_0_791,refute_0_792]) ).
cnf(refute_0_794,plain,
join(complement(complement(B)),X_148) = join(B,X_148),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_735,refute_0_793]) ).
cnf(refute_0_795,plain,
( join(B,join(X_148,B)) != join(complement(complement(B)),X_148)
| join(complement(complement(B)),X_148) != join(B,X_148)
| join(B,join(X_148,B)) = join(B,X_148) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(B,join(X_148,B)),join(B,X_148)) ),[0],$fot(join(complement(complement(B)),X_148))]]) ).
cnf(refute_0_796,plain,
( join(B,join(X_148,B)) != join(complement(complement(B)),X_148)
| join(B,join(X_148,B)) = join(B,X_148) ),
inference(resolve,[$cnf( $equal(join(complement(complement(B)),X_148),join(B,X_148)) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
( join(B,join(X_148,complement(complement(B)))) != join(complement(complement(B)),X_148)
| join(B,join(X_148,B)) = join(B,X_148) ),
inference(resolve,[$cnf( $equal(join(B,join(X_148,B)),join(complement(complement(B)),X_148)) )],[refute_0_790,refute_0_796]) ).
cnf(refute_0_798,plain,
join(B,join(X_148,B)) = join(B,X_148),
inference(resolve,[$cnf( $equal(join(B,join(X_148,complement(complement(B)))),join(complement(complement(B)),X_148)) )],[refute_0_780,refute_0_797]) ).
cnf(refute_0_799,plain,
join(one,join(X_220,one)) = join(one,X_220),
inference(subst,[],[refute_0_798:[bind(B,$fot(one)),bind(X_148,$fot(X_220))]]) ).
cnf(refute_0_800,plain,
composition(join(one,join(X_220,one)),B) = composition(join(one,join(X_220,one)),B),
introduced(tautology,[refl,[$fot(composition(join(one,join(X_220,one)),B))]]) ).
cnf(refute_0_801,plain,
( composition(join(one,join(X_220,one)),B) != composition(join(one,join(X_220,one)),B)
| join(one,join(X_220,one)) != join(one,X_220)
| composition(join(one,join(X_220,one)),B) = composition(join(one,X_220),B) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(X_220,one)),B),composition(join(one,join(X_220,one)),B)) ),[1,0],$fot(join(one,X_220))]]) ).
cnf(refute_0_802,plain,
( join(one,join(X_220,one)) != join(one,X_220)
| composition(join(one,join(X_220,one)),B) = composition(join(one,X_220),B) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_220,one)),B),composition(join(one,join(X_220,one)),B)) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
composition(join(one,join(X_220,one)),B) = composition(join(one,X_220),B),
inference(resolve,[$cnf( $equal(join(one,join(X_220,one)),join(one,X_220)) )],[refute_0_799,refute_0_802]) ).
cnf(refute_0_804,plain,
composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = join(composition(converse(complement(composition(X_124,top))),X_124),composition(X_123,X_124)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(converse(complement(composition(X_124,top))))),bind(B,$fot(X_123)),bind(C,$fot(X_124))]]) ).
cnf(refute_0_805,plain,
converse(composition(converse(X_85),complement(composition(X_85,top)))) = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(X_85))),bind(B,$fot(complement(composition(X_85,top))))]]) ).
cnf(refute_0_806,plain,
composition(converse(X_85),complement(composition(X_85,top))) = zero,
inference(subst,[],[refute_0_296:[bind(A,$fot(X_85))]]) ).
cnf(refute_0_807,plain,
( composition(converse(X_85),complement(composition(X_85,top))) != zero
| converse(composition(converse(X_85),complement(composition(X_85,top)))) != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| converse(zero) = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_85),complement(composition(X_85,top)))),composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_808,plain,
( converse(composition(converse(X_85),complement(composition(X_85,top)))) != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| converse(zero) = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) ),
inference(resolve,[$cnf( $equal(composition(converse(X_85),complement(composition(X_85,top))),zero) )],[refute_0_806,refute_0_807]) ).
cnf(refute_0_809,plain,
converse(zero) = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_85),complement(composition(X_85,top)))),composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) )],[refute_0_805,refute_0_808]) ).
cnf(refute_0_810,plain,
( converse(zero) != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| converse(zero) != zero
| zero = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) ),[0],$fot(zero)]]) ).
cnf(refute_0_811,plain,
( converse(zero) != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| zero = composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) ),
inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_629,refute_0_810]) ).
cnf(refute_0_812,plain,
converse(composition(converse(X_85),complement(composition(X_85,top)))) = composition(converse(complement(composition(X_85,top))),X_85),
inference(subst,[],[refute_0_82:[bind(A,$fot(X_85)),bind(X_6,$fot(complement(composition(X_85,top))))]]) ).
cnf(refute_0_813,plain,
composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) = converse(composition(converse(X_85),complement(composition(X_85,top)))),
inference(subst,[],[refute_0_634:[bind(A,$fot(converse(X_85))),bind(B,$fot(complement(composition(X_85,top))))]]) ).
cnf(refute_0_814,plain,
( composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) != converse(composition(converse(X_85),complement(composition(X_85,top))))
| converse(composition(converse(X_85),complement(composition(X_85,top)))) != composition(converse(complement(composition(X_85,top))),X_85)
| composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) = composition(converse(complement(composition(X_85,top))),X_85) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(complement(composition(X_85,top))),converse(converse(X_85))))),bind(Y,$fot(converse(composition(converse(X_85),complement(composition(X_85,top)))))),bind(Z,$fot(composition(converse(complement(composition(X_85,top))),X_85)))]]) ).
cnf(refute_0_815,plain,
( converse(composition(converse(X_85),complement(composition(X_85,top)))) != composition(converse(complement(composition(X_85,top))),X_85)
| composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) = composition(converse(complement(composition(X_85,top))),X_85) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_85,top))),converse(converse(X_85))),converse(composition(converse(X_85),complement(composition(X_85,top))))) )],[refute_0_813,refute_0_814]) ).
cnf(refute_0_816,plain,
composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) = composition(converse(complement(composition(X_85,top))),X_85),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_85),complement(composition(X_85,top)))),composition(converse(complement(composition(X_85,top))),X_85)) )],[refute_0_812,refute_0_815]) ).
cnf(refute_0_817,plain,
( composition(converse(complement(composition(X_85,top))),converse(converse(X_85))) != composition(converse(complement(composition(X_85,top))),X_85)
| zero != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| zero = composition(converse(complement(composition(X_85,top))),X_85) ),
introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) ),[1],$fot(composition(converse(complement(composition(X_85,top))),X_85))]]) ).
cnf(refute_0_818,plain,
( zero != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| zero = composition(converse(complement(composition(X_85,top))),X_85) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_85,top))),converse(converse(X_85))),composition(converse(complement(composition(X_85,top))),X_85)) )],[refute_0_816,refute_0_817]) ).
cnf(refute_0_819,plain,
( converse(zero) != composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))
| zero = composition(converse(complement(composition(X_85,top))),X_85) ),
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) )],[refute_0_811,refute_0_818]) ).
cnf(refute_0_820,plain,
zero = composition(converse(complement(composition(X_85,top))),X_85),
inference(resolve,[$cnf( $equal(converse(zero),composition(converse(complement(composition(X_85,top))),converse(converse(X_85)))) )],[refute_0_809,refute_0_819]) ).
cnf(refute_0_821,plain,
zero = composition(converse(complement(composition(X_124,top))),X_124),
inference(subst,[],[refute_0_820:[bind(X_85,$fot(X_124))]]) ).
cnf(refute_0_822,plain,
( zero != composition(converse(complement(composition(X_124,top))),X_124)
| composition(converse(complement(composition(X_124,top))),X_124) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(composition(converse(complement(composition(X_124,top))),X_124)))]]) ).
cnf(refute_0_823,plain,
composition(converse(complement(composition(X_124,top))),X_124) = zero,
inference(resolve,[$cnf( $equal(zero,composition(converse(complement(composition(X_124,top))),X_124)) )],[refute_0_821,refute_0_822]) ).
cnf(refute_0_824,plain,
( composition(converse(complement(composition(X_124,top))),X_124) != zero
| composition(join(converse(complement(composition(X_124,top))),X_123),X_124) != join(composition(converse(complement(composition(X_124,top))),X_124),composition(X_123,X_124))
| composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = join(zero,composition(X_123,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),X_123),X_124),join(composition(converse(complement(composition(X_124,top))),X_124),composition(X_123,X_124))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_825,plain,
( composition(join(converse(complement(composition(X_124,top))),X_123),X_124) != join(composition(converse(complement(composition(X_124,top))),X_124),composition(X_123,X_124))
| composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = join(zero,composition(X_123,X_124)) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_124,top))),X_124),zero) )],[refute_0_823,refute_0_824]) ).
cnf(refute_0_826,plain,
composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = join(zero,composition(X_123,X_124)),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),X_123),X_124),join(composition(converse(complement(composition(X_124,top))),X_124),composition(X_123,X_124))) )],[refute_0_804,refute_0_825]) ).
cnf(refute_0_827,plain,
join(zero,composition(X_123,X_124)) = composition(X_123,X_124),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(composition(X_123,X_124)))]]) ).
cnf(refute_0_828,plain,
( composition(join(converse(complement(composition(X_124,top))),X_123),X_124) != join(zero,composition(X_123,X_124))
| join(zero,composition(X_123,X_124)) != composition(X_123,X_124)
| composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = composition(X_123,X_124) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(converse(complement(composition(X_124,top))),X_123),X_124),composition(X_123,X_124)) ),[0],$fot(join(zero,composition(X_123,X_124)))]]) ).
cnf(refute_0_829,plain,
( composition(join(converse(complement(composition(X_124,top))),X_123),X_124) != join(zero,composition(X_123,X_124))
| composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = composition(X_123,X_124) ),
inference(resolve,[$cnf( $equal(join(zero,composition(X_123,X_124)),composition(X_123,X_124)) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
composition(join(converse(complement(composition(X_124,top))),X_123),X_124) = composition(X_123,X_124),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),X_123),X_124),join(zero,composition(X_123,X_124))) )],[refute_0_826,refute_0_829]) ).
cnf(refute_0_831,plain,
composition(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),X_124) = composition(join(X_200,X_198),X_124),
inference(subst,[],[refute_0_830:[bind(X_123,$fot(join(X_200,X_198)))]]) ).
cnf(refute_0_832,plain,
join(X_198,join(converse(complement(composition(X_124,top))),X_200)) = join(converse(complement(composition(X_124,top))),join(X_200,X_198)),
inference(subst,[],[refute_0_404:[bind(A,$fot(X_198)),bind(X_49,$fot(converse(complement(composition(X_124,top))))),bind(X_50,$fot(X_200))]]) ).
cnf(refute_0_833,plain,
( join(X_198,join(converse(complement(composition(X_124,top))),X_200)) != join(converse(complement(composition(X_124,top))),join(X_200,X_198))
| join(converse(complement(composition(X_124,top))),join(X_200,X_198)) = join(X_198,join(converse(complement(composition(X_124,top))),X_200)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_198,join(converse(complement(composition(X_124,top))),X_200)))),bind(Y,$fot(join(converse(complement(composition(X_124,top))),join(X_200,X_198))))]]) ).
cnf(refute_0_834,plain,
join(converse(complement(composition(X_124,top))),join(X_200,X_198)) = join(X_198,join(converse(complement(composition(X_124,top))),X_200)),
inference(resolve,[$cnf( $equal(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),join(converse(complement(composition(X_124,top))),join(X_200,X_198))) )],[refute_0_832,refute_0_833]) ).
cnf(refute_0_835,plain,
( composition(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),X_124) != composition(join(X_200,X_198),X_124)
| join(converse(complement(composition(X_124,top))),join(X_200,X_198)) != join(X_198,join(converse(complement(composition(X_124,top))),X_200))
| composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) = composition(join(X_200,X_198),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),X_124),composition(join(X_200,X_198),X_124)) ),[0,0],$fot(join(X_198,join(converse(complement(composition(X_124,top))),X_200)))]]) ).
cnf(refute_0_836,plain,
( composition(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),X_124) != composition(join(X_200,X_198),X_124)
| composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) = composition(join(X_200,X_198),X_124) ),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),join(X_198,join(converse(complement(composition(X_124,top))),X_200))) )],[refute_0_834,refute_0_835]) ).
cnf(refute_0_837,plain,
composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) = composition(join(X_200,X_198),X_124),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),join(X_200,X_198)),X_124),composition(join(X_200,X_198),X_124)) )],[refute_0_831,refute_0_836]) ).
cnf(refute_0_838,plain,
composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = join(composition(A,C),composition(join(converse(complement(composition(C,top))),X_133),C)),
inference(subst,[],[composition_distributivity_7:[bind(B,$fot(join(converse(complement(composition(C,top))),X_133)))]]) ).
cnf(refute_0_839,plain,
composition(join(converse(complement(composition(C,top))),X_133),C) = composition(X_133,C),
inference(subst,[],[refute_0_830:[bind(X_123,$fot(X_133)),bind(X_124,$fot(C))]]) ).
cnf(refute_0_840,plain,
( composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) != join(composition(A,C),composition(join(converse(complement(composition(C,top))),X_133),C))
| composition(join(converse(complement(composition(C,top))),X_133),C) != composition(X_133,C)
| composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = join(composition(A,C),composition(X_133,C)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,join(converse(complement(composition(C,top))),X_133)),C),join(composition(A,C),composition(join(converse(complement(composition(C,top))),X_133),C))) ),[1,1],$fot(composition(X_133,C))]]) ).
cnf(refute_0_841,plain,
( composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) != join(composition(A,C),composition(join(converse(complement(composition(C,top))),X_133),C))
| composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = join(composition(A,C),composition(X_133,C)) ),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(composition(C,top))),X_133),C),composition(X_133,C)) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = join(composition(A,C),composition(X_133,C)),
inference(resolve,[$cnf( $equal(composition(join(A,join(converse(complement(composition(C,top))),X_133)),C),join(composition(A,C),composition(join(converse(complement(composition(C,top))),X_133),C))) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
( composition(join(A,B),C) != join(composition(A,C),composition(B,C))
| join(composition(A,C),composition(B,C)) = composition(join(A,B),C) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(A,B),C))),bind(Y,$fot(join(composition(A,C),composition(B,C))))]]) ).
cnf(refute_0_844,plain,
join(composition(A,C),composition(B,C)) = composition(join(A,B),C),
inference(resolve,[$cnf( $equal(composition(join(A,B),C),join(composition(A,C),composition(B,C))) )],[composition_distributivity_7,refute_0_843]) ).
cnf(refute_0_845,plain,
join(composition(A,C),composition(X_133,C)) = composition(join(A,X_133),C),
inference(subst,[],[refute_0_844:[bind(B,$fot(X_133))]]) ).
cnf(refute_0_846,plain,
( composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) != join(composition(A,C),composition(X_133,C))
| join(composition(A,C),composition(X_133,C)) != composition(join(A,X_133),C)
| composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = composition(join(A,X_133),C) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,join(converse(complement(composition(C,top))),X_133)),C),composition(join(A,X_133),C)) ),[0],$fot(join(composition(A,C),composition(X_133,C)))]]) ).
cnf(refute_0_847,plain,
( composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) != join(composition(A,C),composition(X_133,C))
| composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = composition(join(A,X_133),C) ),
inference(resolve,[$cnf( $equal(join(composition(A,C),composition(X_133,C)),composition(join(A,X_133),C)) )],[refute_0_845,refute_0_846]) ).
cnf(refute_0_848,plain,
composition(join(A,join(converse(complement(composition(C,top))),X_133)),C) = composition(join(A,X_133),C),
inference(resolve,[$cnf( $equal(composition(join(A,join(converse(complement(composition(C,top))),X_133)),C),join(composition(A,C),composition(X_133,C))) )],[refute_0_842,refute_0_847]) ).
cnf(refute_0_849,plain,
composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) = composition(join(X_198,X_200),X_124),
inference(subst,[],[refute_0_848:[bind(A,$fot(X_198)),bind(C,$fot(X_124)),bind(X_133,$fot(X_200))]]) ).
cnf(refute_0_850,plain,
( composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) != composition(join(X_198,X_200),X_124)
| composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) != composition(join(X_200,X_198),X_124)
| composition(join(X_198,X_200),X_124) = composition(join(X_200,X_198),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124),composition(join(X_200,X_198),X_124)) ),[0],$fot(composition(join(X_198,X_200),X_124))]]) ).
cnf(refute_0_851,plain,
( composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124) != composition(join(X_200,X_198),X_124)
| composition(join(X_198,X_200),X_124) = composition(join(X_200,X_198),X_124) ),
inference(resolve,[$cnf( $equal(composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124),composition(join(X_198,X_200),X_124)) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
composition(join(X_198,X_200),X_124) = composition(join(X_200,X_198),X_124),
inference(resolve,[$cnf( $equal(composition(join(X_198,join(converse(complement(composition(X_124,top))),X_200)),X_124),composition(join(X_200,X_198),X_124)) )],[refute_0_837,refute_0_851]) ).
cnf(refute_0_853,plain,
( composition(join(X_198,X_200),X_124) != composition(join(X_200,X_198),X_124)
| composition(join(X_200,X_198),X_124) = composition(join(X_198,X_200),X_124) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(X_198,X_200),X_124))),bind(Y,$fot(composition(join(X_200,X_198),X_124)))]]) ).
cnf(refute_0_854,plain,
composition(join(X_200,X_198),X_124) = composition(join(X_198,X_200),X_124),
inference(resolve,[$cnf( $equal(composition(join(X_198,X_200),X_124),composition(join(X_200,X_198),X_124)) )],[refute_0_852,refute_0_853]) ).
cnf(refute_0_855,plain,
composition(join(join(X_220,one),one),B) = composition(join(one,join(X_220,one)),B),
inference(subst,[],[refute_0_854:[bind(X_124,$fot(B)),bind(X_198,$fot(one)),bind(X_200,$fot(join(X_220,one)))]]) ).
cnf(refute_0_856,plain,
( composition(join(X_122,one),X_124) != join(X_124,composition(X_122,X_124))
| join(X_124,composition(X_122,X_124)) = composition(join(X_122,one),X_124) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(X_122,one),X_124))),bind(Y,$fot(join(X_124,composition(X_122,X_124))))]]) ).
cnf(refute_0_857,plain,
join(X_124,composition(X_122,X_124)) = composition(join(X_122,one),X_124),
inference(resolve,[$cnf( $equal(composition(join(X_122,one),X_124),join(X_124,composition(X_122,X_124))) )],[refute_0_698,refute_0_856]) ).
cnf(refute_0_858,plain,
join(B,composition(join(X_220,one),B)) = composition(join(join(X_220,one),one),B),
inference(subst,[],[refute_0_857:[bind(X_122,$fot(join(X_220,one))),bind(X_124,$fot(B))]]) ).
cnf(refute_0_859,plain,
( composition(join(join(X_220,one),one),B) != composition(join(one,join(X_220,one)),B)
| join(B,composition(join(X_220,one),B)) != composition(join(join(X_220,one),one),B)
| join(B,composition(join(X_220,one),B)) = composition(join(one,join(X_220,one)),B) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,composition(join(X_220,one),B)))),bind(Y,$fot(composition(join(join(X_220,one),one),B))),bind(Z,$fot(composition(join(one,join(X_220,one)),B)))]]) ).
cnf(refute_0_860,plain,
( composition(join(join(X_220,one),one),B) != composition(join(one,join(X_220,one)),B)
| join(B,composition(join(X_220,one),B)) = composition(join(one,join(X_220,one)),B) ),
inference(resolve,[$cnf( $equal(join(B,composition(join(X_220,one),B)),composition(join(join(X_220,one),one),B)) )],[refute_0_858,refute_0_859]) ).
cnf(refute_0_861,plain,
join(B,composition(join(X_220,one),B)) = composition(join(one,join(X_220,one)),B),
inference(resolve,[$cnf( $equal(composition(join(join(X_220,one),one),B),composition(join(one,join(X_220,one)),B)) )],[refute_0_855,refute_0_860]) ).
cnf(refute_0_862,plain,
join(composition(X_220,X_50),join(X_49,X_50)) = join(X_49,join(X_50,composition(X_220,X_50))),
inference(subst,[],[refute_0_404:[bind(A,$fot(composition(X_220,X_50)))]]) ).
cnf(refute_0_863,plain,
composition(join(X_220,one),X_50) = join(X_50,composition(X_220,X_50)),
inference(subst,[],[refute_0_698:[bind(X_122,$fot(X_220)),bind(X_124,$fot(X_50))]]) ).
cnf(refute_0_864,plain,
( composition(join(X_220,one),X_50) != join(X_50,composition(X_220,X_50))
| join(X_50,composition(X_220,X_50)) = composition(join(X_220,one),X_50) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(X_220,one),X_50))),bind(Y,$fot(join(X_50,composition(X_220,X_50))))]]) ).
cnf(refute_0_865,plain,
join(X_50,composition(X_220,X_50)) = composition(join(X_220,one),X_50),
inference(resolve,[$cnf( $equal(composition(join(X_220,one),X_50),join(X_50,composition(X_220,X_50))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
( join(X_50,composition(X_220,X_50)) != composition(join(X_220,one),X_50)
| join(composition(X_220,X_50),join(X_49,X_50)) != join(X_49,join(X_50,composition(X_220,X_50)))
| join(composition(X_220,X_50),join(X_49,X_50)) = join(X_49,composition(join(X_220,one),X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_220,X_50),join(X_49,X_50)),join(X_49,join(X_50,composition(X_220,X_50)))) ),[1,1],$fot(composition(join(X_220,one),X_50))]]) ).
cnf(refute_0_867,plain,
( join(composition(X_220,X_50),join(X_49,X_50)) != join(X_49,join(X_50,composition(X_220,X_50)))
| join(composition(X_220,X_50),join(X_49,X_50)) = join(X_49,composition(join(X_220,one),X_50)) ),
inference(resolve,[$cnf( $equal(join(X_50,composition(X_220,X_50)),composition(join(X_220,one),X_50)) )],[refute_0_865,refute_0_866]) ).
cnf(refute_0_868,plain,
join(composition(X_220,X_50),join(X_49,X_50)) = join(X_49,composition(join(X_220,one),X_50)),
inference(resolve,[$cnf( $equal(join(composition(X_220,X_50),join(X_49,X_50)),join(X_49,join(X_50,composition(X_220,X_50)))) )],[refute_0_862,refute_0_867]) ).
cnf(refute_0_869,plain,
join(X_198,join(X_199,X_200)) = join(X_199,join(X_200,X_198)),
inference(subst,[],[refute_0_404:[bind(A,$fot(X_198)),bind(X_49,$fot(X_199)),bind(X_50,$fot(X_200))]]) ).
cnf(refute_0_870,plain,
join(X_200,X_199) = join(X_199,X_200),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_200)),bind(B,$fot(X_199))]]) ).
cnf(refute_0_871,plain,
( join(X_200,X_199) != join(X_199,X_200)
| join(X_199,X_200) = join(X_200,X_199) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_200,X_199))),bind(Y,$fot(join(X_199,X_200)))]]) ).
cnf(refute_0_872,plain,
join(X_199,X_200) = join(X_200,X_199),
inference(resolve,[$cnf( $equal(join(X_200,X_199),join(X_199,X_200)) )],[refute_0_870,refute_0_871]) ).
cnf(refute_0_873,plain,
( join(X_198,join(X_199,X_200)) != join(X_199,join(X_200,X_198))
| join(X_199,X_200) != join(X_200,X_199)
| join(X_198,join(X_200,X_199)) = join(X_199,join(X_200,X_198)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_198,join(X_199,X_200)),join(X_199,join(X_200,X_198))) ),[0,1],$fot(join(X_200,X_199))]]) ).
cnf(refute_0_874,plain,
( join(X_198,join(X_199,X_200)) != join(X_199,join(X_200,X_198))
| join(X_198,join(X_200,X_199)) = join(X_199,join(X_200,X_198)) ),
inference(resolve,[$cnf( $equal(join(X_199,X_200),join(X_200,X_199)) )],[refute_0_872,refute_0_873]) ).
cnf(refute_0_875,plain,
join(X_198,join(X_200,X_199)) = join(X_199,join(X_200,X_198)),
inference(resolve,[$cnf( $equal(join(X_198,join(X_199,X_200)),join(X_199,join(X_200,X_198))) )],[refute_0_869,refute_0_874]) ).
cnf(refute_0_876,plain,
( join(X_198,join(X_200,X_199)) != join(X_199,join(X_200,X_198))
| join(X_199,join(X_200,X_198)) = join(X_198,join(X_200,X_199)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_198,join(X_200,X_199)))),bind(Y,$fot(join(X_199,join(X_200,X_198))))]]) ).
cnf(refute_0_877,plain,
join(X_199,join(X_200,X_198)) = join(X_198,join(X_200,X_199)),
inference(resolve,[$cnf( $equal(join(X_198,join(X_200,X_199)),join(X_199,join(X_200,X_198))) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
join(composition(X_220,X_50),join(X_49,X_50)) = join(X_50,join(X_49,composition(X_220,X_50))),
inference(subst,[],[refute_0_877:[bind(X_198,$fot(X_50)),bind(X_199,$fot(composition(X_220,X_50))),bind(X_200,$fot(X_49))]]) ).
cnf(refute_0_879,plain,
( join(composition(X_220,X_50),join(X_49,X_50)) != join(X_49,composition(join(X_220,one),X_50))
| join(composition(X_220,X_50),join(X_49,X_50)) != join(X_50,join(X_49,composition(X_220,X_50)))
| join(X_50,join(X_49,composition(X_220,X_50))) = join(X_49,composition(join(X_220,one),X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_220,X_50),join(X_49,X_50)),join(X_49,composition(join(X_220,one),X_50))) ),[0],$fot(join(X_50,join(X_49,composition(X_220,X_50))))]]) ).
cnf(refute_0_880,plain,
( join(composition(X_220,X_50),join(X_49,X_50)) != join(X_49,composition(join(X_220,one),X_50))
| join(X_50,join(X_49,composition(X_220,X_50))) = join(X_49,composition(join(X_220,one),X_50)) ),
inference(resolve,[$cnf( $equal(join(composition(X_220,X_50),join(X_49,X_50)),join(X_50,join(X_49,composition(X_220,X_50)))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
join(X_50,join(X_49,composition(X_220,X_50))) = join(X_49,composition(join(X_220,one),X_50)),
inference(resolve,[$cnf( $equal(join(composition(X_220,X_50),join(X_49,X_50)),join(X_49,composition(join(X_220,one),X_50))) )],[refute_0_868,refute_0_880]) ).
cnf(refute_0_882,plain,
join(B,join(B,composition(X_220,B))) = join(B,composition(join(X_220,one),B)),
inference(subst,[],[refute_0_881:[bind(X_49,$fot(B)),bind(X_50,$fot(B))]]) ).
cnf(refute_0_883,plain,
( join(B,composition(join(X_220,one),B)) != composition(join(one,join(X_220,one)),B)
| join(B,join(B,composition(X_220,B))) != join(B,composition(join(X_220,one),B))
| join(B,join(B,composition(X_220,B))) = composition(join(one,join(X_220,one)),B) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,join(B,composition(X_220,B))))),bind(Y,$fot(join(B,composition(join(X_220,one),B)))),bind(Z,$fot(composition(join(one,join(X_220,one)),B)))]]) ).
cnf(refute_0_884,plain,
( join(B,composition(join(X_220,one),B)) != composition(join(one,join(X_220,one)),B)
| join(B,join(B,composition(X_220,B))) = composition(join(one,join(X_220,one)),B) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(X_220,B))),join(B,composition(join(X_220,one),B))) )],[refute_0_882,refute_0_883]) ).
cnf(refute_0_885,plain,
join(B,join(B,composition(X_220,B))) = composition(join(one,join(X_220,one)),B),
inference(resolve,[$cnf( $equal(join(B,composition(join(X_220,one),B)),composition(join(one,join(X_220,one)),B)) )],[refute_0_861,refute_0_884]) ).
cnf(refute_0_886,plain,
( composition(join(one,join(X_220,one)),B) != composition(join(one,X_220),B)
| join(B,join(B,composition(X_220,B))) != composition(join(one,join(X_220,one)),B)
| join(B,join(B,composition(X_220,B))) = composition(join(one,X_220),B) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,join(B,composition(X_220,B))))),bind(Y,$fot(composition(join(one,join(X_220,one)),B))),bind(Z,$fot(composition(join(one,X_220),B)))]]) ).
cnf(refute_0_887,plain,
( composition(join(one,join(X_220,one)),B) != composition(join(one,X_220),B)
| join(B,join(B,composition(X_220,B))) = composition(join(one,X_220),B) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(X_220,B))),composition(join(one,join(X_220,one)),B)) )],[refute_0_885,refute_0_886]) ).
cnf(refute_0_888,plain,
join(B,join(B,composition(X_220,B))) = composition(join(one,X_220),B),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_220,one)),B),composition(join(one,X_220),B)) )],[refute_0_803,refute_0_887]) ).
cnf(refute_0_889,plain,
( join(B,join(B,composition(X_220,B))) != composition(join(X_220,one),B)
| join(B,join(B,composition(X_220,B))) != composition(join(one,X_220),B)
| composition(join(one,X_220),B) = composition(join(X_220,one),B) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,composition(X_220,B))),composition(join(X_220,one),B)) ),[0],$fot(composition(join(one,X_220),B))]]) ).
cnf(refute_0_890,plain,
( join(B,join(B,composition(X_220,B))) != composition(join(X_220,one),B)
| composition(join(one,X_220),B) = composition(join(X_220,one),B) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(X_220,B))),composition(join(one,X_220),B)) )],[refute_0_888,refute_0_889]) ).
cnf(refute_0_891,plain,
composition(join(one,X_220),B) = composition(join(X_220,one),B),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(X_220,B))),composition(join(X_220,one),B)) )],[refute_0_763,refute_0_890]) ).
cnf(refute_0_892,plain,
( composition(join(one,X_220),B) != composition(join(X_220,one),B)
| composition(join(X_220,one),B) = composition(join(one,X_220),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(one,X_220),B))),bind(Y,$fot(composition(join(X_220,one),B)))]]) ).
cnf(refute_0_893,plain,
composition(join(X_220,one),B) = composition(join(one,X_220),B),
inference(resolve,[$cnf( $equal(composition(join(one,X_220),B),composition(join(X_220,one),B)) )],[refute_0_891,refute_0_892]) ).
cnf(refute_0_894,plain,
composition(join(composition(A,B),one),X_221) = composition(join(one,composition(A,B)),X_221),
inference(subst,[],[refute_0_893:[bind(B,$fot(X_221)),bind(X_220,$fot(composition(A,B)))]]) ).
cnf(refute_0_895,plain,
( composition(join(composition(A,B),one),X_221) != composition(join(one,composition(A,B)),X_221)
| composition(join(composition(A,B),one),X_221) != join(X_221,composition(A,composition(B,X_221)))
| composition(join(one,composition(A,B)),X_221) = join(X_221,composition(A,composition(B,X_221))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(composition(A,B),one),X_221),join(X_221,composition(A,composition(B,X_221)))) ),[0],$fot(composition(join(one,composition(A,B)),X_221))]]) ).
cnf(refute_0_896,plain,
( composition(join(composition(A,B),one),X_221) != join(X_221,composition(A,composition(B,X_221)))
| composition(join(one,composition(A,B)),X_221) = join(X_221,composition(A,composition(B,X_221))) ),
inference(resolve,[$cnf( $equal(composition(join(composition(A,B),one),X_221),composition(join(one,composition(A,B)),X_221)) )],[refute_0_894,refute_0_895]) ).
cnf(refute_0_897,plain,
composition(join(one,composition(A,B)),X_221) = join(X_221,composition(A,composition(B,X_221))),
inference(resolve,[$cnf( $equal(composition(join(composition(A,B),one),X_221),join(X_221,composition(A,composition(B,X_221)))) )],[refute_0_705,refute_0_896]) ).
cnf(refute_0_898,plain,
( composition(join(one,composition(A,B)),X_221) != join(X_221,composition(A,composition(B,X_221)))
| join(X_221,composition(A,composition(B,X_221))) = composition(join(one,composition(A,B)),X_221) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(one,composition(A,B)),X_221))),bind(Y,$fot(join(X_221,composition(A,composition(B,X_221)))))]]) ).
cnf(refute_0_899,plain,
join(X_221,composition(A,composition(B,X_221))) = composition(join(one,composition(A,B)),X_221),
inference(resolve,[$cnf( $equal(composition(join(one,composition(A,B)),X_221),join(X_221,composition(A,composition(B,X_221)))) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) = composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),
inference(subst,[],[refute_0_899:[bind(A,$fot(converse(complement(composition(sk1,complement(one)))))),bind(B,$fot(sk1)),bind(X_221,$fot(complement(one)))]]) ).
cnf(refute_0_901,plain,
complement(complement(composition(sk1,complement(one)))) = composition(sk1,complement(one)),
inference(subst,[],[refute_0_735:[bind(B,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_902,plain,
composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))),
introduced(tautology,[refl,[$fot(composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))))]]) ).
cnf(refute_0_903,plain,
( complement(complement(composition(sk1,complement(one)))) != composition(sk1,complement(one))
| composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one)))))
| composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one)))))) ),[1,1],$fot(composition(sk1,complement(one)))]]) ).
cnf(refute_0_904,plain,
( complement(complement(composition(sk1,complement(one)))) != composition(sk1,complement(one))
| composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one)))))) )],[refute_0_902,refute_0_903]) ).
cnf(refute_0_905,plain,
composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(complement(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) )],[refute_0_901,refute_0_904]) ).
cnf(refute_0_906,plain,
converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) = converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),
introduced(tautology,[refl,[$fot(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))))]]) ).
cnf(refute_0_907,plain,
( converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) != converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)))
| join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) != complement(composition(sk1,complement(one)))
| converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) = converse(complement(composition(sk1,complement(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)))) ),[1,0],$fot(complement(composition(sk1,complement(one))))]]) ).
cnf(refute_0_908,plain,
( join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)) != complement(composition(sk1,complement(one)))
| converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) = converse(complement(composition(sk1,complement(one)))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)))) )],[refute_0_906,refute_0_907]) ).
cnf(refute_0_909,plain,
converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) = converse(complement(composition(sk1,complement(one)))),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top)),complement(composition(sk1,complement(one)))) )],[refute_0_684,refute_0_908]) ).
cnf(refute_0_910,plain,
composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),
introduced(tautology,[refl,[$fot(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))))]]) ).
cnf(refute_0_911,plain,
( composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) != composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one)))))
| converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) != converse(complement(composition(sk1,complement(one))))
| composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one)))))) ),[1,0],$fot(converse(complement(composition(sk1,complement(one)))))]]) ).
cnf(refute_0_912,plain,
( converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))) != converse(complement(composition(sk1,complement(one))))
| composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one)))))) )],[refute_0_910,refute_0_911]) ).
cnf(refute_0_913,plain,
composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),converse(complement(composition(sk1,complement(one))))) )],[refute_0_909,refute_0_912]) ).
cnf(refute_0_914,plain,
( composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one)))))
| composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))))),bind(Y,$fot(composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))))),bind(Z,$fot(composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_915,plain,
( composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one)))))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) )],[refute_0_905,refute_0_915]) ).
cnf(refute_0_917,plain,
composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) = composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),
inference(subst,[],[refute_0_320:[bind(A,$fot(complement(complement(composition(sk1,complement(one)))))),bind(X_47,$fot(complement(composition(sk1,complement(one))))),bind(X_48,$fot(composition(complement(composition(complement(sk1),top)),top)))]]) ).
cnf(refute_0_918,plain,
( composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) != composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one)))))
| composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))))),bind(Y,$fot(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))))),bind(Z,$fot(composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_919,plain,
( composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))),composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one)))))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) = composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(composition(converse(join(complement(composition(sk1,complement(one))),composition(complement(composition(complement(sk1),top)),top))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) )],[refute_0_916,refute_0_919]) ).
cnf(refute_0_921,plain,
join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_922,plain,
( composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) != join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))))) ),[1,1],$fot(composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))))]]) ).
cnf(refute_0_923,plain,
( composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))) != composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))))) )],[refute_0_921,refute_0_922]) ).
cnf(refute_0_924,plain,
join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))),
inference(resolve,[$cnf( $equal(composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one))))),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) )],[refute_0_920,refute_0_923]) ).
cnf(refute_0_925,plain,
( join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) != composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) != join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))))),bind(Y,$fot(join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))))),bind(Z,$fot(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))))]]) ).
cnf(refute_0_926,plain,
( join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))) != composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one))))) )],[refute_0_924,refute_0_925]) ).
cnf(refute_0_927,plain,
join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) = composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(complement(composition(sk1,complement(one)))),composition(sk1,complement(one)))),composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))) )],[refute_0_900,refute_0_926]) ).
cnf(refute_0_928,plain,
( join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) != complement(one)
| join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) != composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))
| composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),complement(one)) ),[0],$fot(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)))]]) ).
cnf(refute_0_929,plain,
( join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))) != complement(one)
| composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))) )],[refute_0_927,refute_0_928]) ).
cnf(refute_0_930,plain,
composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(composition(complement(composition(complement(sk1),top)),top),complement(composition(sk1,complement(one))))),complement(complement(composition(sk1,complement(one)))))),complement(one)) )],[refute_0_687,refute_0_929]) ).
cnf(refute_0_931,plain,
join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) = join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))),
inference(subst,[],[refute_0_756:[bind(B,$fot(complement(X_347))),bind(C,$fot(meet(X_347,converse(complement(converse(X_347))))))]]) ).
cnf(refute_0_932,plain,
X_74 = join(meet(X_74,X_75),complement(join(complement(X_74),X_75))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(X_75))]]) ).
cnf(refute_0_933,plain,
meet(X_75,X_74) = meet(X_74,X_75),
inference(subst,[],[refute_0_272:[bind(X_27,$fot(X_75)),bind(X_28,$fot(X_74))]]) ).
cnf(refute_0_934,plain,
( meet(X_75,X_74) != meet(X_74,X_75)
| meet(X_74,X_75) = meet(X_75,X_74) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_75,X_74))),bind(Y,$fot(meet(X_74,X_75)))]]) ).
cnf(refute_0_935,plain,
meet(X_74,X_75) = meet(X_75,X_74),
inference(resolve,[$cnf( $equal(meet(X_75,X_74),meet(X_74,X_75)) )],[refute_0_933,refute_0_934]) ).
cnf(refute_0_936,plain,
( X_74 != join(meet(X_74,X_75),complement(join(complement(X_74),X_75)))
| meet(X_74,X_75) != meet(X_75,X_74)
| X_74 = join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,X_75),complement(join(complement(X_74),X_75)))) ),[1,0],$fot(meet(X_75,X_74))]]) ).
cnf(refute_0_937,plain,
( X_74 != join(meet(X_74,X_75),complement(join(complement(X_74),X_75)))
| X_74 = join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) ),
inference(resolve,[$cnf( $equal(meet(X_74,X_75),meet(X_75,X_74)) )],[refute_0_935,refute_0_936]) ).
cnf(refute_0_938,plain,
X_74 = join(meet(X_75,X_74),complement(join(complement(X_74),X_75))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,X_75),complement(join(complement(X_74),X_75)))) )],[refute_0_932,refute_0_937]) ).
cnf(refute_0_939,plain,
meet(A,join(zero,complement(X_32))) = complement(join(complement(A),complement(join(zero,complement(X_32))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_32))))]]) ).
cnf(refute_0_940,plain,
meet(top,X_32) = complement(join(zero,complement(X_32))),
inference(subst,[],[refute_0_247:[bind(B,$fot(X_32))]]) ).
cnf(refute_0_941,plain,
( meet(top,X_32) != complement(join(zero,complement(X_32)))
| complement(join(zero,complement(X_32))) = meet(top,X_32) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(top,X_32))),bind(Y,$fot(complement(join(zero,complement(X_32)))))]]) ).
cnf(refute_0_942,plain,
complement(join(zero,complement(X_32))) = meet(top,X_32),
inference(resolve,[$cnf( $equal(meet(top,X_32),complement(join(zero,complement(X_32)))) )],[refute_0_940,refute_0_941]) ).
cnf(refute_0_943,plain,
( complement(join(zero,complement(X_32))) != meet(top,X_32)
| meet(A,join(zero,complement(X_32))) != complement(join(complement(A),complement(join(zero,complement(X_32)))))
| meet(A,join(zero,complement(X_32))) = complement(join(complement(A),meet(top,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_32))),complement(join(complement(A),complement(join(zero,complement(X_32)))))) ),[1,0,1],$fot(meet(top,X_32))]]) ).
cnf(refute_0_944,plain,
( meet(A,join(zero,complement(X_32))) != complement(join(complement(A),complement(join(zero,complement(X_32)))))
| meet(A,join(zero,complement(X_32))) = complement(join(complement(A),meet(top,X_32))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_32))),meet(top,X_32)) )],[refute_0_942,refute_0_943]) ).
cnf(refute_0_945,plain,
meet(A,join(zero,complement(X_32))) = complement(join(complement(A),meet(top,X_32))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_32))),complement(join(complement(A),complement(join(zero,complement(X_32)))))) )],[refute_0_939,refute_0_944]) ).
cnf(refute_0_946,plain,
join(zero,complement(X_32)) = complement(X_32),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(complement(X_32)))]]) ).
cnf(refute_0_947,plain,
meet(A,join(zero,complement(X_32))) = meet(A,join(zero,complement(X_32))),
introduced(tautology,[refl,[$fot(meet(A,join(zero,complement(X_32))))]]) ).
cnf(refute_0_948,plain,
( join(zero,complement(X_32)) != complement(X_32)
| meet(A,join(zero,complement(X_32))) != meet(A,join(zero,complement(X_32)))
| meet(A,join(zero,complement(X_32))) = meet(A,complement(X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_32))),meet(A,join(zero,complement(X_32)))) ),[1,1],$fot(complement(X_32))]]) ).
cnf(refute_0_949,plain,
( join(zero,complement(X_32)) != complement(X_32)
| meet(A,join(zero,complement(X_32))) = meet(A,complement(X_32)) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_32))),meet(A,join(zero,complement(X_32)))) )],[refute_0_947,refute_0_948]) ).
cnf(refute_0_950,plain,
meet(A,join(zero,complement(X_32))) = meet(A,complement(X_32)),
inference(resolve,[$cnf( $equal(join(zero,complement(X_32)),complement(X_32)) )],[refute_0_946,refute_0_949]) ).
cnf(refute_0_951,plain,
( meet(A,join(zero,complement(X_32))) != complement(join(complement(A),meet(top,X_32)))
| meet(A,join(zero,complement(X_32))) != meet(A,complement(X_32))
| meet(A,complement(X_32)) = complement(join(complement(A),meet(top,X_32))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_32))),complement(join(complement(A),meet(top,X_32)))) ),[0],$fot(meet(A,complement(X_32)))]]) ).
cnf(refute_0_952,plain,
( meet(A,join(zero,complement(X_32))) != complement(join(complement(A),meet(top,X_32)))
| meet(A,complement(X_32)) = complement(join(complement(A),meet(top,X_32))) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_32))),meet(A,complement(X_32))) )],[refute_0_950,refute_0_951]) ).
cnf(refute_0_953,plain,
meet(top,X_32) = X_32,
inference(subst,[],[refute_0_284:[bind(X_76,$fot(X_32))]]) ).
cnf(refute_0_954,plain,
join(complement(A),meet(top,X_32)) = join(complement(A),meet(top,X_32)),
introduced(tautology,[refl,[$fot(join(complement(A),meet(top,X_32)))]]) ).
cnf(refute_0_955,plain,
( join(complement(A),meet(top,X_32)) != join(complement(A),meet(top,X_32))
| meet(top,X_32) != X_32
| join(complement(A),meet(top,X_32)) = join(complement(A),X_32) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),meet(top,X_32)),join(complement(A),meet(top,X_32))) ),[1,1],$fot(X_32)]]) ).
cnf(refute_0_956,plain,
( meet(top,X_32) != X_32
| join(complement(A),meet(top,X_32)) = join(complement(A),X_32) ),
inference(resolve,[$cnf( $equal(join(complement(A),meet(top,X_32)),join(complement(A),meet(top,X_32))) )],[refute_0_954,refute_0_955]) ).
cnf(refute_0_957,plain,
join(complement(A),meet(top,X_32)) = join(complement(A),X_32),
inference(resolve,[$cnf( $equal(meet(top,X_32),X_32) )],[refute_0_953,refute_0_956]) ).
cnf(refute_0_958,plain,
complement(join(complement(A),meet(top,X_32))) = complement(join(complement(A),meet(top,X_32))),
introduced(tautology,[refl,[$fot(complement(join(complement(A),meet(top,X_32))))]]) ).
cnf(refute_0_959,plain,
( complement(join(complement(A),meet(top,X_32))) != complement(join(complement(A),meet(top,X_32)))
| join(complement(A),meet(top,X_32)) != join(complement(A),X_32)
| complement(join(complement(A),meet(top,X_32))) = complement(join(complement(A),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),meet(top,X_32))),complement(join(complement(A),meet(top,X_32)))) ),[1,0],$fot(join(complement(A),X_32))]]) ).
cnf(refute_0_960,plain,
( join(complement(A),meet(top,X_32)) != join(complement(A),X_32)
| complement(join(complement(A),meet(top,X_32))) = complement(join(complement(A),X_32)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_32))),complement(join(complement(A),meet(top,X_32)))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
complement(join(complement(A),meet(top,X_32))) = complement(join(complement(A),X_32)),
inference(resolve,[$cnf( $equal(join(complement(A),meet(top,X_32)),join(complement(A),X_32)) )],[refute_0_957,refute_0_960]) ).
cnf(refute_0_962,plain,
( complement(join(complement(A),meet(top,X_32))) != complement(join(complement(A),X_32))
| meet(A,complement(X_32)) != complement(join(complement(A),meet(top,X_32)))
| meet(A,complement(X_32)) = complement(join(complement(A),X_32)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,complement(X_32)),complement(join(complement(A),meet(top,X_32)))) ),[1],$fot(complement(join(complement(A),X_32)))]]) ).
cnf(refute_0_963,plain,
( meet(A,complement(X_32)) != complement(join(complement(A),meet(top,X_32)))
| meet(A,complement(X_32)) = complement(join(complement(A),X_32)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_32))),complement(join(complement(A),X_32))) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
( meet(A,join(zero,complement(X_32))) != complement(join(complement(A),meet(top,X_32)))
| meet(A,complement(X_32)) = complement(join(complement(A),X_32)) ),
inference(resolve,[$cnf( $equal(meet(A,complement(X_32)),complement(join(complement(A),meet(top,X_32)))) )],[refute_0_952,refute_0_963]) ).
cnf(refute_0_965,plain,
meet(A,complement(X_32)) = complement(join(complement(A),X_32)),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_32))),complement(join(complement(A),meet(top,X_32)))) )],[refute_0_945,refute_0_964]) ).
cnf(refute_0_966,plain,
( meet(A,complement(X_32)) != complement(join(complement(A),X_32))
| complement(join(complement(A),X_32)) = meet(A,complement(X_32)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(A,complement(X_32)))),bind(Y,$fot(complement(join(complement(A),X_32))))]]) ).
cnf(refute_0_967,plain,
complement(join(complement(A),X_32)) = meet(A,complement(X_32)),
inference(resolve,[$cnf( $equal(meet(A,complement(X_32)),complement(join(complement(A),X_32))) )],[refute_0_965,refute_0_966]) ).
cnf(refute_0_968,plain,
complement(join(complement(X_74),X_75)) = meet(X_74,complement(X_75)),
inference(subst,[],[refute_0_967:[bind(A,$fot(X_74)),bind(X_32,$fot(X_75))]]) ).
cnf(refute_0_969,plain,
join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) = join(meet(X_75,X_74),complement(join(complement(X_74),X_75))),
introduced(tautology,[refl,[$fot(join(meet(X_75,X_74),complement(join(complement(X_74),X_75))))]]) ).
cnf(refute_0_970,plain,
( complement(join(complement(X_74),X_75)) != meet(X_74,complement(X_75))
| join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) != join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))
| join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) = join(meet(X_75,X_74),meet(X_74,complement(X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_75,X_74),complement(join(complement(X_74),X_75))),join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))) ),[1,1],$fot(meet(X_74,complement(X_75)))]]) ).
cnf(refute_0_971,plain,
( complement(join(complement(X_74),X_75)) != meet(X_74,complement(X_75))
| join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) = join(meet(X_75,X_74),meet(X_74,complement(X_75))) ),
inference(resolve,[$cnf( $equal(join(meet(X_75,X_74),complement(join(complement(X_74),X_75))),join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))) )],[refute_0_969,refute_0_970]) ).
cnf(refute_0_972,plain,
join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) = join(meet(X_75,X_74),meet(X_74,complement(X_75))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_74),X_75)),meet(X_74,complement(X_75))) )],[refute_0_968,refute_0_971]) ).
cnf(refute_0_973,plain,
( X_74 != join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))
| join(meet(X_75,X_74),complement(join(complement(X_74),X_75))) != join(meet(X_75,X_74),meet(X_74,complement(X_75)))
| X_74 = join(meet(X_75,X_74),meet(X_74,complement(X_75))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(meet(X_75,X_74),meet(X_74,complement(X_75)))) ),[0],$fot(join(meet(X_75,X_74),complement(join(complement(X_74),X_75))))]]) ).
cnf(refute_0_974,plain,
( X_74 != join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))
| X_74 = join(meet(X_75,X_74),meet(X_74,complement(X_75))) ),
inference(resolve,[$cnf( $equal(join(meet(X_75,X_74),complement(join(complement(X_74),X_75))),join(meet(X_75,X_74),meet(X_74,complement(X_75)))) )],[refute_0_972,refute_0_973]) ).
cnf(refute_0_975,plain,
X_74 = join(meet(X_75,X_74),meet(X_74,complement(X_75))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_75,X_74),complement(join(complement(X_74),X_75)))) )],[refute_0_938,refute_0_974]) ).
cnf(refute_0_976,plain,
converse(complement(converse(X_84))) = join(meet(complement(X_84),converse(complement(converse(X_84)))),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),
inference(subst,[],[refute_0_975:[bind(X_74,$fot(converse(complement(converse(X_84))))),bind(X_75,$fot(complement(X_84)))]]) ).
cnf(refute_0_977,plain,
X_74 = join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(join(complement(X_74),converse(complement(converse(complement(X_74))))))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(converse(complement(converse(complement(X_74))))))]]) ).
cnf(refute_0_978,plain,
top = join(complement(X_74),converse(complement(converse(complement(X_74))))),
inference(subst,[],[refute_0_572:[bind(X_13,$fot(complement(X_74)))]]) ).
cnf(refute_0_979,plain,
( top != join(complement(X_74),converse(complement(converse(complement(X_74)))))
| join(complement(X_74),converse(complement(converse(complement(X_74))))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_74),converse(complement(converse(complement(X_74)))))))]]) ).
cnf(refute_0_980,plain,
join(complement(X_74),converse(complement(converse(complement(X_74))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_74),converse(complement(converse(complement(X_74)))))) )],[refute_0_978,refute_0_979]) ).
cnf(refute_0_981,plain,
( X_74 != join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(join(complement(X_74),converse(complement(converse(complement(X_74)))))))
| join(complement(X_74),converse(complement(converse(complement(X_74))))) != top
| X_74 = join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(join(complement(X_74),converse(complement(converse(complement(X_74)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_982,plain,
( X_74 != join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(join(complement(X_74),converse(complement(converse(complement(X_74)))))))
| X_74 = join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_74),converse(complement(converse(complement(X_74))))),top) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
X_74 = join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(join(complement(X_74),converse(complement(converse(complement(X_74)))))))) )],[refute_0_977,refute_0_982]) ).
cnf(refute_0_984,plain,
join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) = join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))))]]) ).
cnf(refute_0_985,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) != join(complement(top),meet(X_74,converse(complement(converse(complement(X_74))))))
| join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))),join(complement(top),meet(X_74,converse(complement(converse(complement(X_74))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_986,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))),join(complement(top),meet(X_74,converse(complement(converse(complement(X_74))))))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_986]) ).
cnf(refute_0_988,plain,
join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) = join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_74,converse(complement(converse(complement(X_74)))))))]]) ).
cnf(refute_0_989,plain,
( join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) != join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))
| join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) != join(complement(top),meet(X_74,converse(complement(converse(complement(X_74))))))
| join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))))),bind(Z,$fot(join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))))]]) ).
cnf(refute_0_990,plain,
( join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))) != join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))
| join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)),join(complement(top),meet(X_74,converse(complement(converse(complement(X_74))))))) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,converse(complement(converse(complement(X_74)))))),join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))) )],[refute_0_987,refute_0_990]) ).
cnf(refute_0_992,plain,
( X_74 != join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top))
| join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)) != join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))
| X_74 = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))) ),[0],$fot(join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)))]]) ).
cnf(refute_0_993,plain,
( X_74 != join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top))
| X_74 = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top)),join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
X_74 = join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,converse(complement(converse(complement(X_74))))),complement(top))) )],[refute_0_983,refute_0_993]) ).
cnf(refute_0_995,plain,
join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) = meet(X_74,converse(complement(converse(complement(X_74))))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(X_74,converse(complement(converse(complement(X_74)))))))]]) ).
cnf(refute_0_996,plain,
( X_74 != join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))
| join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))) != meet(X_74,converse(complement(converse(complement(X_74)))))
| X_74 = meet(X_74,converse(complement(converse(complement(X_74))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,meet(X_74,converse(complement(converse(complement(X_74)))))) ),[0],$fot(join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))))]]) ).
cnf(refute_0_997,plain,
( X_74 != join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))
| X_74 = meet(X_74,converse(complement(converse(complement(X_74))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_74,converse(complement(converse(complement(X_74)))))),meet(X_74,converse(complement(converse(complement(X_74)))))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
X_74 = meet(X_74,converse(complement(converse(complement(X_74))))),
inference(resolve,[$cnf( $equal(X_74,join(zero,meet(X_74,converse(complement(converse(complement(X_74))))))) )],[refute_0_994,refute_0_997]) ).
cnf(refute_0_999,plain,
complement(X_84) = meet(complement(X_84),converse(complement(converse(complement(complement(X_84)))))),
inference(subst,[],[refute_0_998:[bind(X_74,$fot(complement(X_84)))]]) ).
cnf(refute_0_1000,plain,
X_84 = complement(complement(X_84)),
inference(subst,[],[refute_0_733:[bind(B,$fot(X_84))]]) ).
cnf(refute_0_1001,plain,
( X_84 != complement(complement(X_84))
| complement(complement(X_84)) = X_84 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_84)),bind(Y,$fot(complement(complement(X_84))))]]) ).
cnf(refute_0_1002,plain,
complement(complement(X_84)) = X_84,
inference(resolve,[$cnf( $equal(X_84,complement(complement(X_84))) )],[refute_0_1000,refute_0_1001]) ).
cnf(refute_0_1003,plain,
( complement(X_84) != meet(complement(X_84),converse(complement(converse(complement(complement(X_84))))))
| complement(complement(X_84)) != X_84
| complement(X_84) = meet(complement(X_84),converse(complement(converse(X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_84),meet(complement(X_84),converse(complement(converse(complement(complement(X_84))))))) ),[1,1,0,0,0],$fot(X_84)]]) ).
cnf(refute_0_1004,plain,
( complement(X_84) != meet(complement(X_84),converse(complement(converse(complement(complement(X_84))))))
| complement(X_84) = meet(complement(X_84),converse(complement(converse(X_84)))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),X_84) )],[refute_0_1002,refute_0_1003]) ).
cnf(refute_0_1005,plain,
complement(X_84) = meet(complement(X_84),converse(complement(converse(X_84)))),
inference(resolve,[$cnf( $equal(complement(X_84),meet(complement(X_84),converse(complement(converse(complement(complement(X_84))))))) )],[refute_0_999,refute_0_1004]) ).
cnf(refute_0_1006,plain,
( complement(X_84) != meet(complement(X_84),converse(complement(converse(X_84))))
| meet(complement(X_84),converse(complement(converse(X_84)))) = complement(X_84) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(X_84))),bind(Y,$fot(meet(complement(X_84),converse(complement(converse(X_84))))))]]) ).
cnf(refute_0_1007,plain,
meet(complement(X_84),converse(complement(converse(X_84)))) = complement(X_84),
inference(resolve,[$cnf( $equal(complement(X_84),meet(complement(X_84),converse(complement(converse(X_84))))) )],[refute_0_1005,refute_0_1006]) ).
cnf(refute_0_1008,plain,
( converse(complement(converse(X_84))) != join(meet(complement(X_84),converse(complement(converse(X_84)))),meet(converse(complement(converse(X_84))),complement(complement(X_84))))
| meet(complement(X_84),converse(complement(converse(X_84)))) != complement(X_84)
| converse(complement(converse(X_84))) = join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(X_84))),join(meet(complement(X_84),converse(complement(converse(X_84)))),meet(converse(complement(converse(X_84))),complement(complement(X_84))))) ),[1,0],$fot(complement(X_84))]]) ).
cnf(refute_0_1009,plain,
( converse(complement(converse(X_84))) != join(meet(complement(X_84),converse(complement(converse(X_84)))),meet(converse(complement(converse(X_84))),complement(complement(X_84))))
| converse(complement(converse(X_84))) = join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_84),converse(complement(converse(X_84)))),complement(X_84)) )],[refute_0_1007,refute_0_1008]) ).
cnf(refute_0_1010,plain,
converse(complement(converse(X_84))) = join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_84))),join(meet(complement(X_84),converse(complement(converse(X_84)))),meet(converse(complement(converse(X_84))),complement(complement(X_84))))) )],[refute_0_976,refute_0_1009]) ).
cnf(refute_0_1011,plain,
meet(complement(complement(X_84)),converse(complement(converse(X_84)))) = meet(complement(complement(X_84)),converse(complement(converse(X_84)))),
introduced(tautology,[refl,[$fot(meet(complement(complement(X_84)),converse(complement(converse(X_84)))))]]) ).
cnf(refute_0_1012,plain,
( complement(complement(X_84)) != X_84
| meet(complement(complement(X_84)),converse(complement(converse(X_84)))) != meet(complement(complement(X_84)),converse(complement(converse(X_84))))
| meet(complement(complement(X_84)),converse(complement(converse(X_84)))) = meet(X_84,converse(complement(converse(X_84)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(complement(X_84)),converse(complement(converse(X_84)))),meet(complement(complement(X_84)),converse(complement(converse(X_84))))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_1013,plain,
( complement(complement(X_84)) != X_84
| meet(complement(complement(X_84)),converse(complement(converse(X_84)))) = meet(X_84,converse(complement(converse(X_84)))) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_84)),converse(complement(converse(X_84)))),meet(complement(complement(X_84)),converse(complement(converse(X_84))))) )],[refute_0_1011,refute_0_1012]) ).
cnf(refute_0_1014,plain,
meet(complement(complement(X_84)),converse(complement(converse(X_84)))) = meet(X_84,converse(complement(converse(X_84)))),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),X_84) )],[refute_0_1002,refute_0_1013]) ).
cnf(refute_0_1015,plain,
( meet(X_27,X_28) != meet(X_28,X_27)
| meet(X_28,X_27) = meet(X_27,X_28) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_27,X_28))),bind(Y,$fot(meet(X_28,X_27)))]]) ).
cnf(refute_0_1016,plain,
meet(X_28,X_27) = meet(X_27,X_28),
inference(resolve,[$cnf( $equal(meet(X_27,X_28),meet(X_28,X_27)) )],[refute_0_272,refute_0_1015]) ).
cnf(refute_0_1017,plain,
meet(converse(complement(converse(X_84))),complement(complement(X_84))) = meet(complement(complement(X_84)),converse(complement(converse(X_84)))),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(complement(complement(X_84)))),bind(X_28,$fot(converse(complement(converse(X_84)))))]]) ).
cnf(refute_0_1018,plain,
( meet(complement(complement(X_84)),converse(complement(converse(X_84)))) != meet(X_84,converse(complement(converse(X_84))))
| meet(converse(complement(converse(X_84))),complement(complement(X_84))) != meet(complement(complement(X_84)),converse(complement(converse(X_84))))
| meet(converse(complement(converse(X_84))),complement(complement(X_84))) = meet(X_84,converse(complement(converse(X_84)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(meet(converse(complement(converse(X_84))),complement(complement(X_84))))),bind(Y,$fot(meet(complement(complement(X_84)),converse(complement(converse(X_84)))))),bind(Z,$fot(meet(X_84,converse(complement(converse(X_84))))))]]) ).
cnf(refute_0_1019,plain,
( meet(complement(complement(X_84)),converse(complement(converse(X_84)))) != meet(X_84,converse(complement(converse(X_84))))
| meet(converse(complement(converse(X_84))),complement(complement(X_84))) = meet(X_84,converse(complement(converse(X_84)))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(X_84))),complement(complement(X_84))),meet(complement(complement(X_84)),converse(complement(converse(X_84))))) )],[refute_0_1017,refute_0_1018]) ).
cnf(refute_0_1020,plain,
meet(converse(complement(converse(X_84))),complement(complement(X_84))) = meet(X_84,converse(complement(converse(X_84)))),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_84)),converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) )],[refute_0_1014,refute_0_1019]) ).
cnf(refute_0_1021,plain,
join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) = join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),
introduced(tautology,[refl,[$fot(join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))))]]) ).
cnf(refute_0_1022,plain,
( join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) != join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))
| meet(converse(complement(converse(X_84))),complement(complement(X_84))) != meet(X_84,converse(complement(converse(X_84))))
| join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))) ),[1,1],$fot(meet(X_84,converse(complement(converse(X_84)))))]]) ).
cnf(refute_0_1023,plain,
( meet(converse(complement(converse(X_84))),complement(complement(X_84))) != meet(X_84,converse(complement(converse(X_84))))
| join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))) )],[refute_0_1021,refute_0_1022]) ).
cnf(refute_0_1024,plain,
join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(X_84))),complement(complement(X_84))),meet(X_84,converse(complement(converse(X_84))))) )],[refute_0_1020,refute_0_1023]) ).
cnf(refute_0_1025,plain,
( converse(complement(converse(X_84))) != join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))
| join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))) != join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))
| converse(complement(converse(X_84))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(X_84))),join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))) ),[0],$fot(join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))))]]) ).
cnf(refute_0_1026,plain,
( converse(complement(converse(X_84))) != join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))
| converse(complement(converse(X_84))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84)))),join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))) )],[refute_0_1024,refute_0_1025]) ).
cnf(refute_0_1027,plain,
converse(complement(converse(X_84))) = join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_84))),join(complement(X_84),meet(converse(complement(converse(X_84))),complement(complement(X_84))))) )],[refute_0_1010,refute_0_1026]) ).
cnf(refute_0_1028,plain,
converse(complement(converse(X_347))) = join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))),
inference(subst,[],[refute_0_1027:[bind(X_84,$fot(X_347))]]) ).
cnf(refute_0_1029,plain,
( converse(complement(converse(X_347))) != join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))
| join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))) = converse(complement(converse(X_347))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(complement(converse(X_347))))),bind(Y,$fot(join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))))]]) ).
cnf(refute_0_1030,plain,
join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))) = converse(complement(converse(X_347))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_347))),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) )],[refute_0_1028,refute_0_1029]) ).
cnf(refute_0_1031,plain,
( join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) != join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))
| join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))) != converse(complement(converse(X_347)))
| join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) = converse(complement(converse(X_347))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),converse(complement(converse(X_347)))) ),[0],$fot(join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))))]]) ).
cnf(refute_0_1032,plain,
( join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) != join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))
| join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) = converse(complement(converse(X_347))) ),
inference(resolve,[$cnf( $equal(join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))),converse(complement(converse(X_347)))) )],[refute_0_1030,refute_0_1031]) ).
cnf(refute_0_1033,plain,
join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) = converse(complement(converse(X_347))),
inference(resolve,[$cnf( $equal(join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) )],[refute_0_931,refute_0_1032]) ).
cnf(refute_0_1034,plain,
join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) = join(X_49,join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),
inference(subst,[],[refute_0_404:[bind(A,$fot(meet(X_347,converse(complement(converse(X_347)))))),bind(X_50,$fot(complement(X_347)))]]) ).
cnf(refute_0_1035,plain,
( join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))) != converse(complement(converse(X_347)))
| join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) != join(X_49,join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))))
| join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) = join(X_49,converse(complement(converse(X_347)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))),join(X_49,join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))))) ),[1,1],$fot(converse(complement(converse(X_347))))]]) ).
cnf(refute_0_1036,plain,
( join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) != join(X_49,join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))))
| join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) = join(X_49,converse(complement(converse(X_347)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))),converse(complement(converse(X_347)))) )],[refute_0_1030,refute_0_1035]) ).
cnf(refute_0_1037,plain,
join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) = join(X_49,converse(complement(converse(X_347)))),
inference(resolve,[$cnf( $equal(join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))),join(X_49,join(complement(X_347),meet(X_347,converse(complement(converse(X_347))))))) )],[refute_0_1034,refute_0_1036]) ).
cnf(refute_0_1038,plain,
join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) = join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347)))))),
inference(subst,[],[refute_0_877:[bind(X_198,$fot(complement(X_347))),bind(X_199,$fot(meet(X_347,converse(complement(converse(X_347)))))),bind(X_200,$fot(X_49))]]) ).
cnf(refute_0_1039,plain,
( join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) != join(X_49,converse(complement(converse(X_347))))
| join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) != join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347))))))
| join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347)))))) = join(X_49,converse(complement(converse(X_347)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))),join(X_49,converse(complement(converse(X_347))))) ),[0],$fot(join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347)))))))]]) ).
cnf(refute_0_1040,plain,
( join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))) != join(X_49,converse(complement(converse(X_347))))
| join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347)))))) = join(X_49,converse(complement(converse(X_347)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))),join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347))))))) )],[refute_0_1038,refute_0_1039]) ).
cnf(refute_0_1041,plain,
join(complement(X_347),join(X_49,meet(X_347,converse(complement(converse(X_347)))))) = join(X_49,converse(complement(converse(X_347)))),
inference(resolve,[$cnf( $equal(join(meet(X_347,converse(complement(converse(X_347)))),join(X_49,complement(X_347))),join(X_49,converse(complement(converse(X_347))))) )],[refute_0_1037,refute_0_1040]) ).
cnf(refute_0_1042,plain,
join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) = join(complement(X_347),converse(complement(converse(X_347)))),
inference(subst,[],[refute_0_1041:[bind(X_49,$fot(complement(X_347)))]]) ).
cnf(refute_0_1043,plain,
( join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) != converse(complement(converse(X_347)))
| join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) != join(complement(X_347),converse(complement(converse(X_347))))
| join(complement(X_347),converse(complement(converse(X_347)))) = converse(complement(converse(X_347))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),converse(complement(converse(X_347)))) ),[0],$fot(join(complement(X_347),converse(complement(converse(X_347)))))]]) ).
cnf(refute_0_1044,plain,
( join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))) != converse(complement(converse(X_347)))
| join(complement(X_347),converse(complement(converse(X_347)))) = converse(complement(converse(X_347))) ),
inference(resolve,[$cnf( $equal(join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),join(complement(X_347),converse(complement(converse(X_347))))) )],[refute_0_1042,refute_0_1043]) ).
cnf(refute_0_1045,plain,
join(complement(X_347),converse(complement(converse(X_347)))) = converse(complement(converse(X_347))),
inference(resolve,[$cnf( $equal(join(complement(X_347),join(complement(X_347),meet(X_347,converse(complement(converse(X_347)))))),converse(complement(converse(X_347)))) )],[refute_0_1033,refute_0_1044]) ).
cnf(refute_0_1046,plain,
join(complement(converse(A)),converse(complement(converse(converse(A))))) = converse(complement(converse(converse(A)))),
inference(subst,[],[refute_0_1045:[bind(X_347,$fot(converse(A)))]]) ).
cnf(refute_0_1047,plain,
( converse(converse(A)) != A
| join(complement(converse(A)),converse(complement(converse(converse(A))))) != converse(complement(converse(converse(A))))
| join(complement(converse(A)),converse(complement(A))) = converse(complement(converse(converse(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(A)),converse(complement(converse(converse(A))))),converse(complement(converse(converse(A))))) ),[0,1,0,0],$fot(A)]]) ).
cnf(refute_0_1048,plain,
( join(complement(converse(A)),converse(complement(converse(converse(A))))) != converse(complement(converse(converse(A))))
| join(complement(converse(A)),converse(complement(A))) = converse(complement(converse(converse(A)))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1047]) ).
cnf(refute_0_1049,plain,
join(complement(converse(A)),converse(complement(A))) = converse(complement(converse(converse(A)))),
inference(resolve,[$cnf( $equal(join(complement(converse(A)),converse(complement(converse(converse(A))))),converse(complement(converse(converse(A))))) )],[refute_0_1046,refute_0_1048]) ).
cnf(refute_0_1050,plain,
converse(join(converse(complement(converse(X_478))),complement(X_478))) = converse(join(complement(X_478),converse(complement(converse(X_478))))),
inference(subst,[],[refute_0_29:[bind(X_10,$fot(converse(complement(converse(X_478))))),bind(X_9,$fot(complement(X_478)))]]) ).
cnf(refute_0_1051,plain,
join(complement(X_478),converse(complement(converse(X_478)))) = converse(complement(converse(X_478))),
inference(subst,[],[refute_0_1045:[bind(X_347,$fot(X_478))]]) ).
cnf(refute_0_1052,plain,
( converse(join(converse(complement(converse(X_478))),complement(X_478))) != converse(join(complement(X_478),converse(complement(converse(X_478)))))
| join(complement(X_478),converse(complement(converse(X_478)))) != converse(complement(converse(X_478)))
| converse(join(converse(complement(converse(X_478))),complement(X_478))) = converse(converse(complement(converse(X_478)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(X_478))),complement(X_478))),converse(join(complement(X_478),converse(complement(converse(X_478)))))) ),[1,0],$fot(converse(complement(converse(X_478))))]]) ).
cnf(refute_0_1053,plain,
( converse(join(converse(complement(converse(X_478))),complement(X_478))) != converse(join(complement(X_478),converse(complement(converse(X_478)))))
| converse(join(converse(complement(converse(X_478))),complement(X_478))) = converse(converse(complement(converse(X_478)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_478),converse(complement(converse(X_478)))),converse(complement(converse(X_478)))) )],[refute_0_1051,refute_0_1052]) ).
cnf(refute_0_1054,plain,
converse(join(converse(complement(converse(X_478))),complement(X_478))) = converse(converse(complement(converse(X_478)))),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_478))),complement(X_478))),converse(join(complement(X_478),converse(complement(converse(X_478)))))) )],[refute_0_1050,refute_0_1053]) ).
cnf(refute_0_1055,plain,
converse(join(converse(complement(converse(X_478))),complement(X_478))) = join(complement(converse(X_478)),converse(complement(X_478))),
inference(subst,[],[refute_0_335:[bind(A,$fot(complement(converse(X_478)))),bind(X_10,$fot(complement(X_478)))]]) ).
cnf(refute_0_1056,plain,
( converse(join(converse(complement(converse(X_478))),complement(X_478))) != converse(converse(complement(converse(X_478))))
| converse(join(converse(complement(converse(X_478))),complement(X_478))) != join(complement(converse(X_478)),converse(complement(X_478)))
| join(complement(converse(X_478)),converse(complement(X_478))) = converse(converse(complement(converse(X_478)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(X_478))),complement(X_478))),converse(converse(complement(converse(X_478))))) ),[0],$fot(join(complement(converse(X_478)),converse(complement(X_478))))]]) ).
cnf(refute_0_1057,plain,
( converse(join(converse(complement(converse(X_478))),complement(X_478))) != converse(converse(complement(converse(X_478))))
| join(complement(converse(X_478)),converse(complement(X_478))) = converse(converse(complement(converse(X_478)))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_478))),complement(X_478))),join(complement(converse(X_478)),converse(complement(X_478)))) )],[refute_0_1055,refute_0_1056]) ).
cnf(refute_0_1058,plain,
converse(converse(complement(converse(X_478)))) = complement(converse(X_478)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(X_478))))]]) ).
cnf(refute_0_1059,plain,
( converse(converse(complement(converse(X_478)))) != complement(converse(X_478))
| join(complement(converse(X_478)),converse(complement(X_478))) != converse(converse(complement(converse(X_478))))
| join(complement(converse(X_478)),converse(complement(X_478))) = complement(converse(X_478)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X_478)),converse(complement(X_478))),converse(converse(complement(converse(X_478))))) ),[1],$fot(complement(converse(X_478)))]]) ).
cnf(refute_0_1060,plain,
( join(complement(converse(X_478)),converse(complement(X_478))) != converse(converse(complement(converse(X_478))))
| join(complement(converse(X_478)),converse(complement(X_478))) = complement(converse(X_478)) ),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(X_478)))),complement(converse(X_478))) )],[refute_0_1058,refute_0_1059]) ).
cnf(refute_0_1061,plain,
( converse(join(converse(complement(converse(X_478))),complement(X_478))) != converse(converse(complement(converse(X_478))))
| join(complement(converse(X_478)),converse(complement(X_478))) = complement(converse(X_478)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_478)),converse(complement(X_478))),converse(converse(complement(converse(X_478))))) )],[refute_0_1057,refute_0_1060]) ).
cnf(refute_0_1062,plain,
join(complement(converse(X_478)),converse(complement(X_478))) = complement(converse(X_478)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_478))),complement(X_478))),converse(converse(complement(converse(X_478))))) )],[refute_0_1054,refute_0_1061]) ).
cnf(refute_0_1063,plain,
join(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(subst,[],[refute_0_1062:[bind(X_478,$fot(A))]]) ).
cnf(refute_0_1064,plain,
( join(complement(converse(A)),converse(complement(A))) != complement(converse(A))
| join(complement(converse(A)),converse(complement(A))) != converse(complement(converse(converse(A))))
| complement(converse(A)) = converse(complement(converse(converse(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(A)),converse(complement(A))),converse(complement(converse(converse(A))))) ),[0],$fot(complement(converse(A)))]]) ).
cnf(refute_0_1065,plain,
( join(complement(converse(A)),converse(complement(A))) != converse(complement(converse(converse(A))))
| complement(converse(A)) = converse(complement(converse(converse(A)))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(A)),converse(complement(A))),complement(converse(A))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
complement(converse(converse(A))) = complement(converse(converse(A))),
introduced(tautology,[refl,[$fot(complement(converse(converse(A))))]]) ).
cnf(refute_0_1067,plain,
( complement(converse(converse(A))) != complement(converse(converse(A)))
| converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1068,plain,
( converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) )],[refute_0_1066,refute_0_1067]) ).
cnf(refute_0_1069,plain,
complement(converse(converse(A))) = complement(A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1068]) ).
cnf(refute_0_1070,plain,
converse(complement(converse(converse(A)))) = converse(complement(converse(converse(A)))),
introduced(tautology,[refl,[$fot(converse(complement(converse(converse(A)))))]]) ).
cnf(refute_0_1071,plain,
( complement(converse(converse(A))) != complement(A)
| converse(complement(converse(converse(A)))) != converse(complement(converse(converse(A))))
| converse(complement(converse(converse(A)))) = converse(complement(A)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(converse(converse(A))))) ),[1,0],$fot(complement(A))]]) ).
cnf(refute_0_1072,plain,
( complement(converse(converse(A))) != complement(A)
| converse(complement(converse(converse(A)))) = converse(complement(A)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(converse(converse(A))))) )],[refute_0_1070,refute_0_1071]) ).
cnf(refute_0_1073,plain,
converse(complement(converse(converse(A)))) = converse(complement(A)),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(A)) )],[refute_0_1069,refute_0_1072]) ).
cnf(refute_0_1074,plain,
( complement(converse(A)) != converse(complement(converse(converse(A))))
| converse(complement(converse(converse(A)))) != converse(complement(A))
| complement(converse(A)) = converse(complement(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(converse(A)),converse(complement(A))) ),[0],$fot(converse(complement(converse(converse(A)))))]]) ).
cnf(refute_0_1075,plain,
( complement(converse(A)) != converse(complement(converse(converse(A))))
| complement(converse(A)) = converse(complement(A)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(A))) )],[refute_0_1073,refute_0_1074]) ).
cnf(refute_0_1076,plain,
( join(complement(converse(A)),converse(complement(A))) != converse(complement(converse(converse(A))))
| complement(converse(A)) = converse(complement(A)) ),
inference(resolve,[$cnf( $equal(complement(converse(A)),converse(complement(converse(converse(A))))) )],[refute_0_1065,refute_0_1075]) ).
cnf(refute_0_1077,plain,
complement(converse(A)) = converse(complement(A)),
inference(resolve,[$cnf( $equal(join(complement(converse(A)),converse(complement(A))),converse(complement(converse(converse(A))))) )],[refute_0_1049,refute_0_1076]) ).
cnf(refute_0_1078,plain,
( complement(converse(A)) != converse(complement(A))
| converse(complement(A)) = complement(converse(A)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(converse(A)))),bind(Y,$fot(converse(complement(A))))]]) ).
cnf(refute_0_1079,plain,
converse(complement(A)) = complement(converse(A)),
inference(resolve,[$cnf( $equal(complement(converse(A)),converse(complement(A))) )],[refute_0_1077,refute_0_1078]) ).
cnf(refute_0_1080,plain,
converse(complement(composition(sk1,complement(one)))) = complement(converse(composition(sk1,complement(one)))),
inference(subst,[],[refute_0_1079:[bind(A,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1081,plain,
composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(converse(complement(composition(sk1,complement(one)))),sk1),
introduced(tautology,[refl,[$fot(composition(converse(complement(composition(sk1,complement(one)))),sk1))]]) ).
cnf(refute_0_1082,plain,
( composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(converse(complement(composition(sk1,complement(one)))),sk1)
| converse(complement(composition(sk1,complement(one)))) != complement(converse(composition(sk1,complement(one))))
| composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(complement(converse(composition(sk1,complement(one)))),sk1) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(converse(complement(composition(sk1,complement(one)))),sk1)) ),[1,0],$fot(complement(converse(composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1083,plain,
( converse(complement(composition(sk1,complement(one)))) != complement(converse(composition(sk1,complement(one))))
| composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(complement(converse(composition(sk1,complement(one)))),sk1) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(converse(complement(composition(sk1,complement(one)))),sk1)) )],[refute_0_1081,refute_0_1082]) ).
cnf(refute_0_1084,plain,
composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(complement(converse(composition(sk1,complement(one)))),sk1),
inference(resolve,[$cnf( $equal(converse(complement(composition(sk1,complement(one)))),complement(converse(composition(sk1,complement(one))))) )],[refute_0_1080,refute_0_1083]) ).
cnf(refute_0_1085,plain,
join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) = join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),
introduced(tautology,[refl,[$fot(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)))]]) ).
cnf(refute_0_1086,plain,
( composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(complement(converse(composition(sk1,complement(one)))),sk1)
| join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) != join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1))
| join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1))) ),[1,1],$fot(composition(complement(converse(composition(sk1,complement(one)))),sk1))]]) ).
cnf(refute_0_1087,plain,
( composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(complement(converse(composition(sk1,complement(one)))),sk1)
| join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
inference(resolve,[$cnf( $equal(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1))) )],[refute_0_1085,refute_0_1086]) ).
cnf(refute_0_1088,plain,
join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(complement(converse(composition(sk1,complement(one)))),sk1)) )],[refute_0_1084,refute_0_1087]) ).
cnf(refute_0_1089,plain,
composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),
introduced(tautology,[refl,[$fot(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)))]]) ).
cnf(refute_0_1090,plain,
( composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) != composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))
| join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))) ),[1,0],$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))]]) ).
cnf(refute_0_1091,plain,
( join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one))) )],[refute_0_1089,refute_0_1090]) ).
cnf(refute_0_1092,plain,
composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) = composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)),
inference(resolve,[$cnf( $equal(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_1088,refute_0_1091]) ).
cnf(refute_0_1093,plain,
( composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) != complement(one)
| composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) != composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))
| composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),complement(one)) ),[0],$fot(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)))]]) ).
cnf(refute_0_1094,plain,
( composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)) != complement(one)
| composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))) )],[refute_0_1092,refute_0_1093]) ).
cnf(refute_0_1095,plain,
composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(composition(join(one,composition(converse(complement(composition(sk1,complement(one)))),sk1)),complement(one)),complement(one)) )],[refute_0_930,refute_0_1094]) ).
cnf(refute_0_1096,plain,
( composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)) != complement(one)
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))))),complement(complement(one))) ),[0,1,1,0],$fot(complement(one))]]) ).
cnf(refute_0_1097,plain,
( join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one)),complement(one)) )],[refute_0_1095,refute_0_1096]) ).
cnf(refute_0_1098,plain,
join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(composition(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),complement(one))))),complement(complement(one))) )],[refute_0_10,refute_0_1097]) ).
cnf(refute_0_1099,plain,
composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1100,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_735:[bind(B,$fot(one))]]) ).
cnf(refute_0_1101,plain,
composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))))]]) ).
cnf(refute_0_1102,plain,
( complement(complement(one)) != one
| composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) != composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))
| composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_1103,plain,
( complement(complement(one)) != one
| composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) )],[refute_0_1101,refute_0_1102]) ).
cnf(refute_0_1104,plain,
composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1100,refute_0_1103]) ).
cnf(refute_0_1105,plain,
join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
inference(subst,[],[refute_0_756:[bind(B,$fot(one)),bind(C,$fot(composition(complement(converse(composition(sk1,complement(one)))),sk1)))]]) ).
cnf(refute_0_1106,plain,
converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1107,plain,
( converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))
| join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))) ),[1,0],$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))]]) ).
cnf(refute_0_1108,plain,
( join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))) )],[refute_0_1106,refute_0_1107]) ).
cnf(refute_0_1109,plain,
converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),
inference(resolve,[$cnf( $equal(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_1105,refute_0_1108]) ).
cnf(refute_0_1110,plain,
join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),
inference(subst,[],[refute_0_483:[bind(X_10,$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))]]) ).
cnf(refute_0_1111,plain,
( converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))
| join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))),bind(Y,$fot(converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))),bind(Z,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1112,plain,
( converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))) )],[refute_0_1110,refute_0_1111]) ).
cnf(refute_0_1113,plain,
join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) )],[refute_0_1109,refute_0_1112]) ).
cnf(refute_0_1114,plain,
composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))))]]) ).
cnf(refute_0_1115,plain,
( composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) != composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))
| join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))) ),[1,0],$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))]]) ).
cnf(refute_0_1116,plain,
( join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))) )],[refute_0_1114,refute_0_1115]) ).
cnf(refute_0_1117,plain,
composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) )],[refute_0_1113,refute_0_1116]) ).
cnf(refute_0_1118,plain,
( composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) != composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) != composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))))),bind(Y,$fot(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))))),bind(Z,$fot(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)))]]) ).
cnf(refute_0_1119,plain,
( composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) != composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),
inference(resolve,[$cnf( $equal(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)) )],[refute_0_1104,refute_0_1119]) ).
cnf(refute_0_1121,plain,
( composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) != composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))))),bind(Y,$fot(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one))),bind(Z,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1122,plain,
( composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one)) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),
inference(resolve,[$cnf( $equal(composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) )],[refute_0_1099,refute_0_1122]) ).
cnf(refute_0_1124,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_75),complement(join(complement(join(zero,complement(B))),X_75))),
inference(subst,[],[refute_0_165:[bind(A,$fot(join(zero,complement(B)))),bind(B,$fot(X_75))]]) ).
cnf(refute_0_1125,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_1126,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_247,refute_0_1125]) ).
cnf(refute_0_1127,plain,
( complement(join(zero,complement(B))) != meet(top,B)
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_75),complement(join(complement(join(zero,complement(B))),X_75)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_75),complement(join(complement(join(zero,complement(B))),X_75)))) ),[1,1,0,0],$fot(meet(top,B))]]) ).
cnf(refute_0_1128,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_75),complement(join(complement(join(zero,complement(B))),X_75)))
| join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),meet(top,B)) )],[refute_0_1126,refute_0_1127]) ).
cnf(refute_0_1129,plain,
join(zero,complement(B)) = join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_75),complement(join(complement(join(zero,complement(B))),X_75)))) )],[refute_0_1124,refute_0_1128]) ).
cnf(refute_0_1130,plain,
join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(join(meet(top,B),X_75)))),bind(B,$fot(meet(join(zero,complement(B)),X_75)))]]) ).
cnf(refute_0_1131,plain,
( join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75)))) ),[1],$fot(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)))]]) ).
cnf(refute_0_1132,plain,
( join(zero,complement(B)) != join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75)))
| join(zero,complement(B)) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) ),
inference(resolve,[$cnf( $equal(join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75))),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
join(zero,complement(B)) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(meet(join(zero,complement(B)),X_75),complement(join(meet(top,B),X_75)))) )],[refute_0_1129,refute_0_1132]) ).
cnf(refute_0_1134,plain,
( join(zero,complement(B)) != complement(B)
| join(zero,complement(B)) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| complement(B) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) ),[0],$fot(complement(B))]]) ).
cnf(refute_0_1135,plain,
( join(zero,complement(B)) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| complement(B) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_725,refute_0_1134]) ).
cnf(refute_0_1136,plain,
meet(join(zero,complement(B)),X_75) = meet(join(zero,complement(B)),X_75),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(B)),X_75))]]) ).
cnf(refute_0_1137,plain,
( join(zero,complement(B)) != complement(B)
| meet(join(zero,complement(B)),X_75) != meet(join(zero,complement(B)),X_75)
| meet(join(zero,complement(B)),X_75) = meet(complement(B),X_75) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(B)),X_75),meet(join(zero,complement(B)),X_75)) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_1138,plain,
( join(zero,complement(B)) != complement(B)
| meet(join(zero,complement(B)),X_75) = meet(complement(B),X_75) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),X_75),meet(join(zero,complement(B)),X_75)) )],[refute_0_1136,refute_0_1137]) ).
cnf(refute_0_1139,plain,
meet(join(zero,complement(B)),X_75) = meet(complement(B),X_75),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_725,refute_0_1138]) ).
cnf(refute_0_1140,plain,
join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)),
introduced(tautology,[refl,[$fot(join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)))]]) ).
cnf(refute_0_1141,plain,
( join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75))
| meet(join(zero,complement(B)),X_75) != meet(complement(B),X_75)
| join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75))) ),[1,1],$fot(meet(complement(B),X_75))]]) ).
cnf(refute_0_1142,plain,
( meet(join(zero,complement(B)),X_75) != meet(complement(B),X_75)
| join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1140,refute_0_1141]) ).
cnf(refute_0_1143,plain,
join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(B)),X_75),meet(complement(B),X_75)) )],[refute_0_1139,refute_0_1142]) ).
cnf(refute_0_1144,plain,
join(meet(top,B),X_75) = join(meet(top,B),X_75),
introduced(tautology,[refl,[$fot(join(meet(top,B),X_75))]]) ).
cnf(refute_0_1145,plain,
( join(meet(top,B),X_75) != join(meet(top,B),X_75)
| meet(top,B) != B
| join(meet(top,B),X_75) = join(B,X_75) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,B),X_75),join(meet(top,B),X_75)) ),[1,0],$fot(B)]]) ).
cnf(refute_0_1146,plain,
( meet(top,B) != B
| join(meet(top,B),X_75) = join(B,X_75) ),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_75),join(meet(top,B),X_75)) )],[refute_0_1144,refute_0_1145]) ).
cnf(refute_0_1147,plain,
join(meet(top,B),X_75) = join(B,X_75),
inference(resolve,[$cnf( $equal(meet(top,B),B) )],[refute_0_722,refute_0_1146]) ).
cnf(refute_0_1148,plain,
complement(join(meet(top,B),X_75)) = complement(join(meet(top,B),X_75)),
introduced(tautology,[refl,[$fot(complement(join(meet(top,B),X_75)))]]) ).
cnf(refute_0_1149,plain,
( complement(join(meet(top,B),X_75)) != complement(join(meet(top,B),X_75))
| join(meet(top,B),X_75) != join(B,X_75)
| complement(join(meet(top,B),X_75)) = complement(join(B,X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,B),X_75)),complement(join(meet(top,B),X_75))) ),[1,0],$fot(join(B,X_75))]]) ).
cnf(refute_0_1150,plain,
( join(meet(top,B),X_75) != join(B,X_75)
| complement(join(meet(top,B),X_75)) = complement(join(B,X_75)) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_75)),complement(join(meet(top,B),X_75))) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
complement(join(meet(top,B),X_75)) = complement(join(B,X_75)),
inference(resolve,[$cnf( $equal(join(meet(top,B),X_75),join(B,X_75)) )],[refute_0_1147,refute_0_1150]) ).
cnf(refute_0_1152,plain,
join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),
introduced(tautology,[refl,[$fot(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)))]]) ).
cnf(refute_0_1153,plain,
( complement(join(meet(top,B),X_75)) != complement(join(B,X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) ),[1,0],$fot(complement(join(B,X_75)))]]) ).
cnf(refute_0_1154,plain,
( complement(join(meet(top,B),X_75)) != complement(join(B,X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)),
inference(resolve,[$cnf( $equal(complement(join(meet(top,B),X_75)),complement(join(B,X_75))) )],[refute_0_1151,refute_0_1154]) ).
cnf(refute_0_1156,plain,
( join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(B,X_75)),meet(complement(B),X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)))),bind(Y,$fot(join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)))),bind(Z,$fot(join(complement(join(B,X_75)),meet(complement(B),X_75))))]]) ).
cnf(refute_0_1157,plain,
( join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(B,X_75)),meet(complement(B),X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1155,refute_0_1156]) ).
cnf(refute_0_1158,plain,
join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) = join(complement(join(B,X_75)),meet(complement(B),X_75)),
inference(resolve,[$cnf( $equal(join(complement(join(B,X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(B,X_75)),meet(complement(B),X_75))) )],[refute_0_1143,refute_0_1157]) ).
cnf(refute_0_1159,plain,
( complement(B) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)) != join(complement(join(B,X_75)),meet(complement(B),X_75))
| complement(B) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(B),join(complement(join(B,X_75)),meet(complement(B),X_75))) ),[0],$fot(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)))]]) ).
cnf(refute_0_1160,plain,
( complement(B) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| complement(B) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75)),join(complement(join(B,X_75)),meet(complement(B),X_75))) )],[refute_0_1158,refute_0_1159]) ).
cnf(refute_0_1161,plain,
( join(zero,complement(B)) != join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))
| complement(B) = join(complement(join(B,X_75)),meet(complement(B),X_75)) ),
inference(resolve,[$cnf( $equal(complement(B),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1135,refute_0_1160]) ).
cnf(refute_0_1162,plain,
complement(B) = join(complement(join(B,X_75)),meet(complement(B),X_75)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),join(complement(join(meet(top,B),X_75)),meet(join(zero,complement(B)),X_75))) )],[refute_0_1133,refute_0_1161]) ).
cnf(refute_0_1163,plain,
complement(complement(X_84)) = join(complement(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),
inference(subst,[],[refute_0_1162:[bind(B,$fot(complement(X_84))),bind(X_75,$fot(meet(X_84,converse(complement(converse(X_84))))))]]) ).
cnf(refute_0_1164,plain,
( converse(complement(converse(X_84))) != join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))
| join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) = converse(complement(converse(X_84))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(complement(converse(X_84))))),bind(Y,$fot(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))))]]) ).
cnf(refute_0_1165,plain,
join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) = converse(complement(converse(X_84))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_84))),join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))) )],[refute_0_1027,refute_0_1164]) ).
cnf(refute_0_1166,plain,
( complement(complement(X_84)) != join(complement(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))) != converse(complement(converse(X_84)))
| complement(complement(X_84)) = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(X_84)),join(complement(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) ),[1,0,0],$fot(converse(complement(converse(X_84))))]]) ).
cnf(refute_0_1167,plain,
( complement(complement(X_84)) != join(complement(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| complement(complement(X_84)) = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_84),meet(X_84,converse(complement(converse(X_84))))),converse(complement(converse(X_84)))) )],[refute_0_1165,refute_0_1166]) ).
cnf(refute_0_1168,plain,
complement(complement(X_84)) = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),join(complement(join(complement(X_84),meet(X_84,converse(complement(converse(X_84)))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) )],[refute_0_1163,refute_0_1167]) ).
cnf(refute_0_1169,plain,
( complement(complement(X_84)) != X_84
| complement(complement(X_84)) != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| X_84 = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(complement(X_84)),join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) ),[0],$fot(X_84)]]) ).
cnf(refute_0_1170,plain,
( complement(complement(X_84)) != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| X_84 = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) ),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),X_84) )],[refute_0_1002,refute_0_1169]) ).
cnf(refute_0_1171,plain,
X_74 = join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),join(complement(X_74),X_51)))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(join(complement(X_74),X_51)))]]) ).
cnf(refute_0_1172,plain,
join(complement(X_74),join(complement(X_74),X_51)) = join(complement(X_74),X_51),
inference(subst,[],[refute_0_768:[bind(X_24,$fot(X_74))]]) ).
cnf(refute_0_1173,plain,
( X_74 != join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),join(complement(X_74),X_51))))
| join(complement(X_74),join(complement(X_74),X_51)) != join(complement(X_74),X_51)
| X_74 = join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),join(complement(X_74),X_51))))) ),[1,1,0],$fot(join(complement(X_74),X_51))]]) ).
cnf(refute_0_1174,plain,
( X_74 != join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),join(complement(X_74),X_51))))
| X_74 = join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))) ),
inference(resolve,[$cnf( $equal(join(complement(X_74),join(complement(X_74),X_51)),join(complement(X_74),X_51)) )],[refute_0_1172,refute_0_1173]) ).
cnf(refute_0_1175,plain,
X_74 = join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),join(complement(X_74),X_51))))) )],[refute_0_1171,refute_0_1174]) ).
cnf(refute_0_1176,plain,
join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))) = join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(join(complement(X_74),X_51)))),bind(B,$fot(meet(X_74,join(complement(X_74),X_51))))]]) ).
cnf(refute_0_1177,plain,
( X_74 != join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51)))
| join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))) != join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))
| X_74 = join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))) ),[0],$fot(join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))))]]) ).
cnf(refute_0_1178,plain,
( X_74 != join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51)))
| X_74 = join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51))),join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))) )],[refute_0_1176,refute_0_1177]) ).
cnf(refute_0_1179,plain,
X_74 = join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,join(complement(X_74),X_51)),complement(join(complement(X_74),X_51)))) )],[refute_0_1175,refute_0_1178]) ).
cnf(refute_0_1180,plain,
complement(join(complement(X_74),X_51)) = meet(X_74,complement(X_51)),
inference(subst,[],[refute_0_967:[bind(A,$fot(X_74)),bind(X_32,$fot(X_51))]]) ).
cnf(refute_0_1181,plain,
join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) = join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))))]]) ).
cnf(refute_0_1182,plain,
( complement(join(complement(X_74),X_51)) != meet(X_74,complement(X_51))
| join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) != join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))
| join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))) ),[1,0],$fot(meet(X_74,complement(X_51)))]]) ).
cnf(refute_0_1183,plain,
( complement(join(complement(X_74),X_51)) != meet(X_74,complement(X_51))
| join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))) )],[refute_0_1181,refute_0_1182]) ).
cnf(refute_0_1184,plain,
join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_74),X_51)),meet(X_74,complement(X_51))) )],[refute_0_1180,refute_0_1183]) ).
cnf(refute_0_1185,plain,
( X_74 != join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))
| join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))) != join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51)))
| X_74 = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51)))) ),[0],$fot(join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))))]]) ).
cnf(refute_0_1186,plain,
( X_74 != join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))
| X_74 = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51))),join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51)))) )],[refute_0_1184,refute_0_1185]) ).
cnf(refute_0_1187,plain,
X_74 = join(meet(X_74,complement(X_51)),meet(X_74,join(complement(X_74),X_51))),
inference(resolve,[$cnf( $equal(X_74,join(complement(join(complement(X_74),X_51)),meet(X_74,join(complement(X_74),X_51)))) )],[refute_0_1179,refute_0_1186]) ).
cnf(refute_0_1188,plain,
X_172 = join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,join(complement(X_172),meet(complement(X_172),B)))),
inference(subst,[],[refute_0_1187:[bind(X_51,$fot(meet(complement(X_172),B))),bind(X_74,$fot(X_172))]]) ).
cnf(refute_0_1189,plain,
join(meet(X_74,B),join(meet(X_74,B),meet(X_74,complement(B)))) = join(meet(X_74,B),meet(X_74,complement(B))),
inference(subst,[],[refute_0_756:[bind(B,$fot(meet(X_74,B))),bind(C,$fot(meet(X_74,complement(B))))]]) ).
cnf(refute_0_1190,plain,
X_74 = join(meet(X_74,complement(B)),complement(join(complement(X_74),complement(B)))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_1191,plain,
meet(X_74,B) = complement(join(complement(X_74),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_74))]]) ).
cnf(refute_0_1192,plain,
( meet(X_74,B) != complement(join(complement(X_74),complement(B)))
| complement(join(complement(X_74),complement(B))) = meet(X_74,B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_74,B))),bind(Y,$fot(complement(join(complement(X_74),complement(B)))))]]) ).
cnf(refute_0_1193,plain,
complement(join(complement(X_74),complement(B))) = meet(X_74,B),
inference(resolve,[$cnf( $equal(meet(X_74,B),complement(join(complement(X_74),complement(B)))) )],[refute_0_1191,refute_0_1192]) ).
cnf(refute_0_1194,plain,
( X_74 != join(meet(X_74,complement(B)),complement(join(complement(X_74),complement(B))))
| complement(join(complement(X_74),complement(B))) != meet(X_74,B)
| X_74 = join(meet(X_74,complement(B)),meet(X_74,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,complement(B)),complement(join(complement(X_74),complement(B))))) ),[1,1],$fot(meet(X_74,B))]]) ).
cnf(refute_0_1195,plain,
( X_74 != join(meet(X_74,complement(B)),complement(join(complement(X_74),complement(B))))
| X_74 = join(meet(X_74,complement(B)),meet(X_74,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_74),complement(B))),meet(X_74,B)) )],[refute_0_1193,refute_0_1194]) ).
cnf(refute_0_1196,plain,
X_74 = join(meet(X_74,complement(B)),meet(X_74,B)),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,complement(B)),complement(join(complement(X_74),complement(B))))) )],[refute_0_1190,refute_0_1195]) ).
cnf(refute_0_1197,plain,
join(meet(X_74,complement(B)),meet(X_74,B)) = join(meet(X_74,B),meet(X_74,complement(B))),
inference(subst,[],[refute_0_5:[bind(A,$fot(meet(X_74,B))),bind(B,$fot(meet(X_74,complement(B))))]]) ).
cnf(refute_0_1198,plain,
( X_74 != join(meet(X_74,complement(B)),meet(X_74,B))
| join(meet(X_74,complement(B)),meet(X_74,B)) != join(meet(X_74,B),meet(X_74,complement(B)))
| X_74 = join(meet(X_74,B),meet(X_74,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(meet(X_74,B),meet(X_74,complement(B)))) ),[0],$fot(join(meet(X_74,complement(B)),meet(X_74,B)))]]) ).
cnf(refute_0_1199,plain,
( X_74 != join(meet(X_74,complement(B)),meet(X_74,B))
| X_74 = join(meet(X_74,B),meet(X_74,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,complement(B)),meet(X_74,B)),join(meet(X_74,B),meet(X_74,complement(B)))) )],[refute_0_1197,refute_0_1198]) ).
cnf(refute_0_1200,plain,
X_74 = join(meet(X_74,B),meet(X_74,complement(B))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,complement(B)),meet(X_74,B))) )],[refute_0_1196,refute_0_1199]) ).
cnf(refute_0_1201,plain,
( X_74 != join(meet(X_74,B),meet(X_74,complement(B)))
| join(meet(X_74,B),meet(X_74,complement(B))) = X_74 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_74)),bind(Y,$fot(join(meet(X_74,B),meet(X_74,complement(B)))))]]) ).
cnf(refute_0_1202,plain,
join(meet(X_74,B),meet(X_74,complement(B))) = X_74,
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,B),meet(X_74,complement(B)))) )],[refute_0_1200,refute_0_1201]) ).
cnf(refute_0_1203,plain,
( join(meet(X_74,B),join(meet(X_74,B),meet(X_74,complement(B)))) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(meet(X_74,B),meet(X_74,complement(B))) != X_74
| join(meet(X_74,B),X_74) = join(meet(X_74,B),meet(X_74,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_74,B),join(meet(X_74,B),meet(X_74,complement(B)))),join(meet(X_74,B),meet(X_74,complement(B)))) ),[0,1],$fot(X_74)]]) ).
cnf(refute_0_1204,plain,
( join(meet(X_74,B),join(meet(X_74,B),meet(X_74,complement(B)))) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(meet(X_74,B),X_74) = join(meet(X_74,B),meet(X_74,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,B),meet(X_74,complement(B))),X_74) )],[refute_0_1202,refute_0_1203]) ).
cnf(refute_0_1205,plain,
join(meet(X_74,B),X_74) = join(meet(X_74,B),meet(X_74,complement(B))),
inference(resolve,[$cnf( $equal(join(meet(X_74,B),join(meet(X_74,B),meet(X_74,complement(B)))),join(meet(X_74,B),meet(X_74,complement(B)))) )],[refute_0_1189,refute_0_1204]) ).
cnf(refute_0_1206,plain,
join(meet(X_74,B),X_74) = join(X_74,meet(X_74,B)),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_74)),bind(B,$fot(meet(X_74,B)))]]) ).
cnf(refute_0_1207,plain,
( join(meet(X_74,B),X_74) != join(X_74,meet(X_74,B))
| join(meet(X_74,B),X_74) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(X_74,meet(X_74,B)) = join(meet(X_74,B),meet(X_74,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_74,B),X_74),join(meet(X_74,B),meet(X_74,complement(B)))) ),[0],$fot(join(X_74,meet(X_74,B)))]]) ).
cnf(refute_0_1208,plain,
( join(meet(X_74,B),X_74) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(X_74,meet(X_74,B)) = join(meet(X_74,B),meet(X_74,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,B),X_74),join(X_74,meet(X_74,B))) )],[refute_0_1206,refute_0_1207]) ).
cnf(refute_0_1209,plain,
( join(X_74,meet(X_74,B)) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(meet(X_74,B),meet(X_74,complement(B))) != X_74
| join(X_74,meet(X_74,B)) = X_74 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_74,meet(X_74,B)),X_74) ),[0],$fot(join(meet(X_74,B),meet(X_74,complement(B))))]]) ).
cnf(refute_0_1210,plain,
( join(X_74,meet(X_74,B)) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(X_74,meet(X_74,B)) = X_74 ),
inference(resolve,[$cnf( $equal(join(meet(X_74,B),meet(X_74,complement(B))),X_74) )],[refute_0_1202,refute_0_1209]) ).
cnf(refute_0_1211,plain,
( join(meet(X_74,B),X_74) != join(meet(X_74,B),meet(X_74,complement(B)))
| join(X_74,meet(X_74,B)) = X_74 ),
inference(resolve,[$cnf( $equal(join(X_74,meet(X_74,B)),join(meet(X_74,B),meet(X_74,complement(B)))) )],[refute_0_1208,refute_0_1210]) ).
cnf(refute_0_1212,plain,
join(X_74,meet(X_74,B)) = X_74,
inference(resolve,[$cnf( $equal(join(meet(X_74,B),X_74),join(meet(X_74,B),meet(X_74,complement(B)))) )],[refute_0_1205,refute_0_1211]) ).
cnf(refute_0_1213,plain,
join(complement(X_172),meet(complement(X_172),B)) = complement(X_172),
inference(subst,[],[refute_0_1212:[bind(X_74,$fot(complement(X_172)))]]) ).
cnf(refute_0_1214,plain,
( X_172 != join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,join(complement(X_172),meet(complement(X_172),B))))
| join(complement(X_172),meet(complement(X_172),B)) != complement(X_172)
| X_172 = join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) ),
introduced(tautology,[equality,[$cnf( $equal(X_172,join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,join(complement(X_172),meet(complement(X_172),B))))) ),[1,1,1],$fot(complement(X_172))]]) ).
cnf(refute_0_1215,plain,
( X_172 != join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,join(complement(X_172),meet(complement(X_172),B))))
| X_172 = join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) ),
inference(resolve,[$cnf( $equal(join(complement(X_172),meet(complement(X_172),B)),complement(X_172)) )],[refute_0_1213,refute_0_1214]) ).
cnf(refute_0_1216,plain,
X_172 = join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))),
inference(resolve,[$cnf( $equal(X_172,join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,join(complement(X_172),meet(complement(X_172),B))))) )],[refute_0_1188,refute_0_1215]) ).
cnf(refute_0_1217,plain,
join(zero,meet(X_172,complement(meet(complement(X_172),B)))) = meet(X_172,complement(meet(complement(X_172),B))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(X_172,complement(meet(complement(X_172),B)))))]]) ).
cnf(refute_0_1218,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_1219,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_1218]) ).
cnf(refute_0_1220,plain,
meet(X_172,complement(X_172)) = zero,
inference(subst,[],[refute_0_1219:[bind(A,$fot(X_172))]]) ).
cnf(refute_0_1221,plain,
join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),
introduced(tautology,[refl,[$fot(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))))]]) ).
cnf(refute_0_1222,plain,
( join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) != join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B))))
| meet(X_172,complement(X_172)) != zero
| join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = join(zero,meet(X_172,complement(meet(complement(X_172),B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1223,plain,
( meet(X_172,complement(X_172)) != zero
| join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = join(zero,meet(X_172,complement(meet(complement(X_172),B)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B))))) )],[refute_0_1221,refute_0_1222]) ).
cnf(refute_0_1224,plain,
join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = join(zero,meet(X_172,complement(meet(complement(X_172),B)))),
inference(resolve,[$cnf( $equal(meet(X_172,complement(X_172)),zero) )],[refute_0_1220,refute_0_1223]) ).
cnf(refute_0_1225,plain,
( join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) != join(zero,meet(X_172,complement(meet(complement(X_172),B))))
| join(zero,meet(X_172,complement(meet(complement(X_172),B)))) != meet(X_172,complement(meet(complement(X_172),B)))
| join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = meet(X_172,complement(meet(complement(X_172),B))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))))),bind(Y,$fot(join(zero,meet(X_172,complement(meet(complement(X_172),B)))))),bind(Z,$fot(meet(X_172,complement(meet(complement(X_172),B)))))]]) ).
cnf(refute_0_1226,plain,
( join(zero,meet(X_172,complement(meet(complement(X_172),B)))) != meet(X_172,complement(meet(complement(X_172),B)))
| join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = meet(X_172,complement(meet(complement(X_172),B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),join(zero,meet(X_172,complement(meet(complement(X_172),B))))) )],[refute_0_1224,refute_0_1225]) ).
cnf(refute_0_1227,plain,
join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) = meet(X_172,complement(meet(complement(X_172),B))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_172,complement(meet(complement(X_172),B)))),meet(X_172,complement(meet(complement(X_172),B)))) )],[refute_0_1217,refute_0_1226]) ).
cnf(refute_0_1228,plain,
join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) = join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),
inference(subst,[],[refute_0_5:[bind(A,$fot(meet(X_172,complement(X_172)))),bind(B,$fot(meet(X_172,complement(meet(complement(X_172),B)))))]]) ).
cnf(refute_0_1229,plain,
( join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) != meet(X_172,complement(meet(complement(X_172),B)))
| join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) != join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B))))
| join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) = meet(X_172,complement(meet(complement(X_172),B))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))))),bind(Y,$fot(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))))),bind(Z,$fot(meet(X_172,complement(meet(complement(X_172),B)))))]]) ).
cnf(refute_0_1230,plain,
( join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))) != meet(X_172,complement(meet(complement(X_172),B)))
| join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) = meet(X_172,complement(meet(complement(X_172),B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))),join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B))))) )],[refute_0_1228,refute_0_1229]) ).
cnf(refute_0_1231,plain,
join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) = meet(X_172,complement(meet(complement(X_172),B))),
inference(resolve,[$cnf( $equal(join(meet(X_172,complement(X_172)),meet(X_172,complement(meet(complement(X_172),B)))),meet(X_172,complement(meet(complement(X_172),B)))) )],[refute_0_1227,refute_0_1230]) ).
cnf(refute_0_1232,plain,
( X_172 != join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172)))
| join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))) != meet(X_172,complement(meet(complement(X_172),B)))
| X_172 = meet(X_172,complement(meet(complement(X_172),B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_172,meet(X_172,complement(meet(complement(X_172),B)))) ),[0],$fot(join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))))]]) ).
cnf(refute_0_1233,plain,
( X_172 != join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172)))
| X_172 = meet(X_172,complement(meet(complement(X_172),B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172))),meet(X_172,complement(meet(complement(X_172),B)))) )],[refute_0_1231,refute_0_1232]) ).
cnf(refute_0_1234,plain,
X_172 = meet(X_172,complement(meet(complement(X_172),B))),
inference(resolve,[$cnf( $equal(X_172,join(meet(X_172,complement(meet(complement(X_172),B))),meet(X_172,complement(X_172)))) )],[refute_0_1216,refute_0_1233]) ).
cnf(refute_0_1235,plain,
X_174 = meet(X_174,complement(meet(complement(X_174),X_173))),
inference(subst,[],[refute_0_1234:[bind(B,$fot(X_173)),bind(X_172,$fot(X_174))]]) ).
cnf(refute_0_1236,plain,
meet(X_173,complement(X_174)) = meet(complement(X_174),X_173),
inference(subst,[],[refute_0_272:[bind(X_27,$fot(X_173)),bind(X_28,$fot(complement(X_174)))]]) ).
cnf(refute_0_1237,plain,
( meet(X_173,complement(X_174)) != meet(complement(X_174),X_173)
| meet(complement(X_174),X_173) = meet(X_173,complement(X_174)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_173,complement(X_174)))),bind(Y,$fot(meet(complement(X_174),X_173)))]]) ).
cnf(refute_0_1238,plain,
meet(complement(X_174),X_173) = meet(X_173,complement(X_174)),
inference(resolve,[$cnf( $equal(meet(X_173,complement(X_174)),meet(complement(X_174),X_173)) )],[refute_0_1236,refute_0_1237]) ).
cnf(refute_0_1239,plain,
( X_174 != meet(X_174,complement(meet(complement(X_174),X_173)))
| meet(complement(X_174),X_173) != meet(X_173,complement(X_174))
| X_174 = meet(X_174,complement(meet(X_173,complement(X_174)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_174,meet(X_174,complement(meet(complement(X_174),X_173)))) ),[1,1,0],$fot(meet(X_173,complement(X_174)))]]) ).
cnf(refute_0_1240,plain,
( X_174 != meet(X_174,complement(meet(complement(X_174),X_173)))
| X_174 = meet(X_174,complement(meet(X_173,complement(X_174)))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_174),X_173),meet(X_173,complement(X_174))) )],[refute_0_1238,refute_0_1239]) ).
cnf(refute_0_1241,plain,
X_174 = meet(X_174,complement(meet(X_173,complement(X_174)))),
inference(resolve,[$cnf( $equal(X_174,meet(X_174,complement(meet(complement(X_174),X_173)))) )],[refute_0_1235,refute_0_1240]) ).
cnf(refute_0_1242,plain,
meet(X_253,X_254) = meet(meet(X_253,X_254),complement(meet(complement(X_253),complement(meet(X_253,X_254))))),
inference(subst,[],[refute_0_1241:[bind(X_173,$fot(complement(X_253))),bind(X_174,$fot(meet(X_253,X_254)))]]) ).
cnf(refute_0_1243,plain,
complement(B) = meet(complement(B),complement(meet(complement(complement(B)),X_173))),
inference(subst,[],[refute_0_1234:[bind(B,$fot(X_173)),bind(X_172,$fot(complement(B)))]]) ).
cnf(refute_0_1244,plain,
( complement(B) != meet(complement(B),complement(meet(complement(complement(B)),X_173)))
| complement(complement(B)) != B
| complement(B) = meet(complement(B),complement(meet(B,X_173))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(B),meet(complement(B),complement(meet(complement(complement(B)),X_173)))) ),[1,1,0,0],$fot(B)]]) ).
cnf(refute_0_1245,plain,
( complement(B) != meet(complement(B),complement(meet(complement(complement(B)),X_173)))
| complement(B) = meet(complement(B),complement(meet(B,X_173))) ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_735,refute_0_1244]) ).
cnf(refute_0_1246,plain,
complement(B) = meet(complement(B),complement(meet(B,X_173))),
inference(resolve,[$cnf( $equal(complement(B),meet(complement(B),complement(meet(complement(complement(B)),X_173)))) )],[refute_0_1243,refute_0_1245]) ).
cnf(refute_0_1247,plain,
complement(X_253) = meet(complement(X_253),complement(meet(X_253,X_254))),
inference(subst,[],[refute_0_1246:[bind(B,$fot(X_253)),bind(X_173,$fot(X_254))]]) ).
cnf(refute_0_1248,plain,
( complement(X_253) != meet(complement(X_253),complement(meet(X_253,X_254)))
| meet(complement(X_253),complement(meet(X_253,X_254))) = complement(X_253) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(X_253))),bind(Y,$fot(meet(complement(X_253),complement(meet(X_253,X_254)))))]]) ).
cnf(refute_0_1249,plain,
meet(complement(X_253),complement(meet(X_253,X_254))) = complement(X_253),
inference(resolve,[$cnf( $equal(complement(X_253),meet(complement(X_253),complement(meet(X_253,X_254)))) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
( meet(X_253,X_254) != meet(meet(X_253,X_254),complement(meet(complement(X_253),complement(meet(X_253,X_254)))))
| meet(complement(X_253),complement(meet(X_253,X_254))) != complement(X_253)
| meet(X_253,X_254) = meet(meet(X_253,X_254),complement(complement(X_253))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_253,X_254),meet(meet(X_253,X_254),complement(meet(complement(X_253),complement(meet(X_253,X_254)))))) ),[1,1,0],$fot(complement(X_253))]]) ).
cnf(refute_0_1251,plain,
( meet(X_253,X_254) != meet(meet(X_253,X_254),complement(meet(complement(X_253),complement(meet(X_253,X_254)))))
| meet(X_253,X_254) = meet(meet(X_253,X_254),complement(complement(X_253))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_253),complement(meet(X_253,X_254))),complement(X_253)) )],[refute_0_1249,refute_0_1250]) ).
cnf(refute_0_1252,plain,
meet(X_253,X_254) = meet(meet(X_253,X_254),complement(complement(X_253))),
inference(resolve,[$cnf( $equal(meet(X_253,X_254),meet(meet(X_253,X_254),complement(meet(complement(X_253),complement(meet(X_253,X_254)))))) )],[refute_0_1242,refute_0_1251]) ).
cnf(refute_0_1253,plain,
complement(complement(X_253)) = X_253,
inference(subst,[],[refute_0_735:[bind(B,$fot(X_253))]]) ).
cnf(refute_0_1254,plain,
meet(complement(complement(X_253)),meet(X_253,X_254)) = meet(complement(complement(X_253)),meet(X_253,X_254)),
introduced(tautology,[refl,[$fot(meet(complement(complement(X_253)),meet(X_253,X_254)))]]) ).
cnf(refute_0_1255,plain,
( complement(complement(X_253)) != X_253
| meet(complement(complement(X_253)),meet(X_253,X_254)) != meet(complement(complement(X_253)),meet(X_253,X_254))
| meet(complement(complement(X_253)),meet(X_253,X_254)) = meet(X_253,meet(X_253,X_254)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(complement(X_253)),meet(X_253,X_254)),meet(complement(complement(X_253)),meet(X_253,X_254))) ),[1,0],$fot(X_253)]]) ).
cnf(refute_0_1256,plain,
( complement(complement(X_253)) != X_253
| meet(complement(complement(X_253)),meet(X_253,X_254)) = meet(X_253,meet(X_253,X_254)) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_253)),meet(X_253,X_254)),meet(complement(complement(X_253)),meet(X_253,X_254))) )],[refute_0_1254,refute_0_1255]) ).
cnf(refute_0_1257,plain,
meet(complement(complement(X_253)),meet(X_253,X_254)) = meet(X_253,meet(X_253,X_254)),
inference(resolve,[$cnf( $equal(complement(complement(X_253)),X_253) )],[refute_0_1253,refute_0_1256]) ).
cnf(refute_0_1258,plain,
meet(meet(X_253,X_254),complement(complement(X_253))) = meet(complement(complement(X_253)),meet(X_253,X_254)),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(complement(complement(X_253)))),bind(X_28,$fot(meet(X_253,X_254)))]]) ).
cnf(refute_0_1259,plain,
( meet(complement(complement(X_253)),meet(X_253,X_254)) != meet(X_253,meet(X_253,X_254))
| meet(meet(X_253,X_254),complement(complement(X_253))) != meet(complement(complement(X_253)),meet(X_253,X_254))
| meet(meet(X_253,X_254),complement(complement(X_253))) = meet(X_253,meet(X_253,X_254)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(meet(meet(X_253,X_254),complement(complement(X_253))))),bind(Y,$fot(meet(complement(complement(X_253)),meet(X_253,X_254)))),bind(Z,$fot(meet(X_253,meet(X_253,X_254))))]]) ).
cnf(refute_0_1260,plain,
( meet(complement(complement(X_253)),meet(X_253,X_254)) != meet(X_253,meet(X_253,X_254))
| meet(meet(X_253,X_254),complement(complement(X_253))) = meet(X_253,meet(X_253,X_254)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_253,X_254),complement(complement(X_253))),meet(complement(complement(X_253)),meet(X_253,X_254))) )],[refute_0_1258,refute_0_1259]) ).
cnf(refute_0_1261,plain,
meet(meet(X_253,X_254),complement(complement(X_253))) = meet(X_253,meet(X_253,X_254)),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_253)),meet(X_253,X_254)),meet(X_253,meet(X_253,X_254))) )],[refute_0_1257,refute_0_1260]) ).
cnf(refute_0_1262,plain,
( meet(X_253,X_254) != meet(meet(X_253,X_254),complement(complement(X_253)))
| meet(meet(X_253,X_254),complement(complement(X_253))) != meet(X_253,meet(X_253,X_254))
| meet(X_253,X_254) = meet(X_253,meet(X_253,X_254)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X_253,X_254),meet(X_253,meet(X_253,X_254))) ),[0],$fot(meet(meet(X_253,X_254),complement(complement(X_253))))]]) ).
cnf(refute_0_1263,plain,
( meet(X_253,X_254) != meet(meet(X_253,X_254),complement(complement(X_253)))
| meet(X_253,X_254) = meet(X_253,meet(X_253,X_254)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_253,X_254),complement(complement(X_253))),meet(X_253,meet(X_253,X_254))) )],[refute_0_1261,refute_0_1262]) ).
cnf(refute_0_1264,plain,
meet(X_253,X_254) = meet(X_253,meet(X_253,X_254)),
inference(resolve,[$cnf( $equal(meet(X_253,X_254),meet(meet(X_253,X_254),complement(complement(X_253)))) )],[refute_0_1252,refute_0_1263]) ).
cnf(refute_0_1265,plain,
( meet(X_253,X_254) != meet(X_253,meet(X_253,X_254))
| meet(X_253,meet(X_253,X_254)) = meet(X_253,X_254) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_253,X_254))),bind(Y,$fot(meet(X_253,meet(X_253,X_254))))]]) ).
cnf(refute_0_1266,plain,
meet(X_253,meet(X_253,X_254)) = meet(X_253,X_254),
inference(resolve,[$cnf( $equal(meet(X_253,X_254),meet(X_253,meet(X_253,X_254))) )],[refute_0_1264,refute_0_1265]) ).
cnf(refute_0_1267,plain,
meet(X_84,meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,converse(complement(converse(X_84)))),
inference(subst,[],[refute_0_1266:[bind(X_253,$fot(X_84)),bind(X_254,$fot(converse(complement(converse(X_84)))))]]) ).
cnf(refute_0_1268,plain,
meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))),
introduced(tautology,[refl,[$fot(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))]]) ).
cnf(refute_0_1269,plain,
( complement(complement(X_84)) != X_84
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) != meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,meet(X_84,converse(complement(converse(X_84))))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) ),[1,0],$fot(X_84)]]) ).
cnf(refute_0_1270,plain,
( complement(complement(X_84)) != X_84
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,meet(X_84,converse(complement(converse(X_84))))),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),X_84) )],[refute_0_1002,refute_0_1270]) ).
cnf(refute_0_1272,plain,
( meet(X_84,meet(X_84,converse(complement(converse(X_84))))) != meet(X_84,converse(complement(converse(X_84))))
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) != meet(X_84,meet(X_84,converse(complement(converse(X_84)))))
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,converse(complement(converse(X_84)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))),bind(Y,$fot(meet(X_84,meet(X_84,converse(complement(converse(X_84))))))),bind(Z,$fot(meet(X_84,converse(complement(converse(X_84))))))]]) ).
cnf(refute_0_1273,plain,
( meet(X_84,meet(X_84,converse(complement(converse(X_84))))) != meet(X_84,converse(complement(converse(X_84))))
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,converse(complement(converse(X_84)))) ),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))),meet(X_84,meet(X_84,converse(complement(converse(X_84)))))) )],[refute_0_1271,refute_0_1272]) ).
cnf(refute_0_1274,plain,
meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) = meet(X_84,converse(complement(converse(X_84)))),
inference(resolve,[$cnf( $equal(meet(X_84,meet(X_84,converse(complement(converse(X_84))))),meet(X_84,converse(complement(converse(X_84))))) )],[refute_0_1267,refute_0_1273]) ).
cnf(refute_0_1275,plain,
join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) = join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))))]]) ).
cnf(refute_0_1276,plain,
( join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) != meet(X_84,converse(complement(converse(X_84))))
| join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) ),[1,1],$fot(meet(X_84,converse(complement(converse(X_84)))))]]) ).
cnf(refute_0_1277,plain,
( meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))) != meet(X_84,converse(complement(converse(X_84))))
| join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) )],[refute_0_1275,refute_0_1276]) ).
cnf(refute_0_1278,plain,
join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))),
inference(resolve,[$cnf( $equal(meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))),meet(X_84,converse(complement(converse(X_84))))) )],[refute_0_1274,refute_0_1277]) ).
cnf(refute_0_1279,plain,
( X_84 != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))) != join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84)))))
| X_84 = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_84,join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84)))))) ),[0],$fot(join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))))]]) ).
cnf(refute_0_1280,plain,
( X_84 != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| X_84 = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84)))))),join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84)))))) )],[refute_0_1278,refute_0_1279]) ).
cnf(refute_0_1281,plain,
( complement(complement(X_84)) != join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))
| X_84 = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))) ),
inference(resolve,[$cnf( $equal(X_84,join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) )],[refute_0_1170,refute_0_1280]) ).
cnf(refute_0_1282,plain,
X_84 = join(complement(converse(complement(converse(X_84)))),meet(X_84,converse(complement(converse(X_84))))),
inference(resolve,[$cnf( $equal(complement(complement(X_84)),join(complement(converse(complement(converse(X_84)))),meet(complement(complement(X_84)),meet(X_84,converse(complement(converse(X_84))))))) )],[refute_0_1168,refute_0_1281]) ).
cnf(refute_0_1283,plain,
composition(join(one,X_409),X_408) = join(complement(converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),
inference(subst,[],[refute_0_1282:[bind(X_84,$fot(composition(join(one,X_409),X_408)))]]) ).
cnf(refute_0_1284,plain,
converse(composition(join(X_12,converse(X_11)),B)) = composition(converse(B),converse(join(X_12,converse(X_11)))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(join(X_12,converse(X_11))))]]) ).
cnf(refute_0_1285,plain,
converse(join(X_12,converse(X_11))) = join(converse(X_12),X_11),
inference(subst,[],[refute_0_370:[bind(A,$fot(X_11)),bind(X_9,$fot(X_12))]]) ).
cnf(refute_0_1286,plain,
( converse(composition(join(X_12,converse(X_11)),B)) != composition(converse(B),converse(join(X_12,converse(X_11))))
| converse(join(X_12,converse(X_11))) != join(converse(X_12),X_11)
| converse(composition(join(X_12,converse(X_11)),B)) = composition(converse(B),join(converse(X_12),X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_12,converse(X_11)),B)),composition(converse(B),converse(join(X_12,converse(X_11))))) ),[1,1],$fot(join(converse(X_12),X_11))]]) ).
cnf(refute_0_1287,plain,
( converse(composition(join(X_12,converse(X_11)),B)) != composition(converse(B),converse(join(X_12,converse(X_11))))
| converse(composition(join(X_12,converse(X_11)),B)) = composition(converse(B),join(converse(X_12),X_11)) ),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(X_11))),join(converse(X_12),X_11)) )],[refute_0_1285,refute_0_1286]) ).
cnf(refute_0_1288,plain,
converse(composition(join(X_12,converse(X_11)),B)) = composition(converse(B),join(converse(X_12),X_11)),
inference(resolve,[$cnf( $equal(converse(composition(join(X_12,converse(X_11)),B)),composition(converse(B),converse(join(X_12,converse(X_11))))) )],[refute_0_1284,refute_0_1287]) ).
cnf(refute_0_1289,plain,
converse(composition(join(X_282,converse(one)),X_280)) = composition(converse(X_280),join(converse(X_282),one)),
inference(subst,[],[refute_0_1288:[bind(B,$fot(X_280)),bind(X_11,$fot(one)),bind(X_12,$fot(X_282))]]) ).
cnf(refute_0_1290,plain,
( converse(composition(join(X_282,converse(one)),X_280)) != composition(converse(X_280),join(converse(X_282),one))
| converse(one) != one
| converse(composition(join(X_282,one),X_280)) = composition(converse(X_280),join(converse(X_282),one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_282,converse(one)),X_280)),composition(converse(X_280),join(converse(X_282),one))) ),[0,0,0,1],$fot(one)]]) ).
cnf(refute_0_1291,plain,
( converse(composition(join(X_282,converse(one)),X_280)) != composition(converse(X_280),join(converse(X_282),one))
| converse(composition(join(X_282,one),X_280)) = composition(converse(X_280),join(converse(X_282),one)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_1290]) ).
cnf(refute_0_1292,plain,
converse(composition(join(X_282,one),X_280)) = composition(converse(X_280),join(converse(X_282),one)),
inference(resolve,[$cnf( $equal(converse(composition(join(X_282,converse(one)),X_280)),composition(converse(X_280),join(converse(X_282),one))) )],[refute_0_1289,refute_0_1291]) ).
cnf(refute_0_1293,plain,
join(converse(one),X_282) = join(converse(one),X_282),
introduced(tautology,[refl,[$fot(join(converse(one),X_282))]]) ).
cnf(refute_0_1294,plain,
( converse(one) != one
| join(converse(one),X_282) != join(converse(one),X_282)
| join(converse(one),X_282) = join(one,X_282) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),X_282),join(converse(one),X_282)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1295,plain,
( converse(one) != one
| join(converse(one),X_282) = join(one,X_282) ),
inference(resolve,[$cnf( $equal(join(converse(one),X_282),join(converse(one),X_282)) )],[refute_0_1293,refute_0_1294]) ).
cnf(refute_0_1296,plain,
join(converse(one),X_282) = join(one,X_282),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_1295]) ).
cnf(refute_0_1297,plain,
composition(join(converse(one),X_282),X_280) = composition(join(converse(one),X_282),X_280),
introduced(tautology,[refl,[$fot(composition(join(converse(one),X_282),X_280))]]) ).
cnf(refute_0_1298,plain,
( composition(join(converse(one),X_282),X_280) != composition(join(converse(one),X_282),X_280)
| join(converse(one),X_282) != join(one,X_282)
| composition(join(converse(one),X_282),X_280) = composition(join(one,X_282),X_280) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(one),X_282),X_280),composition(join(converse(one),X_282),X_280)) ),[1,0],$fot(join(one,X_282))]]) ).
cnf(refute_0_1299,plain,
( join(converse(one),X_282) != join(one,X_282)
| composition(join(converse(one),X_282),X_280) = composition(join(one,X_282),X_280) ),
inference(resolve,[$cnf( $equal(composition(join(converse(one),X_282),X_280),composition(join(converse(one),X_282),X_280)) )],[refute_0_1297,refute_0_1298]) ).
cnf(refute_0_1300,plain,
composition(join(converse(one),X_282),X_280) = composition(join(one,X_282),X_280),
inference(resolve,[$cnf( $equal(join(converse(one),X_282),join(one,X_282)) )],[refute_0_1296,refute_0_1299]) ).
cnf(refute_0_1301,plain,
converse(composition(join(converse(one),X_282),X_280)) = converse(composition(join(converse(one),X_282),X_280)),
introduced(tautology,[refl,[$fot(converse(composition(join(converse(one),X_282),X_280)))]]) ).
cnf(refute_0_1302,plain,
( composition(join(converse(one),X_282),X_280) != composition(join(one,X_282),X_280)
| converse(composition(join(converse(one),X_282),X_280)) != converse(composition(join(converse(one),X_282),X_280))
| converse(composition(join(converse(one),X_282),X_280)) = converse(composition(join(one,X_282),X_280)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(converse(one),X_282),X_280)),converse(composition(join(converse(one),X_282),X_280))) ),[1,0],$fot(composition(join(one,X_282),X_280))]]) ).
cnf(refute_0_1303,plain,
( composition(join(converse(one),X_282),X_280) != composition(join(one,X_282),X_280)
| converse(composition(join(converse(one),X_282),X_280)) = converse(composition(join(one,X_282),X_280)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(one),X_282),X_280)),converse(composition(join(converse(one),X_282),X_280))) )],[refute_0_1301,refute_0_1302]) ).
cnf(refute_0_1304,plain,
converse(composition(join(converse(one),X_282),X_280)) = converse(composition(join(one,X_282),X_280)),
inference(resolve,[$cnf( $equal(composition(join(converse(one),X_282),X_280),composition(join(one,X_282),X_280)) )],[refute_0_1300,refute_0_1303]) ).
cnf(refute_0_1305,plain,
converse(composition(join(converse(X_13),X_14),B)) = composition(converse(B),converse(join(converse(X_13),X_14))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(join(converse(X_13),X_14)))]]) ).
cnf(refute_0_1306,plain,
converse(join(converse(X_13),X_14)) = join(X_13,converse(X_14)),
inference(subst,[],[refute_0_335:[bind(A,$fot(X_13)),bind(X_10,$fot(X_14))]]) ).
cnf(refute_0_1307,plain,
( converse(composition(join(converse(X_13),X_14),B)) != composition(converse(B),converse(join(converse(X_13),X_14)))
| converse(join(converse(X_13),X_14)) != join(X_13,converse(X_14))
| converse(composition(join(converse(X_13),X_14),B)) = composition(converse(B),join(X_13,converse(X_14))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(converse(X_13),X_14),B)),composition(converse(B),converse(join(converse(X_13),X_14)))) ),[1,1],$fot(join(X_13,converse(X_14)))]]) ).
cnf(refute_0_1308,plain,
( converse(composition(join(converse(X_13),X_14),B)) != composition(converse(B),converse(join(converse(X_13),X_14)))
| converse(composition(join(converse(X_13),X_14),B)) = composition(converse(B),join(X_13,converse(X_14))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(X_13),X_14)),join(X_13,converse(X_14))) )],[refute_0_1306,refute_0_1307]) ).
cnf(refute_0_1309,plain,
converse(composition(join(converse(X_13),X_14),B)) = composition(converse(B),join(X_13,converse(X_14))),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(X_13),X_14),B)),composition(converse(B),converse(join(converse(X_13),X_14)))) )],[refute_0_1305,refute_0_1308]) ).
cnf(refute_0_1310,plain,
( converse(composition(join(converse(X_13),X_14),B)) != composition(converse(B),join(X_13,converse(X_14)))
| composition(converse(B),join(X_13,converse(X_14))) = converse(composition(join(converse(X_13),X_14),B)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(composition(join(converse(X_13),X_14),B)))),bind(Y,$fot(composition(converse(B),join(X_13,converse(X_14)))))]]) ).
cnf(refute_0_1311,plain,
composition(converse(B),join(X_13,converse(X_14))) = converse(composition(join(converse(X_13),X_14),B)),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(X_13),X_14),B)),composition(converse(B),join(X_13,converse(X_14)))) )],[refute_0_1309,refute_0_1310]) ).
cnf(refute_0_1312,plain,
composition(converse(X_280),join(one,converse(X_282))) = converse(composition(join(converse(one),X_282),X_280)),
inference(subst,[],[refute_0_1311:[bind(B,$fot(X_280)),bind(X_13,$fot(one)),bind(X_14,$fot(X_282))]]) ).
cnf(refute_0_1313,plain,
converse(composition(converse(join(X_47,X_48)),X_6)) = composition(converse(X_6),join(X_47,X_48)),
inference(subst,[],[refute_0_82:[bind(A,$fot(join(X_47,X_48)))]]) ).
cnf(refute_0_1314,plain,
( converse(composition(converse(join(X_47,X_48)),X_6)) != composition(converse(X_6),join(X_47,X_48))
| converse(join(X_47,X_48)) != converse(join(X_48,X_47))
| converse(composition(converse(join(X_48,X_47)),X_6)) = composition(converse(X_6),join(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(join(X_47,X_48)),X_6)),composition(converse(X_6),join(X_47,X_48))) ),[0,0,0],$fot(converse(join(X_48,X_47)))]]) ).
cnf(refute_0_1315,plain,
( converse(composition(converse(join(X_47,X_48)),X_6)) != composition(converse(X_6),join(X_47,X_48))
| converse(composition(converse(join(X_48,X_47)),X_6)) = composition(converse(X_6),join(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(converse(join(X_47,X_48)),converse(join(X_48,X_47))) )],[refute_0_30,refute_0_1314]) ).
cnf(refute_0_1316,plain,
converse(composition(converse(join(X_48,X_47)),X_6)) = composition(converse(X_6),join(X_47,X_48)),
inference(resolve,[$cnf( $equal(converse(composition(converse(join(X_47,X_48)),X_6)),composition(converse(X_6),join(X_47,X_48))) )],[refute_0_1313,refute_0_1315]) ).
cnf(refute_0_1317,plain,
converse(composition(converse(join(X_48,X_47)),X_6)) = composition(converse(X_6),join(X_48,X_47)),
inference(subst,[],[refute_0_82:[bind(A,$fot(join(X_48,X_47)))]]) ).
cnf(refute_0_1318,plain,
( converse(composition(converse(join(X_48,X_47)),X_6)) != composition(converse(X_6),join(X_47,X_48))
| converse(composition(converse(join(X_48,X_47)),X_6)) != composition(converse(X_6),join(X_48,X_47))
| composition(converse(X_6),join(X_48,X_47)) = composition(converse(X_6),join(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(join(X_48,X_47)),X_6)),composition(converse(X_6),join(X_47,X_48))) ),[0],$fot(composition(converse(X_6),join(X_48,X_47)))]]) ).
cnf(refute_0_1319,plain,
( converse(composition(converse(join(X_48,X_47)),X_6)) != composition(converse(X_6),join(X_47,X_48))
| composition(converse(X_6),join(X_48,X_47)) = composition(converse(X_6),join(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(join(X_48,X_47)),X_6)),composition(converse(X_6),join(X_48,X_47))) )],[refute_0_1317,refute_0_1318]) ).
cnf(refute_0_1320,plain,
composition(converse(X_6),join(X_48,X_47)) = composition(converse(X_6),join(X_47,X_48)),
inference(resolve,[$cnf( $equal(converse(composition(converse(join(X_48,X_47)),X_6)),composition(converse(X_6),join(X_47,X_48))) )],[refute_0_1316,refute_0_1319]) ).
cnf(refute_0_1321,plain,
( composition(converse(X_6),join(X_48,X_47)) != composition(converse(X_6),join(X_47,X_48))
| composition(converse(X_6),join(X_47,X_48)) = composition(converse(X_6),join(X_48,X_47)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(converse(X_6),join(X_48,X_47)))),bind(Y,$fot(composition(converse(X_6),join(X_47,X_48))))]]) ).
cnf(refute_0_1322,plain,
composition(converse(X_6),join(X_47,X_48)) = composition(converse(X_6),join(X_48,X_47)),
inference(resolve,[$cnf( $equal(composition(converse(X_6),join(X_48,X_47)),composition(converse(X_6),join(X_47,X_48))) )],[refute_0_1320,refute_0_1321]) ).
cnf(refute_0_1323,plain,
composition(converse(X_280),join(converse(X_282),one)) = composition(converse(X_280),join(one,converse(X_282))),
inference(subst,[],[refute_0_1322:[bind(X_47,$fot(converse(X_282))),bind(X_48,$fot(one)),bind(X_6,$fot(X_280))]]) ).
cnf(refute_0_1324,plain,
( composition(converse(X_280),join(converse(X_282),one)) != composition(converse(X_280),join(one,converse(X_282)))
| composition(converse(X_280),join(one,converse(X_282))) != converse(composition(join(converse(one),X_282),X_280))
| composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(converse(one),X_282),X_280)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(X_280),join(converse(X_282),one)))),bind(Y,$fot(composition(converse(X_280),join(one,converse(X_282))))),bind(Z,$fot(converse(composition(join(converse(one),X_282),X_280))))]]) ).
cnf(refute_0_1325,plain,
( composition(converse(X_280),join(one,converse(X_282))) != converse(composition(join(converse(one),X_282),X_280))
| composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(converse(one),X_282),X_280)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_280),join(converse(X_282),one)),composition(converse(X_280),join(one,converse(X_282)))) )],[refute_0_1323,refute_0_1324]) ).
cnf(refute_0_1326,plain,
composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(converse(one),X_282),X_280)),
inference(resolve,[$cnf( $equal(composition(converse(X_280),join(one,converse(X_282))),converse(composition(join(converse(one),X_282),X_280))) )],[refute_0_1312,refute_0_1325]) ).
cnf(refute_0_1327,plain,
( composition(converse(X_280),join(converse(X_282),one)) != converse(composition(join(converse(one),X_282),X_280))
| converse(composition(join(converse(one),X_282),X_280)) != converse(composition(join(one,X_282),X_280))
| composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(one,X_282),X_280)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(converse(X_280),join(converse(X_282),one)))),bind(Y,$fot(converse(composition(join(converse(one),X_282),X_280)))),bind(Z,$fot(converse(composition(join(one,X_282),X_280))))]]) ).
cnf(refute_0_1328,plain,
( converse(composition(join(converse(one),X_282),X_280)) != converse(composition(join(one,X_282),X_280))
| composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(one,X_282),X_280)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_280),join(converse(X_282),one)),converse(composition(join(converse(one),X_282),X_280))) )],[refute_0_1326,refute_0_1327]) ).
cnf(refute_0_1329,plain,
composition(converse(X_280),join(converse(X_282),one)) = converse(composition(join(one,X_282),X_280)),
inference(resolve,[$cnf( $equal(converse(composition(join(converse(one),X_282),X_280)),converse(composition(join(one,X_282),X_280))) )],[refute_0_1304,refute_0_1328]) ).
cnf(refute_0_1330,plain,
( composition(converse(X_280),join(converse(X_282),one)) != converse(composition(join(one,X_282),X_280))
| converse(composition(join(X_282,one),X_280)) != composition(converse(X_280),join(converse(X_282),one))
| converse(composition(join(X_282,one),X_280)) = converse(composition(join(one,X_282),X_280)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_282,one),X_280)),composition(converse(X_280),join(converse(X_282),one))) ),[1],$fot(converse(composition(join(one,X_282),X_280)))]]) ).
cnf(refute_0_1331,plain,
( converse(composition(join(X_282,one),X_280)) != composition(converse(X_280),join(converse(X_282),one))
| converse(composition(join(X_282,one),X_280)) = converse(composition(join(one,X_282),X_280)) ),
inference(resolve,[$cnf( $equal(composition(converse(X_280),join(converse(X_282),one)),converse(composition(join(one,X_282),X_280))) )],[refute_0_1329,refute_0_1330]) ).
cnf(refute_0_1332,plain,
converse(composition(join(X_282,one),X_280)) = converse(composition(join(one,X_282),X_280)),
inference(resolve,[$cnf( $equal(converse(composition(join(X_282,one),X_280)),composition(converse(X_280),join(converse(X_282),one))) )],[refute_0_1292,refute_0_1331]) ).
cnf(refute_0_1333,plain,
converse(composition(join(X_409,one),X_408)) = converse(composition(join(one,X_409),X_408)),
inference(subst,[],[refute_0_1332:[bind(X_280,$fot(X_408)),bind(X_282,$fot(X_409))]]) ).
cnf(refute_0_1334,plain,
( converse(composition(join(X_409,one),X_408)) != converse(composition(join(one,X_409),X_408))
| converse(composition(join(one,X_409),X_408)) = converse(composition(join(X_409,one),X_408)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(composition(join(X_409,one),X_408)))),bind(Y,$fot(converse(composition(join(one,X_409),X_408))))]]) ).
cnf(refute_0_1335,plain,
converse(composition(join(one,X_409),X_408)) = converse(composition(join(X_409,one),X_408)),
inference(resolve,[$cnf( $equal(converse(composition(join(X_409,one),X_408)),converse(composition(join(one,X_409),X_408))) )],[refute_0_1333,refute_0_1334]) ).
cnf(refute_0_1336,plain,
( composition(join(one,X_409),X_408) != join(complement(converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| converse(composition(join(one,X_409),X_408)) != converse(composition(join(X_409,one),X_408))
| composition(join(one,X_409),X_408) = join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,X_409),X_408),join(complement(converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) ),[1,0,0,0,0],$fot(converse(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1337,plain,
( composition(join(one,X_409),X_408) != join(complement(converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| composition(join(one,X_409),X_408) = join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,X_409),X_408)),converse(composition(join(X_409,one),X_408))) )],[refute_0_1335,refute_0_1336]) ).
cnf(refute_0_1338,plain,
composition(join(one,X_409),X_408) = join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),
inference(resolve,[$cnf( $equal(composition(join(one,X_409),X_408),join(complement(converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) )],[refute_0_1283,refute_0_1337]) ).
cnf(refute_0_1339,plain,
join(zero,composition(join(X_409,one),X_408)) = composition(join(X_409,one),X_408),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1340,plain,
join(A,join(X_49,complement(converse(complement(converse(X_49)))))) = join(X_49,join(complement(converse(complement(converse(X_49)))),A)),
inference(subst,[],[refute_0_404:[bind(X_50,$fot(complement(converse(complement(converse(X_49))))))]]) ).
cnf(refute_0_1341,plain,
join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))),
inference(subst,[],[refute_0_756:[bind(B,$fot(complement(converse(complement(converse(X_375)))))),bind(C,$fot(meet(X_375,converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1342,plain,
X_375 = join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))),
inference(subst,[],[refute_0_1282:[bind(X_84,$fot(X_375))]]) ).
cnf(refute_0_1343,plain,
( X_375 != join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))
| join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))) = X_375 ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_375)),bind(Y,$fot(join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))))]]) ).
cnf(refute_0_1344,plain,
join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))) = X_375,
inference(resolve,[$cnf( $equal(X_375,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
( join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))
| join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))) != X_375
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = X_375 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),X_375) ),[0],$fot(join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1346,plain,
( join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = X_375 ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))),X_375) )],[refute_0_1344,refute_0_1345]) ).
cnf(refute_0_1347,plain,
join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = X_375,
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) )],[refute_0_1341,refute_0_1346]) ).
cnf(refute_0_1348,plain,
join(complement(converse(complement(converse(X_375)))),X_375) = join(X_375,complement(converse(complement(converse(X_375))))),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_375)),bind(B,$fot(complement(converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1349,plain,
join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) = join(X_49,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),
inference(subst,[],[refute_0_404:[bind(A,$fot(meet(X_375,converse(complement(converse(X_375)))))),bind(X_50,$fot(complement(converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1350,plain,
( join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))) != X_375
| join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) != join(X_49,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))))
| join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) = join(X_49,X_375) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))),join(X_49,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))))) ),[1,1],$fot(X_375)]]) ).
cnf(refute_0_1351,plain,
( join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) != join(X_49,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))))
| join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) = join(X_49,X_375) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))),X_375) )],[refute_0_1344,refute_0_1350]) ).
cnf(refute_0_1352,plain,
join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) = join(X_49,X_375),
inference(resolve,[$cnf( $equal(join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))),join(X_49,join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375))))))) )],[refute_0_1349,refute_0_1351]) ).
cnf(refute_0_1353,plain,
join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) = join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375)))))),
inference(subst,[],[refute_0_877:[bind(X_198,$fot(complement(converse(complement(converse(X_375)))))),bind(X_199,$fot(meet(X_375,converse(complement(converse(X_375)))))),bind(X_200,$fot(X_49))]]) ).
cnf(refute_0_1354,plain,
( join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) != join(X_49,X_375)
| join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) != join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375))))))
| join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375)))))) = join(X_49,X_375) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))),join(X_49,X_375)) ),[0],$fot(join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375)))))))]]) ).
cnf(refute_0_1355,plain,
( join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))) != join(X_49,X_375)
| join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375)))))) = join(X_49,X_375) ),
inference(resolve,[$cnf( $equal(join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))),join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375))))))) )],[refute_0_1353,refute_0_1354]) ).
cnf(refute_0_1356,plain,
join(complement(converse(complement(converse(X_375)))),join(X_49,meet(X_375,converse(complement(converse(X_375)))))) = join(X_49,X_375),
inference(resolve,[$cnf( $equal(join(meet(X_375,converse(complement(converse(X_375)))),join(X_49,complement(converse(complement(converse(X_375)))))),join(X_49,X_375)) )],[refute_0_1352,refute_0_1355]) ).
cnf(refute_0_1357,plain,
join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = join(complement(converse(complement(converse(X_375)))),X_375),
inference(subst,[],[refute_0_1356:[bind(X_49,$fot(complement(converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1358,plain,
( join(complement(converse(complement(converse(X_375)))),X_375) != join(X_375,complement(converse(complement(converse(X_375)))))
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != join(complement(converse(complement(converse(X_375)))),X_375)
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = join(X_375,complement(converse(complement(converse(X_375))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))))),bind(Y,$fot(join(complement(converse(complement(converse(X_375)))),X_375))),bind(Z,$fot(join(X_375,complement(converse(complement(converse(X_375)))))))]]) ).
cnf(refute_0_1359,plain,
( join(complement(converse(complement(converse(X_375)))),X_375) != join(X_375,complement(converse(complement(converse(X_375)))))
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = join(X_375,complement(converse(complement(converse(X_375))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),join(complement(converse(complement(converse(X_375)))),X_375)) )],[refute_0_1357,refute_0_1358]) ).
cnf(refute_0_1360,plain,
join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) = join(X_375,complement(converse(complement(converse(X_375))))),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),X_375),join(X_375,complement(converse(complement(converse(X_375)))))) )],[refute_0_1348,refute_0_1359]) ).
cnf(refute_0_1361,plain,
( join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != X_375
| join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != join(X_375,complement(converse(complement(converse(X_375)))))
| join(X_375,complement(converse(complement(converse(X_375))))) = X_375 ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),X_375) ),[0],$fot(join(X_375,complement(converse(complement(converse(X_375))))))]]) ).
cnf(refute_0_1362,plain,
( join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))) != X_375
| join(X_375,complement(converse(complement(converse(X_375))))) = X_375 ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),join(X_375,complement(converse(complement(converse(X_375)))))) )],[refute_0_1360,refute_0_1361]) ).
cnf(refute_0_1363,plain,
join(X_375,complement(converse(complement(converse(X_375))))) = X_375,
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_375)))),join(complement(converse(complement(converse(X_375)))),meet(X_375,converse(complement(converse(X_375)))))),X_375) )],[refute_0_1347,refute_0_1362]) ).
cnf(refute_0_1364,plain,
join(X_49,complement(converse(complement(converse(X_49))))) = X_49,
inference(subst,[],[refute_0_1363:[bind(X_375,$fot(X_49))]]) ).
cnf(refute_0_1365,plain,
( join(A,join(X_49,complement(converse(complement(converse(X_49)))))) != join(X_49,join(complement(converse(complement(converse(X_49)))),A))
| join(X_49,complement(converse(complement(converse(X_49))))) != X_49
| join(A,X_49) = join(X_49,join(complement(converse(complement(converse(X_49)))),A)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(X_49,complement(converse(complement(converse(X_49)))))),join(X_49,join(complement(converse(complement(converse(X_49)))),A))) ),[0,1],$fot(X_49)]]) ).
cnf(refute_0_1366,plain,
( join(A,join(X_49,complement(converse(complement(converse(X_49)))))) != join(X_49,join(complement(converse(complement(converse(X_49)))),A))
| join(A,X_49) = join(X_49,join(complement(converse(complement(converse(X_49)))),A)) ),
inference(resolve,[$cnf( $equal(join(X_49,complement(converse(complement(converse(X_49))))),X_49) )],[refute_0_1364,refute_0_1365]) ).
cnf(refute_0_1367,plain,
join(A,X_49) = join(X_49,join(complement(converse(complement(converse(X_49)))),A)),
inference(resolve,[$cnf( $equal(join(A,join(X_49,complement(converse(complement(converse(X_49)))))),join(X_49,join(complement(converse(complement(converse(X_49)))),A))) )],[refute_0_1340,refute_0_1366]) ).
cnf(refute_0_1368,plain,
join(X_49,join(X_49,A)) = join(X_49,A),
inference(subst,[],[refute_0_756:[bind(B,$fot(X_49)),bind(C,$fot(A))]]) ).
cnf(refute_0_1369,plain,
complement(complement(X_49)) = X_49,
inference(subst,[],[refute_0_735:[bind(B,$fot(X_49))]]) ).
cnf(refute_0_1370,plain,
converse(converse(X_49)) = X_49,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_49))]]) ).
cnf(refute_0_1371,plain,
complement(converse(converse(X_49))) = complement(converse(converse(X_49))),
introduced(tautology,[refl,[$fot(complement(converse(converse(X_49))))]]) ).
cnf(refute_0_1372,plain,
( complement(converse(converse(X_49))) != complement(converse(converse(X_49)))
| converse(converse(X_49)) != X_49
| complement(converse(converse(X_49))) = complement(X_49) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(X_49))),complement(converse(converse(X_49)))) ),[1,0],$fot(X_49)]]) ).
cnf(refute_0_1373,plain,
( converse(converse(X_49)) != X_49
| complement(converse(converse(X_49))) = complement(X_49) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(X_49))),complement(converse(converse(X_49)))) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
complement(converse(converse(X_49))) = complement(X_49),
inference(resolve,[$cnf( $equal(converse(converse(X_49)),X_49) )],[refute_0_1370,refute_0_1373]) ).
cnf(refute_0_1375,plain,
converse(complement(converse(X_49))) = complement(converse(converse(X_49))),
inference(subst,[],[refute_0_1079:[bind(A,$fot(converse(X_49)))]]) ).
cnf(refute_0_1376,plain,
( complement(converse(converse(X_49))) != complement(X_49)
| converse(complement(converse(X_49))) != complement(converse(converse(X_49)))
| converse(complement(converse(X_49))) = complement(X_49) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(complement(converse(X_49))))),bind(Y,$fot(complement(converse(converse(X_49))))),bind(Z,$fot(complement(X_49)))]]) ).
cnf(refute_0_1377,plain,
( complement(converse(converse(X_49))) != complement(X_49)
| converse(complement(converse(X_49))) = complement(X_49) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_49))),complement(converse(converse(X_49)))) )],[refute_0_1375,refute_0_1376]) ).
cnf(refute_0_1378,plain,
converse(complement(converse(X_49))) = complement(X_49),
inference(resolve,[$cnf( $equal(complement(converse(converse(X_49))),complement(X_49)) )],[refute_0_1374,refute_0_1377]) ).
cnf(refute_0_1379,plain,
complement(converse(complement(converse(X_49)))) = complement(converse(complement(converse(X_49)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(converse(X_49)))))]]) ).
cnf(refute_0_1380,plain,
( complement(converse(complement(converse(X_49)))) != complement(converse(complement(converse(X_49))))
| converse(complement(converse(X_49))) != complement(X_49)
| complement(converse(complement(converse(X_49)))) = complement(complement(X_49)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(converse(X_49)))),complement(converse(complement(converse(X_49))))) ),[1,0],$fot(complement(X_49))]]) ).
cnf(refute_0_1381,plain,
( converse(complement(converse(X_49))) != complement(X_49)
| complement(converse(complement(converse(X_49)))) = complement(complement(X_49)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(X_49)))),complement(converse(complement(converse(X_49))))) )],[refute_0_1379,refute_0_1380]) ).
cnf(refute_0_1382,plain,
complement(converse(complement(converse(X_49)))) = complement(complement(X_49)),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_49))),complement(X_49)) )],[refute_0_1378,refute_0_1381]) ).
cnf(refute_0_1383,plain,
( complement(complement(X_49)) != X_49
| complement(converse(complement(converse(X_49)))) != complement(complement(X_49))
| complement(converse(complement(converse(X_49)))) = X_49 ),
inference(subst,[],[refute_0_58:[bind(X,$fot(complement(converse(complement(converse(X_49)))))),bind(Y,$fot(complement(complement(X_49)))),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_1384,plain,
( complement(complement(X_49)) != X_49
| complement(converse(complement(converse(X_49)))) = X_49 ),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(X_49)))),complement(complement(X_49))) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
complement(converse(complement(converse(X_49)))) = X_49,
inference(resolve,[$cnf( $equal(complement(complement(X_49)),X_49) )],[refute_0_1369,refute_0_1384]) ).
cnf(refute_0_1386,plain,
join(complement(converse(complement(converse(X_49)))),A) = join(complement(converse(complement(converse(X_49)))),A),
introduced(tautology,[refl,[$fot(join(complement(converse(complement(converse(X_49)))),A))]]) ).
cnf(refute_0_1387,plain,
( complement(converse(complement(converse(X_49)))) != X_49
| join(complement(converse(complement(converse(X_49)))),A) != join(complement(converse(complement(converse(X_49)))),A)
| join(complement(converse(complement(converse(X_49)))),A) = join(X_49,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(complement(converse(X_49)))),A),join(complement(converse(complement(converse(X_49)))),A)) ),[1,0],$fot(X_49)]]) ).
cnf(refute_0_1388,plain,
( complement(converse(complement(converse(X_49)))) != X_49
| join(complement(converse(complement(converse(X_49)))),A) = join(X_49,A) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_49)))),A),join(complement(converse(complement(converse(X_49)))),A)) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
join(complement(converse(complement(converse(X_49)))),A) = join(X_49,A),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(X_49)))),X_49) )],[refute_0_1385,refute_0_1388]) ).
cnf(refute_0_1390,plain,
join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,join(complement(converse(complement(converse(X_49)))),A)),
introduced(tautology,[refl,[$fot(join(X_49,join(complement(converse(complement(converse(X_49)))),A)))]]) ).
cnf(refute_0_1391,plain,
( join(X_49,join(complement(converse(complement(converse(X_49)))),A)) != join(X_49,join(complement(converse(complement(converse(X_49)))),A))
| join(complement(converse(complement(converse(X_49)))),A) != join(X_49,A)
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,join(X_49,A)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_49,join(complement(converse(complement(converse(X_49)))),A)),join(X_49,join(complement(converse(complement(converse(X_49)))),A))) ),[1,1],$fot(join(X_49,A))]]) ).
cnf(refute_0_1392,plain,
( join(complement(converse(complement(converse(X_49)))),A) != join(X_49,A)
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,join(X_49,A)) ),
inference(resolve,[$cnf( $equal(join(X_49,join(complement(converse(complement(converse(X_49)))),A)),join(X_49,join(complement(converse(complement(converse(X_49)))),A))) )],[refute_0_1390,refute_0_1391]) ).
cnf(refute_0_1393,plain,
join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,join(X_49,A)),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(X_49)))),A),join(X_49,A)) )],[refute_0_1389,refute_0_1392]) ).
cnf(refute_0_1394,plain,
( join(X_49,join(X_49,A)) != join(X_49,A)
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) != join(X_49,join(X_49,A))
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,A) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(X_49,join(complement(converse(complement(converse(X_49)))),A)))),bind(Y,$fot(join(X_49,join(X_49,A)))),bind(Z,$fot(join(X_49,A)))]]) ).
cnf(refute_0_1395,plain,
( join(X_49,join(X_49,A)) != join(X_49,A)
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,A) ),
inference(resolve,[$cnf( $equal(join(X_49,join(complement(converse(complement(converse(X_49)))),A)),join(X_49,join(X_49,A))) )],[refute_0_1393,refute_0_1394]) ).
cnf(refute_0_1396,plain,
join(X_49,join(complement(converse(complement(converse(X_49)))),A)) = join(X_49,A),
inference(resolve,[$cnf( $equal(join(X_49,join(X_49,A)),join(X_49,A)) )],[refute_0_1368,refute_0_1395]) ).
cnf(refute_0_1397,plain,
( join(A,X_49) != join(X_49,join(complement(converse(complement(converse(X_49)))),A))
| join(X_49,join(complement(converse(complement(converse(X_49)))),A)) != join(X_49,A)
| join(A,X_49) = join(X_49,A) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,X_49),join(X_49,A)) ),[0],$fot(join(X_49,join(complement(converse(complement(converse(X_49)))),A)))]]) ).
cnf(refute_0_1398,plain,
( join(A,X_49) != join(X_49,join(complement(converse(complement(converse(X_49)))),A))
| join(A,X_49) = join(X_49,A) ),
inference(resolve,[$cnf( $equal(join(X_49,join(complement(converse(complement(converse(X_49)))),A)),join(X_49,A)) )],[refute_0_1396,refute_0_1397]) ).
cnf(refute_0_1399,plain,
join(A,X_49) = join(X_49,A),
inference(resolve,[$cnf( $equal(join(A,X_49),join(X_49,join(complement(converse(complement(converse(X_49)))),A))) )],[refute_0_1367,refute_0_1398]) ).
cnf(refute_0_1400,plain,
( join(A,X_49) != join(X_49,A)
| join(X_49,A) = join(A,X_49) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,X_49))),bind(Y,$fot(join(X_49,A)))]]) ).
cnf(refute_0_1401,plain,
join(X_49,A) = join(A,X_49),
inference(resolve,[$cnf( $equal(join(A,X_49),join(X_49,A)) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
join(composition(join(X_409,one),X_408),zero) = join(zero,composition(join(X_409,one),X_408)),
inference(subst,[],[refute_0_1401:[bind(A,$fot(zero)),bind(X_49,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1403,plain,
( join(composition(join(X_409,one),X_408),zero) != join(zero,composition(join(X_409,one),X_408))
| join(zero,composition(join(X_409,one),X_408)) != composition(join(X_409,one),X_408)
| join(composition(join(X_409,one),X_408),zero) = composition(join(X_409,one),X_408) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(composition(join(X_409,one),X_408),zero))),bind(Y,$fot(join(zero,composition(join(X_409,one),X_408)))),bind(Z,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1404,plain,
( join(zero,composition(join(X_409,one),X_408)) != composition(join(X_409,one),X_408)
| join(composition(join(X_409,one),X_408),zero) = composition(join(X_409,one),X_408) ),
inference(resolve,[$cnf( $equal(join(composition(join(X_409,one),X_408),zero),join(zero,composition(join(X_409,one),X_408))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
join(composition(join(X_409,one),X_408),zero) = composition(join(X_409,one),X_408),
inference(resolve,[$cnf( $equal(join(zero,composition(join(X_409,one),X_408)),composition(join(X_409,one),X_408)) )],[refute_0_1339,refute_0_1404]) ).
cnf(refute_0_1406,plain,
meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))) = zero,
inference(subst,[],[refute_0_1219:[bind(A,$fot(composition(join(one,X_409),X_408)))]]) ).
cnf(refute_0_1407,plain,
converse(converse(composition(join(one,X_409),X_408))) = composition(join(one,X_409),X_408),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(join(one,X_409),X_408)))]]) ).
cnf(refute_0_1408,plain,
complement(converse(converse(composition(join(one,X_409),X_408)))) = complement(converse(converse(composition(join(one,X_409),X_408)))),
introduced(tautology,[refl,[$fot(complement(converse(converse(composition(join(one,X_409),X_408)))))]]) ).
cnf(refute_0_1409,plain,
( complement(converse(converse(composition(join(one,X_409),X_408)))) != complement(converse(converse(composition(join(one,X_409),X_408))))
| converse(converse(composition(join(one,X_409),X_408))) != composition(join(one,X_409),X_408)
| complement(converse(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(composition(join(one,X_409),X_408)))),complement(converse(converse(composition(join(one,X_409),X_408))))) ),[1,0],$fot(composition(join(one,X_409),X_408))]]) ).
cnf(refute_0_1410,plain,
( converse(converse(composition(join(one,X_409),X_408))) != composition(join(one,X_409),X_408)
| complement(converse(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(join(one,X_409),X_408)))),complement(converse(converse(composition(join(one,X_409),X_408))))) )],[refute_0_1408,refute_0_1409]) ).
cnf(refute_0_1411,plain,
complement(converse(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)),
inference(resolve,[$cnf( $equal(converse(converse(composition(join(one,X_409),X_408))),composition(join(one,X_409),X_408)) )],[refute_0_1407,refute_0_1410]) ).
cnf(refute_0_1412,plain,
converse(complement(converse(composition(join(one,X_409),X_408)))) = complement(converse(converse(composition(join(one,X_409),X_408)))),
inference(subst,[],[refute_0_1079:[bind(A,$fot(converse(composition(join(one,X_409),X_408))))]]) ).
cnf(refute_0_1413,plain,
( complement(converse(converse(composition(join(one,X_409),X_408)))) != complement(composition(join(one,X_409),X_408))
| converse(complement(converse(composition(join(one,X_409),X_408)))) != complement(converse(converse(composition(join(one,X_409),X_408))))
| converse(complement(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(complement(converse(composition(join(one,X_409),X_408)))))),bind(Y,$fot(complement(converse(converse(composition(join(one,X_409),X_408)))))),bind(Z,$fot(complement(composition(join(one,X_409),X_408))))]]) ).
cnf(refute_0_1414,plain,
( complement(converse(converse(composition(join(one,X_409),X_408)))) != complement(composition(join(one,X_409),X_408))
| converse(complement(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(join(one,X_409),X_408)))),complement(converse(converse(composition(join(one,X_409),X_408))))) )],[refute_0_1412,refute_0_1413]) ).
cnf(refute_0_1415,plain,
converse(complement(converse(composition(join(one,X_409),X_408)))) = complement(composition(join(one,X_409),X_408)),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(join(one,X_409),X_408)))),complement(composition(join(one,X_409),X_408))) )],[refute_0_1411,refute_0_1414]) ).
cnf(refute_0_1416,plain,
meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))),
introduced(tautology,[refl,[$fot(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))]]) ).
cnf(refute_0_1417,plain,
( converse(complement(converse(composition(join(one,X_409),X_408)))) != complement(composition(join(one,X_409),X_408))
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) != meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) ),[1,1],$fot(complement(composition(join(one,X_409),X_408)))]]) ).
cnf(refute_0_1418,plain,
( converse(complement(converse(composition(join(one,X_409),X_408)))) != complement(composition(join(one,X_409),X_408))
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))) ),
inference(resolve,[$cnf( $equal(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) )],[refute_0_1416,refute_0_1417]) ).
cnf(refute_0_1419,plain,
meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(join(one,X_409),X_408)))),complement(composition(join(one,X_409),X_408))) )],[refute_0_1415,refute_0_1418]) ).
cnf(refute_0_1420,plain,
( meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))) != zero
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) != meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408)))
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = zero ),
inference(subst,[],[refute_0_58:[bind(X,$fot(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))),bind(Y,$fot(meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_1421,plain,
( meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))) != zero
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = zero ),
inference(resolve,[$cnf( $equal(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))),meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408)))) )],[refute_0_1419,refute_0_1420]) ).
cnf(refute_0_1422,plain,
meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) = zero,
inference(resolve,[$cnf( $equal(meet(composition(join(one,X_409),X_408),complement(composition(join(one,X_409),X_408))),zero) )],[refute_0_1406,refute_0_1421]) ).
cnf(refute_0_1423,plain,
join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),
introduced(tautology,[refl,[$fot(join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))]]) ).
cnf(refute_0_1424,plain,
( join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) != zero
| join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1425,plain,
( meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))) != zero
| join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero) ),
inference(resolve,[$cnf( $equal(join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) )],[refute_0_1423,refute_0_1424]) ).
cnf(refute_0_1426,plain,
join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero),
inference(resolve,[$cnf( $equal(meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))),zero) )],[refute_0_1422,refute_0_1425]) ).
cnf(refute_0_1427,plain,
complement(complement(composition(join(X_409,one),X_408))) = composition(join(X_409,one),X_408),
inference(subst,[],[refute_0_735:[bind(B,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1428,plain,
converse(converse(composition(join(X_409,one),X_408))) = composition(join(X_409,one),X_408),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1429,plain,
complement(converse(converse(composition(join(X_409,one),X_408)))) = complement(converse(converse(composition(join(X_409,one),X_408)))),
introduced(tautology,[refl,[$fot(complement(converse(converse(composition(join(X_409,one),X_408)))))]]) ).
cnf(refute_0_1430,plain,
( complement(converse(converse(composition(join(X_409,one),X_408)))) != complement(converse(converse(composition(join(X_409,one),X_408))))
| converse(converse(composition(join(X_409,one),X_408))) != composition(join(X_409,one),X_408)
| complement(converse(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(composition(join(X_409,one),X_408)))),complement(converse(converse(composition(join(X_409,one),X_408))))) ),[1,0],$fot(composition(join(X_409,one),X_408))]]) ).
cnf(refute_0_1431,plain,
( converse(converse(composition(join(X_409,one),X_408))) != composition(join(X_409,one),X_408)
| complement(converse(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(join(X_409,one),X_408)))),complement(converse(converse(composition(join(X_409,one),X_408))))) )],[refute_0_1429,refute_0_1430]) ).
cnf(refute_0_1432,plain,
complement(converse(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)),
inference(resolve,[$cnf( $equal(converse(converse(composition(join(X_409,one),X_408))),composition(join(X_409,one),X_408)) )],[refute_0_1428,refute_0_1431]) ).
cnf(refute_0_1433,plain,
converse(complement(converse(composition(join(X_409,one),X_408)))) = complement(converse(converse(composition(join(X_409,one),X_408)))),
inference(subst,[],[refute_0_1079:[bind(A,$fot(converse(composition(join(X_409,one),X_408))))]]) ).
cnf(refute_0_1434,plain,
( complement(converse(converse(composition(join(X_409,one),X_408)))) != complement(composition(join(X_409,one),X_408))
| converse(complement(converse(composition(join(X_409,one),X_408)))) != complement(converse(converse(composition(join(X_409,one),X_408))))
| converse(complement(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(complement(converse(composition(join(X_409,one),X_408)))))),bind(Y,$fot(complement(converse(converse(composition(join(X_409,one),X_408)))))),bind(Z,$fot(complement(composition(join(X_409,one),X_408))))]]) ).
cnf(refute_0_1435,plain,
( complement(converse(converse(composition(join(X_409,one),X_408)))) != complement(composition(join(X_409,one),X_408))
| converse(complement(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(join(X_409,one),X_408)))),complement(converse(converse(composition(join(X_409,one),X_408))))) )],[refute_0_1433,refute_0_1434]) ).
cnf(refute_0_1436,plain,
converse(complement(converse(composition(join(X_409,one),X_408)))) = complement(composition(join(X_409,one),X_408)),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(join(X_409,one),X_408)))),complement(composition(join(X_409,one),X_408))) )],[refute_0_1432,refute_0_1435]) ).
cnf(refute_0_1437,plain,
complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = complement(converse(complement(converse(composition(join(X_409,one),X_408))))),
introduced(tautology,[refl,[$fot(complement(converse(complement(converse(composition(join(X_409,one),X_408))))))]]) ).
cnf(refute_0_1438,plain,
( complement(converse(complement(converse(composition(join(X_409,one),X_408))))) != complement(converse(complement(converse(composition(join(X_409,one),X_408)))))
| converse(complement(converse(composition(join(X_409,one),X_408)))) != complement(composition(join(X_409,one),X_408))
| complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = complement(complement(composition(join(X_409,one),X_408))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),complement(converse(complement(converse(composition(join(X_409,one),X_408)))))) ),[1,0],$fot(complement(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1439,plain,
( converse(complement(converse(composition(join(X_409,one),X_408)))) != complement(composition(join(X_409,one),X_408))
| complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = complement(complement(composition(join(X_409,one),X_408))) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),complement(converse(complement(converse(composition(join(X_409,one),X_408)))))) )],[refute_0_1437,refute_0_1438]) ).
cnf(refute_0_1440,plain,
complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = complement(complement(composition(join(X_409,one),X_408))),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(join(X_409,one),X_408)))),complement(composition(join(X_409,one),X_408))) )],[refute_0_1436,refute_0_1439]) ).
cnf(refute_0_1441,plain,
( complement(complement(composition(join(X_409,one),X_408))) != composition(join(X_409,one),X_408)
| complement(converse(complement(converse(composition(join(X_409,one),X_408))))) != complement(complement(composition(join(X_409,one),X_408)))
| complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = composition(join(X_409,one),X_408) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(complement(converse(complement(converse(composition(join(X_409,one),X_408))))))),bind(Y,$fot(complement(complement(composition(join(X_409,one),X_408))))),bind(Z,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1442,plain,
( complement(complement(composition(join(X_409,one),X_408))) != composition(join(X_409,one),X_408)
| complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = composition(join(X_409,one),X_408) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),complement(complement(composition(join(X_409,one),X_408)))) )],[refute_0_1440,refute_0_1441]) ).
cnf(refute_0_1443,plain,
complement(converse(complement(converse(composition(join(X_409,one),X_408))))) = composition(join(X_409,one),X_408),
inference(resolve,[$cnf( $equal(complement(complement(composition(join(X_409,one),X_408))),composition(join(X_409,one),X_408)) )],[refute_0_1427,refute_0_1442]) ).
cnf(refute_0_1444,plain,
join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),
introduced(tautology,[refl,[$fot(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))]]) ).
cnf(refute_0_1445,plain,
( complement(converse(complement(converse(composition(join(X_409,one),X_408))))) != composition(join(X_409,one),X_408)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) ),[1,0],$fot(composition(join(X_409,one),X_408))]]) ).
cnf(refute_0_1446,plain,
( complement(converse(complement(converse(composition(join(X_409,one),X_408))))) != composition(join(X_409,one),X_408)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) )],[refute_0_1444,refute_0_1445]) ).
cnf(refute_0_1447,plain,
join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),
inference(resolve,[$cnf( $equal(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),composition(join(X_409,one),X_408)) )],[refute_0_1443,refute_0_1446]) ).
cnf(refute_0_1448,plain,
( join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(composition(join(X_409,one),X_408),zero)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))),bind(Y,$fot(join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))),bind(Z,$fot(join(composition(join(X_409,one),X_408),zero)))]]) ).
cnf(refute_0_1449,plain,
( join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(composition(join(X_409,one),X_408),zero)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) )],[refute_0_1447,refute_0_1448]) ).
cnf(refute_0_1450,plain,
join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = join(composition(join(X_409,one),X_408),zero),
inference(resolve,[$cnf( $equal(join(composition(join(X_409,one),X_408),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(composition(join(X_409,one),X_408),zero)) )],[refute_0_1426,refute_0_1449]) ).
cnf(refute_0_1451,plain,
( join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != join(composition(join(X_409,one),X_408),zero)
| join(composition(join(X_409,one),X_408),zero) != composition(join(X_409,one),X_408)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = composition(join(X_409,one),X_408) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))),bind(Y,$fot(join(composition(join(X_409,one),X_408),zero))),bind(Z,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1452,plain,
( join(composition(join(X_409,one),X_408),zero) != composition(join(X_409,one),X_408)
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = composition(join(X_409,one),X_408) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),join(composition(join(X_409,one),X_408),zero)) )],[refute_0_1450,refute_0_1451]) ).
cnf(refute_0_1453,plain,
join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) = composition(join(X_409,one),X_408),
inference(resolve,[$cnf( $equal(join(composition(join(X_409,one),X_408),zero),composition(join(X_409,one),X_408)) )],[refute_0_1405,refute_0_1452]) ).
cnf(refute_0_1454,plain,
( composition(join(one,X_409),X_408) != join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))) != composition(join(X_409,one),X_408)
| composition(join(one,X_409),X_408) = composition(join(X_409,one),X_408) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_409),X_408),composition(join(X_409,one),X_408)) ),[0],$fot(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))))]]) ).
cnf(refute_0_1455,plain,
( composition(join(one,X_409),X_408) != join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))
| composition(join(one,X_409),X_408) = composition(join(X_409,one),X_408) ),
inference(resolve,[$cnf( $equal(join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408)))))),composition(join(X_409,one),X_408)) )],[refute_0_1453,refute_0_1454]) ).
cnf(refute_0_1456,plain,
composition(join(one,X_409),X_408) = composition(join(X_409,one),X_408),
inference(resolve,[$cnf( $equal(composition(join(one,X_409),X_408),join(complement(converse(complement(converse(composition(join(X_409,one),X_408))))),meet(composition(join(one,X_409),X_408),converse(complement(converse(composition(join(one,X_409),X_408))))))) )],[refute_0_1338,refute_0_1455]) ).
cnf(refute_0_1457,plain,
( composition(join(one,X_409),X_408) != composition(join(X_409,one),X_408)
| composition(join(X_409,one),X_408) = composition(join(one,X_409),X_408) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(one,X_409),X_408))),bind(Y,$fot(composition(join(X_409,one),X_408)))]]) ).
cnf(refute_0_1458,plain,
composition(join(X_409,one),X_408) = composition(join(one,X_409),X_408),
inference(resolve,[$cnf( $equal(composition(join(one,X_409),X_408),composition(join(X_409,one),X_408)) )],[refute_0_1456,refute_0_1457]) ).
cnf(refute_0_1459,plain,
composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))) = composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),
inference(subst,[],[refute_0_1458:[bind(X_408,$fot(complement(complement(one)))),bind(X_409,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1460,plain,
join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))),
inference(subst,[],[refute_0_857:[bind(X_122,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))),bind(X_124,$fot(complement(complement(one))))]]) ).
cnf(refute_0_1461,plain,
( composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))) != composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))))),bind(Y,$fot(composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))))),bind(Z,$fot(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))))]]) ).
cnf(refute_0_1462,plain,
( composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))) != composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))),composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one)))) )],[refute_0_1460,refute_0_1461]) ).
cnf(refute_0_1463,plain,
join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),
inference(resolve,[$cnf( $equal(composition(join(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one),complement(complement(one))),composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))) )],[refute_0_1459,refute_0_1462]) ).
cnf(refute_0_1464,plain,
( composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))))),bind(Y,$fot(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))))),bind(Z,$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))))]]) ).
cnf(refute_0_1465,plain,
( composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))),composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one)))) )],[refute_0_1463,refute_0_1464]) ).
cnf(refute_0_1466,plain,
join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) = converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),complement(complement(one))),converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) )],[refute_0_1123,refute_0_1465]) ).
cnf(refute_0_1467,plain,
( join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))),complement(complement(one))) ),[0],$fot(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))))]]) ).
cnf(refute_0_1468,plain,
( join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != complement(complement(one))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))),converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) )],[refute_0_1466,refute_0_1467]) ).
cnf(refute_0_1469,plain,
( complement(complement(one)) != one
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) != complement(complement(one))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = one ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1470,plain,
( converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) != complement(complement(one))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_1100,refute_0_1469]) ).
cnf(refute_0_1471,plain,
( join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))) != complement(complement(one))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = one ),
inference(resolve,[$cnf( $equal(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one))) )],[refute_0_1468,refute_0_1470]) ).
cnf(refute_0_1472,plain,
converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) = one,
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),complement(complement(one)))),complement(complement(one))) )],[refute_0_1098,refute_0_1471]) ).
cnf(refute_0_1473,plain,
( converse(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) != one
| converse(one) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),[0,0],$fot(one)]]) ).
cnf(refute_0_1474,plain,
( converse(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| converse(one) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
inference(resolve,[$cnf( $equal(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))),one) )],[refute_0_1472,refute_0_1473]) ).
cnf(refute_0_1475,plain,
converse(one) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
inference(resolve,[$cnf( $equal(converse(converse(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_0,refute_0_1474]) ).
cnf(refute_0_1476,plain,
( converse(one) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| converse(one) != one
| one = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(one),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),[0],$fot(one)]]) ).
cnf(refute_0_1477,plain,
( converse(one) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| one = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_1476]) ).
cnf(refute_0_1478,plain,
one = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
inference(resolve,[$cnf( $equal(converse(one),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_1475,refute_0_1477]) ).
cnf(refute_0_1479,plain,
composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = join(composition(X_122,X_124),composition(converse(complement(composition(X_124,top))),X_124)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_122)),bind(B,$fot(converse(complement(composition(X_124,top))))),bind(C,$fot(X_124))]]) ).
cnf(refute_0_1480,plain,
( composition(converse(complement(composition(X_124,top))),X_124) != zero
| composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) != join(composition(X_122,X_124),composition(converse(complement(composition(X_124,top))),X_124))
| composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = join(composition(X_122,X_124),zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_122,converse(complement(composition(X_124,top)))),X_124),join(composition(X_122,X_124),composition(converse(complement(composition(X_124,top))),X_124))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_1481,plain,
( composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) != join(composition(X_122,X_124),composition(converse(complement(composition(X_124,top))),X_124))
| composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = join(composition(X_122,X_124),zero) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(X_124,top))),X_124),zero) )],[refute_0_823,refute_0_1480]) ).
cnf(refute_0_1482,plain,
composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = join(composition(X_122,X_124),zero),
inference(resolve,[$cnf( $equal(composition(join(X_122,converse(complement(composition(X_124,top)))),X_124),join(composition(X_122,X_124),composition(converse(complement(composition(X_124,top))),X_124))) )],[refute_0_1479,refute_0_1481]) ).
cnf(refute_0_1483,plain,
join(join(zero,X_53),zero) = join(zero,join(zero,X_53)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(zero,X_53))),bind(B,$fot(zero))]]) ).
cnf(refute_0_1484,plain,
join(zero,join(zero,X_53)) = join(zero,X_53),
inference(subst,[],[refute_0_147:[bind(X_51,$fot(X_53))]]) ).
cnf(refute_0_1485,plain,
( join(join(zero,X_53),zero) != join(zero,join(zero,X_53))
| join(zero,join(zero,X_53)) != join(zero,X_53)
| join(join(zero,X_53),zero) = join(zero,X_53) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(zero,X_53),zero),join(zero,X_53)) ),[0],$fot(join(zero,join(zero,X_53)))]]) ).
cnf(refute_0_1486,plain,
( join(join(zero,X_53),zero) != join(zero,join(zero,X_53))
| join(join(zero,X_53),zero) = join(zero,X_53) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_53)),join(zero,X_53)) )],[refute_0_1484,refute_0_1485]) ).
cnf(refute_0_1487,plain,
join(join(zero,X_53),zero) = join(zero,X_53),
inference(resolve,[$cnf( $equal(join(join(zero,X_53),zero),join(zero,join(zero,X_53))) )],[refute_0_1483,refute_0_1486]) ).
cnf(refute_0_1488,plain,
join(join(zero,X_53),zero) = join(zero,join(X_53,zero)),
inference(subst,[],[refute_0_180:[bind(A,$fot(zero)),bind(B,$fot(X_53)),bind(C,$fot(zero))]]) ).
cnf(refute_0_1489,plain,
( join(join(zero,X_53),zero) != join(zero,X_53)
| join(join(zero,X_53),zero) != join(zero,join(X_53,zero))
| join(zero,join(X_53,zero)) = join(zero,X_53) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_53),zero),join(zero,X_53)) ),[0],$fot(join(zero,join(X_53,zero)))]]) ).
cnf(refute_0_1490,plain,
( join(join(zero,X_53),zero) != join(zero,X_53)
| join(zero,join(X_53,zero)) = join(zero,X_53) ),
inference(resolve,[$cnf( $equal(join(join(zero,X_53),zero),join(zero,join(X_53,zero))) )],[refute_0_1488,refute_0_1489]) ).
cnf(refute_0_1491,plain,
join(zero,join(X_53,zero)) = join(zero,X_53),
inference(resolve,[$cnf( $equal(join(join(zero,X_53),zero),join(zero,X_53)) )],[refute_0_1487,refute_0_1490]) ).
cnf(refute_0_1492,plain,
join(zero,join(meet(X_76,top),zero)) = join(zero,meet(X_76,top)),
inference(subst,[],[refute_0_1491:[bind(X_53,$fot(meet(X_76,top)))]]) ).
cnf(refute_0_1493,plain,
( join(zero,join(meet(X_76,top),zero)) != join(zero,meet(X_76,top))
| join(zero,meet(X_76,top)) != X_76
| join(zero,join(meet(X_76,top),zero)) = X_76 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,join(meet(X_76,top),zero)),X_76) ),[0],$fot(join(zero,meet(X_76,top)))]]) ).
cnf(refute_0_1494,plain,
( join(zero,join(meet(X_76,top),zero)) != join(zero,meet(X_76,top))
| join(zero,join(meet(X_76,top),zero)) = X_76 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_76,top)),X_76) )],[refute_0_232,refute_0_1493]) ).
cnf(refute_0_1495,plain,
join(zero,join(meet(X_76,top),zero)) = X_76,
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_76,top),zero)),join(zero,meet(X_76,top))) )],[refute_0_1492,refute_0_1494]) ).
cnf(refute_0_1496,plain,
join(zero,join(meet(X_76,top),C)) = join(join(zero,meet(X_76,top)),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(meet(X_76,top)))]]) ).
cnf(refute_0_1497,plain,
( join(zero,join(meet(X_76,top),C)) != join(join(zero,meet(X_76,top)),C)
| join(zero,meet(X_76,top)) != X_76
| join(zero,join(meet(X_76,top),C)) = join(X_76,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_76,top),C)),join(join(zero,meet(X_76,top)),C)) ),[1,0],$fot(X_76)]]) ).
cnf(refute_0_1498,plain,
( join(zero,join(meet(X_76,top),C)) != join(join(zero,meet(X_76,top)),C)
| join(zero,join(meet(X_76,top),C)) = join(X_76,C) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_76,top)),X_76) )],[refute_0_232,refute_0_1497]) ).
cnf(refute_0_1499,plain,
join(zero,join(meet(X_76,top),C)) = join(X_76,C),
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_76,top),C)),join(join(zero,meet(X_76,top)),C)) )],[refute_0_1496,refute_0_1498]) ).
cnf(refute_0_1500,plain,
join(zero,join(meet(X_76,top),zero)) = join(X_76,zero),
inference(subst,[],[refute_0_1499:[bind(C,$fot(zero))]]) ).
cnf(refute_0_1501,plain,
( join(zero,join(meet(X_76,top),zero)) != X_76
| join(zero,join(meet(X_76,top),zero)) != join(X_76,zero)
| join(X_76,zero) = X_76 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_76,top),zero)),X_76) ),[0],$fot(join(X_76,zero))]]) ).
cnf(refute_0_1502,plain,
( join(zero,join(meet(X_76,top),zero)) != X_76
| join(X_76,zero) = X_76 ),
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_76,top),zero)),join(X_76,zero)) )],[refute_0_1500,refute_0_1501]) ).
cnf(refute_0_1503,plain,
join(X_76,zero) = X_76,
inference(resolve,[$cnf( $equal(join(zero,join(meet(X_76,top),zero)),X_76) )],[refute_0_1495,refute_0_1502]) ).
cnf(refute_0_1504,plain,
join(composition(X_122,X_124),zero) = composition(X_122,X_124),
inference(subst,[],[refute_0_1503:[bind(X_76,$fot(composition(X_122,X_124)))]]) ).
cnf(refute_0_1505,plain,
( composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) != join(composition(X_122,X_124),zero)
| join(composition(X_122,X_124),zero) != composition(X_122,X_124)
| composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = composition(X_122,X_124) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_122,converse(complement(composition(X_124,top)))),X_124),composition(X_122,X_124)) ),[0],$fot(join(composition(X_122,X_124),zero))]]) ).
cnf(refute_0_1506,plain,
( composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) != join(composition(X_122,X_124),zero)
| composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = composition(X_122,X_124) ),
inference(resolve,[$cnf( $equal(join(composition(X_122,X_124),zero),composition(X_122,X_124)) )],[refute_0_1504,refute_0_1505]) ).
cnf(refute_0_1507,plain,
composition(join(X_122,converse(complement(composition(X_124,top)))),X_124) = composition(X_122,X_124),
inference(resolve,[$cnf( $equal(composition(join(X_122,converse(complement(composition(X_124,top)))),X_124),join(composition(X_122,X_124),zero)) )],[refute_0_1482,refute_0_1506]) ).
cnf(refute_0_1508,plain,
composition(join(converse(A),converse(complement(composition(X_388,top)))),X_388) = composition(converse(A),X_388),
inference(subst,[],[refute_0_1507:[bind(X_122,$fot(converse(A))),bind(X_124,$fot(X_388))]]) ).
cnf(refute_0_1509,plain,
converse(join(A,complement(composition(X_388,top)))) = join(converse(A),converse(complement(composition(X_388,top)))),
inference(subst,[],[converse_additivity_9:[bind(B,$fot(complement(composition(X_388,top))))]]) ).
cnf(refute_0_1510,plain,
( converse(join(A,complement(composition(X_388,top)))) != join(converse(A),converse(complement(composition(X_388,top))))
| join(converse(A),converse(complement(composition(X_388,top)))) = converse(join(A,complement(composition(X_388,top)))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(converse(join(A,complement(composition(X_388,top)))))),bind(Y,$fot(join(converse(A),converse(complement(composition(X_388,top))))))]]) ).
cnf(refute_0_1511,plain,
join(converse(A),converse(complement(composition(X_388,top)))) = converse(join(A,complement(composition(X_388,top)))),
inference(resolve,[$cnf( $equal(converse(join(A,complement(composition(X_388,top)))),join(converse(A),converse(complement(composition(X_388,top))))) )],[refute_0_1509,refute_0_1510]) ).
cnf(refute_0_1512,plain,
( composition(join(converse(A),converse(complement(composition(X_388,top)))),X_388) != composition(converse(A),X_388)
| join(converse(A),converse(complement(composition(X_388,top)))) != converse(join(A,complement(composition(X_388,top))))
| composition(converse(join(A,complement(composition(X_388,top)))),X_388) = composition(converse(A),X_388) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(A),converse(complement(composition(X_388,top)))),X_388),composition(converse(A),X_388)) ),[0,0],$fot(converse(join(A,complement(composition(X_388,top)))))]]) ).
cnf(refute_0_1513,plain,
( composition(join(converse(A),converse(complement(composition(X_388,top)))),X_388) != composition(converse(A),X_388)
| composition(converse(join(A,complement(composition(X_388,top)))),X_388) = composition(converse(A),X_388) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(complement(composition(X_388,top)))),converse(join(A,complement(composition(X_388,top))))) )],[refute_0_1511,refute_0_1512]) ).
cnf(refute_0_1514,plain,
composition(converse(join(A,complement(composition(X_388,top)))),X_388) = composition(converse(A),X_388),
inference(resolve,[$cnf( $equal(composition(join(converse(A),converse(complement(composition(X_388,top)))),X_388),composition(converse(A),X_388)) )],[refute_0_1508,refute_0_1513]) ).
cnf(refute_0_1515,plain,
composition(converse(join(sk1,complement(composition(sk1,top)))),sk1) = composition(converse(sk1),sk1),
inference(subst,[],[refute_0_1514:[bind(A,$fot(sk1)),bind(X_388,$fot(sk1))]]) ).
cnf(refute_0_1516,plain,
complement(composition(sk1,complement(one))) = join(complement(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
inference(subst,[],[refute_0_1162:[bind(B,$fot(composition(sk1,complement(one)))),bind(X_75,$fot(complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1517,plain,
complement(sk1) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(sk1),composition(sk1,complement(one)))),
inference(subst,[],[refute_0_1162:[bind(B,$fot(sk1)),bind(X_75,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1518,plain,
composition(sk1,complement(one)) = join(meet(sk1,composition(sk1,complement(one))),meet(composition(sk1,complement(one)),complement(sk1))),
inference(subst,[],[refute_0_975:[bind(X_74,$fot(composition(sk1,complement(one)))),bind(X_75,$fot(sk1))]]) ).
cnf(refute_0_1519,plain,
( composition(sk1,complement(one)) != join(meet(sk1,composition(sk1,complement(one))),meet(composition(sk1,complement(one)),complement(sk1)))
| meet(sk1,composition(sk1,complement(one))) != zero
| composition(sk1,complement(one)) = join(zero,meet(composition(sk1,complement(one)),complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(sk1,complement(one)),join(meet(sk1,composition(sk1,complement(one))),meet(composition(sk1,complement(one)),complement(sk1)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1520,plain,
( composition(sk1,complement(one)) != join(meet(sk1,composition(sk1,complement(one))),meet(composition(sk1,complement(one)),complement(sk1)))
| composition(sk1,complement(one)) = join(zero,meet(composition(sk1,complement(one)),complement(sk1))) ),
inference(resolve,[$cnf( $equal(meet(sk1,composition(sk1,complement(one))),zero) )],[refute_0_254,refute_0_1519]) ).
cnf(refute_0_1521,plain,
composition(sk1,complement(one)) = join(zero,meet(composition(sk1,complement(one)),complement(sk1))),
inference(resolve,[$cnf( $equal(composition(sk1,complement(one)),join(meet(sk1,composition(sk1,complement(one))),meet(composition(sk1,complement(one)),complement(sk1)))) )],[refute_0_1518,refute_0_1520]) ).
cnf(refute_0_1522,plain,
meet(composition(sk1,complement(one)),complement(sk1)) = meet(complement(sk1),composition(sk1,complement(one))),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(complement(sk1))),bind(X_28,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1523,plain,
join(zero,meet(composition(sk1,complement(one)),complement(sk1))) = meet(composition(sk1,complement(one)),complement(sk1)),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(composition(sk1,complement(one)),complement(sk1))))]]) ).
cnf(refute_0_1524,plain,
( join(zero,meet(composition(sk1,complement(one)),complement(sk1))) != meet(composition(sk1,complement(one)),complement(sk1))
| meet(composition(sk1,complement(one)),complement(sk1)) != meet(complement(sk1),composition(sk1,complement(one)))
| join(zero,meet(composition(sk1,complement(one)),complement(sk1))) = meet(complement(sk1),composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(zero,meet(composition(sk1,complement(one)),complement(sk1))))),bind(Y,$fot(meet(composition(sk1,complement(one)),complement(sk1)))),bind(Z,$fot(meet(complement(sk1),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1525,plain,
( meet(composition(sk1,complement(one)),complement(sk1)) != meet(complement(sk1),composition(sk1,complement(one)))
| join(zero,meet(composition(sk1,complement(one)),complement(sk1))) = meet(complement(sk1),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(composition(sk1,complement(one)),complement(sk1))),meet(composition(sk1,complement(one)),complement(sk1))) )],[refute_0_1523,refute_0_1524]) ).
cnf(refute_0_1526,plain,
join(zero,meet(composition(sk1,complement(one)),complement(sk1))) = meet(complement(sk1),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(meet(composition(sk1,complement(one)),complement(sk1)),meet(complement(sk1),composition(sk1,complement(one)))) )],[refute_0_1522,refute_0_1525]) ).
cnf(refute_0_1527,plain,
( composition(sk1,complement(one)) != join(zero,meet(composition(sk1,complement(one)),complement(sk1)))
| join(zero,meet(composition(sk1,complement(one)),complement(sk1))) != meet(complement(sk1),composition(sk1,complement(one)))
| composition(sk1,complement(one)) = meet(complement(sk1),composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(sk1,complement(one)),meet(complement(sk1),composition(sk1,complement(one)))) ),[0],$fot(join(zero,meet(composition(sk1,complement(one)),complement(sk1))))]]) ).
cnf(refute_0_1528,plain,
( composition(sk1,complement(one)) != join(zero,meet(composition(sk1,complement(one)),complement(sk1)))
| composition(sk1,complement(one)) = meet(complement(sk1),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(composition(sk1,complement(one)),complement(sk1))),meet(complement(sk1),composition(sk1,complement(one)))) )],[refute_0_1526,refute_0_1527]) ).
cnf(refute_0_1529,plain,
composition(sk1,complement(one)) = meet(complement(sk1),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(composition(sk1,complement(one)),join(zero,meet(composition(sk1,complement(one)),complement(sk1)))) )],[refute_0_1521,refute_0_1528]) ).
cnf(refute_0_1530,plain,
( composition(sk1,complement(one)) != meet(complement(sk1),composition(sk1,complement(one)))
| meet(complement(sk1),composition(sk1,complement(one))) = composition(sk1,complement(one)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(sk1,complement(one)))),bind(Y,$fot(meet(complement(sk1),composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1531,plain,
meet(complement(sk1),composition(sk1,complement(one))) = composition(sk1,complement(one)),
inference(resolve,[$cnf( $equal(composition(sk1,complement(one)),meet(complement(sk1),composition(sk1,complement(one)))) )],[refute_0_1529,refute_0_1530]) ).
cnf(refute_0_1532,plain,
( complement(sk1) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(sk1),composition(sk1,complement(one))))
| meet(complement(sk1),composition(sk1,complement(one))) != composition(sk1,complement(one))
| complement(sk1) = join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(sk1),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(sk1),composition(sk1,complement(one))))) ),[1,1],$fot(composition(sk1,complement(one)))]]) ).
cnf(refute_0_1533,plain,
( complement(sk1) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(sk1),composition(sk1,complement(one))))
| complement(sk1) = join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(meet(complement(sk1),composition(sk1,complement(one))),composition(sk1,complement(one))) )],[refute_0_1531,refute_0_1532]) ).
cnf(refute_0_1534,plain,
complement(sk1) = join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(complement(sk1),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(sk1),composition(sk1,complement(one))))) )],[refute_0_1517,refute_0_1533]) ).
cnf(refute_0_1535,plain,
join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))) = join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))),
inference(subst,[],[refute_0_5:[bind(A,$fot(composition(sk1,complement(one)))),bind(B,$fot(complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1536,plain,
( complement(sk1) != join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one)))
| join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))) != join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))
| complement(sk1) = join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(sk1),join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))) ),[0],$fot(join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))))]]) ).
cnf(refute_0_1537,plain,
( complement(sk1) != join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one)))
| complement(sk1) = join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))),join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1535,refute_0_1536]) ).
cnf(refute_0_1538,plain,
complement(sk1) = join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(complement(sk1),join(complement(join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one)))) )],[refute_0_1534,refute_0_1537]) ).
cnf(refute_0_1539,plain,
( complement(sk1) != join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))
| join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))) = complement(sk1) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(sk1))),bind(Y,$fot(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1540,plain,
join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))) = complement(sk1),
inference(resolve,[$cnf( $equal(complement(sk1),join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1538,refute_0_1539]) ).
cnf(refute_0_1541,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))) != complement(sk1)
| complement(composition(sk1,complement(one))) = join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) ),[1,0,0],$fot(complement(sk1))]]) ).
cnf(refute_0_1542,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one))))),complement(sk1)) )],[refute_0_1540,refute_0_1541]) ).
cnf(refute_0_1543,plain,
complement(composition(sk1,complement(one))) = join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(composition(sk1,complement(one)),complement(join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1516,refute_0_1542]) ).
cnf(refute_0_1544,plain,
complement(complement(sk1)) = sk1,
inference(subst,[],[refute_0_735:[bind(B,$fot(sk1))]]) ).
cnf(refute_0_1545,plain,
join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
introduced(tautology,[refl,[$fot(join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1546,plain,
( complement(complement(sk1)) != sk1
| join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_1547,plain,
( complement(complement(sk1)) != sk1
| join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1545,refute_0_1546]) ).
cnf(refute_0_1548,plain,
join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
inference(resolve,[$cnf( $equal(complement(complement(sk1)),sk1) )],[refute_0_1544,refute_0_1547]) ).
cnf(refute_0_1549,plain,
( complement(composition(sk1,complement(one))) != join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,complement(one))),join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) ),[0],$fot(join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1550,plain,
( complement(composition(sk1,complement(one))) != join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1548,refute_0_1549]) ).
cnf(refute_0_1551,plain,
complement(composition(sk1,complement(one))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(complement(sk1)),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1543,refute_0_1550]) ).
cnf(refute_0_1552,plain,
meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) = complement(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))),
inference(subst,[],[refute_0_733:[bind(B,$fot(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1553,plain,
join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)),
inference(subst,[],[refute_0_756:[bind(B,$fot(complement(join(X_348,X_349)))),bind(C,$fot(meet(complement(X_348),X_349)))]]) ).
cnf(refute_0_1554,plain,
complement(X_348) = join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)),
inference(subst,[],[refute_0_1162:[bind(B,$fot(X_348)),bind(X_75,$fot(X_349))]]) ).
cnf(refute_0_1555,plain,
( complement(X_348) != join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))
| join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)) = complement(X_348) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(X_348))),bind(Y,$fot(join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))))]]) ).
cnf(refute_0_1556,plain,
join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)) = complement(X_348),
inference(resolve,[$cnf( $equal(complement(X_348),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) )],[refute_0_1554,refute_0_1555]) ).
cnf(refute_0_1557,plain,
( join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))
| join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)) != complement(X_348)
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(X_348) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),complement(X_348)) ),[0],$fot(join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)))]]) ).
cnf(refute_0_1558,plain,
( join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(X_348) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)),complement(X_348)) )],[refute_0_1556,refute_0_1557]) ).
cnf(refute_0_1559,plain,
join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(X_348),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) )],[refute_0_1553,refute_0_1558]) ).
cnf(refute_0_1560,plain,
meet(join(X_348,X_349),X_348) = meet(X_348,join(X_348,X_349)),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(X_348)),bind(X_28,$fot(join(X_348,X_349)))]]) ).
cnf(refute_0_1561,plain,
complement(meet(join(X_348,X_349),X_348)) = complement(meet(join(X_348,X_349),X_348)),
introduced(tautology,[refl,[$fot(complement(meet(join(X_348,X_349),X_348)))]]) ).
cnf(refute_0_1562,plain,
( complement(meet(join(X_348,X_349),X_348)) != complement(meet(join(X_348,X_349),X_348))
| meet(join(X_348,X_349),X_348) != meet(X_348,join(X_348,X_349))
| complement(meet(join(X_348,X_349),X_348)) = complement(meet(X_348,join(X_348,X_349))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(join(X_348,X_349),X_348)),complement(meet(join(X_348,X_349),X_348))) ),[1,0],$fot(meet(X_348,join(X_348,X_349)))]]) ).
cnf(refute_0_1563,plain,
( meet(join(X_348,X_349),X_348) != meet(X_348,join(X_348,X_349))
| complement(meet(join(X_348,X_349),X_348)) = complement(meet(X_348,join(X_348,X_349))) ),
inference(resolve,[$cnf( $equal(complement(meet(join(X_348,X_349),X_348)),complement(meet(join(X_348,X_349),X_348))) )],[refute_0_1561,refute_0_1562]) ).
cnf(refute_0_1564,plain,
complement(meet(join(X_348,X_349),X_348)) = complement(meet(X_348,join(X_348,X_349))),
inference(resolve,[$cnf( $equal(meet(join(X_348,X_349),X_348),meet(X_348,join(X_348,X_349))) )],[refute_0_1560,refute_0_1563]) ).
cnf(refute_0_1565,plain,
join(complement(A),complement(B)) = join(meet(join(complement(A),complement(B)),X_75),complement(join(complement(join(complement(A),complement(B))),X_75))),
inference(subst,[],[refute_0_165:[bind(A,$fot(join(complement(A),complement(B)))),bind(B,$fot(X_75))]]) ).
cnf(refute_0_1566,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(meet(join(complement(A),complement(B)),X_75),complement(join(complement(join(complement(A),complement(B))),X_75)))
| join(complement(A),complement(B)) = join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(meet(join(complement(A),complement(B)),X_75),complement(join(complement(join(complement(A),complement(B))),X_75)))) ),[1,1,0,0],$fot(meet(A,B))]]) ).
cnf(refute_0_1567,plain,
( join(complement(A),complement(B)) != join(meet(join(complement(A),complement(B)),X_75),complement(join(complement(join(complement(A),complement(B))),X_75)))
| join(complement(A),complement(B)) = join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_155,refute_0_1566]) ).
cnf(refute_0_1568,plain,
join(complement(A),complement(B)) = join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(meet(join(complement(A),complement(B)),X_75),complement(join(complement(join(complement(A),complement(B))),X_75)))) )],[refute_0_1565,refute_0_1567]) ).
cnf(refute_0_1569,plain,
meet(join(complement(A),complement(B)),X_75) = complement(join(meet(A,B),complement(X_75))),
inference(subst,[],[refute_0_55:[bind(B,$fot(X_75)),bind(X_27,$fot(A)),bind(X_28,$fot(B))]]) ).
cnf(refute_0_1570,plain,
join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) = join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)),
introduced(tautology,[refl,[$fot(join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)))]]) ).
cnf(refute_0_1571,plain,
( join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) != join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75))
| meet(join(complement(A),complement(B)),X_75) != complement(join(meet(A,B),complement(X_75)))
| join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)),join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75))) ),[1,1],$fot(complement(join(meet(A,B),complement(X_75))))]]) ).
cnf(refute_0_1572,plain,
( meet(join(complement(A),complement(B)),X_75) != complement(join(meet(A,B),complement(X_75)))
| join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)),join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75))) )],[refute_0_1570,refute_0_1571]) ).
cnf(refute_0_1573,plain,
join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),
inference(resolve,[$cnf( $equal(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),complement(X_75)))) )],[refute_0_1569,refute_0_1572]) ).
cnf(refute_0_1574,plain,
join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) = join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(join(meet(A,B),X_75)))),bind(B,$fot(meet(join(complement(A),complement(B)),X_75)))]]) ).
cnf(refute_0_1575,plain,
( join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) != join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75))
| join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))))),bind(Y,$fot(join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)))),bind(Z,$fot(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))))]]) ).
cnf(refute_0_1576,plain,
( join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))),join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75))) )],[refute_0_1574,refute_0_1575]) ).
cnf(refute_0_1577,plain,
join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),
inference(resolve,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),meet(join(complement(A),complement(B)),X_75)),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) )],[refute_0_1573,refute_0_1576]) ).
cnf(refute_0_1578,plain,
( join(complement(A),complement(B)) != join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75)))
| join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) ),[0],$fot(join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))))]]) ).
cnf(refute_0_1579,plain,
( join(complement(A),complement(B)) != join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75)))
| join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) ),
inference(resolve,[$cnf( $equal(join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75))),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) )],[refute_0_1577,refute_0_1578]) ).
cnf(refute_0_1580,plain,
join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(meet(join(complement(A),complement(B)),X_75),complement(join(meet(A,B),X_75)))) )],[refute_0_1568,refute_0_1579]) ).
cnf(refute_0_1581,plain,
meet(join(zero,complement(X_32)),B) = complement(join(complement(join(zero,complement(X_32))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(zero,complement(X_32))))]]) ).
cnf(refute_0_1582,plain,
( complement(join(zero,complement(X_32))) != meet(top,X_32)
| meet(join(zero,complement(X_32)),B) != complement(join(complement(join(zero,complement(X_32))),complement(B)))
| meet(join(zero,complement(X_32)),B) = complement(join(meet(top,X_32),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_32)),B),complement(join(complement(join(zero,complement(X_32))),complement(B)))) ),[1,0,0],$fot(meet(top,X_32))]]) ).
cnf(refute_0_1583,plain,
( meet(join(zero,complement(X_32)),B) != complement(join(complement(join(zero,complement(X_32))),complement(B)))
| meet(join(zero,complement(X_32)),B) = complement(join(meet(top,X_32),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_32))),meet(top,X_32)) )],[refute_0_942,refute_0_1582]) ).
cnf(refute_0_1584,plain,
meet(join(zero,complement(X_32)),B) = complement(join(meet(top,X_32),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_32)),B),complement(join(complement(join(zero,complement(X_32))),complement(B)))) )],[refute_0_1581,refute_0_1583]) ).
cnf(refute_0_1585,plain,
meet(join(zero,complement(X_32)),B) = meet(join(zero,complement(X_32)),B),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(X_32)),B))]]) ).
cnf(refute_0_1586,plain,
( join(zero,complement(X_32)) != complement(X_32)
| meet(join(zero,complement(X_32)),B) != meet(join(zero,complement(X_32)),B)
| meet(join(zero,complement(X_32)),B) = meet(complement(X_32),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_32)),B),meet(join(zero,complement(X_32)),B)) ),[1,0],$fot(complement(X_32))]]) ).
cnf(refute_0_1587,plain,
( join(zero,complement(X_32)) != complement(X_32)
| meet(join(zero,complement(X_32)),B) = meet(complement(X_32),B) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_32)),B),meet(join(zero,complement(X_32)),B)) )],[refute_0_1585,refute_0_1586]) ).
cnf(refute_0_1588,plain,
meet(join(zero,complement(X_32)),B) = meet(complement(X_32),B),
inference(resolve,[$cnf( $equal(join(zero,complement(X_32)),complement(X_32)) )],[refute_0_946,refute_0_1587]) ).
cnf(refute_0_1589,plain,
( meet(join(zero,complement(X_32)),B) != complement(join(meet(top,X_32),complement(B)))
| meet(join(zero,complement(X_32)),B) != meet(complement(X_32),B)
| meet(complement(X_32),B) = complement(join(meet(top,X_32),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_32)),B),complement(join(meet(top,X_32),complement(B)))) ),[0],$fot(meet(complement(X_32),B))]]) ).
cnf(refute_0_1590,plain,
( meet(join(zero,complement(X_32)),B) != complement(join(meet(top,X_32),complement(B)))
| meet(complement(X_32),B) = complement(join(meet(top,X_32),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_32)),B),meet(complement(X_32),B)) )],[refute_0_1588,refute_0_1589]) ).
cnf(refute_0_1591,plain,
join(meet(top,X_32),complement(B)) = join(meet(top,X_32),complement(B)),
introduced(tautology,[refl,[$fot(join(meet(top,X_32),complement(B)))]]) ).
cnf(refute_0_1592,plain,
( join(meet(top,X_32),complement(B)) != join(meet(top,X_32),complement(B))
| meet(top,X_32) != X_32
| join(meet(top,X_32),complement(B)) = join(X_32,complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_32),complement(B)),join(meet(top,X_32),complement(B))) ),[1,0],$fot(X_32)]]) ).
cnf(refute_0_1593,plain,
( meet(top,X_32) != X_32
| join(meet(top,X_32),complement(B)) = join(X_32,complement(B)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_32),complement(B)),join(meet(top,X_32),complement(B))) )],[refute_0_1591,refute_0_1592]) ).
cnf(refute_0_1594,plain,
join(meet(top,X_32),complement(B)) = join(X_32,complement(B)),
inference(resolve,[$cnf( $equal(meet(top,X_32),X_32) )],[refute_0_953,refute_0_1593]) ).
cnf(refute_0_1595,plain,
complement(join(meet(top,X_32),complement(B))) = complement(join(meet(top,X_32),complement(B))),
introduced(tautology,[refl,[$fot(complement(join(meet(top,X_32),complement(B))))]]) ).
cnf(refute_0_1596,plain,
( complement(join(meet(top,X_32),complement(B))) != complement(join(meet(top,X_32),complement(B)))
| join(meet(top,X_32),complement(B)) != join(X_32,complement(B))
| complement(join(meet(top,X_32),complement(B))) = complement(join(X_32,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,X_32),complement(B))),complement(join(meet(top,X_32),complement(B)))) ),[1,0],$fot(join(X_32,complement(B)))]]) ).
cnf(refute_0_1597,plain,
( join(meet(top,X_32),complement(B)) != join(X_32,complement(B))
| complement(join(meet(top,X_32),complement(B))) = complement(join(X_32,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_32),complement(B))),complement(join(meet(top,X_32),complement(B)))) )],[refute_0_1595,refute_0_1596]) ).
cnf(refute_0_1598,plain,
complement(join(meet(top,X_32),complement(B))) = complement(join(X_32,complement(B))),
inference(resolve,[$cnf( $equal(join(meet(top,X_32),complement(B)),join(X_32,complement(B))) )],[refute_0_1594,refute_0_1597]) ).
cnf(refute_0_1599,plain,
( complement(join(meet(top,X_32),complement(B))) != complement(join(X_32,complement(B)))
| meet(complement(X_32),B) != complement(join(meet(top,X_32),complement(B)))
| meet(complement(X_32),B) = complement(join(X_32,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_32),B),complement(join(meet(top,X_32),complement(B)))) ),[1],$fot(complement(join(X_32,complement(B))))]]) ).
cnf(refute_0_1600,plain,
( meet(complement(X_32),B) != complement(join(meet(top,X_32),complement(B)))
| meet(complement(X_32),B) = complement(join(X_32,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_32),complement(B))),complement(join(X_32,complement(B)))) )],[refute_0_1598,refute_0_1599]) ).
cnf(refute_0_1601,plain,
( meet(join(zero,complement(X_32)),B) != complement(join(meet(top,X_32),complement(B)))
| meet(complement(X_32),B) = complement(join(X_32,complement(B))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_32),B),complement(join(meet(top,X_32),complement(B)))) )],[refute_0_1590,refute_0_1600]) ).
cnf(refute_0_1602,plain,
meet(complement(X_32),B) = complement(join(X_32,complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_32)),B),complement(join(meet(top,X_32),complement(B)))) )],[refute_0_1584,refute_0_1601]) ).
cnf(refute_0_1603,plain,
( meet(complement(X_32),B) != complement(join(X_32,complement(B)))
| complement(join(X_32,complement(B))) = meet(complement(X_32),B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(complement(X_32),B))),bind(Y,$fot(complement(join(X_32,complement(B)))))]]) ).
cnf(refute_0_1604,plain,
complement(join(X_32,complement(B))) = meet(complement(X_32),B),
inference(resolve,[$cnf( $equal(meet(complement(X_32),B),complement(join(X_32,complement(B)))) )],[refute_0_1602,refute_0_1603]) ).
cnf(refute_0_1605,plain,
complement(join(meet(A,B),complement(X_75))) = meet(complement(meet(A,B)),X_75),
inference(subst,[],[refute_0_1604:[bind(B,$fot(X_75)),bind(X_32,$fot(meet(A,B)))]]) ).
cnf(refute_0_1606,plain,
join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) = join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),
introduced(tautology,[refl,[$fot(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))))]]) ).
cnf(refute_0_1607,plain,
( complement(join(meet(A,B),complement(X_75))) != meet(complement(meet(A,B)),X_75)
| join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) ),[1,1],$fot(meet(complement(meet(A,B)),X_75))]]) ).
cnf(refute_0_1608,plain,
( complement(join(meet(A,B),complement(X_75))) != meet(complement(meet(A,B)),X_75)
| join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) )],[refute_0_1606,refute_0_1607]) ).
cnf(refute_0_1609,plain,
join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)),
inference(resolve,[$cnf( $equal(complement(join(meet(A,B),complement(X_75))),meet(complement(meet(A,B)),X_75)) )],[refute_0_1605,refute_0_1608]) ).
cnf(refute_0_1610,plain,
( join(complement(A),complement(B)) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))) != join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))
| join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))) ),[0],$fot(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))))]]) ).
cnf(refute_0_1611,plain,
( join(complement(A),complement(B)) != join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))
| join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75)))),join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))) )],[refute_0_1609,refute_0_1610]) ).
cnf(refute_0_1612,plain,
join(complement(A),complement(B)) = join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(complement(join(meet(A,B),X_75)),complement(join(meet(A,B),complement(X_75))))) )],[refute_0_1580,refute_0_1611]) ).
cnf(refute_0_1613,plain,
( complement(B) != join(complement(join(B,X_75)),meet(complement(B),X_75))
| join(complement(join(B,X_75)),meet(complement(B),X_75)) = complement(B) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(B))),bind(Y,$fot(join(complement(join(B,X_75)),meet(complement(B),X_75))))]]) ).
cnf(refute_0_1614,plain,
join(complement(join(B,X_75)),meet(complement(B),X_75)) = complement(B),
inference(resolve,[$cnf( $equal(complement(B),join(complement(join(B,X_75)),meet(complement(B),X_75))) )],[refute_0_1162,refute_0_1613]) ).
cnf(refute_0_1615,plain,
join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) = complement(meet(A,B)),
inference(subst,[],[refute_0_1614:[bind(B,$fot(meet(A,B)))]]) ).
cnf(refute_0_1616,plain,
( join(complement(A),complement(B)) != join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))
| join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)))]]) ).
cnf(refute_0_1617,plain,
( join(complement(A),complement(B)) != join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75)),complement(meet(A,B))) )],[refute_0_1615,refute_0_1616]) ).
cnf(refute_0_1618,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(complement(join(meet(A,B),X_75)),meet(complement(meet(A,B)),X_75))) )],[refute_0_1612,refute_0_1617]) ).
cnf(refute_0_1619,plain,
join(complement(join(X_348,X_349)),complement(X_348)) = complement(meet(join(X_348,X_349),X_348)),
inference(subst,[],[refute_0_1618:[bind(A,$fot(join(X_348,X_349))),bind(B,$fot(X_348))]]) ).
cnf(refute_0_1620,plain,
join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) = join(X_49,join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),
inference(subst,[],[refute_0_404:[bind(A,$fot(meet(complement(X_348),X_349))),bind(X_50,$fot(complement(join(X_348,X_349))))]]) ).
cnf(refute_0_1621,plain,
( join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)) != complement(X_348)
| join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) != join(X_49,join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)))
| join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) = join(X_49,complement(X_348)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))),join(X_49,join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)))) ),[1,1],$fot(complement(X_348))]]) ).
cnf(refute_0_1622,plain,
( join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) != join(X_49,join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)))
| join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) = join(X_49,complement(X_348)) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)),complement(X_348)) )],[refute_0_1556,refute_0_1621]) ).
cnf(refute_0_1623,plain,
join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) = join(X_49,complement(X_348)),
inference(resolve,[$cnf( $equal(join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))),join(X_49,join(complement(join(X_348,X_349)),meet(complement(X_348),X_349)))) )],[refute_0_1620,refute_0_1622]) ).
cnf(refute_0_1624,plain,
join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) = join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349))),
inference(subst,[],[refute_0_877:[bind(X_198,$fot(complement(join(X_348,X_349)))),bind(X_199,$fot(meet(complement(X_348),X_349))),bind(X_200,$fot(X_49))]]) ).
cnf(refute_0_1625,plain,
( join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) != join(X_49,complement(X_348))
| join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) != join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349)))
| join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349))) = join(X_49,complement(X_348)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))),join(X_49,complement(X_348))) ),[0],$fot(join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349))))]]) ).
cnf(refute_0_1626,plain,
( join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))) != join(X_49,complement(X_348))
| join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349))) = join(X_49,complement(X_348)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))),join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349)))) )],[refute_0_1624,refute_0_1625]) ).
cnf(refute_0_1627,plain,
join(complement(join(X_348,X_349)),join(X_49,meet(complement(X_348),X_349))) = join(X_49,complement(X_348)),
inference(resolve,[$cnf( $equal(join(meet(complement(X_348),X_349),join(X_49,complement(join(X_348,X_349)))),join(X_49,complement(X_348))) )],[refute_0_1623,refute_0_1626]) ).
cnf(refute_0_1628,plain,
join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = join(complement(join(X_348,X_349)),complement(X_348)),
inference(subst,[],[refute_0_1627:[bind(X_49,$fot(complement(join(X_348,X_349))))]]) ).
cnf(refute_0_1629,plain,
( join(complement(join(X_348,X_349)),complement(X_348)) != complement(meet(join(X_348,X_349),X_348))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != join(complement(join(X_348,X_349)),complement(X_348))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(join(X_348,X_349),X_348)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))))),bind(Y,$fot(join(complement(join(X_348,X_349)),complement(X_348)))),bind(Z,$fot(complement(meet(join(X_348,X_349),X_348))))]]) ).
cnf(refute_0_1630,plain,
( join(complement(join(X_348,X_349)),complement(X_348)) != complement(meet(join(X_348,X_349),X_348))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(join(X_348,X_349),X_348)) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),join(complement(join(X_348,X_349)),complement(X_348))) )],[refute_0_1628,refute_0_1629]) ).
cnf(refute_0_1631,plain,
join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(join(X_348,X_349),X_348)),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),complement(X_348)),complement(meet(join(X_348,X_349),X_348))) )],[refute_0_1619,refute_0_1630]) ).
cnf(refute_0_1632,plain,
( complement(meet(join(X_348,X_349),X_348)) != complement(meet(X_348,join(X_348,X_349)))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != complement(meet(join(X_348,X_349),X_348))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(X_348,join(X_348,X_349))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))))),bind(Y,$fot(complement(meet(join(X_348,X_349),X_348)))),bind(Z,$fot(complement(meet(X_348,join(X_348,X_349)))))]]) ).
cnf(refute_0_1633,plain,
( complement(meet(join(X_348,X_349),X_348)) != complement(meet(X_348,join(X_348,X_349)))
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(X_348,join(X_348,X_349))) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),complement(meet(join(X_348,X_349),X_348))) )],[refute_0_1631,refute_0_1632]) ).
cnf(refute_0_1634,plain,
join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) = complement(meet(X_348,join(X_348,X_349))),
inference(resolve,[$cnf( $equal(complement(meet(join(X_348,X_349),X_348)),complement(meet(X_348,join(X_348,X_349)))) )],[refute_0_1564,refute_0_1633]) ).
cnf(refute_0_1635,plain,
( join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != complement(X_348)
| join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != complement(meet(X_348,join(X_348,X_349)))
| complement(meet(X_348,join(X_348,X_349))) = complement(X_348) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),complement(X_348)) ),[0],$fot(complement(meet(X_348,join(X_348,X_349))))]]) ).
cnf(refute_0_1636,plain,
( join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))) != complement(X_348)
| complement(meet(X_348,join(X_348,X_349))) = complement(X_348) ),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),complement(meet(X_348,join(X_348,X_349)))) )],[refute_0_1634,refute_0_1635]) ).
cnf(refute_0_1637,plain,
complement(meet(X_348,join(X_348,X_349))) = complement(X_348),
inference(resolve,[$cnf( $equal(join(complement(join(X_348,X_349)),join(complement(join(X_348,X_349)),meet(complement(X_348),X_349))),complement(X_348)) )],[refute_0_1559,refute_0_1636]) ).
cnf(refute_0_1638,plain,
complement(meet(complement(join(sk1,composition(sk1,complement(one)))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) = complement(complement(join(sk1,composition(sk1,complement(one))))),
inference(subst,[],[refute_0_1637:[bind(X_348,$fot(complement(join(sk1,composition(sk1,complement(one)))))),bind(X_349,$fot(meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1639,plain,
complement(composition(sk1,complement(one))) = join(complement(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),
inference(subst,[],[refute_0_1162:[bind(B,$fot(composition(sk1,complement(one)))),bind(X_75,$fot(meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1640,plain,
join(sk1,composition(sk1,complement(one))) = join(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),
inference(subst,[],[refute_0_975:[bind(X_74,$fot(join(sk1,composition(sk1,complement(one))))),bind(X_75,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1641,plain,
X_74 = join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))))),
inference(subst,[],[refute_0_165:[bind(A,$fot(X_74)),bind(B,$fot(join(X_50,complement(join(complement(X_74),X_50)))))]]) ).
cnf(refute_0_1642,plain,
top = join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))),
inference(subst,[],[refute_0_173:[bind(X_49,$fot(complement(X_74)))]]) ).
cnf(refute_0_1643,plain,
( top != join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))
| join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))) = top ),
inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))))]]) ).
cnf(refute_0_1644,plain,
join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))) )],[refute_0_1642,refute_0_1643]) ).
cnf(refute_0_1645,plain,
( X_74 != join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))))
| join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))) != top
| X_74 = join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_74,join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_1646,plain,
( X_74 != join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))))
| X_74 = join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50)))),top) )],[refute_0_1644,refute_0_1645]) ).
cnf(refute_0_1647,plain,
X_74 = join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(join(complement(X_74),join(X_50,complement(join(complement(X_74),X_50))))))) )],[refute_0_1641,refute_0_1646]) ).
cnf(refute_0_1648,plain,
join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))]]) ).
cnf(refute_0_1649,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) != join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1650,plain,
( complement(top) != zero
| join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) )],[refute_0_1648,refute_0_1649]) ).
cnf(refute_0_1651,plain,
join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_66,refute_0_1650]) ).
cnf(refute_0_1652,plain,
join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) = join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),
inference(subst,[],[refute_0_5:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))]]) ).
cnf(refute_0_1653,plain,
( join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) != join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) != join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))),bind(Z,$fot(join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))))]]) ).
cnf(refute_0_1654,plain,
( join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) != join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)),join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) )],[refute_0_1652,refute_0_1653]) ).
cnf(refute_0_1655,plain,
join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) )],[refute_0_1651,refute_0_1654]) ).
cnf(refute_0_1656,plain,
( X_74 != join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top))
| join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)) != join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| X_74 = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) ),[0],$fot(join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)))]]) ).
cnf(refute_0_1657,plain,
( X_74 != join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top))
| X_74 = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top)),join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) )],[refute_0_1655,refute_0_1656]) ).
cnf(refute_0_1658,plain,
X_74 = join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),
inference(resolve,[$cnf( $equal(X_74,join(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),complement(top))) )],[refute_0_1647,refute_0_1657]) ).
cnf(refute_0_1659,plain,
complement(join(complement(X_74),X_50)) = meet(X_74,complement(X_50)),
inference(subst,[],[refute_0_967:[bind(A,$fot(X_74)),bind(X_32,$fot(X_50))]]) ).
cnf(refute_0_1660,plain,
join(X_50,complement(join(complement(X_74),X_50))) = join(X_50,complement(join(complement(X_74),X_50))),
introduced(tautology,[refl,[$fot(join(X_50,complement(join(complement(X_74),X_50))))]]) ).
cnf(refute_0_1661,plain,
( complement(join(complement(X_74),X_50)) != meet(X_74,complement(X_50))
| join(X_50,complement(join(complement(X_74),X_50))) != join(X_50,complement(join(complement(X_74),X_50)))
| join(X_50,complement(join(complement(X_74),X_50))) = join(X_50,meet(X_74,complement(X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_50,complement(join(complement(X_74),X_50))),join(X_50,complement(join(complement(X_74),X_50)))) ),[1,1],$fot(meet(X_74,complement(X_50)))]]) ).
cnf(refute_0_1662,plain,
( complement(join(complement(X_74),X_50)) != meet(X_74,complement(X_50))
| join(X_50,complement(join(complement(X_74),X_50))) = join(X_50,meet(X_74,complement(X_50))) ),
inference(resolve,[$cnf( $equal(join(X_50,complement(join(complement(X_74),X_50))),join(X_50,complement(join(complement(X_74),X_50)))) )],[refute_0_1660,refute_0_1661]) ).
cnf(refute_0_1663,plain,
join(X_50,complement(join(complement(X_74),X_50))) = join(X_50,meet(X_74,complement(X_50))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_74),X_50)),meet(X_74,complement(X_50))) )],[refute_0_1659,refute_0_1662]) ).
cnf(refute_0_1664,plain,
meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) = meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),
introduced(tautology,[refl,[$fot(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))]]) ).
cnf(refute_0_1665,plain,
( join(X_50,complement(join(complement(X_74),X_50))) != join(X_50,meet(X_74,complement(X_50)))
| meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) != meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))
| meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) ),[1,1],$fot(join(X_50,meet(X_74,complement(X_50))))]]) ).
cnf(refute_0_1666,plain,
( join(X_50,complement(join(complement(X_74),X_50))) != join(X_50,meet(X_74,complement(X_50)))
| meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
inference(resolve,[$cnf( $equal(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) )],[refute_0_1664,refute_0_1665]) ).
cnf(refute_0_1667,plain,
meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))),
inference(resolve,[$cnf( $equal(join(X_50,complement(join(complement(X_74),X_50))),join(X_50,meet(X_74,complement(X_50)))) )],[refute_0_1663,refute_0_1666]) ).
cnf(refute_0_1668,plain,
join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),
inference(subst,[],[refute_0_238:[bind(X_76,$fot(meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))]]) ).
cnf(refute_0_1669,plain,
( join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) != meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))
| meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) != meet(X_74,join(X_50,meet(X_74,complement(X_50))))
| join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))),bind(Y,$fot(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))),bind(Z,$fot(meet(X_74,join(X_50,meet(X_74,complement(X_50))))))]]) ).
cnf(refute_0_1670,plain,
( meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))) != meet(X_74,join(X_50,meet(X_74,complement(X_50))))
| join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) )],[refute_0_1668,refute_0_1669]) ).
cnf(refute_0_1671,plain,
join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) = meet(X_74,join(X_50,meet(X_74,complement(X_50)))),
inference(resolve,[$cnf( $equal(meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))),meet(X_74,join(X_50,meet(X_74,complement(X_50))))) )],[refute_0_1667,refute_0_1670]) ).
cnf(refute_0_1672,plain,
( X_74 != join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))) != meet(X_74,join(X_50,meet(X_74,complement(X_50))))
| X_74 = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_74,meet(X_74,join(X_50,meet(X_74,complement(X_50))))) ),[0],$fot(join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))))]]) ).
cnf(refute_0_1673,plain,
( X_74 != join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))
| X_74 = meet(X_74,join(X_50,meet(X_74,complement(X_50)))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50))))),meet(X_74,join(X_50,meet(X_74,complement(X_50))))) )],[refute_0_1671,refute_0_1672]) ).
cnf(refute_0_1674,plain,
X_74 = meet(X_74,join(X_50,meet(X_74,complement(X_50)))),
inference(resolve,[$cnf( $equal(X_74,join(zero,meet(X_74,join(X_50,complement(join(complement(X_74),X_50)))))) )],[refute_0_1658,refute_0_1673]) ).
cnf(refute_0_1675,plain,
X_101 = meet(X_101,join(X_100,meet(X_101,complement(X_100)))),
inference(subst,[],[refute_0_1674:[bind(X_50,$fot(X_100)),bind(X_74,$fot(X_101))]]) ).
cnf(refute_0_1676,plain,
meet(complement(X_100),X_101) = meet(X_101,complement(X_100)),
inference(subst,[],[refute_0_272:[bind(X_27,$fot(complement(X_100))),bind(X_28,$fot(X_101))]]) ).
cnf(refute_0_1677,plain,
( meet(complement(X_100),X_101) != meet(X_101,complement(X_100))
| meet(X_101,complement(X_100)) = meet(complement(X_100),X_101) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(meet(complement(X_100),X_101))),bind(Y,$fot(meet(X_101,complement(X_100))))]]) ).
cnf(refute_0_1678,plain,
meet(X_101,complement(X_100)) = meet(complement(X_100),X_101),
inference(resolve,[$cnf( $equal(meet(complement(X_100),X_101),meet(X_101,complement(X_100))) )],[refute_0_1676,refute_0_1677]) ).
cnf(refute_0_1679,plain,
( X_101 != meet(X_101,join(X_100,meet(X_101,complement(X_100))))
| meet(X_101,complement(X_100)) != meet(complement(X_100),X_101)
| X_101 = meet(X_101,join(X_100,meet(complement(X_100),X_101))) ),
introduced(tautology,[equality,[$cnf( $equal(X_101,meet(X_101,join(X_100,meet(X_101,complement(X_100))))) ),[1,1,1],$fot(meet(complement(X_100),X_101))]]) ).
cnf(refute_0_1680,plain,
( X_101 != meet(X_101,join(X_100,meet(X_101,complement(X_100))))
| X_101 = meet(X_101,join(X_100,meet(complement(X_100),X_101))) ),
inference(resolve,[$cnf( $equal(meet(X_101,complement(X_100)),meet(complement(X_100),X_101)) )],[refute_0_1678,refute_0_1679]) ).
cnf(refute_0_1681,plain,
X_101 = meet(X_101,join(X_100,meet(complement(X_100),X_101))),
inference(resolve,[$cnf( $equal(X_101,meet(X_101,join(X_100,meet(X_101,complement(X_100))))) )],[refute_0_1675,refute_0_1680]) ).
cnf(refute_0_1682,plain,
composition(sk1,complement(one)) = meet(composition(sk1,complement(one)),join(sk1,meet(complement(sk1),composition(sk1,complement(one))))),
inference(subst,[],[refute_0_1681:[bind(X_100,$fot(sk1)),bind(X_101,$fot(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1683,plain,
( composition(sk1,complement(one)) != meet(composition(sk1,complement(one)),join(sk1,meet(complement(sk1),composition(sk1,complement(one)))))
| meet(complement(sk1),composition(sk1,complement(one))) != composition(sk1,complement(one))
| composition(sk1,complement(one)) = meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(sk1,complement(one)),meet(composition(sk1,complement(one)),join(sk1,meet(complement(sk1),composition(sk1,complement(one)))))) ),[1,1,1],$fot(composition(sk1,complement(one)))]]) ).
cnf(refute_0_1684,plain,
( composition(sk1,complement(one)) != meet(composition(sk1,complement(one)),join(sk1,meet(complement(sk1),composition(sk1,complement(one)))))
| composition(sk1,complement(one)) = meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))) ),
inference(resolve,[$cnf( $equal(meet(complement(sk1),composition(sk1,complement(one))),composition(sk1,complement(one))) )],[refute_0_1531,refute_0_1683]) ).
cnf(refute_0_1685,plain,
composition(sk1,complement(one)) = meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),
inference(resolve,[$cnf( $equal(composition(sk1,complement(one)),meet(composition(sk1,complement(one)),join(sk1,meet(complement(sk1),composition(sk1,complement(one)))))) )],[refute_0_1682,refute_0_1684]) ).
cnf(refute_0_1686,plain,
( composition(sk1,complement(one)) != meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one))))
| meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))) = composition(sk1,complement(one)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(sk1,complement(one)))),bind(Y,$fot(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1687,plain,
meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))) = composition(sk1,complement(one)),
inference(resolve,[$cnf( $equal(composition(sk1,complement(one)),meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one))))) )],[refute_0_1685,refute_0_1686]) ).
cnf(refute_0_1688,plain,
( join(sk1,composition(sk1,complement(one))) != join(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))
| meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))) != composition(sk1,complement(one))
| join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),join(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) ),[1,0],$fot(composition(sk1,complement(one)))]]) ).
cnf(refute_0_1689,plain,
( join(sk1,composition(sk1,complement(one))) != join(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))
| join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),composition(sk1,complement(one))) )],[refute_0_1687,refute_0_1688]) ).
cnf(refute_0_1690,plain,
join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),join(meet(composition(sk1,complement(one)),join(sk1,composition(sk1,complement(one)))),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) )],[refute_0_1640,refute_0_1689]) ).
cnf(refute_0_1691,plain,
meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))) = meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(complement(composition(sk1,complement(one))))),bind(X_28,$fot(join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1692,plain,
join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) = join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),
introduced(tautology,[refl,[$fot(join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1693,plain,
( join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) != join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))
| meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))) != meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))
| join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) ),[1,1],$fot(meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1694,plain,
( meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))) != meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))
| join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) )],[refute_0_1692,refute_0_1693]) ).
cnf(refute_0_1695,plain,
join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) )],[refute_0_1691,refute_0_1694]) ).
cnf(refute_0_1696,plain,
( join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))) != join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))
| join(sk1,composition(sk1,complement(one))) != join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))
| join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) ),[1],$fot(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1697,plain,
( join(sk1,composition(sk1,complement(one))) != join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))
| join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one))))),join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1695,refute_0_1696]) ).
cnf(refute_0_1698,plain,
join(sk1,composition(sk1,complement(one))) = join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),join(composition(sk1,complement(one)),meet(join(sk1,composition(sk1,complement(one))),complement(composition(sk1,complement(one)))))) )],[refute_0_1690,refute_0_1697]) ).
cnf(refute_0_1699,plain,
( join(sk1,composition(sk1,complement(one))) != join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))
| join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) = join(sk1,composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(join(sk1,composition(sk1,complement(one))))),bind(Y,$fot(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1700,plain,
join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) = join(sk1,composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1698,refute_0_1699]) ).
cnf(refute_0_1701,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))
| join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) != join(sk1,composition(sk1,complement(one)))
| complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) ),[1,0,0],$fot(join(sk1,composition(sk1,complement(one))))]]) ).
cnf(refute_0_1702,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),join(sk1,composition(sk1,complement(one)))) )],[refute_0_1700,refute_0_1701]) ).
cnf(refute_0_1703,plain,
complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(composition(sk1,complement(one)),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1639,refute_0_1702]) ).
cnf(refute_0_1704,plain,
meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) = meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))),
inference(subst,[],[refute_0_1266:[bind(X_253,$fot(complement(composition(sk1,complement(one))))),bind(X_254,$fot(join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1705,plain,
join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),
introduced(tautology,[refl,[$fot(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1706,plain,
( join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))
| meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) != meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))
| join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) ),[1,1],$fot(meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1707,plain,
( meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) != meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))
| join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1705,refute_0_1706]) ).
cnf(refute_0_1708,plain,
join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) )],[refute_0_1704,refute_0_1707]) ).
cnf(refute_0_1709,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))
| join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))
| complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,complement(one))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) ),[0],$fot(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1710,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1708,refute_0_1709]) ).
cnf(refute_0_1711,plain,
complement(composition(sk1,complement(one))) = join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1703,refute_0_1710]) ).
cnf(refute_0_1712,plain,
( complement(composition(sk1,complement(one))) != join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))
| join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) = complement(composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(composition(sk1,complement(one))))),bind(Y,$fot(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1713,plain,
join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) = complement(composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1711,refute_0_1712]) ).
cnf(refute_0_1714,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))) != complement(composition(sk1,complement(one)))
| complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(complement(join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) ),[0,0,1],$fot(complement(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1715,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(complement(join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))),complement(composition(sk1,complement(one)))) )],[refute_0_1713,refute_0_1714]) ).
cnf(refute_0_1716,plain,
complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(complement(join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),join(complement(join(sk1,composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),join(sk1,composition(sk1,complement(one))))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1638,refute_0_1715]) ).
cnf(refute_0_1717,plain,
meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))) = meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))),
inference(subst,[],[refute_0_1016:[bind(X_27,$fot(complement(composition(sk1,complement(one))))),bind(X_28,$fot(complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1718,plain,
complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),
introduced(tautology,[refl,[$fot(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1719,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) != complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))))
| meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))) != meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))))) ),[1,0],$fot(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1720,plain,
( meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))) != meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) ),
inference(resolve,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))))) )],[refute_0_1718,refute_0_1719]) ).
cnf(refute_0_1721,plain,
complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) = complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
inference(resolve,[$cnf( $equal(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one)))),meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1717,refute_0_1720]) ).
cnf(refute_0_1722,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) != complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = complement(complement(join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) ),[0],$fot(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1723,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = complement(complement(join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1721,refute_0_1722]) ).
cnf(refute_0_1724,plain,
complement(complement(join(sk1,composition(sk1,complement(one))))) = join(sk1,composition(sk1,complement(one))),
inference(subst,[],[refute_0_735:[bind(B,$fot(join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1725,plain,
( complement(complement(join(sk1,composition(sk1,complement(one))))) != join(sk1,composition(sk1,complement(one)))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,composition(sk1,complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) ),[1],$fot(join(sk1,composition(sk1,complement(one))))]]) ).
cnf(refute_0_1726,plain,
( complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(complement(complement(join(sk1,composition(sk1,complement(one))))),join(sk1,composition(sk1,complement(one)))) )],[refute_0_1724,refute_0_1725]) ).
cnf(refute_0_1727,plain,
( complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))) != complement(complement(join(sk1,composition(sk1,complement(one)))))
| complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,composition(sk1,complement(one))) ),
inference(resolve,[$cnf( $equal(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1723,refute_0_1726]) ).
cnf(refute_0_1728,plain,
complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(complement(meet(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,complement(one))))),complement(complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1716,refute_0_1727]) ).
cnf(refute_0_1729,plain,
( complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != join(sk1,composition(sk1,complement(one)))
| meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) != complement(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))
| meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) = complement(join(sk1,composition(sk1,complement(one)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))),complement(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))) ),[1,0],$fot(join(sk1,composition(sk1,complement(one))))]]) ).
cnf(refute_0_1730,plain,
( meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) != complement(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))
| meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) = complement(join(sk1,composition(sk1,complement(one)))) ),
inference(resolve,[$cnf( $equal(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(sk1,composition(sk1,complement(one)))) )],[refute_0_1728,refute_0_1729]) ).
cnf(refute_0_1731,plain,
meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) = complement(join(sk1,composition(sk1,complement(one)))),
inference(resolve,[$cnf( $equal(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))),complement(complement(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))) )],[refute_0_1552,refute_0_1730]) ).
cnf(refute_0_1732,plain,
join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),
introduced(tautology,[refl,[$fot(join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1733,plain,
( join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) != complement(join(sk1,composition(sk1,complement(one))))
| join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) ),[1,1],$fot(complement(join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1734,plain,
( meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))) != complement(join(sk1,composition(sk1,complement(one))))
| join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1732,refute_0_1733]) ).
cnf(refute_0_1735,plain,
join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))),complement(join(sk1,composition(sk1,complement(one))))) )],[refute_0_1731,refute_0_1734]) ).
cnf(refute_0_1736,plain,
( complement(composition(sk1,complement(one))) != join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))) != join(sk1,complement(join(sk1,composition(sk1,complement(one)))))
| complement(composition(sk1,complement(one))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,complement(one))),join(sk1,complement(join(sk1,composition(sk1,complement(one)))))) ),[0],$fot(join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))))]]) ).
cnf(refute_0_1737,plain,
( complement(composition(sk1,complement(one))) != join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))
| complement(composition(sk1,complement(one))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))) ),
inference(resolve,[$cnf( $equal(join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one)))))),join(sk1,complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1735,refute_0_1736]) ).
cnf(refute_0_1738,plain,
complement(composition(sk1,complement(one))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(sk1,meet(complement(composition(sk1,complement(one))),complement(join(sk1,composition(sk1,complement(one))))))) )],[refute_0_1551,refute_0_1737]) ).
cnf(refute_0_1739,plain,
join(one,complement(one)) = top,
inference(subst,[],[refute_0_46:[bind(A,$fot(one))]]) ).
cnf(refute_0_1740,plain,
composition(sk1,join(one,complement(one))) = composition(sk1,join(one,complement(one))),
introduced(tautology,[refl,[$fot(composition(sk1,join(one,complement(one))))]]) ).
cnf(refute_0_1741,plain,
( composition(sk1,join(one,complement(one))) != composition(sk1,join(one,complement(one)))
| join(one,complement(one)) != top
| composition(sk1,join(one,complement(one))) = composition(sk1,top) ),
introduced(tautology,[equality,[$cnf( $equal(composition(sk1,join(one,complement(one))),composition(sk1,join(one,complement(one)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_1742,plain,
( join(one,complement(one)) != top
| composition(sk1,join(one,complement(one))) = composition(sk1,top) ),
inference(resolve,[$cnf( $equal(composition(sk1,join(one,complement(one))),composition(sk1,join(one,complement(one)))) )],[refute_0_1740,refute_0_1741]) ).
cnf(refute_0_1743,plain,
composition(sk1,join(one,complement(one))) = composition(sk1,top),
inference(resolve,[$cnf( $equal(join(one,complement(one)),top) )],[refute_0_1739,refute_0_1742]) ).
cnf(refute_0_1744,plain,
converse(join(converse(A),composition(X_220,converse(A)))) = join(A,converse(composition(X_220,converse(A)))),
inference(subst,[],[refute_0_335:[bind(X_10,$fot(composition(X_220,converse(A))))]]) ).
cnf(refute_0_1745,plain,
composition(join(X_220,one),converse(A)) = join(converse(A),composition(X_220,converse(A))),
inference(subst,[],[refute_0_698:[bind(X_122,$fot(X_220)),bind(X_124,$fot(converse(A)))]]) ).
cnf(refute_0_1746,plain,
( composition(join(X_220,one),converse(A)) != join(converse(A),composition(X_220,converse(A)))
| join(converse(A),composition(X_220,converse(A))) = composition(join(X_220,one),converse(A)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(join(X_220,one),converse(A)))),bind(Y,$fot(join(converse(A),composition(X_220,converse(A)))))]]) ).
cnf(refute_0_1747,plain,
join(converse(A),composition(X_220,converse(A))) = composition(join(X_220,one),converse(A)),
inference(resolve,[$cnf( $equal(composition(join(X_220,one),converse(A)),join(converse(A),composition(X_220,converse(A)))) )],[refute_0_1745,refute_0_1746]) ).
cnf(refute_0_1748,plain,
( converse(join(converse(A),composition(X_220,converse(A)))) != join(A,converse(composition(X_220,converse(A))))
| join(converse(A),composition(X_220,converse(A))) != composition(join(X_220,one),converse(A))
| converse(composition(join(X_220,one),converse(A))) = join(A,converse(composition(X_220,converse(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),composition(X_220,converse(A)))),join(A,converse(composition(X_220,converse(A))))) ),[0,0],$fot(composition(join(X_220,one),converse(A)))]]) ).
cnf(refute_0_1749,plain,
( converse(join(converse(A),composition(X_220,converse(A)))) != join(A,converse(composition(X_220,converse(A))))
| converse(composition(join(X_220,one),converse(A))) = join(A,converse(composition(X_220,converse(A)))) ),
inference(resolve,[$cnf( $equal(join(converse(A),composition(X_220,converse(A))),composition(join(X_220,one),converse(A))) )],[refute_0_1747,refute_0_1748]) ).
cnf(refute_0_1750,plain,
converse(composition(join(X_220,one),converse(A))) = join(A,converse(composition(X_220,converse(A)))),
inference(resolve,[$cnf( $equal(converse(join(converse(A),composition(X_220,converse(A)))),join(A,converse(composition(X_220,converse(A))))) )],[refute_0_1744,refute_0_1749]) ).
cnf(refute_0_1751,plain,
converse(composition(X_5,converse(A))) = composition(converse(converse(A)),converse(X_5)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_5)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_1752,plain,
( converse(composition(X_5,converse(A))) != composition(converse(converse(A)),converse(X_5))
| converse(converse(A)) != A
| converse(composition(X_5,converse(A))) = composition(A,converse(X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_5,converse(A))),composition(converse(converse(A)),converse(X_5))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1753,plain,
( converse(composition(X_5,converse(A))) != composition(converse(converse(A)),converse(X_5))
| converse(composition(X_5,converse(A))) = composition(A,converse(X_5)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1752]) ).
cnf(refute_0_1754,plain,
converse(composition(X_5,converse(A))) = composition(A,converse(X_5)),
inference(resolve,[$cnf( $equal(converse(composition(X_5,converse(A))),composition(converse(converse(A)),converse(X_5))) )],[refute_0_1751,refute_0_1753]) ).
cnf(refute_0_1755,plain,
converse(composition(join(X_220,one),converse(A))) = composition(A,converse(join(X_220,one))),
inference(subst,[],[refute_0_1754:[bind(X_5,$fot(join(X_220,one)))]]) ).
cnf(refute_0_1756,plain,
( converse(composition(join(X_220,one),converse(A))) != composition(A,converse(join(X_220,one)))
| converse(composition(join(X_220,one),converse(A))) != join(A,converse(composition(X_220,converse(A))))
| composition(A,converse(join(X_220,one))) = join(A,converse(composition(X_220,converse(A)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_220,one),converse(A))),join(A,converse(composition(X_220,converse(A))))) ),[0],$fot(composition(A,converse(join(X_220,one))))]]) ).
cnf(refute_0_1757,plain,
( converse(composition(join(X_220,one),converse(A))) != join(A,converse(composition(X_220,converse(A))))
| composition(A,converse(join(X_220,one))) = join(A,converse(composition(X_220,converse(A)))) ),
inference(resolve,[$cnf( $equal(converse(composition(join(X_220,one),converse(A))),composition(A,converse(join(X_220,one)))) )],[refute_0_1755,refute_0_1756]) ).
cnf(refute_0_1758,plain,
converse(composition(X_220,converse(A))) = composition(A,converse(X_220)),
inference(subst,[],[refute_0_1754:[bind(X_5,$fot(X_220))]]) ).
cnf(refute_0_1759,plain,
join(A,converse(composition(X_220,converse(A)))) = join(A,converse(composition(X_220,converse(A)))),
introduced(tautology,[refl,[$fot(join(A,converse(composition(X_220,converse(A)))))]]) ).
cnf(refute_0_1760,plain,
( converse(composition(X_220,converse(A))) != composition(A,converse(X_220))
| join(A,converse(composition(X_220,converse(A)))) != join(A,converse(composition(X_220,converse(A))))
| join(A,converse(composition(X_220,converse(A)))) = join(A,composition(A,converse(X_220))) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(composition(X_220,converse(A)))),join(A,converse(composition(X_220,converse(A))))) ),[1,1],$fot(composition(A,converse(X_220)))]]) ).
cnf(refute_0_1761,plain,
( converse(composition(X_220,converse(A))) != composition(A,converse(X_220))
| join(A,converse(composition(X_220,converse(A)))) = join(A,composition(A,converse(X_220))) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(X_220,converse(A)))),join(A,converse(composition(X_220,converse(A))))) )],[refute_0_1759,refute_0_1760]) ).
cnf(refute_0_1762,plain,
join(A,converse(composition(X_220,converse(A)))) = join(A,composition(A,converse(X_220))),
inference(resolve,[$cnf( $equal(converse(composition(X_220,converse(A))),composition(A,converse(X_220))) )],[refute_0_1758,refute_0_1761]) ).
cnf(refute_0_1763,plain,
( composition(A,converse(join(X_220,one))) != join(A,converse(composition(X_220,converse(A))))
| join(A,converse(composition(X_220,converse(A)))) != join(A,composition(A,converse(X_220)))
| composition(A,converse(join(X_220,one))) = join(A,composition(A,converse(X_220))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(A,converse(join(X_220,one))),join(A,composition(A,converse(X_220)))) ),[0],$fot(join(A,converse(composition(X_220,converse(A)))))]]) ).
cnf(refute_0_1764,plain,
( composition(A,converse(join(X_220,one))) != join(A,converse(composition(X_220,converse(A))))
| composition(A,converse(join(X_220,one))) = join(A,composition(A,converse(X_220))) ),
inference(resolve,[$cnf( $equal(join(A,converse(composition(X_220,converse(A)))),join(A,composition(A,converse(X_220)))) )],[refute_0_1762,refute_0_1763]) ).
cnf(refute_0_1765,plain,
( converse(composition(join(X_220,one),converse(A))) != join(A,converse(composition(X_220,converse(A))))
| composition(A,converse(join(X_220,one))) = join(A,composition(A,converse(X_220))) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(X_220,one))),join(A,converse(composition(X_220,converse(A))))) )],[refute_0_1757,refute_0_1764]) ).
cnf(refute_0_1766,plain,
composition(A,converse(join(X_220,one))) = join(A,composition(A,converse(X_220))),
inference(resolve,[$cnf( $equal(converse(composition(join(X_220,one),converse(A))),join(A,converse(composition(X_220,converse(A))))) )],[refute_0_1750,refute_0_1765]) ).
cnf(refute_0_1767,plain,
composition(X_403,converse(join(converse(A),one))) = join(X_403,composition(X_403,converse(converse(A)))),
inference(subst,[],[refute_0_1766:[bind(A,$fot(X_403)),bind(X_220,$fot(converse(A)))]]) ).
cnf(refute_0_1768,plain,
( composition(X_403,converse(join(converse(A),one))) != join(X_403,composition(X_403,converse(converse(A))))
| converse(converse(A)) != A
| composition(X_403,converse(join(converse(A),one))) = join(X_403,composition(X_403,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),join(X_403,composition(X_403,converse(converse(A))))) ),[1,1,1],$fot(A)]]) ).
cnf(refute_0_1769,plain,
( composition(X_403,converse(join(converse(A),one))) != join(X_403,composition(X_403,converse(converse(A))))
| composition(X_403,converse(join(converse(A),one))) = join(X_403,composition(X_403,A)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1768]) ).
cnf(refute_0_1770,plain,
composition(X_403,converse(join(converse(A),one))) = join(X_403,composition(X_403,A)),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),join(X_403,composition(X_403,converse(converse(A))))) )],[refute_0_1767,refute_0_1769]) ).
cnf(refute_0_1771,plain,
join(converse(one),A) = join(converse(one),A),
introduced(tautology,[refl,[$fot(join(converse(one),A))]]) ).
cnf(refute_0_1772,plain,
( converse(one) != one
| join(converse(one),A) != join(converse(one),A)
| join(converse(one),A) = join(one,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),A),join(converse(one),A)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1773,plain,
( converse(one) != one
| join(converse(one),A) = join(one,A) ),
inference(resolve,[$cnf( $equal(join(converse(one),A),join(converse(one),A)) )],[refute_0_1771,refute_0_1772]) ).
cnf(refute_0_1774,plain,
join(converse(one),A) = join(one,A),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_100,refute_0_1773]) ).
cnf(refute_0_1775,plain,
converse(join(one,converse(A))) = join(converse(one),A),
inference(subst,[],[refute_0_370:[bind(X_9,$fot(one))]]) ).
cnf(refute_0_1776,plain,
( converse(join(one,converse(A))) != join(converse(one),A)
| join(converse(one),A) != join(one,A)
| converse(join(one,converse(A))) = join(one,A) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(converse(join(one,converse(A))))),bind(Y,$fot(join(converse(one),A))),bind(Z,$fot(join(one,A)))]]) ).
cnf(refute_0_1777,plain,
( join(converse(one),A) != join(one,A)
| converse(join(one,converse(A))) = join(one,A) ),
inference(resolve,[$cnf( $equal(converse(join(one,converse(A))),join(converse(one),A)) )],[refute_0_1775,refute_0_1776]) ).
cnf(refute_0_1778,plain,
converse(join(one,converse(A))) = join(one,A),
inference(resolve,[$cnf( $equal(join(converse(one),A),join(one,A)) )],[refute_0_1774,refute_0_1777]) ).
cnf(refute_0_1779,plain,
composition(X_403,converse(join(one,converse(A)))) = composition(X_403,converse(join(one,converse(A)))),
introduced(tautology,[refl,[$fot(composition(X_403,converse(join(one,converse(A)))))]]) ).
cnf(refute_0_1780,plain,
( composition(X_403,converse(join(one,converse(A)))) != composition(X_403,converse(join(one,converse(A))))
| converse(join(one,converse(A))) != join(one,A)
| composition(X_403,converse(join(one,converse(A)))) = composition(X_403,join(one,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_403,converse(join(one,converse(A)))),composition(X_403,converse(join(one,converse(A))))) ),[1,1],$fot(join(one,A))]]) ).
cnf(refute_0_1781,plain,
( converse(join(one,converse(A))) != join(one,A)
| composition(X_403,converse(join(one,converse(A)))) = composition(X_403,join(one,A)) ),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(one,converse(A)))),composition(X_403,converse(join(one,converse(A))))) )],[refute_0_1779,refute_0_1780]) ).
cnf(refute_0_1782,plain,
composition(X_403,converse(join(one,converse(A)))) = composition(X_403,join(one,A)),
inference(resolve,[$cnf( $equal(converse(join(one,converse(A))),join(one,A)) )],[refute_0_1778,refute_0_1781]) ).
cnf(refute_0_1783,plain,
join(B,join(B,composition(B,converse(X_404)))) = join(B,composition(B,converse(X_404))),
inference(subst,[],[refute_0_756:[bind(C,$fot(composition(B,converse(X_404))))]]) ).
cnf(refute_0_1784,plain,
composition(B,converse(join(X_404,one))) = join(B,composition(B,converse(X_404))),
inference(subst,[],[refute_0_1766:[bind(A,$fot(B)),bind(X_220,$fot(X_404))]]) ).
cnf(refute_0_1785,plain,
( composition(B,converse(join(X_404,one))) != join(B,composition(B,converse(X_404)))
| join(B,composition(B,converse(X_404))) = composition(B,converse(join(X_404,one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(B,converse(join(X_404,one))))),bind(Y,$fot(join(B,composition(B,converse(X_404)))))]]) ).
cnf(refute_0_1786,plain,
join(B,composition(B,converse(X_404))) = composition(B,converse(join(X_404,one))),
inference(resolve,[$cnf( $equal(composition(B,converse(join(X_404,one))),join(B,composition(B,converse(X_404)))) )],[refute_0_1784,refute_0_1785]) ).
cnf(refute_0_1787,plain,
( join(B,composition(B,converse(X_404))) != composition(B,converse(join(X_404,one)))
| join(B,join(B,composition(B,converse(X_404)))) != join(B,composition(B,converse(X_404)))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(X_404,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),join(B,composition(B,converse(X_404)))) ),[1],$fot(composition(B,converse(join(X_404,one))))]]) ).
cnf(refute_0_1788,plain,
( join(B,join(B,composition(B,converse(X_404)))) != join(B,composition(B,converse(X_404)))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(X_404,one))) ),
inference(resolve,[$cnf( $equal(join(B,composition(B,converse(X_404))),composition(B,converse(join(X_404,one)))) )],[refute_0_1786,refute_0_1787]) ).
cnf(refute_0_1789,plain,
join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(X_404,one))),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),join(B,composition(B,converse(X_404)))) )],[refute_0_1783,refute_0_1788]) ).
cnf(refute_0_1790,plain,
join(one,join(X_404,one)) = join(one,X_404),
inference(subst,[],[refute_0_798:[bind(B,$fot(one)),bind(X_148,$fot(X_404))]]) ).
cnf(refute_0_1791,plain,
converse(join(one,join(X_404,one))) = converse(join(one,join(X_404,one))),
introduced(tautology,[refl,[$fot(converse(join(one,join(X_404,one))))]]) ).
cnf(refute_0_1792,plain,
( converse(join(one,join(X_404,one))) != converse(join(one,join(X_404,one)))
| join(one,join(X_404,one)) != join(one,X_404)
| converse(join(one,join(X_404,one))) = converse(join(one,X_404)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(X_404,one))),converse(join(one,join(X_404,one)))) ),[1,0],$fot(join(one,X_404))]]) ).
cnf(refute_0_1793,plain,
( join(one,join(X_404,one)) != join(one,X_404)
| converse(join(one,join(X_404,one))) = converse(join(one,X_404)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(X_404,one))),converse(join(one,join(X_404,one)))) )],[refute_0_1791,refute_0_1792]) ).
cnf(refute_0_1794,plain,
converse(join(one,join(X_404,one))) = converse(join(one,X_404)),
inference(resolve,[$cnf( $equal(join(one,join(X_404,one)),join(one,X_404)) )],[refute_0_1790,refute_0_1793]) ).
cnf(refute_0_1795,plain,
composition(B,converse(join(one,join(X_404,one)))) = composition(B,converse(join(one,join(X_404,one)))),
introduced(tautology,[refl,[$fot(composition(B,converse(join(one,join(X_404,one)))))]]) ).
cnf(refute_0_1796,plain,
( composition(B,converse(join(one,join(X_404,one)))) != composition(B,converse(join(one,join(X_404,one))))
| converse(join(one,join(X_404,one))) != converse(join(one,X_404))
| composition(B,converse(join(one,join(X_404,one)))) = composition(B,converse(join(one,X_404))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(B,converse(join(one,join(X_404,one)))),composition(B,converse(join(one,join(X_404,one))))) ),[1,1],$fot(converse(join(one,X_404)))]]) ).
cnf(refute_0_1797,plain,
( converse(join(one,join(X_404,one))) != converse(join(one,X_404))
| composition(B,converse(join(one,join(X_404,one)))) = composition(B,converse(join(one,X_404))) ),
inference(resolve,[$cnf( $equal(composition(B,converse(join(one,join(X_404,one)))),composition(B,converse(join(one,join(X_404,one))))) )],[refute_0_1795,refute_0_1796]) ).
cnf(refute_0_1798,plain,
composition(B,converse(join(one,join(X_404,one)))) = composition(B,converse(join(one,X_404))),
inference(resolve,[$cnf( $equal(converse(join(one,join(X_404,one))),converse(join(one,X_404))) )],[refute_0_1794,refute_0_1797]) ).
cnf(refute_0_1799,plain,
converse(composition(join(one,X_390),converse(A))) = composition(A,converse(join(one,X_390))),
inference(subst,[],[refute_0_1754:[bind(X_5,$fot(join(one,X_390)))]]) ).
cnf(refute_0_1800,plain,
composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = join(X_124,composition(join(X_387,converse(complement(composition(X_124,top)))),X_124)),
inference(subst,[],[refute_0_698:[bind(X_122,$fot(join(X_387,converse(complement(composition(X_124,top))))))]]) ).
cnf(refute_0_1801,plain,
composition(join(X_387,converse(complement(composition(X_124,top)))),X_124) = composition(X_387,X_124),
inference(subst,[],[refute_0_1507:[bind(X_122,$fot(X_387))]]) ).
cnf(refute_0_1802,plain,
( composition(join(X_387,converse(complement(composition(X_124,top)))),X_124) != composition(X_387,X_124)
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != join(X_124,composition(join(X_387,converse(complement(composition(X_124,top)))),X_124))
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = join(X_124,composition(X_387,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),join(X_124,composition(join(X_387,converse(complement(composition(X_124,top)))),X_124))) ),[1,1],$fot(composition(X_387,X_124))]]) ).
cnf(refute_0_1803,plain,
( composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != join(X_124,composition(join(X_387,converse(complement(composition(X_124,top)))),X_124))
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = join(X_124,composition(X_387,X_124)) ),
inference(resolve,[$cnf( $equal(composition(join(X_387,converse(complement(composition(X_124,top)))),X_124),composition(X_387,X_124)) )],[refute_0_1801,refute_0_1802]) ).
cnf(refute_0_1804,plain,
composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = join(X_124,composition(X_387,X_124)),
inference(resolve,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),join(X_124,composition(join(X_387,converse(complement(composition(X_124,top)))),X_124))) )],[refute_0_1800,refute_0_1803]) ).
cnf(refute_0_1805,plain,
composition(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),X_124) = composition(join(X_199,X_200),X_124),
inference(subst,[],[refute_0_830:[bind(X_123,$fot(join(X_199,X_200)))]]) ).
cnf(refute_0_1806,plain,
join(converse(complement(composition(X_124,top))),join(X_199,X_200)) = join(X_199,join(X_200,converse(complement(composition(X_124,top))))),
inference(subst,[],[refute_0_404:[bind(A,$fot(converse(complement(composition(X_124,top))))),bind(X_49,$fot(X_199)),bind(X_50,$fot(X_200))]]) ).
cnf(refute_0_1807,plain,
( composition(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),X_124) != composition(join(X_199,X_200),X_124)
| join(converse(complement(composition(X_124,top))),join(X_199,X_200)) != join(X_199,join(X_200,converse(complement(composition(X_124,top)))))
| composition(join(X_199,join(X_200,converse(complement(composition(X_124,top))))),X_124) = composition(join(X_199,X_200),X_124) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),X_124),composition(join(X_199,X_200),X_124)) ),[0,0],$fot(join(X_199,join(X_200,converse(complement(composition(X_124,top))))))]]) ).
cnf(refute_0_1808,plain,
( composition(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),X_124) != composition(join(X_199,X_200),X_124)
| composition(join(X_199,join(X_200,converse(complement(composition(X_124,top))))),X_124) = composition(join(X_199,X_200),X_124) ),
inference(resolve,[$cnf( $equal(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),join(X_199,join(X_200,converse(complement(composition(X_124,top)))))) )],[refute_0_1806,refute_0_1807]) ).
cnf(refute_0_1809,plain,
composition(join(X_199,join(X_200,converse(complement(composition(X_124,top))))),X_124) = composition(join(X_199,X_200),X_124),
inference(resolve,[$cnf( $equal(composition(join(converse(complement(composition(X_124,top))),join(X_199,X_200)),X_124),composition(join(X_199,X_200),X_124)) )],[refute_0_1805,refute_0_1808]) ).
cnf(refute_0_1810,plain,
composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124) = composition(join(one,X_387),X_124),
inference(subst,[],[refute_0_1809:[bind(X_199,$fot(one)),bind(X_200,$fot(X_387))]]) ).
cnf(refute_0_1811,plain,
composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124),
inference(subst,[],[refute_0_893:[bind(B,$fot(X_124)),bind(X_220,$fot(join(X_387,converse(complement(composition(X_124,top))))))]]) ).
cnf(refute_0_1812,plain,
( composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124)
| composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124) != composition(join(one,X_387),X_124)
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = composition(join(one,X_387),X_124) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124))),bind(Y,$fot(composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124))),bind(Z,$fot(composition(join(one,X_387),X_124)))]]) ).
cnf(refute_0_1813,plain,
( composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124) != composition(join(one,X_387),X_124)
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = composition(join(one,X_387),X_124) ),
inference(resolve,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124)) )],[refute_0_1811,refute_0_1812]) ).
cnf(refute_0_1814,plain,
composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) = composition(join(one,X_387),X_124),
inference(resolve,[$cnf( $equal(composition(join(one,join(X_387,converse(complement(composition(X_124,top))))),X_124),composition(join(one,X_387),X_124)) )],[refute_0_1810,refute_0_1813]) ).
cnf(refute_0_1815,plain,
( composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != composition(join(one,X_387),X_124)
| composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != join(X_124,composition(X_387,X_124))
| composition(join(one,X_387),X_124) = join(X_124,composition(X_387,X_124)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),join(X_124,composition(X_387,X_124))) ),[0],$fot(composition(join(one,X_387),X_124))]]) ).
cnf(refute_0_1816,plain,
( composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != join(X_124,composition(X_387,X_124))
| composition(join(one,X_387),X_124) = join(X_124,composition(X_387,X_124)) ),
inference(resolve,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),composition(join(one,X_387),X_124)) )],[refute_0_1814,refute_0_1815]) ).
cnf(refute_0_1817,plain,
join(X_124,composition(X_387,X_124)) = composition(join(X_387,one),X_124),
inference(subst,[],[refute_0_857:[bind(X_122,$fot(X_387))]]) ).
cnf(refute_0_1818,plain,
( composition(join(one,X_387),X_124) != join(X_124,composition(X_387,X_124))
| join(X_124,composition(X_387,X_124)) != composition(join(X_387,one),X_124)
| composition(join(one,X_387),X_124) = composition(join(X_387,one),X_124) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_387),X_124),composition(join(X_387,one),X_124)) ),[0],$fot(join(X_124,composition(X_387,X_124)))]]) ).
cnf(refute_0_1819,plain,
( composition(join(one,X_387),X_124) != join(X_124,composition(X_387,X_124))
| composition(join(one,X_387),X_124) = composition(join(X_387,one),X_124) ),
inference(resolve,[$cnf( $equal(join(X_124,composition(X_387,X_124)),composition(join(X_387,one),X_124)) )],[refute_0_1817,refute_0_1818]) ).
cnf(refute_0_1820,plain,
( composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124) != join(X_124,composition(X_387,X_124))
| composition(join(one,X_387),X_124) = composition(join(X_387,one),X_124) ),
inference(resolve,[$cnf( $equal(composition(join(one,X_387),X_124),join(X_124,composition(X_387,X_124))) )],[refute_0_1816,refute_0_1819]) ).
cnf(refute_0_1821,plain,
composition(join(one,X_387),X_124) = composition(join(X_387,one),X_124),
inference(resolve,[$cnf( $equal(composition(join(join(X_387,converse(complement(composition(X_124,top)))),one),X_124),join(X_124,composition(X_387,X_124))) )],[refute_0_1804,refute_0_1820]) ).
cnf(refute_0_1822,plain,
composition(join(one,X_390),converse(A)) = composition(join(X_390,one),converse(A)),
inference(subst,[],[refute_0_1821:[bind(X_124,$fot(converse(A))),bind(X_387,$fot(X_390))]]) ).
cnf(refute_0_1823,plain,
( composition(join(one,X_390),converse(A)) != composition(join(X_390,one),converse(A))
| converse(composition(join(one,X_390),converse(A))) != composition(A,converse(join(one,X_390)))
| converse(composition(join(X_390,one),converse(A))) = composition(A,converse(join(one,X_390))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(one,X_390),converse(A))),composition(A,converse(join(one,X_390)))) ),[0,0],$fot(composition(join(X_390,one),converse(A)))]]) ).
cnf(refute_0_1824,plain,
( converse(composition(join(one,X_390),converse(A))) != composition(A,converse(join(one,X_390)))
| converse(composition(join(X_390,one),converse(A))) = composition(A,converse(join(one,X_390))) ),
inference(resolve,[$cnf( $equal(composition(join(one,X_390),converse(A)),composition(join(X_390,one),converse(A))) )],[refute_0_1822,refute_0_1823]) ).
cnf(refute_0_1825,plain,
converse(composition(join(X_390,one),converse(A))) = composition(A,converse(join(one,X_390))),
inference(resolve,[$cnf( $equal(converse(composition(join(one,X_390),converse(A))),composition(A,converse(join(one,X_390)))) )],[refute_0_1799,refute_0_1824]) ).
cnf(refute_0_1826,plain,
converse(composition(join(X_390,one),converse(A))) = composition(A,converse(join(X_390,one))),
inference(subst,[],[refute_0_1754:[bind(X_5,$fot(join(X_390,one)))]]) ).
cnf(refute_0_1827,plain,
( converse(composition(join(X_390,one),converse(A))) != composition(A,converse(join(X_390,one)))
| converse(composition(join(X_390,one),converse(A))) != composition(A,converse(join(one,X_390)))
| composition(A,converse(join(X_390,one))) = composition(A,converse(join(one,X_390))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(X_390,one),converse(A))),composition(A,converse(join(one,X_390)))) ),[0],$fot(composition(A,converse(join(X_390,one))))]]) ).
cnf(refute_0_1828,plain,
( converse(composition(join(X_390,one),converse(A))) != composition(A,converse(join(one,X_390)))
| composition(A,converse(join(X_390,one))) = composition(A,converse(join(one,X_390))) ),
inference(resolve,[$cnf( $equal(converse(composition(join(X_390,one),converse(A))),composition(A,converse(join(X_390,one)))) )],[refute_0_1826,refute_0_1827]) ).
cnf(refute_0_1829,plain,
composition(A,converse(join(X_390,one))) = composition(A,converse(join(one,X_390))),
inference(resolve,[$cnf( $equal(converse(composition(join(X_390,one),converse(A))),composition(A,converse(join(one,X_390)))) )],[refute_0_1825,refute_0_1828]) ).
cnf(refute_0_1830,plain,
composition(B,converse(join(join(X_404,one),one))) = composition(B,converse(join(one,join(X_404,one)))),
inference(subst,[],[refute_0_1829:[bind(A,$fot(B)),bind(X_390,$fot(join(X_404,one)))]]) ).
cnf(refute_0_1831,plain,
( composition(A,converse(join(X_220,one))) != join(A,composition(A,converse(X_220)))
| join(A,composition(A,converse(X_220))) = composition(A,converse(join(X_220,one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(A,converse(join(X_220,one))))),bind(Y,$fot(join(A,composition(A,converse(X_220)))))]]) ).
cnf(refute_0_1832,plain,
join(A,composition(A,converse(X_220))) = composition(A,converse(join(X_220,one))),
inference(resolve,[$cnf( $equal(composition(A,converse(join(X_220,one))),join(A,composition(A,converse(X_220)))) )],[refute_0_1766,refute_0_1831]) ).
cnf(refute_0_1833,plain,
join(B,composition(B,converse(join(X_404,one)))) = composition(B,converse(join(join(X_404,one),one))),
inference(subst,[],[refute_0_1832:[bind(A,$fot(B)),bind(X_220,$fot(join(X_404,one)))]]) ).
cnf(refute_0_1834,plain,
( composition(B,converse(join(join(X_404,one),one))) != composition(B,converse(join(one,join(X_404,one))))
| join(B,composition(B,converse(join(X_404,one)))) != composition(B,converse(join(join(X_404,one),one)))
| join(B,composition(B,converse(join(X_404,one)))) = composition(B,converse(join(one,join(X_404,one)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,composition(B,converse(join(X_404,one)))))),bind(Y,$fot(composition(B,converse(join(join(X_404,one),one))))),bind(Z,$fot(composition(B,converse(join(one,join(X_404,one))))))]]) ).
cnf(refute_0_1835,plain,
( composition(B,converse(join(join(X_404,one),one))) != composition(B,converse(join(one,join(X_404,one))))
| join(B,composition(B,converse(join(X_404,one)))) = composition(B,converse(join(one,join(X_404,one)))) ),
inference(resolve,[$cnf( $equal(join(B,composition(B,converse(join(X_404,one)))),composition(B,converse(join(join(X_404,one),one)))) )],[refute_0_1833,refute_0_1834]) ).
cnf(refute_0_1836,plain,
join(B,composition(B,converse(join(X_404,one)))) = composition(B,converse(join(one,join(X_404,one)))),
inference(resolve,[$cnf( $equal(composition(B,converse(join(join(X_404,one),one))),composition(B,converse(join(one,join(X_404,one))))) )],[refute_0_1830,refute_0_1835]) ).
cnf(refute_0_1837,plain,
join(composition(X_50,converse(X_404)),join(X_49,X_50)) = join(X_49,join(X_50,composition(X_50,converse(X_404)))),
inference(subst,[],[refute_0_404:[bind(A,$fot(composition(X_50,converse(X_404))))]]) ).
cnf(refute_0_1838,plain,
composition(X_50,converse(join(X_404,one))) = join(X_50,composition(X_50,converse(X_404))),
inference(subst,[],[refute_0_1766:[bind(A,$fot(X_50)),bind(X_220,$fot(X_404))]]) ).
cnf(refute_0_1839,plain,
( composition(X_50,converse(join(X_404,one))) != join(X_50,composition(X_50,converse(X_404)))
| join(X_50,composition(X_50,converse(X_404))) = composition(X_50,converse(join(X_404,one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(X_50,converse(join(X_404,one))))),bind(Y,$fot(join(X_50,composition(X_50,converse(X_404)))))]]) ).
cnf(refute_0_1840,plain,
join(X_50,composition(X_50,converse(X_404))) = composition(X_50,converse(join(X_404,one))),
inference(resolve,[$cnf( $equal(composition(X_50,converse(join(X_404,one))),join(X_50,composition(X_50,converse(X_404)))) )],[refute_0_1838,refute_0_1839]) ).
cnf(refute_0_1841,plain,
( join(X_50,composition(X_50,converse(X_404))) != composition(X_50,converse(join(X_404,one)))
| join(composition(X_50,converse(X_404)),join(X_49,X_50)) != join(X_49,join(X_50,composition(X_50,converse(X_404))))
| join(composition(X_50,converse(X_404)),join(X_49,X_50)) = join(X_49,composition(X_50,converse(join(X_404,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_50,converse(X_404)),join(X_49,X_50)),join(X_49,join(X_50,composition(X_50,converse(X_404))))) ),[1,1],$fot(composition(X_50,converse(join(X_404,one))))]]) ).
cnf(refute_0_1842,plain,
( join(composition(X_50,converse(X_404)),join(X_49,X_50)) != join(X_49,join(X_50,composition(X_50,converse(X_404))))
| join(composition(X_50,converse(X_404)),join(X_49,X_50)) = join(X_49,composition(X_50,converse(join(X_404,one)))) ),
inference(resolve,[$cnf( $equal(join(X_50,composition(X_50,converse(X_404))),composition(X_50,converse(join(X_404,one)))) )],[refute_0_1840,refute_0_1841]) ).
cnf(refute_0_1843,plain,
join(composition(X_50,converse(X_404)),join(X_49,X_50)) = join(X_49,composition(X_50,converse(join(X_404,one)))),
inference(resolve,[$cnf( $equal(join(composition(X_50,converse(X_404)),join(X_49,X_50)),join(X_49,join(X_50,composition(X_50,converse(X_404))))) )],[refute_0_1837,refute_0_1842]) ).
cnf(refute_0_1844,plain,
join(composition(X_50,converse(X_404)),join(X_49,X_50)) = join(X_50,join(X_49,composition(X_50,converse(X_404)))),
inference(subst,[],[refute_0_877:[bind(X_198,$fot(X_50)),bind(X_199,$fot(composition(X_50,converse(X_404)))),bind(X_200,$fot(X_49))]]) ).
cnf(refute_0_1845,plain,
( join(composition(X_50,converse(X_404)),join(X_49,X_50)) != join(X_49,composition(X_50,converse(join(X_404,one))))
| join(composition(X_50,converse(X_404)),join(X_49,X_50)) != join(X_50,join(X_49,composition(X_50,converse(X_404))))
| join(X_50,join(X_49,composition(X_50,converse(X_404)))) = join(X_49,composition(X_50,converse(join(X_404,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(X_50,converse(X_404)),join(X_49,X_50)),join(X_49,composition(X_50,converse(join(X_404,one))))) ),[0],$fot(join(X_50,join(X_49,composition(X_50,converse(X_404)))))]]) ).
cnf(refute_0_1846,plain,
( join(composition(X_50,converse(X_404)),join(X_49,X_50)) != join(X_49,composition(X_50,converse(join(X_404,one))))
| join(X_50,join(X_49,composition(X_50,converse(X_404)))) = join(X_49,composition(X_50,converse(join(X_404,one)))) ),
inference(resolve,[$cnf( $equal(join(composition(X_50,converse(X_404)),join(X_49,X_50)),join(X_50,join(X_49,composition(X_50,converse(X_404))))) )],[refute_0_1844,refute_0_1845]) ).
cnf(refute_0_1847,plain,
join(X_50,join(X_49,composition(X_50,converse(X_404)))) = join(X_49,composition(X_50,converse(join(X_404,one)))),
inference(resolve,[$cnf( $equal(join(composition(X_50,converse(X_404)),join(X_49,X_50)),join(X_49,composition(X_50,converse(join(X_404,one))))) )],[refute_0_1843,refute_0_1846]) ).
cnf(refute_0_1848,plain,
join(B,join(B,composition(B,converse(X_404)))) = join(B,composition(B,converse(join(X_404,one)))),
inference(subst,[],[refute_0_1847:[bind(X_49,$fot(B)),bind(X_50,$fot(B))]]) ).
cnf(refute_0_1849,plain,
( join(B,composition(B,converse(join(X_404,one)))) != composition(B,converse(join(one,join(X_404,one))))
| join(B,join(B,composition(B,converse(X_404)))) != join(B,composition(B,converse(join(X_404,one))))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,join(X_404,one)))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,join(B,composition(B,converse(X_404)))))),bind(Y,$fot(join(B,composition(B,converse(join(X_404,one)))))),bind(Z,$fot(composition(B,converse(join(one,join(X_404,one))))))]]) ).
cnf(refute_0_1850,plain,
( join(B,composition(B,converse(join(X_404,one)))) != composition(B,converse(join(one,join(X_404,one))))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,join(X_404,one)))) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),join(B,composition(B,converse(join(X_404,one))))) )],[refute_0_1848,refute_0_1849]) ).
cnf(refute_0_1851,plain,
join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,join(X_404,one)))),
inference(resolve,[$cnf( $equal(join(B,composition(B,converse(join(X_404,one)))),composition(B,converse(join(one,join(X_404,one))))) )],[refute_0_1836,refute_0_1850]) ).
cnf(refute_0_1852,plain,
( composition(B,converse(join(one,join(X_404,one)))) != composition(B,converse(join(one,X_404)))
| join(B,join(B,composition(B,converse(X_404)))) != composition(B,converse(join(one,join(X_404,one))))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,X_404))) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(B,join(B,composition(B,converse(X_404)))))),bind(Y,$fot(composition(B,converse(join(one,join(X_404,one)))))),bind(Z,$fot(composition(B,converse(join(one,X_404)))))]]) ).
cnf(refute_0_1853,plain,
( composition(B,converse(join(one,join(X_404,one)))) != composition(B,converse(join(one,X_404)))
| join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,X_404))) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),composition(B,converse(join(one,join(X_404,one))))) )],[refute_0_1851,refute_0_1852]) ).
cnf(refute_0_1854,plain,
join(B,join(B,composition(B,converse(X_404)))) = composition(B,converse(join(one,X_404))),
inference(resolve,[$cnf( $equal(composition(B,converse(join(one,join(X_404,one)))),composition(B,converse(join(one,X_404)))) )],[refute_0_1798,refute_0_1853]) ).
cnf(refute_0_1855,plain,
( join(B,join(B,composition(B,converse(X_404)))) != composition(B,converse(join(X_404,one)))
| join(B,join(B,composition(B,converse(X_404)))) != composition(B,converse(join(one,X_404)))
| composition(B,converse(join(one,X_404))) = composition(B,converse(join(X_404,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),composition(B,converse(join(X_404,one)))) ),[0],$fot(composition(B,converse(join(one,X_404))))]]) ).
cnf(refute_0_1856,plain,
( join(B,join(B,composition(B,converse(X_404)))) != composition(B,converse(join(X_404,one)))
| composition(B,converse(join(one,X_404))) = composition(B,converse(join(X_404,one))) ),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),composition(B,converse(join(one,X_404)))) )],[refute_0_1854,refute_0_1855]) ).
cnf(refute_0_1857,plain,
composition(B,converse(join(one,X_404))) = composition(B,converse(join(X_404,one))),
inference(resolve,[$cnf( $equal(join(B,join(B,composition(B,converse(X_404)))),composition(B,converse(join(X_404,one)))) )],[refute_0_1789,refute_0_1856]) ).
cnf(refute_0_1858,plain,
( composition(B,converse(join(one,X_404))) != composition(B,converse(join(X_404,one)))
| composition(B,converse(join(X_404,one))) = composition(B,converse(join(one,X_404))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(B,converse(join(one,X_404))))),bind(Y,$fot(composition(B,converse(join(X_404,one)))))]]) ).
cnf(refute_0_1859,plain,
composition(B,converse(join(X_404,one))) = composition(B,converse(join(one,X_404))),
inference(resolve,[$cnf( $equal(composition(B,converse(join(one,X_404))),composition(B,converse(join(X_404,one)))) )],[refute_0_1857,refute_0_1858]) ).
cnf(refute_0_1860,plain,
composition(X_403,converse(join(converse(A),one))) = composition(X_403,converse(join(one,converse(A)))),
inference(subst,[],[refute_0_1859:[bind(B,$fot(X_403)),bind(X_404,$fot(converse(A)))]]) ).
cnf(refute_0_1861,plain,
( composition(X_403,converse(join(converse(A),one))) != composition(X_403,converse(join(one,converse(A))))
| composition(X_403,converse(join(one,converse(A)))) != composition(X_403,join(one,A))
| composition(X_403,converse(join(converse(A),one))) = composition(X_403,join(one,A)) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(composition(X_403,converse(join(converse(A),one))))),bind(Y,$fot(composition(X_403,converse(join(one,converse(A)))))),bind(Z,$fot(composition(X_403,join(one,A))))]]) ).
cnf(refute_0_1862,plain,
( composition(X_403,converse(join(one,converse(A)))) != composition(X_403,join(one,A))
| composition(X_403,converse(join(converse(A),one))) = composition(X_403,join(one,A)) ),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),composition(X_403,converse(join(one,converse(A))))) )],[refute_0_1860,refute_0_1861]) ).
cnf(refute_0_1863,plain,
composition(X_403,converse(join(converse(A),one))) = composition(X_403,join(one,A)),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(one,converse(A)))),composition(X_403,join(one,A))) )],[refute_0_1782,refute_0_1862]) ).
cnf(refute_0_1864,plain,
( composition(X_403,converse(join(converse(A),one))) != composition(X_403,join(one,A))
| composition(X_403,converse(join(converse(A),one))) != join(X_403,composition(X_403,A))
| composition(X_403,join(one,A)) = join(X_403,composition(X_403,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),join(X_403,composition(X_403,A))) ),[0],$fot(composition(X_403,join(one,A)))]]) ).
cnf(refute_0_1865,plain,
( composition(X_403,converse(join(converse(A),one))) != join(X_403,composition(X_403,A))
| composition(X_403,join(one,A)) = join(X_403,composition(X_403,A)) ),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),composition(X_403,join(one,A))) )],[refute_0_1863,refute_0_1864]) ).
cnf(refute_0_1866,plain,
composition(X_403,join(one,A)) = join(X_403,composition(X_403,A)),
inference(resolve,[$cnf( $equal(composition(X_403,converse(join(converse(A),one))),join(X_403,composition(X_403,A))) )],[refute_0_1770,refute_0_1865]) ).
cnf(refute_0_1867,plain,
( composition(X_403,join(one,A)) != join(X_403,composition(X_403,A))
| join(X_403,composition(X_403,A)) = composition(X_403,join(one,A)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(composition(X_403,join(one,A)))),bind(Y,$fot(join(X_403,composition(X_403,A))))]]) ).
cnf(refute_0_1868,plain,
join(X_403,composition(X_403,A)) = composition(X_403,join(one,A)),
inference(resolve,[$cnf( $equal(composition(X_403,join(one,A)),join(X_403,composition(X_403,A))) )],[refute_0_1866,refute_0_1867]) ).
cnf(refute_0_1869,plain,
join(sk1,composition(sk1,complement(one))) = composition(sk1,join(one,complement(one))),
inference(subst,[],[refute_0_1868:[bind(A,$fot(complement(one))),bind(X_403,$fot(sk1))]]) ).
cnf(refute_0_1870,plain,
( composition(sk1,join(one,complement(one))) != composition(sk1,top)
| join(sk1,composition(sk1,complement(one))) != composition(sk1,join(one,complement(one)))
| join(sk1,composition(sk1,complement(one))) = composition(sk1,top) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(join(sk1,composition(sk1,complement(one))))),bind(Y,$fot(composition(sk1,join(one,complement(one))))),bind(Z,$fot(composition(sk1,top)))]]) ).
cnf(refute_0_1871,plain,
( composition(sk1,join(one,complement(one))) != composition(sk1,top)
| join(sk1,composition(sk1,complement(one))) = composition(sk1,top) ),
inference(resolve,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),composition(sk1,join(one,complement(one)))) )],[refute_0_1869,refute_0_1870]) ).
cnf(refute_0_1872,plain,
join(sk1,composition(sk1,complement(one))) = composition(sk1,top),
inference(resolve,[$cnf( $equal(composition(sk1,join(one,complement(one))),composition(sk1,top)) )],[refute_0_1743,refute_0_1871]) ).
cnf(refute_0_1873,plain,
complement(join(sk1,composition(sk1,complement(one)))) = complement(join(sk1,composition(sk1,complement(one)))),
introduced(tautology,[refl,[$fot(complement(join(sk1,composition(sk1,complement(one)))))]]) ).
cnf(refute_0_1874,plain,
( complement(join(sk1,composition(sk1,complement(one)))) != complement(join(sk1,composition(sk1,complement(one))))
| join(sk1,composition(sk1,complement(one))) != composition(sk1,top)
| complement(join(sk1,composition(sk1,complement(one)))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(sk1,composition(sk1,complement(one)))),complement(join(sk1,composition(sk1,complement(one))))) ),[1,0],$fot(composition(sk1,top))]]) ).
cnf(refute_0_1875,plain,
( join(sk1,composition(sk1,complement(one))) != composition(sk1,top)
| complement(join(sk1,composition(sk1,complement(one)))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(complement(join(sk1,composition(sk1,complement(one)))),complement(join(sk1,composition(sk1,complement(one))))) )],[refute_0_1873,refute_0_1874]) ).
cnf(refute_0_1876,plain,
complement(join(sk1,composition(sk1,complement(one)))) = complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(join(sk1,composition(sk1,complement(one))),composition(sk1,top)) )],[refute_0_1872,refute_0_1875]) ).
cnf(refute_0_1877,plain,
join(sk1,complement(join(sk1,composition(sk1,complement(one))))) = join(sk1,complement(join(sk1,composition(sk1,complement(one))))),
introduced(tautology,[refl,[$fot(join(sk1,complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1878,plain,
( complement(join(sk1,composition(sk1,complement(one)))) != complement(composition(sk1,top))
| join(sk1,complement(join(sk1,composition(sk1,complement(one))))) != join(sk1,complement(join(sk1,composition(sk1,complement(one)))))
| join(sk1,complement(join(sk1,composition(sk1,complement(one))))) = join(sk1,complement(composition(sk1,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk1,complement(join(sk1,composition(sk1,complement(one))))),join(sk1,complement(join(sk1,composition(sk1,complement(one)))))) ),[1,1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1879,plain,
( complement(join(sk1,composition(sk1,complement(one)))) != complement(composition(sk1,top))
| join(sk1,complement(join(sk1,composition(sk1,complement(one))))) = join(sk1,complement(composition(sk1,top))) ),
inference(resolve,[$cnf( $equal(join(sk1,complement(join(sk1,composition(sk1,complement(one))))),join(sk1,complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1877,refute_0_1878]) ).
cnf(refute_0_1880,plain,
join(sk1,complement(join(sk1,composition(sk1,complement(one))))) = join(sk1,complement(composition(sk1,top))),
inference(resolve,[$cnf( $equal(complement(join(sk1,composition(sk1,complement(one)))),complement(composition(sk1,top))) )],[refute_0_1876,refute_0_1879]) ).
cnf(refute_0_1881,plain,
( complement(composition(sk1,complement(one))) != join(sk1,complement(join(sk1,composition(sk1,complement(one)))))
| join(sk1,complement(join(sk1,composition(sk1,complement(one))))) != join(sk1,complement(composition(sk1,top)))
| complement(composition(sk1,complement(one))) = join(sk1,complement(composition(sk1,top))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(composition(sk1,complement(one))),join(sk1,complement(composition(sk1,top)))) ),[0],$fot(join(sk1,complement(join(sk1,composition(sk1,complement(one))))))]]) ).
cnf(refute_0_1882,plain,
( complement(composition(sk1,complement(one))) != join(sk1,complement(join(sk1,composition(sk1,complement(one)))))
| complement(composition(sk1,complement(one))) = join(sk1,complement(composition(sk1,top))) ),
inference(resolve,[$cnf( $equal(join(sk1,complement(join(sk1,composition(sk1,complement(one))))),join(sk1,complement(composition(sk1,top)))) )],[refute_0_1880,refute_0_1881]) ).
cnf(refute_0_1883,plain,
complement(composition(sk1,complement(one))) = join(sk1,complement(composition(sk1,top))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(sk1,complement(join(sk1,composition(sk1,complement(one)))))) )],[refute_0_1738,refute_0_1882]) ).
cnf(refute_0_1884,plain,
( complement(composition(sk1,complement(one))) != join(sk1,complement(composition(sk1,top)))
| join(sk1,complement(composition(sk1,top))) = complement(composition(sk1,complement(one))) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(complement(composition(sk1,complement(one))))),bind(Y,$fot(join(sk1,complement(composition(sk1,top)))))]]) ).
cnf(refute_0_1885,plain,
join(sk1,complement(composition(sk1,top))) = complement(composition(sk1,complement(one))),
inference(resolve,[$cnf( $equal(complement(composition(sk1,complement(one))),join(sk1,complement(composition(sk1,top)))) )],[refute_0_1883,refute_0_1884]) ).
cnf(refute_0_1886,plain,
( composition(converse(join(sk1,complement(composition(sk1,top)))),sk1) != composition(converse(sk1),sk1)
| join(sk1,complement(composition(sk1,top))) != complement(composition(sk1,complement(one)))
| composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(sk1,complement(composition(sk1,top)))),sk1),composition(converse(sk1),sk1)) ),[0,0,0],$fot(complement(composition(sk1,complement(one))))]]) ).
cnf(refute_0_1887,plain,
( composition(converse(join(sk1,complement(composition(sk1,top)))),sk1) != composition(converse(sk1),sk1)
| composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1) ),
inference(resolve,[$cnf( $equal(join(sk1,complement(composition(sk1,top))),complement(composition(sk1,complement(one)))) )],[refute_0_1885,refute_0_1886]) ).
cnf(refute_0_1888,plain,
composition(converse(complement(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1),
inference(resolve,[$cnf( $equal(composition(converse(join(sk1,complement(composition(sk1,top)))),sk1),composition(converse(sk1),sk1)) )],[refute_0_1515,refute_0_1887]) ).
cnf(refute_0_1889,plain,
( composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(complement(converse(composition(sk1,complement(one)))),sk1)
| composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(converse(sk1),sk1)
| composition(complement(converse(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(converse(sk1),sk1)) ),[0],$fot(composition(complement(converse(composition(sk1,complement(one)))),sk1))]]) ).
cnf(refute_0_1890,plain,
( composition(converse(complement(composition(sk1,complement(one)))),sk1) != composition(converse(sk1),sk1)
| composition(complement(converse(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1) ),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(complement(converse(composition(sk1,complement(one)))),sk1)) )],[refute_0_1084,refute_0_1889]) ).
cnf(refute_0_1891,plain,
composition(complement(converse(composition(sk1,complement(one)))),sk1) = composition(converse(sk1),sk1),
inference(resolve,[$cnf( $equal(composition(converse(complement(composition(sk1,complement(one)))),sk1),composition(converse(sk1),sk1)) )],[refute_0_1888,refute_0_1890]) ).
cnf(refute_0_1892,plain,
join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) = join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),
introduced(tautology,[refl,[$fot(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)))]]) ).
cnf(refute_0_1893,plain,
( composition(complement(converse(composition(sk1,complement(one)))),sk1) != composition(converse(sk1),sk1)
| join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) = join(one,composition(converse(sk1),sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),[1,1],$fot(composition(converse(sk1),sk1))]]) ).
cnf(refute_0_1894,plain,
( composition(complement(converse(composition(sk1,complement(one)))),sk1) != composition(converse(sk1),sk1)
| join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) = join(one,composition(converse(sk1),sk1)) ),
inference(resolve,[$cnf( $equal(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_1892,refute_0_1893]) ).
cnf(refute_0_1895,plain,
join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) = join(one,composition(converse(sk1),sk1)),
inference(resolve,[$cnf( $equal(composition(complement(converse(composition(sk1,complement(one)))),sk1),composition(converse(sk1),sk1)) )],[refute_0_1891,refute_0_1894]) ).
cnf(refute_0_1896,plain,
( join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)) != join(one,composition(converse(sk1),sk1))
| one != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| one = join(one,composition(converse(sk1),sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) ),[1],$fot(join(one,composition(converse(sk1),sk1)))]]) ).
cnf(refute_0_1897,plain,
( one != join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))
| one = join(one,composition(converse(sk1),sk1)) ),
inference(resolve,[$cnf( $equal(join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1)),join(one,composition(converse(sk1),sk1))) )],[refute_0_1895,refute_0_1896]) ).
cnf(refute_0_1898,plain,
one = join(one,composition(converse(sk1),sk1)),
inference(resolve,[$cnf( $equal(one,join(one,composition(complement(converse(composition(sk1,complement(one)))),sk1))) )],[refute_0_1478,refute_0_1897]) ).
cnf(refute_0_1899,plain,
join(composition(converse(sk1),sk1),one) = join(one,composition(converse(sk1),sk1)),
inference(subst,[],[refute_0_5:[bind(A,$fot(one)),bind(B,$fot(composition(converse(sk1),sk1)))]]) ).
cnf(refute_0_1900,plain,
( join(composition(converse(sk1),sk1),one) != join(one,composition(converse(sk1),sk1))
| join(one,composition(converse(sk1),sk1)) != one
| join(composition(converse(sk1),sk1),one) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(composition(converse(sk1),sk1),one),one) ),[0],$fot(join(one,composition(converse(sk1),sk1)))]]) ).
cnf(refute_0_1901,plain,
( join(one,composition(converse(sk1),sk1)) != one
| join(composition(converse(sk1),sk1),one) = one ),
inference(resolve,[$cnf( $equal(join(composition(converse(sk1),sk1),one),join(one,composition(converse(sk1),sk1))) )],[refute_0_1899,refute_0_1900]) ).
cnf(refute_0_1902,plain,
join(one,composition(converse(sk1),sk1)) != one,
inference(resolve,[$cnf( $equal(join(composition(converse(sk1),sk1),one),one) )],[refute_0_1901,goals_15]) ).
cnf(refute_0_1903,plain,
( one != join(one,composition(converse(sk1),sk1))
| join(one,composition(converse(sk1),sk1)) = one ),
inference(subst,[],[refute_0_3:[bind(X,$fot(one)),bind(Y,$fot(join(one,composition(converse(sk1),sk1))))]]) ).
cnf(refute_0_1904,plain,
one != join(one,composition(converse(sk1),sk1)),
inference(resolve,[$cnf( $equal(join(one,composition(converse(sk1),sk1)),one) )],[refute_0_1903,refute_0_1902]) ).
cnf(refute_0_1905,plain,
$false,
inference(resolve,[$cnf( $equal(one,join(one,composition(converse(sk1),sk1))) )],[refute_0_1898,refute_0_1904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : REL042-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n020.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 : Fri Jul 8 10:10:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 16.53/16.74 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.53/16.74
% 16.53/16.74 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.75/16.98
%------------------------------------------------------------------------------