TSTP Solution File: REL007-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL007-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:09 EDT 2022
% Result : Unsatisfiable 6.06s 6.27s
% Output : CNFRefutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 180
% Syntax : Number of clauses : 739 ( 373 unt; 0 nHn; 450 RR)
% Number of literals : 1263 (1262 equ; 526 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 860 ( 13 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(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(sk1,converse(sk2)) = zero ).
cnf(goals_15,negated_conjecture,
meet(converse(sk1),sk2) != zero ).
cnf(refute_0_0,plain,
meet(A,join(zero,complement(X_16))) = complement(join(complement(A),complement(join(zero,complement(X_16))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(join(zero,complement(X_16))))]]) ).
cnf(refute_0_1,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_2,plain,
zero = meet(join(complement(X_4),complement(X_5)),complement(join(complement(X_4),complement(X_5)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_4),complement(X_5))))]]) ).
cnf(refute_0_3,plain,
meet(X_4,X_5) = complement(join(complement(X_4),complement(X_5))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_4)),bind(B,$fot(X_5))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( meet(X_4,X_5) != complement(join(complement(X_4),complement(X_5)))
| complement(join(complement(X_4),complement(X_5))) = meet(X_4,X_5) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(X_4,X_5))),bind(Y,$fot(complement(join(complement(X_4),complement(X_5)))))]]) ).
cnf(refute_0_8,plain,
complement(join(complement(X_4),complement(X_5))) = meet(X_4,X_5),
inference(resolve,[$cnf( $equal(meet(X_4,X_5),complement(join(complement(X_4),complement(X_5)))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( complement(join(complement(X_4),complement(X_5))) != meet(X_4,X_5)
| zero != meet(join(complement(X_4),complement(X_5)),complement(join(complement(X_4),complement(X_5))))
| zero = meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_4),complement(X_5)),complement(join(complement(X_4),complement(X_5))))) ),[1,1],$fot(meet(X_4,X_5))]]) ).
cnf(refute_0_10,plain,
( zero != meet(join(complement(X_4),complement(X_5)),complement(join(complement(X_4),complement(X_5))))
| zero = meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_4),complement(X_5))),meet(X_4,X_5)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
zero = meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_4),complement(X_5)),complement(join(complement(X_4),complement(X_5))))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_13,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_12]) ).
cnf(refute_0_14,plain,
join(meet(X_4,X_5),complement(meet(X_4,X_5))) = top,
inference(subst,[],[refute_0_13:[bind(A,$fot(meet(X_4,X_5)))]]) ).
cnf(refute_0_15,plain,
complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) = complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))))]]) ).
cnf(refute_0_16,plain,
( complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) != complement(join(meet(X_4,X_5),complement(meet(X_4,X_5))))
| join(meet(X_4,X_5),complement(meet(X_4,X_5))) != top
| complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))),complement(join(meet(X_4,X_5),complement(meet(X_4,X_5))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_17,plain,
( join(meet(X_4,X_5),complement(meet(X_4,X_5))) != top
| complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))),complement(join(meet(X_4,X_5),complement(meet(X_4,X_5))))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_4,X_5),complement(meet(X_4,X_5))),top) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
meet(join(complement(X_4),complement(X_5)),B) = complement(join(complement(join(complement(X_4),complement(X_5))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_4),complement(X_5))))]]) ).
cnf(refute_0_20,plain,
( complement(join(complement(X_4),complement(X_5))) != meet(X_4,X_5)
| meet(join(complement(X_4),complement(X_5)),B) != complement(join(complement(join(complement(X_4),complement(X_5))),complement(B)))
| meet(join(complement(X_4),complement(X_5)),B) = complement(join(meet(X_4,X_5),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_4),complement(X_5)),B),complement(join(complement(join(complement(X_4),complement(X_5))),complement(B)))) ),[1,0,0],$fot(meet(X_4,X_5))]]) ).
cnf(refute_0_21,plain,
( meet(join(complement(X_4),complement(X_5)),B) != complement(join(complement(join(complement(X_4),complement(X_5))),complement(B)))
| meet(join(complement(X_4),complement(X_5)),B) = complement(join(meet(X_4,X_5),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_4),complement(X_5))),meet(X_4,X_5)) )],[refute_0_8,refute_0_20]) ).
cnf(refute_0_22,plain,
meet(join(complement(X_4),complement(X_5)),B) = complement(join(meet(X_4,X_5),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_4),complement(X_5)),B),complement(join(complement(join(complement(X_4),complement(X_5))),complement(B)))) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) = complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))),
inference(subst,[],[refute_0_22:[bind(B,$fot(meet(X_4,X_5)))]]) ).
cnf(refute_0_24,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_25,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_6,refute_0_24]) ).
cnf(refute_0_26,plain,
( complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) != complement(top)
| meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) != complement(join(meet(X_4,X_5),complement(meet(X_4,X_5))))
| meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) = complement(top) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)))),bind(Y,$fot(complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_27,plain,
( complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))) != complement(top)
| meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)),complement(join(meet(X_4,X_5),complement(meet(X_4,X_5))))) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_4,X_5),complement(meet(X_4,X_5)))),complement(top)) )],[refute_0_18,refute_0_27]) ).
cnf(refute_0_29,plain,
( meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)) != complement(top)
| zero != meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_30,plain,
( zero != meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5)),complement(top)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_4),complement(X_5)),meet(X_4,X_5))) )],[refute_0_11,refute_0_30]) ).
cnf(refute_0_32,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_6:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_33,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_35,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_1,refute_0_35]) ).
cnf(refute_0_37,plain,
meet(top,X_16) = complement(join(zero,complement(X_16))),
inference(subst,[],[refute_0_36:[bind(B,$fot(X_16))]]) ).
cnf(refute_0_38,plain,
( meet(top,X_16) != complement(join(zero,complement(X_16)))
| complement(join(zero,complement(X_16))) = meet(top,X_16) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(top,X_16))),bind(Y,$fot(complement(join(zero,complement(X_16)))))]]) ).
cnf(refute_0_39,plain,
complement(join(zero,complement(X_16))) = meet(top,X_16),
inference(resolve,[$cnf( $equal(meet(top,X_16),complement(join(zero,complement(X_16)))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( complement(join(zero,complement(X_16))) != meet(top,X_16)
| meet(A,join(zero,complement(X_16))) != complement(join(complement(A),complement(join(zero,complement(X_16)))))
| meet(A,join(zero,complement(X_16))) = complement(join(complement(A),meet(top,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_16))),complement(join(complement(A),complement(join(zero,complement(X_16)))))) ),[1,0,1],$fot(meet(top,X_16))]]) ).
cnf(refute_0_41,plain,
( meet(A,join(zero,complement(X_16))) != complement(join(complement(A),complement(join(zero,complement(X_16)))))
| meet(A,join(zero,complement(X_16))) = complement(join(complement(A),meet(top,X_16))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_16))),meet(top,X_16)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
meet(A,join(zero,complement(X_16))) = complement(join(complement(A),meet(top,X_16))),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_16))),complement(join(complement(A),complement(join(zero,complement(X_16)))))) )],[refute_0_0,refute_0_41]) ).
cnf(refute_0_43,plain,
join(zero,join(zero,C)) = join(join(zero,zero),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero))]]) ).
cnf(refute_0_44,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_45,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_44]) ).
cnf(refute_0_46,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_45:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_47,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_48,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_48]) ).
cnf(refute_0_50,plain,
join(complement(top),composition(converse(X_14),complement(composition(X_14,top)))) = complement(top),
inference(subst,[],[refute_0_49:[bind(A,$fot(X_14)),bind(B,$fot(top))]]) ).
cnf(refute_0_51,plain,
( complement(top) != zero
| join(complement(top),composition(converse(X_14),complement(composition(X_14,top)))) != complement(top)
| join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_14),complement(composition(X_14,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_52,plain,
( join(complement(top),composition(converse(X_14),complement(composition(X_14,top)))) != complement(top)
| join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_51]) ).
cnf(refute_0_53,plain,
join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_14),complement(composition(X_14,top)))),complement(top)) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
( complement(top) != zero
| join(zero,composition(converse(X_14),complement(composition(X_14,top)))) != complement(top)
| join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_14),complement(composition(X_14,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_55,plain,
( join(zero,composition(converse(X_14),complement(composition(X_14,top)))) != complement(top)
| join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_54]) ).
cnf(refute_0_56,plain,
join(zero,composition(converse(X_14),complement(composition(X_14,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_14),complement(composition(X_14,top)))),complement(top)) )],[refute_0_53,refute_0_55]) ).
cnf(refute_0_57,plain,
join(zero,composition(converse(converse(one)),complement(composition(converse(one),top)))) = zero,
inference(subst,[],[refute_0_56:[bind(X_14,$fot(converse(one)))]]) ).
cnf(refute_0_58,plain,
converse(composition(converse(A),X_19)) = composition(converse(X_19),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_19))]]) ).
cnf(refute_0_59,plain,
( converse(composition(converse(A),X_19)) != composition(converse(X_19),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_19)) = composition(converse(X_19),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_19)),composition(converse(X_19),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_60,plain,
( converse(composition(converse(A),X_19)) != composition(converse(X_19),converse(converse(A)))
| converse(composition(converse(A),X_19)) = composition(converse(X_19),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_59]) ).
cnf(refute_0_61,plain,
converse(composition(converse(A),X_19)) = composition(converse(X_19),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_19)),composition(converse(X_19),converse(converse(A)))) )],[refute_0_58,refute_0_60]) ).
cnf(refute_0_62,plain,
converse(composition(converse(X_46),one)) = composition(converse(one),X_46),
inference(subst,[],[refute_0_61:[bind(A,$fot(X_46)),bind(X_19,$fot(one))]]) ).
cnf(refute_0_63,plain,
composition(converse(X_46),one) = converse(X_46),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_46)))]]) ).
cnf(refute_0_64,plain,
( composition(converse(X_46),one) != converse(X_46)
| converse(composition(converse(X_46),one)) != composition(converse(one),X_46)
| converse(converse(X_46)) = composition(converse(one),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_46),one)),composition(converse(one),X_46)) ),[0,0],$fot(converse(X_46))]]) ).
cnf(refute_0_65,plain,
( converse(composition(converse(X_46),one)) != composition(converse(one),X_46)
| converse(converse(X_46)) = composition(converse(one),X_46) ),
inference(resolve,[$cnf( $equal(composition(converse(X_46),one),converse(X_46)) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
converse(converse(X_46)) = composition(converse(one),X_46),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_46),one)),composition(converse(one),X_46)) )],[refute_0_62,refute_0_65]) ).
cnf(refute_0_67,plain,
converse(converse(X_46)) = X_46,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_46))]]) ).
cnf(refute_0_68,plain,
( converse(converse(X_46)) != X_46
| converse(converse(X_46)) != composition(converse(one),X_46)
| X_46 = composition(converse(one),X_46) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_46)),composition(converse(one),X_46)) ),[0],$fot(X_46)]]) ).
cnf(refute_0_69,plain,
( converse(converse(X_46)) != composition(converse(one),X_46)
| X_46 = composition(converse(one),X_46) ),
inference(resolve,[$cnf( $equal(converse(converse(X_46)),X_46) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
X_46 = composition(converse(one),X_46),
inference(resolve,[$cnf( $equal(converse(converse(X_46)),composition(converse(one),X_46)) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
top = composition(converse(one),top),
inference(subst,[],[refute_0_70:[bind(X_46,$fot(top))]]) ).
cnf(refute_0_72,plain,
( top != composition(converse(one),top)
| composition(converse(one),top) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(composition(converse(one),top)))]]) ).
cnf(refute_0_73,plain,
composition(converse(one),top) = top,
inference(resolve,[$cnf( $equal(top,composition(converse(one),top)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( composition(converse(one),top) != top
| join(zero,composition(converse(converse(one)),complement(composition(converse(one),top)))) != zero
| join(zero,composition(converse(converse(one)),complement(top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(composition(converse(one),top)))),zero) ),[0,1,1,0],$fot(top)]]) ).
cnf(refute_0_75,plain,
( join(zero,composition(converse(converse(one)),complement(composition(converse(one),top)))) != zero
| join(zero,composition(converse(converse(one)),complement(top))) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(one),top),top) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
join(zero,composition(converse(converse(one)),complement(top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(composition(converse(one),top)))),zero) )],[refute_0_57,refute_0_75]) ).
cnf(refute_0_77,plain,
composition(X_25,composition(one,X_27)) = composition(composition(X_25,one),X_27),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(X_25)),bind(B,$fot(one)),bind(C,$fot(X_27))]]) ).
cnf(refute_0_78,plain,
composition(X_25,one) = X_25,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_25))]]) ).
cnf(refute_0_79,plain,
( composition(X_25,composition(one,X_27)) != composition(composition(X_25,one),X_27)
| composition(X_25,one) != X_25
| composition(X_25,composition(one,X_27)) = composition(X_25,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_25,composition(one,X_27)),composition(composition(X_25,one),X_27)) ),[1,0],$fot(X_25)]]) ).
cnf(refute_0_80,plain,
( composition(X_25,composition(one,X_27)) != composition(composition(X_25,one),X_27)
| composition(X_25,composition(one,X_27)) = composition(X_25,X_27) ),
inference(resolve,[$cnf( $equal(composition(X_25,one),X_25) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
composition(X_25,composition(one,X_27)) = composition(X_25,X_27),
inference(resolve,[$cnf( $equal(composition(X_25,composition(one,X_27)),composition(composition(X_25,one),X_27)) )],[refute_0_77,refute_0_80]) ).
cnf(refute_0_82,plain,
composition(converse(one),composition(one,X_27)) = composition(converse(one),X_27),
inference(subst,[],[refute_0_81:[bind(X_25,$fot(converse(one)))]]) ).
cnf(refute_0_83,plain,
composition(one,X_27) = composition(converse(one),composition(one,X_27)),
inference(subst,[],[refute_0_70:[bind(X_46,$fot(composition(one,X_27)))]]) ).
cnf(refute_0_84,plain,
( composition(one,X_27) != composition(converse(one),composition(one,X_27))
| composition(converse(one),composition(one,X_27)) = composition(one,X_27) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(composition(one,X_27))),bind(Y,$fot(composition(converse(one),composition(one,X_27))))]]) ).
cnf(refute_0_85,plain,
composition(converse(one),composition(one,X_27)) = composition(one,X_27),
inference(resolve,[$cnf( $equal(composition(one,X_27),composition(converse(one),composition(one,X_27))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
( composition(converse(one),composition(one,X_27)) != composition(converse(one),X_27)
| composition(converse(one),composition(one,X_27)) != composition(one,X_27)
| composition(one,X_27) = composition(converse(one),X_27) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),composition(one,X_27)),composition(converse(one),X_27)) ),[0],$fot(composition(one,X_27))]]) ).
cnf(refute_0_87,plain,
( composition(converse(one),composition(one,X_27)) != composition(converse(one),X_27)
| composition(one,X_27) = composition(converse(one),X_27) ),
inference(resolve,[$cnf( $equal(composition(converse(one),composition(one,X_27)),composition(one,X_27)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
composition(one,X_27) = composition(converse(one),X_27),
inference(resolve,[$cnf( $equal(composition(converse(one),composition(one,X_27)),composition(converse(one),X_27)) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
( X_46 != composition(converse(one),X_46)
| composition(converse(one),X_46) = X_46 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_46)),bind(Y,$fot(composition(converse(one),X_46)))]]) ).
cnf(refute_0_90,plain,
composition(converse(one),X_46) = X_46,
inference(resolve,[$cnf( $equal(X_46,composition(converse(one),X_46)) )],[refute_0_70,refute_0_89]) ).
cnf(refute_0_91,plain,
composition(converse(one),X_27) = X_27,
inference(subst,[],[refute_0_90:[bind(X_46,$fot(X_27))]]) ).
cnf(refute_0_92,plain,
( composition(converse(one),X_27) != X_27
| composition(one,X_27) != composition(converse(one),X_27)
| composition(one,X_27) = X_27 ),
introduced(tautology,[equality,[$cnf( $equal(composition(one,X_27),composition(converse(one),X_27)) ),[1],$fot(X_27)]]) ).
cnf(refute_0_93,plain,
( composition(one,X_27) != composition(converse(one),X_27)
| composition(one,X_27) = X_27 ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_27),X_27) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
composition(one,X_27) = X_27,
inference(resolve,[$cnf( $equal(composition(one,X_27),composition(converse(one),X_27)) )],[refute_0_88,refute_0_93]) ).
cnf(refute_0_95,plain,
composition(one,zero) = zero,
inference(subst,[],[refute_0_94:[bind(X_27,$fot(zero))]]) ).
cnf(refute_0_96,plain,
composition(one,complement(top)) = composition(one,complement(top)),
introduced(tautology,[refl,[$fot(composition(one,complement(top)))]]) ).
cnf(refute_0_97,plain,
( complement(top) != zero
| composition(one,complement(top)) != composition(one,complement(top))
| composition(one,complement(top)) = composition(one,zero) ),
introduced(tautology,[equality,[$cnf( $equal(composition(one,complement(top)),composition(one,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_98,plain,
( complement(top) != zero
| composition(one,complement(top)) = composition(one,zero) ),
inference(resolve,[$cnf( $equal(composition(one,complement(top)),composition(one,complement(top))) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
composition(one,complement(top)) = composition(one,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_98]) ).
cnf(refute_0_100,plain,
converse(converse(one)) = one,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(one))]]) ).
cnf(refute_0_101,plain,
composition(converse(converse(one)),complement(top)) = composition(converse(converse(one)),complement(top)),
introduced(tautology,[refl,[$fot(composition(converse(converse(one)),complement(top)))]]) ).
cnf(refute_0_102,plain,
( composition(converse(converse(one)),complement(top)) != composition(converse(converse(one)),complement(top))
| converse(converse(one)) != one
| composition(converse(converse(one)),complement(top)) = composition(one,complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(one)),complement(top)),composition(converse(converse(one)),complement(top))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_103,plain,
( converse(converse(one)) != one
| composition(converse(converse(one)),complement(top)) = composition(one,complement(top)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(top)),composition(converse(converse(one)),complement(top))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
composition(converse(converse(one)),complement(top)) = composition(one,complement(top)),
inference(resolve,[$cnf( $equal(converse(converse(one)),one) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
( composition(converse(converse(one)),complement(top)) != composition(one,complement(top))
| composition(one,complement(top)) != composition(one,zero)
| composition(converse(converse(one)),complement(top)) = composition(one,zero) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(composition(converse(converse(one)),complement(top)))),bind(Y,$fot(composition(one,complement(top)))),bind(Z,$fot(composition(one,zero)))]]) ).
cnf(refute_0_106,plain,
( composition(one,complement(top)) != composition(one,zero)
| composition(converse(converse(one)),complement(top)) = composition(one,zero) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(top)),composition(one,complement(top))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
composition(converse(converse(one)),complement(top)) = composition(one,zero),
inference(resolve,[$cnf( $equal(composition(one,complement(top)),composition(one,zero)) )],[refute_0_99,refute_0_106]) ).
cnf(refute_0_108,plain,
( composition(converse(converse(one)),complement(top)) != composition(one,zero)
| composition(one,zero) != zero
| composition(converse(converse(one)),complement(top)) = zero ),
inference(subst,[],[refute_0_25:[bind(X,$fot(composition(converse(converse(one)),complement(top)))),bind(Y,$fot(composition(one,zero))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_109,plain,
( composition(one,zero) != zero
| composition(converse(converse(one)),complement(top)) = zero ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(top)),composition(one,zero)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
composition(converse(converse(one)),complement(top)) = zero,
inference(resolve,[$cnf( $equal(composition(one,zero),zero) )],[refute_0_95,refute_0_109]) ).
cnf(refute_0_111,plain,
join(zero,composition(converse(converse(one)),complement(top))) = join(zero,composition(converse(converse(one)),complement(top))),
introduced(tautology,[refl,[$fot(join(zero,composition(converse(converse(one)),complement(top))))]]) ).
cnf(refute_0_112,plain,
( composition(converse(converse(one)),complement(top)) != zero
| join(zero,composition(converse(converse(one)),complement(top))) != join(zero,composition(converse(converse(one)),complement(top)))
| join(zero,composition(converse(converse(one)),complement(top))) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(top))),join(zero,composition(converse(converse(one)),complement(top)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_113,plain,
( composition(converse(converse(one)),complement(top)) != zero
| join(zero,composition(converse(converse(one)),complement(top))) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(top))),join(zero,composition(converse(converse(one)),complement(top)))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
join(zero,composition(converse(converse(one)),complement(top))) = join(zero,zero),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(top)),zero) )],[refute_0_110,refute_0_113]) ).
cnf(refute_0_115,plain,
( join(zero,composition(converse(converse(one)),complement(top))) != join(zero,zero)
| join(zero,composition(converse(converse(one)),complement(top))) != zero
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(top))),zero) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_116,plain,
( join(zero,composition(converse(converse(one)),complement(top))) != zero
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(top))),join(zero,zero)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(converse(one)),complement(top))),zero) )],[refute_0_76,refute_0_116]) ).
cnf(refute_0_118,plain,
( join(zero,join(zero,C)) != join(join(zero,zero),C)
| join(zero,zero) != zero
| join(zero,join(zero,C)) = join(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_119,plain,
( join(zero,join(zero,C)) != join(join(zero,zero),C)
| join(zero,join(zero,C)) = join(zero,C) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
join(zero,join(zero,C)) = join(zero,C),
inference(resolve,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) )],[refute_0_43,refute_0_119]) ).
cnf(refute_0_121,plain,
join(zero,join(zero,meet(X_95,top))) = join(zero,meet(X_95,top)),
inference(subst,[],[refute_0_120:[bind(C,$fot(meet(X_95,top)))]]) ).
cnf(refute_0_122,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_45:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_123,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_124,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_124]) ).
cnf(refute_0_126,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_45:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_127,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_128,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_127]) ).
cnf(refute_0_129,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_130,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_131,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_25:[bind(X,$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_134,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_126,refute_0_134]) ).
cnf(refute_0_136,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_137,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_125,refute_0_137]) ).
cnf(refute_0_139,plain,
X_93 = join(meet(X_93,top),complement(join(complement(X_93),top))),
inference(subst,[],[refute_0_138:[bind(A,$fot(X_93)),bind(B,$fot(top))]]) ).
cnf(refute_0_140,plain,
join(X_34,join(complement(X_34),X_36)) = join(join(X_34,complement(X_34)),X_36),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_34)),bind(B,$fot(complement(X_34))),bind(C,$fot(X_36))]]) ).
cnf(refute_0_141,plain,
top = join(X_34,complement(X_34)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_34))]]) ).
cnf(refute_0_142,plain,
( top != join(X_34,complement(X_34))
| join(X_34,complement(X_34)) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(X_34,complement(X_34))))]]) ).
cnf(refute_0_143,plain,
join(X_34,complement(X_34)) = top,
inference(resolve,[$cnf( $equal(top,join(X_34,complement(X_34))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( join(X_34,complement(X_34)) != top
| join(X_34,join(complement(X_34),X_36)) != join(join(X_34,complement(X_34)),X_36)
| join(X_34,join(complement(X_34),X_36)) = join(top,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_34,join(complement(X_34),X_36)),join(join(X_34,complement(X_34)),X_36)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_145,plain,
( join(X_34,join(complement(X_34),X_36)) != join(join(X_34,complement(X_34)),X_36)
| join(X_34,join(complement(X_34),X_36)) = join(top,X_36) ),
inference(resolve,[$cnf( $equal(join(X_34,complement(X_34)),top) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
join(X_34,join(complement(X_34),X_36)) = join(top,X_36),
inference(resolve,[$cnf( $equal(join(X_34,join(complement(X_34),X_36)),join(join(X_34,complement(X_34)),X_36)) )],[refute_0_140,refute_0_145]) ).
cnf(refute_0_147,plain,
join(X_41,join(complement(X_41),complement(complement(X_41)))) = join(top,complement(complement(X_41))),
inference(subst,[],[refute_0_146:[bind(X_34,$fot(X_41)),bind(X_36,$fot(complement(complement(X_41))))]]) ).
cnf(refute_0_148,plain,
top = join(complement(X_41),complement(complement(X_41))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_41)))]]) ).
cnf(refute_0_149,plain,
( top != join(complement(X_41),complement(complement(X_41)))
| join(complement(X_41),complement(complement(X_41))) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_41),complement(complement(X_41)))))]]) ).
cnf(refute_0_150,plain,
join(complement(X_41),complement(complement(X_41))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_41),complement(complement(X_41)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( join(X_41,join(complement(X_41),complement(complement(X_41)))) != join(top,complement(complement(X_41)))
| join(complement(X_41),complement(complement(X_41))) != top
| join(X_41,top) = join(top,complement(complement(X_41))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),complement(complement(X_41)))),join(top,complement(complement(X_41)))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_152,plain,
( join(X_41,join(complement(X_41),complement(complement(X_41)))) != join(top,complement(complement(X_41)))
| join(X_41,top) = join(top,complement(complement(X_41))) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),complement(complement(X_41))),top) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
join(X_41,top) = join(top,complement(complement(X_41))),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),complement(complement(X_41)))),join(top,complement(complement(X_41)))) )],[refute_0_147,refute_0_152]) ).
cnf(refute_0_154,plain,
top = join(join(X_34,X_35),complement(join(X_34,X_35))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_34,X_35)))]]) ).
cnf(refute_0_155,plain,
join(X_34,join(X_35,complement(join(X_34,X_35)))) = join(join(X_34,X_35),complement(join(X_34,X_35))),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(complement(join(X_34,X_35))))]]) ).
cnf(refute_0_156,plain,
( join(X_34,join(X_35,complement(join(X_34,X_35)))) != join(join(X_34,X_35),complement(join(X_34,X_35)))
| join(join(X_34,X_35),complement(join(X_34,X_35))) = join(X_34,join(X_35,complement(join(X_34,X_35)))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_34,join(X_35,complement(join(X_34,X_35)))))),bind(Y,$fot(join(join(X_34,X_35),complement(join(X_34,X_35)))))]]) ).
cnf(refute_0_157,plain,
join(join(X_34,X_35),complement(join(X_34,X_35))) = join(X_34,join(X_35,complement(join(X_34,X_35)))),
inference(resolve,[$cnf( $equal(join(X_34,join(X_35,complement(join(X_34,X_35)))),join(join(X_34,X_35),complement(join(X_34,X_35)))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( join(join(X_34,X_35),complement(join(X_34,X_35))) != join(X_34,join(X_35,complement(join(X_34,X_35))))
| top != join(join(X_34,X_35),complement(join(X_34,X_35)))
| top = join(X_34,join(X_35,complement(join(X_34,X_35)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_34,X_35),complement(join(X_34,X_35)))) ),[1],$fot(join(X_34,join(X_35,complement(join(X_34,X_35)))))]]) ).
cnf(refute_0_159,plain,
( top != join(join(X_34,X_35),complement(join(X_34,X_35)))
| top = join(X_34,join(X_35,complement(join(X_34,X_35)))) ),
inference(resolve,[$cnf( $equal(join(join(X_34,X_35),complement(join(X_34,X_35))),join(X_34,join(X_35,complement(join(X_34,X_35))))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
top = join(X_34,join(X_35,complement(join(X_34,X_35)))),
inference(resolve,[$cnf( $equal(top,join(join(X_34,X_35),complement(join(X_34,X_35)))) )],[refute_0_154,refute_0_159]) ).
cnf(refute_0_161,plain,
top = join(complement(X_50),join(complement(X_50),complement(join(complement(X_50),complement(X_50))))),
inference(subst,[],[refute_0_160:[bind(X_34,$fot(complement(X_50))),bind(X_35,$fot(complement(X_50)))]]) ).
cnf(refute_0_162,plain,
join(complement(B),composition(converse(converse(one)),complement(composition(converse(one),B)))) = complement(B),
inference(subst,[],[refute_0_49:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_163,plain,
B = composition(converse(one),B),
inference(subst,[],[refute_0_70:[bind(X_46,$fot(B))]]) ).
cnf(refute_0_164,plain,
( B != composition(converse(one),B)
| composition(converse(one),B) = B ),
inference(subst,[],[refute_0_6:[bind(X,$fot(B)),bind(Y,$fot(composition(converse(one),B)))]]) ).
cnf(refute_0_165,plain,
composition(converse(one),B) = B,
inference(resolve,[$cnf( $equal(B,composition(converse(one),B)) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
( composition(converse(one),B) != B
| join(complement(B),composition(converse(converse(one)),complement(composition(converse(one),B)))) != complement(B)
| join(complement(B),composition(converse(converse(one)),complement(B))) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(composition(converse(one),B)))),complement(B)) ),[0,1,1,0],$fot(B)]]) ).
cnf(refute_0_167,plain,
( join(complement(B),composition(converse(converse(one)),complement(composition(converse(one),B)))) != complement(B)
| join(complement(B),composition(converse(converse(one)),complement(B))) = complement(B) ),
inference(resolve,[$cnf( $equal(composition(converse(one),B),B) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
join(complement(B),composition(converse(converse(one)),complement(B))) = complement(B),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(composition(converse(one),B)))),complement(B)) )],[refute_0_162,refute_0_167]) ).
cnf(refute_0_169,plain,
composition(one,complement(B)) = complement(B),
inference(subst,[],[refute_0_94:[bind(X_27,$fot(complement(B)))]]) ).
cnf(refute_0_170,plain,
composition(converse(converse(one)),complement(B)) = composition(converse(converse(one)),complement(B)),
introduced(tautology,[refl,[$fot(composition(converse(converse(one)),complement(B)))]]) ).
cnf(refute_0_171,plain,
( composition(converse(converse(one)),complement(B)) != composition(converse(converse(one)),complement(B))
| converse(converse(one)) != one
| composition(converse(converse(one)),complement(B)) = composition(one,complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(converse(one)),complement(B)),composition(converse(converse(one)),complement(B))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_172,plain,
( converse(converse(one)) != one
| composition(converse(converse(one)),complement(B)) = composition(one,complement(B)) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(B)),composition(converse(converse(one)),complement(B))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
composition(converse(converse(one)),complement(B)) = composition(one,complement(B)),
inference(resolve,[$cnf( $equal(converse(converse(one)),one) )],[refute_0_100,refute_0_172]) ).
cnf(refute_0_174,plain,
( composition(converse(converse(one)),complement(B)) != composition(one,complement(B))
| composition(one,complement(B)) != complement(B)
| composition(converse(converse(one)),complement(B)) = complement(B) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(composition(converse(converse(one)),complement(B)))),bind(Y,$fot(composition(one,complement(B)))),bind(Z,$fot(complement(B)))]]) ).
cnf(refute_0_175,plain,
( composition(one,complement(B)) != complement(B)
| composition(converse(converse(one)),complement(B)) = complement(B) ),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(B)),composition(one,complement(B))) )],[refute_0_173,refute_0_174]) ).
cnf(refute_0_176,plain,
composition(converse(converse(one)),complement(B)) = complement(B),
inference(resolve,[$cnf( $equal(composition(one,complement(B)),complement(B)) )],[refute_0_169,refute_0_175]) ).
cnf(refute_0_177,plain,
join(complement(B),composition(converse(converse(one)),complement(B))) = join(complement(B),composition(converse(converse(one)),complement(B))),
introduced(tautology,[refl,[$fot(join(complement(B),composition(converse(converse(one)),complement(B))))]]) ).
cnf(refute_0_178,plain,
( composition(converse(converse(one)),complement(B)) != complement(B)
| join(complement(B),composition(converse(converse(one)),complement(B))) != join(complement(B),composition(converse(converse(one)),complement(B)))
| join(complement(B),composition(converse(converse(one)),complement(B))) = join(complement(B),complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(B))),join(complement(B),composition(converse(converse(one)),complement(B)))) ),[1,1],$fot(complement(B))]]) ).
cnf(refute_0_179,plain,
( composition(converse(converse(one)),complement(B)) != complement(B)
| join(complement(B),composition(converse(converse(one)),complement(B))) = join(complement(B),complement(B)) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(B))),join(complement(B),composition(converse(converse(one)),complement(B)))) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
join(complement(B),composition(converse(converse(one)),complement(B))) = join(complement(B),complement(B)),
inference(resolve,[$cnf( $equal(composition(converse(converse(one)),complement(B)),complement(B)) )],[refute_0_176,refute_0_179]) ).
cnf(refute_0_181,plain,
( join(complement(B),composition(converse(converse(one)),complement(B))) != complement(B)
| join(complement(B),composition(converse(converse(one)),complement(B))) != join(complement(B),complement(B))
| join(complement(B),complement(B)) = complement(B) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(B))),complement(B)) ),[0],$fot(join(complement(B),complement(B)))]]) ).
cnf(refute_0_182,plain,
( join(complement(B),composition(converse(converse(one)),complement(B))) != complement(B)
| join(complement(B),complement(B)) = complement(B) ),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(B))),join(complement(B),complement(B))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
join(complement(B),complement(B)) = complement(B),
inference(resolve,[$cnf( $equal(join(complement(B),composition(converse(converse(one)),complement(B))),complement(B)) )],[refute_0_168,refute_0_182]) ).
cnf(refute_0_184,plain,
join(complement(X_50),complement(X_50)) = complement(X_50),
inference(subst,[],[refute_0_183:[bind(B,$fot(X_50))]]) ).
cnf(refute_0_185,plain,
( join(complement(X_50),complement(X_50)) != complement(X_50)
| top != join(complement(X_50),join(complement(X_50),complement(join(complement(X_50),complement(X_50)))))
| top = join(complement(X_50),join(complement(X_50),complement(complement(X_50)))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_50),join(complement(X_50),complement(join(complement(X_50),complement(X_50)))))) ),[1,1,1,0],$fot(complement(X_50))]]) ).
cnf(refute_0_186,plain,
( top != join(complement(X_50),join(complement(X_50),complement(join(complement(X_50),complement(X_50)))))
| top = join(complement(X_50),join(complement(X_50),complement(complement(X_50)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),complement(X_50)),complement(X_50)) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
top = join(complement(X_50),join(complement(X_50),complement(complement(X_50)))),
inference(resolve,[$cnf( $equal(top,join(complement(X_50),join(complement(X_50),complement(join(complement(X_50),complement(X_50)))))) )],[refute_0_161,refute_0_186]) ).
cnf(refute_0_188,plain,
join(X_41,join(complement(X_41),X_42)) = join(top,X_42),
inference(subst,[],[refute_0_146:[bind(X_34,$fot(X_41)),bind(X_36,$fot(X_42))]]) ).
cnf(refute_0_189,plain,
join(X_42,complement(X_41)) = join(complement(X_41),X_42),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_42)),bind(B,$fot(complement(X_41)))]]) ).
cnf(refute_0_190,plain,
( join(X_42,complement(X_41)) != join(complement(X_41),X_42)
| join(complement(X_41),X_42) = join(X_42,complement(X_41)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_42,complement(X_41)))),bind(Y,$fot(join(complement(X_41),X_42)))]]) ).
cnf(refute_0_191,plain,
join(complement(X_41),X_42) = join(X_42,complement(X_41)),
inference(resolve,[$cnf( $equal(join(X_42,complement(X_41)),join(complement(X_41),X_42)) )],[refute_0_189,refute_0_190]) ).
cnf(refute_0_192,plain,
( join(X_41,join(complement(X_41),X_42)) != join(top,X_42)
| join(complement(X_41),X_42) != join(X_42,complement(X_41))
| join(X_41,join(X_42,complement(X_41))) = join(top,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_41,join(complement(X_41),X_42)),join(top,X_42)) ),[0,1],$fot(join(X_42,complement(X_41)))]]) ).
cnf(refute_0_193,plain,
( join(X_41,join(complement(X_41),X_42)) != join(top,X_42)
| join(X_41,join(X_42,complement(X_41))) = join(top,X_42) ),
inference(resolve,[$cnf( $equal(join(complement(X_41),X_42),join(X_42,complement(X_41))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
join(X_41,join(X_42,complement(X_41))) = join(top,X_42),
inference(resolve,[$cnf( $equal(join(X_41,join(complement(X_41),X_42)),join(top,X_42)) )],[refute_0_188,refute_0_193]) ).
cnf(refute_0_195,plain,
join(complement(X_50),join(complement(X_50),complement(complement(X_50)))) = join(top,complement(X_50)),
inference(subst,[],[refute_0_194:[bind(X_41,$fot(complement(X_50))),bind(X_42,$fot(complement(X_50)))]]) ).
cnf(refute_0_196,plain,
( join(complement(X_50),join(complement(X_50),complement(complement(X_50)))) != join(top,complement(X_50))
| top != join(complement(X_50),join(complement(X_50),complement(complement(X_50))))
| top = join(top,complement(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(complement(X_50),join(complement(X_50),complement(complement(X_50))))) ),[1],$fot(join(top,complement(X_50)))]]) ).
cnf(refute_0_197,plain,
( top != join(complement(X_50),join(complement(X_50),complement(complement(X_50))))
| top = join(top,complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),join(complement(X_50),complement(complement(X_50)))),join(top,complement(X_50))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
top = join(top,complement(X_50)),
inference(resolve,[$cnf( $equal(top,join(complement(X_50),join(complement(X_50),complement(complement(X_50))))) )],[refute_0_187,refute_0_197]) ).
cnf(refute_0_199,plain,
( top != join(top,complement(X_50))
| join(top,complement(X_50)) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(X_50))))]]) ).
cnf(refute_0_200,plain,
join(top,complement(X_50)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(X_50))) )],[refute_0_198,refute_0_199]) ).
cnf(refute_0_201,plain,
join(top,complement(complement(X_41))) = top,
inference(subst,[],[refute_0_200:[bind(X_50,$fot(complement(X_41)))]]) ).
cnf(refute_0_202,plain,
( join(X_41,top) != join(top,complement(complement(X_41)))
| join(top,complement(complement(X_41))) != top
| join(X_41,top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_41,top),top) ),[0],$fot(join(top,complement(complement(X_41))))]]) ).
cnf(refute_0_203,plain,
( join(X_41,top) != join(top,complement(complement(X_41)))
| join(X_41,top) = top ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_41))),top) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
join(X_41,top) = top,
inference(resolve,[$cnf( $equal(join(X_41,top),join(top,complement(complement(X_41)))) )],[refute_0_153,refute_0_203]) ).
cnf(refute_0_205,plain,
join(complement(X_93),top) = top,
inference(subst,[],[refute_0_204:[bind(X_41,$fot(complement(X_93)))]]) ).
cnf(refute_0_206,plain,
( X_93 != join(meet(X_93,top),complement(join(complement(X_93),top)))
| join(complement(X_93),top) != top
| X_93 = join(meet(X_93,top),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_93,join(meet(X_93,top),complement(join(complement(X_93),top)))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_207,plain,
( X_93 != join(meet(X_93,top),complement(join(complement(X_93),top)))
| X_93 = join(meet(X_93,top),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_93),top),top) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
X_93 = join(meet(X_93,top),complement(top)),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,top),complement(join(complement(X_93),top)))) )],[refute_0_139,refute_0_207]) ).
cnf(refute_0_209,plain,
join(complement(top),meet(X_93,top)) = join(complement(top),meet(X_93,top)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_93,top)))]]) ).
cnf(refute_0_210,plain,
( complement(top) != zero
| join(complement(top),meet(X_93,top)) != join(complement(top),meet(X_93,top))
| join(complement(top),meet(X_93,top)) = join(zero,meet(X_93,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_93,top)),join(complement(top),meet(X_93,top))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_211,plain,
( complement(top) != zero
| join(complement(top),meet(X_93,top)) = join(zero,meet(X_93,top)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_93,top)),join(complement(top),meet(X_93,top))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
join(complement(top),meet(X_93,top)) = join(zero,meet(X_93,top)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_211]) ).
cnf(refute_0_213,plain,
join(meet(X_93,top),complement(top)) = join(complement(top),meet(X_93,top)),
inference(subst,[],[refute_0_45:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_93,top)))]]) ).
cnf(refute_0_214,plain,
( join(complement(top),meet(X_93,top)) != join(zero,meet(X_93,top))
| join(meet(X_93,top),complement(top)) != join(complement(top),meet(X_93,top))
| join(meet(X_93,top),complement(top)) = join(zero,meet(X_93,top)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(meet(X_93,top),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_93,top)))),bind(Z,$fot(join(zero,meet(X_93,top))))]]) ).
cnf(refute_0_215,plain,
( join(complement(top),meet(X_93,top)) != join(zero,meet(X_93,top))
| join(meet(X_93,top),complement(top)) = join(zero,meet(X_93,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,top),complement(top)),join(complement(top),meet(X_93,top))) )],[refute_0_213,refute_0_214]) ).
cnf(refute_0_216,plain,
join(meet(X_93,top),complement(top)) = join(zero,meet(X_93,top)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_93,top)),join(zero,meet(X_93,top))) )],[refute_0_212,refute_0_215]) ).
cnf(refute_0_217,plain,
( X_93 != join(meet(X_93,top),complement(top))
| join(meet(X_93,top),complement(top)) != join(zero,meet(X_93,top))
| X_93 = join(zero,meet(X_93,top)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_93,join(zero,meet(X_93,top))) ),[0],$fot(join(meet(X_93,top),complement(top)))]]) ).
cnf(refute_0_218,plain,
( X_93 != join(meet(X_93,top),complement(top))
| X_93 = join(zero,meet(X_93,top)) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,top),complement(top)),join(zero,meet(X_93,top))) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
X_93 = join(zero,meet(X_93,top)),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,top),complement(top))) )],[refute_0_208,refute_0_218]) ).
cnf(refute_0_220,plain,
X_95 = join(zero,meet(X_95,top)),
inference(subst,[],[refute_0_219:[bind(X_93,$fot(X_95))]]) ).
cnf(refute_0_221,plain,
( X_95 != join(zero,meet(X_95,top))
| join(zero,meet(X_95,top)) = X_95 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_95)),bind(Y,$fot(join(zero,meet(X_95,top))))]]) ).
cnf(refute_0_222,plain,
join(zero,meet(X_95,top)) = X_95,
inference(resolve,[$cnf( $equal(X_95,join(zero,meet(X_95,top))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
( join(zero,join(zero,meet(X_95,top))) != join(zero,meet(X_95,top))
| join(zero,meet(X_95,top)) != X_95
| join(zero,X_95) = join(zero,meet(X_95,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_95,top))),join(zero,meet(X_95,top))) ),[0,1],$fot(X_95)]]) ).
cnf(refute_0_224,plain,
( join(zero,join(zero,meet(X_95,top))) != join(zero,meet(X_95,top))
| join(zero,X_95) = join(zero,meet(X_95,top)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_95,top)),X_95) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
join(zero,X_95) = join(zero,meet(X_95,top)),
inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_95,top))),join(zero,meet(X_95,top))) )],[refute_0_121,refute_0_224]) ).
cnf(refute_0_226,plain,
( join(zero,X_95) != join(zero,meet(X_95,top))
| join(zero,meet(X_95,top)) != X_95
| join(zero,X_95) = X_95 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_95),X_95) ),[0],$fot(join(zero,meet(X_95,top)))]]) ).
cnf(refute_0_227,plain,
( join(zero,X_95) != join(zero,meet(X_95,top))
| join(zero,X_95) = X_95 ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_95,top)),X_95) )],[refute_0_222,refute_0_226]) ).
cnf(refute_0_228,plain,
join(zero,X_95) = X_95,
inference(resolve,[$cnf( $equal(join(zero,X_95),join(zero,meet(X_95,top))) )],[refute_0_225,refute_0_227]) ).
cnf(refute_0_229,plain,
join(zero,complement(X_16)) = complement(X_16),
inference(subst,[],[refute_0_228:[bind(X_95,$fot(complement(X_16)))]]) ).
cnf(refute_0_230,plain,
meet(A,join(zero,complement(X_16))) = meet(A,join(zero,complement(X_16))),
introduced(tautology,[refl,[$fot(meet(A,join(zero,complement(X_16))))]]) ).
cnf(refute_0_231,plain,
( join(zero,complement(X_16)) != complement(X_16)
| meet(A,join(zero,complement(X_16))) != meet(A,join(zero,complement(X_16)))
| meet(A,join(zero,complement(X_16))) = meet(A,complement(X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_16))),meet(A,join(zero,complement(X_16)))) ),[1,1],$fot(complement(X_16))]]) ).
cnf(refute_0_232,plain,
( join(zero,complement(X_16)) != complement(X_16)
| meet(A,join(zero,complement(X_16))) = meet(A,complement(X_16)) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_16))),meet(A,join(zero,complement(X_16)))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
meet(A,join(zero,complement(X_16))) = meet(A,complement(X_16)),
inference(resolve,[$cnf( $equal(join(zero,complement(X_16)),complement(X_16)) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( meet(A,join(zero,complement(X_16))) != complement(join(complement(A),meet(top,X_16)))
| meet(A,join(zero,complement(X_16))) != meet(A,complement(X_16))
| meet(A,complement(X_16)) = complement(join(complement(A),meet(top,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,join(zero,complement(X_16))),complement(join(complement(A),meet(top,X_16)))) ),[0],$fot(meet(A,complement(X_16)))]]) ).
cnf(refute_0_235,plain,
( meet(A,join(zero,complement(X_16))) != complement(join(complement(A),meet(top,X_16)))
| meet(A,complement(X_16)) = complement(join(complement(A),meet(top,X_16))) ),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_16))),meet(A,complement(X_16))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
join(complement(A),complement(B)) = join(complement(B),complement(A)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(A))),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_237,plain,
( join(complement(A),complement(B)) != join(complement(B),complement(A))
| meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(join(complement(B),complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) ),[1,0],$fot(join(complement(B),complement(A)))]]) ).
cnf(refute_0_238,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| meet(A,B) = complement(join(complement(B),complement(A))) ),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(complement(B),complement(A))) )],[refute_0_236,refute_0_237]) ).
cnf(refute_0_239,plain,
meet(A,B) = complement(join(complement(B),complement(A))),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_238]) ).
cnf(refute_0_240,plain,
complement(join(complement(B),complement(A))) = meet(B,A),
inference(subst,[],[refute_0_128:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_241,plain,
( complement(join(complement(B),complement(A))) != meet(B,A)
| meet(A,B) != complement(join(complement(B),complement(A)))
| meet(A,B) = meet(B,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,B),complement(join(complement(B),complement(A)))) ),[1],$fot(meet(B,A))]]) ).
cnf(refute_0_242,plain,
( meet(A,B) != complement(join(complement(B),complement(A)))
| meet(A,B) = meet(B,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(B),complement(A))),meet(B,A)) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
meet(A,B) = meet(B,A),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(B),complement(A)))) )],[refute_0_239,refute_0_242]) ).
cnf(refute_0_244,plain,
meet(top,X_95) = meet(X_95,top),
inference(subst,[],[refute_0_243:[bind(A,$fot(top)),bind(B,$fot(X_95))]]) ).
cnf(refute_0_245,plain,
( meet(top,X_95) != meet(X_95,top)
| meet(X_95,top) = meet(top,X_95) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(top,X_95))),bind(Y,$fot(meet(X_95,top)))]]) ).
cnf(refute_0_246,plain,
meet(X_95,top) = meet(top,X_95),
inference(resolve,[$cnf( $equal(meet(top,X_95),meet(X_95,top)) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
( X_95 != join(zero,meet(X_95,top))
| meet(X_95,top) != meet(top,X_95)
| X_95 = join(zero,meet(top,X_95)) ),
introduced(tautology,[equality,[$cnf( $equal(X_95,join(zero,meet(X_95,top))) ),[1,1],$fot(meet(top,X_95))]]) ).
cnf(refute_0_248,plain,
( X_95 != join(zero,meet(X_95,top))
| X_95 = join(zero,meet(top,X_95)) ),
inference(resolve,[$cnf( $equal(meet(X_95,top),meet(top,X_95)) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
X_95 = join(zero,meet(top,X_95)),
inference(resolve,[$cnf( $equal(X_95,join(zero,meet(X_95,top))) )],[refute_0_220,refute_0_248]) ).
cnf(refute_0_250,plain,
join(zero,meet(top,X_95)) = meet(top,X_95),
inference(subst,[],[refute_0_228:[bind(X_95,$fot(meet(top,X_95)))]]) ).
cnf(refute_0_251,plain,
( X_95 != join(zero,meet(top,X_95))
| join(zero,meet(top,X_95)) != meet(top,X_95)
| X_95 = meet(top,X_95) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_95,meet(top,X_95)) ),[0],$fot(join(zero,meet(top,X_95)))]]) ).
cnf(refute_0_252,plain,
( X_95 != join(zero,meet(top,X_95))
| X_95 = meet(top,X_95) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,X_95)),meet(top,X_95)) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
X_95 = meet(top,X_95),
inference(resolve,[$cnf( $equal(X_95,join(zero,meet(top,X_95))) )],[refute_0_249,refute_0_252]) ).
cnf(refute_0_254,plain,
( X_95 != meet(top,X_95)
| meet(top,X_95) = X_95 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_95)),bind(Y,$fot(meet(top,X_95)))]]) ).
cnf(refute_0_255,plain,
meet(top,X_95) = X_95,
inference(resolve,[$cnf( $equal(X_95,meet(top,X_95)) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
meet(top,X_16) = X_16,
inference(subst,[],[refute_0_255:[bind(X_95,$fot(X_16))]]) ).
cnf(refute_0_257,plain,
join(complement(A),meet(top,X_16)) = join(complement(A),meet(top,X_16)),
introduced(tautology,[refl,[$fot(join(complement(A),meet(top,X_16)))]]) ).
cnf(refute_0_258,plain,
( join(complement(A),meet(top,X_16)) != join(complement(A),meet(top,X_16))
| meet(top,X_16) != X_16
| join(complement(A),meet(top,X_16)) = join(complement(A),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),meet(top,X_16)),join(complement(A),meet(top,X_16))) ),[1,1],$fot(X_16)]]) ).
cnf(refute_0_259,plain,
( meet(top,X_16) != X_16
| join(complement(A),meet(top,X_16)) = join(complement(A),X_16) ),
inference(resolve,[$cnf( $equal(join(complement(A),meet(top,X_16)),join(complement(A),meet(top,X_16))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
join(complement(A),meet(top,X_16)) = join(complement(A),X_16),
inference(resolve,[$cnf( $equal(meet(top,X_16),X_16) )],[refute_0_256,refute_0_259]) ).
cnf(refute_0_261,plain,
complement(join(complement(A),meet(top,X_16))) = complement(join(complement(A),meet(top,X_16))),
introduced(tautology,[refl,[$fot(complement(join(complement(A),meet(top,X_16))))]]) ).
cnf(refute_0_262,plain,
( complement(join(complement(A),meet(top,X_16))) != complement(join(complement(A),meet(top,X_16)))
| join(complement(A),meet(top,X_16)) != join(complement(A),X_16)
| complement(join(complement(A),meet(top,X_16))) = complement(join(complement(A),X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),meet(top,X_16))),complement(join(complement(A),meet(top,X_16)))) ),[1,0],$fot(join(complement(A),X_16))]]) ).
cnf(refute_0_263,plain,
( join(complement(A),meet(top,X_16)) != join(complement(A),X_16)
| complement(join(complement(A),meet(top,X_16))) = complement(join(complement(A),X_16)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_16))),complement(join(complement(A),meet(top,X_16)))) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
complement(join(complement(A),meet(top,X_16))) = complement(join(complement(A),X_16)),
inference(resolve,[$cnf( $equal(join(complement(A),meet(top,X_16)),join(complement(A),X_16)) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
( complement(join(complement(A),meet(top,X_16))) != complement(join(complement(A),X_16))
| meet(A,complement(X_16)) != complement(join(complement(A),meet(top,X_16)))
| meet(A,complement(X_16)) = complement(join(complement(A),X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,complement(X_16)),complement(join(complement(A),meet(top,X_16)))) ),[1],$fot(complement(join(complement(A),X_16)))]]) ).
cnf(refute_0_266,plain,
( meet(A,complement(X_16)) != complement(join(complement(A),meet(top,X_16)))
| meet(A,complement(X_16)) = complement(join(complement(A),X_16)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),meet(top,X_16))),complement(join(complement(A),X_16))) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
( meet(A,join(zero,complement(X_16))) != complement(join(complement(A),meet(top,X_16)))
| meet(A,complement(X_16)) = complement(join(complement(A),X_16)) ),
inference(resolve,[$cnf( $equal(meet(A,complement(X_16)),complement(join(complement(A),meet(top,X_16)))) )],[refute_0_235,refute_0_266]) ).
cnf(refute_0_268,plain,
meet(A,complement(X_16)) = complement(join(complement(A),X_16)),
inference(resolve,[$cnf( $equal(meet(A,join(zero,complement(X_16))),complement(join(complement(A),meet(top,X_16)))) )],[refute_0_42,refute_0_267]) ).
cnf(refute_0_269,plain,
meet(X_370,complement(join(complement(complement(X_370)),X_36))) = complement(join(complement(X_370),join(complement(complement(X_370)),X_36))),
inference(subst,[],[refute_0_268:[bind(A,$fot(X_370)),bind(X_16,$fot(join(complement(complement(X_370)),X_36)))]]) ).
cnf(refute_0_270,plain,
join(X_34,join(complement(zero),join(zero,zero))) = join(join(X_34,complement(zero)),join(zero,zero)),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_34)),bind(B,$fot(complement(zero))),bind(C,$fot(join(zero,zero)))]]) ).
cnf(refute_0_271,plain,
join(join(complement(X_24),meet(top,X_24)),zero) = join(zero,join(complement(X_24),meet(top,X_24))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_24),meet(top,X_24)))),bind(B,$fot(zero))]]) ).
cnf(refute_0_272,plain,
top = join(join(zero,complement(X_16)),complement(join(zero,complement(X_16)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(zero,complement(X_16))))]]) ).
cnf(refute_0_273,plain,
( complement(join(zero,complement(X_16))) != meet(top,X_16)
| top != join(join(zero,complement(X_16)),complement(join(zero,complement(X_16))))
| top = join(join(zero,complement(X_16)),meet(top,X_16)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,complement(X_16)),complement(join(zero,complement(X_16))))) ),[1,1],$fot(meet(top,X_16))]]) ).
cnf(refute_0_274,plain,
( top != join(join(zero,complement(X_16)),complement(join(zero,complement(X_16))))
| top = join(join(zero,complement(X_16)),meet(top,X_16)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_16))),meet(top,X_16)) )],[refute_0_39,refute_0_273]) ).
cnf(refute_0_275,plain,
top = join(join(zero,complement(X_16)),meet(top,X_16)),
inference(resolve,[$cnf( $equal(top,join(join(zero,complement(X_16)),complement(join(zero,complement(X_16))))) )],[refute_0_272,refute_0_274]) ).
cnf(refute_0_276,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_277,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_276]) ).
cnf(refute_0_278,plain,
join(join(zero,complement(X_16)),meet(top,X_16)) = join(zero,join(complement(X_16),meet(top,X_16))),
inference(subst,[],[refute_0_277:[bind(A,$fot(zero)),bind(B,$fot(complement(X_16))),bind(C,$fot(meet(top,X_16)))]]) ).
cnf(refute_0_279,plain,
( join(join(zero,complement(X_16)),meet(top,X_16)) != join(zero,join(complement(X_16),meet(top,X_16)))
| top != join(join(zero,complement(X_16)),meet(top,X_16))
| top = join(zero,join(complement(X_16),meet(top,X_16))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(zero,complement(X_16)),meet(top,X_16))) ),[1],$fot(join(zero,join(complement(X_16),meet(top,X_16))))]]) ).
cnf(refute_0_280,plain,
( top != join(join(zero,complement(X_16)),meet(top,X_16))
| top = join(zero,join(complement(X_16),meet(top,X_16))) ),
inference(resolve,[$cnf( $equal(join(join(zero,complement(X_16)),meet(top,X_16)),join(zero,join(complement(X_16),meet(top,X_16)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
top = join(zero,join(complement(X_16),meet(top,X_16))),
inference(resolve,[$cnf( $equal(top,join(join(zero,complement(X_16)),meet(top,X_16))) )],[refute_0_275,refute_0_280]) ).
cnf(refute_0_282,plain,
top = join(zero,join(complement(X_24),meet(top,X_24))),
inference(subst,[],[refute_0_281:[bind(X_16,$fot(X_24))]]) ).
cnf(refute_0_283,plain,
( top != join(zero,join(complement(X_24),meet(top,X_24)))
| join(zero,join(complement(X_24),meet(top,X_24))) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(zero,join(complement(X_24),meet(top,X_24)))))]]) ).
cnf(refute_0_284,plain,
join(zero,join(complement(X_24),meet(top,X_24))) = top,
inference(resolve,[$cnf( $equal(top,join(zero,join(complement(X_24),meet(top,X_24)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
( join(join(complement(X_24),meet(top,X_24)),zero) != join(zero,join(complement(X_24),meet(top,X_24)))
| join(zero,join(complement(X_24),meet(top,X_24))) != top
| join(join(complement(X_24),meet(top,X_24)),zero) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(complement(X_24),meet(top,X_24)),zero),top) ),[0],$fot(join(zero,join(complement(X_24),meet(top,X_24))))]]) ).
cnf(refute_0_286,plain,
( join(join(complement(X_24),meet(top,X_24)),zero) != join(zero,join(complement(X_24),meet(top,X_24)))
| join(join(complement(X_24),meet(top,X_24)),zero) = top ),
inference(resolve,[$cnf( $equal(join(zero,join(complement(X_24),meet(top,X_24))),top) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
join(join(complement(X_24),meet(top,X_24)),zero) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_24),meet(top,X_24)),zero),join(zero,join(complement(X_24),meet(top,X_24)))) )],[refute_0_271,refute_0_286]) ).
cnf(refute_0_288,plain,
join(meet(top,X_24),zero) = join(zero,meet(top,X_24)),
inference(subst,[],[refute_0_45:[bind(A,$fot(zero)),bind(B,$fot(meet(top,X_24)))]]) ).
cnf(refute_0_289,plain,
join(complement(X_24),join(meet(top,X_24),zero)) = join(complement(X_24),join(meet(top,X_24),zero)),
introduced(tautology,[refl,[$fot(join(complement(X_24),join(meet(top,X_24),zero)))]]) ).
cnf(refute_0_290,plain,
( join(complement(X_24),join(meet(top,X_24),zero)) != join(complement(X_24),join(meet(top,X_24),zero))
| join(meet(top,X_24),zero) != join(zero,meet(top,X_24))
| join(complement(X_24),join(meet(top,X_24),zero)) = join(complement(X_24),join(zero,meet(top,X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_24),join(meet(top,X_24),zero)),join(complement(X_24),join(meet(top,X_24),zero))) ),[1,1],$fot(join(zero,meet(top,X_24)))]]) ).
cnf(refute_0_291,plain,
( join(meet(top,X_24),zero) != join(zero,meet(top,X_24))
| join(complement(X_24),join(meet(top,X_24),zero)) = join(complement(X_24),join(zero,meet(top,X_24))) ),
inference(resolve,[$cnf( $equal(join(complement(X_24),join(meet(top,X_24),zero)),join(complement(X_24),join(meet(top,X_24),zero))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
join(complement(X_24),join(meet(top,X_24),zero)) = join(complement(X_24),join(zero,meet(top,X_24))),
inference(resolve,[$cnf( $equal(join(meet(top,X_24),zero),join(zero,meet(top,X_24))) )],[refute_0_288,refute_0_291]) ).
cnf(refute_0_293,plain,
join(join(complement(X_24),meet(top,X_24)),zero) = join(complement(X_24),join(meet(top,X_24),zero)),
inference(subst,[],[refute_0_277:[bind(A,$fot(complement(X_24))),bind(B,$fot(meet(top,X_24))),bind(C,$fot(zero))]]) ).
cnf(refute_0_294,plain,
( join(complement(X_24),join(meet(top,X_24),zero)) != join(complement(X_24),join(zero,meet(top,X_24)))
| join(join(complement(X_24),meet(top,X_24)),zero) != join(complement(X_24),join(meet(top,X_24),zero))
| join(join(complement(X_24),meet(top,X_24)),zero) = join(complement(X_24),join(zero,meet(top,X_24))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(join(complement(X_24),meet(top,X_24)),zero))),bind(Y,$fot(join(complement(X_24),join(meet(top,X_24),zero)))),bind(Z,$fot(join(complement(X_24),join(zero,meet(top,X_24)))))]]) ).
cnf(refute_0_295,plain,
( join(complement(X_24),join(meet(top,X_24),zero)) != join(complement(X_24),join(zero,meet(top,X_24)))
| join(join(complement(X_24),meet(top,X_24)),zero) = join(complement(X_24),join(zero,meet(top,X_24))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_24),meet(top,X_24)),zero),join(complement(X_24),join(meet(top,X_24),zero))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
join(join(complement(X_24),meet(top,X_24)),zero) = join(complement(X_24),join(zero,meet(top,X_24))),
inference(resolve,[$cnf( $equal(join(complement(X_24),join(meet(top,X_24),zero)),join(complement(X_24),join(zero,meet(top,X_24)))) )],[refute_0_292,refute_0_295]) ).
cnf(refute_0_297,plain,
( join(join(complement(X_24),meet(top,X_24)),zero) != join(complement(X_24),join(zero,meet(top,X_24)))
| join(join(complement(X_24),meet(top,X_24)),zero) != top
| join(complement(X_24),join(zero,meet(top,X_24))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_24),meet(top,X_24)),zero),top) ),[0],$fot(join(complement(X_24),join(zero,meet(top,X_24))))]]) ).
cnf(refute_0_298,plain,
( join(join(complement(X_24),meet(top,X_24)),zero) != top
| join(complement(X_24),join(zero,meet(top,X_24))) = top ),
inference(resolve,[$cnf( $equal(join(join(complement(X_24),meet(top,X_24)),zero),join(complement(X_24),join(zero,meet(top,X_24)))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
join(complement(X_24),join(zero,meet(top,X_24))) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_24),meet(top,X_24)),zero),top) )],[refute_0_287,refute_0_298]) ).
cnf(refute_0_300,plain,
join(complement(complement(top)),join(zero,meet(top,complement(top)))) = top,
inference(subst,[],[refute_0_299:[bind(X_24,$fot(complement(top)))]]) ).
cnf(refute_0_301,plain,
zero = meet(top,complement(top)),
inference(subst,[],[def_zero_13:[bind(A,$fot(top))]]) ).
cnf(refute_0_302,plain,
( zero != meet(top,complement(top))
| meet(top,complement(top)) = zero ),
inference(subst,[],[refute_0_6:[bind(X,$fot(zero)),bind(Y,$fot(meet(top,complement(top))))]]) ).
cnf(refute_0_303,plain,
meet(top,complement(top)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(top,complement(top))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
( join(complement(complement(top)),join(zero,meet(top,complement(top)))) != top
| meet(top,complement(top)) != zero
| join(complement(complement(top)),join(zero,zero)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(top)),join(zero,meet(top,complement(top)))),top) ),[0,1,1],$fot(zero)]]) ).
cnf(refute_0_305,plain,
( join(complement(complement(top)),join(zero,meet(top,complement(top)))) != top
| join(complement(complement(top)),join(zero,zero)) = top ),
inference(resolve,[$cnf( $equal(meet(top,complement(top)),zero) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
join(complement(complement(top)),join(zero,zero)) = top,
inference(resolve,[$cnf( $equal(join(complement(complement(top)),join(zero,meet(top,complement(top)))),top) )],[refute_0_300,refute_0_305]) ).
cnf(refute_0_307,plain,
complement(complement(top)) = complement(complement(top)),
introduced(tautology,[refl,[$fot(complement(complement(top)))]]) ).
cnf(refute_0_308,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_309,plain,
( complement(top) != zero
| complement(complement(top)) = complement(zero) ),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(complement(top))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
complement(complement(top)) = complement(zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_309]) ).
cnf(refute_0_311,plain,
join(complement(complement(top)),join(zero,zero)) = join(complement(complement(top)),join(zero,zero)),
introduced(tautology,[refl,[$fot(join(complement(complement(top)),join(zero,zero)))]]) ).
cnf(refute_0_312,plain,
( complement(complement(top)) != complement(zero)
| join(complement(complement(top)),join(zero,zero)) != join(complement(complement(top)),join(zero,zero))
| join(complement(complement(top)),join(zero,zero)) = join(complement(zero),join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(top)),join(zero,zero)),join(complement(complement(top)),join(zero,zero))) ),[1,0],$fot(complement(zero))]]) ).
cnf(refute_0_313,plain,
( complement(complement(top)) != complement(zero)
| join(complement(complement(top)),join(zero,zero)) = join(complement(zero),join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(top)),join(zero,zero)),join(complement(complement(top)),join(zero,zero))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
join(complement(complement(top)),join(zero,zero)) = join(complement(zero),join(zero,zero)),
inference(resolve,[$cnf( $equal(complement(complement(top)),complement(zero)) )],[refute_0_310,refute_0_313]) ).
cnf(refute_0_315,plain,
( join(complement(complement(top)),join(zero,zero)) != join(complement(zero),join(zero,zero))
| join(complement(complement(top)),join(zero,zero)) != top
| join(complement(zero),join(zero,zero)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(top)),join(zero,zero)),top) ),[0],$fot(join(complement(zero),join(zero,zero)))]]) ).
cnf(refute_0_316,plain,
( join(complement(complement(top)),join(zero,zero)) != top
| join(complement(zero),join(zero,zero)) = top ),
inference(resolve,[$cnf( $equal(join(complement(complement(top)),join(zero,zero)),join(complement(zero),join(zero,zero))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
join(complement(zero),join(zero,zero)) = top,
inference(resolve,[$cnf( $equal(join(complement(complement(top)),join(zero,zero)),top) )],[refute_0_306,refute_0_316]) ).
cnf(refute_0_318,plain,
( join(X_34,join(complement(zero),join(zero,zero))) != join(join(X_34,complement(zero)),join(zero,zero))
| join(complement(zero),join(zero,zero)) != top
| join(X_34,top) = join(join(X_34,complement(zero)),join(zero,zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_34,join(complement(zero),join(zero,zero))),join(join(X_34,complement(zero)),join(zero,zero))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_319,plain,
( join(X_34,join(complement(zero),join(zero,zero))) != join(join(X_34,complement(zero)),join(zero,zero))
| join(X_34,top) = join(join(X_34,complement(zero)),join(zero,zero)) ),
inference(resolve,[$cnf( $equal(join(complement(zero),join(zero,zero)),top) )],[refute_0_317,refute_0_318]) ).
cnf(refute_0_320,plain,
join(X_34,top) = join(join(X_34,complement(zero)),join(zero,zero)),
inference(resolve,[$cnf( $equal(join(X_34,join(complement(zero),join(zero,zero))),join(join(X_34,complement(zero)),join(zero,zero))) )],[refute_0_270,refute_0_319]) ).
cnf(refute_0_321,plain,
join(A,join(X_34,X_35)) = join(join(X_34,X_35),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_34,X_35)))]]) ).
cnf(refute_0_322,plain,
join(X_34,join(X_35,A)) = join(join(X_34,X_35),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(A))]]) ).
cnf(refute_0_323,plain,
( join(X_34,join(X_35,A)) != join(join(X_34,X_35),A)
| join(join(X_34,X_35),A) = join(X_34,join(X_35,A)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_34,join(X_35,A)))),bind(Y,$fot(join(join(X_34,X_35),A)))]]) ).
cnf(refute_0_324,plain,
join(join(X_34,X_35),A) = join(X_34,join(X_35,A)),
inference(resolve,[$cnf( $equal(join(X_34,join(X_35,A)),join(join(X_34,X_35),A)) )],[refute_0_322,refute_0_323]) ).
cnf(refute_0_325,plain,
( join(A,join(X_34,X_35)) != join(join(X_34,X_35),A)
| join(join(X_34,X_35),A) != join(X_34,join(X_35,A))
| join(A,join(X_34,X_35)) = join(X_34,join(X_35,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_34,X_35)),join(X_34,join(X_35,A))) ),[0],$fot(join(join(X_34,X_35),A))]]) ).
cnf(refute_0_326,plain,
( join(A,join(X_34,X_35)) != join(join(X_34,X_35),A)
| join(A,join(X_34,X_35)) = join(X_34,join(X_35,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_34,X_35),A),join(X_34,join(X_35,A))) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
join(A,join(X_34,X_35)) = join(X_34,join(X_35,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_34,X_35)),join(join(X_34,X_35),A)) )],[refute_0_321,refute_0_326]) ).
cnf(refute_0_328,plain,
( join(A,join(X_34,X_35)) != join(X_34,join(X_35,A))
| join(X_34,join(X_35,A)) = join(A,join(X_34,X_35)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(A,join(X_34,X_35)))),bind(Y,$fot(join(X_34,join(X_35,A))))]]) ).
cnf(refute_0_329,plain,
join(X_34,join(X_35,A)) = join(A,join(X_34,X_35)),
inference(resolve,[$cnf( $equal(join(A,join(X_34,X_35)),join(X_34,join(X_35,A))) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
join(zero,join(join(X_34,complement(zero)),zero)) = join(zero,join(zero,join(X_34,complement(zero)))),
inference(subst,[],[refute_0_329:[bind(A,$fot(zero)),bind(X_34,$fot(zero)),bind(X_35,$fot(join(X_34,complement(zero))))]]) ).
cnf(refute_0_331,plain,
join(join(X_34,complement(zero)),join(zero,zero)) = join(zero,join(join(X_34,complement(zero)),zero)),
inference(subst,[],[refute_0_329:[bind(A,$fot(zero)),bind(X_34,$fot(join(X_34,complement(zero)))),bind(X_35,$fot(zero))]]) ).
cnf(refute_0_332,plain,
( join(join(X_34,complement(zero)),join(zero,zero)) != join(zero,join(join(X_34,complement(zero)),zero))
| join(zero,join(join(X_34,complement(zero)),zero)) != join(zero,join(zero,join(X_34,complement(zero))))
| join(join(X_34,complement(zero)),join(zero,zero)) = join(zero,join(zero,join(X_34,complement(zero)))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(join(X_34,complement(zero)),join(zero,zero)))),bind(Y,$fot(join(zero,join(join(X_34,complement(zero)),zero)))),bind(Z,$fot(join(zero,join(zero,join(X_34,complement(zero))))))]]) ).
cnf(refute_0_333,plain,
( join(zero,join(join(X_34,complement(zero)),zero)) != join(zero,join(zero,join(X_34,complement(zero))))
| join(join(X_34,complement(zero)),join(zero,zero)) = join(zero,join(zero,join(X_34,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(join(X_34,complement(zero)),join(zero,zero)),join(zero,join(join(X_34,complement(zero)),zero))) )],[refute_0_331,refute_0_332]) ).
cnf(refute_0_334,plain,
join(join(X_34,complement(zero)),join(zero,zero)) = join(zero,join(zero,join(X_34,complement(zero)))),
inference(resolve,[$cnf( $equal(join(zero,join(join(X_34,complement(zero)),zero)),join(zero,join(zero,join(X_34,complement(zero))))) )],[refute_0_330,refute_0_333]) ).
cnf(refute_0_335,plain,
( join(X_34,top) != join(join(X_34,complement(zero)),join(zero,zero))
| join(join(X_34,complement(zero)),join(zero,zero)) != join(zero,join(zero,join(X_34,complement(zero))))
| join(X_34,top) = join(zero,join(zero,join(X_34,complement(zero)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,top),join(zero,join(zero,join(X_34,complement(zero))))) ),[0],$fot(join(join(X_34,complement(zero)),join(zero,zero)))]]) ).
cnf(refute_0_336,plain,
( join(X_34,top) != join(join(X_34,complement(zero)),join(zero,zero))
| join(X_34,top) = join(zero,join(zero,join(X_34,complement(zero)))) ),
inference(resolve,[$cnf( $equal(join(join(X_34,complement(zero)),join(zero,zero)),join(zero,join(zero,join(X_34,complement(zero))))) )],[refute_0_334,refute_0_335]) ).
cnf(refute_0_337,plain,
join(X_34,top) = join(zero,join(zero,join(X_34,complement(zero)))),
inference(resolve,[$cnf( $equal(join(X_34,top),join(join(X_34,complement(zero)),join(zero,zero))) )],[refute_0_320,refute_0_336]) ).
cnf(refute_0_338,plain,
join(top,join(zero,X_36)) = join(join(top,zero),X_36),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_339,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_340,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_341,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_340]) ).
cnf(refute_0_342,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_339,refute_0_341]) ).
cnf(refute_0_343,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_344,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
( join(top,join(zero,X_36)) != join(join(top,zero),X_36)
| join(top,zero) != top
| join(top,join(zero,X_36)) = join(top,X_36) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_36)),join(join(top,zero),X_36)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_346,plain,
( join(top,join(zero,X_36)) != join(join(top,zero),X_36)
| join(top,join(zero,X_36)) = join(top,X_36) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
join(top,join(zero,X_36)) = join(top,X_36),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_36)),join(join(top,zero),X_36)) )],[refute_0_338,refute_0_346]) ).
cnf(refute_0_348,plain,
join(top,join(zero,X_34)) = join(top,X_34),
inference(subst,[],[refute_0_347:[bind(X_36,$fot(X_34))]]) ).
cnf(refute_0_349,plain,
join(X_34,join(X_35,X_36)) = join(join(X_34,X_35),X_36),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_34)),bind(B,$fot(X_35)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_350,plain,
join(X_35,X_34) = join(X_34,X_35),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_35)),bind(B,$fot(X_34))]]) ).
cnf(refute_0_351,plain,
( join(X_35,X_34) != join(X_34,X_35)
| join(X_34,X_35) = join(X_35,X_34) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_35,X_34))),bind(Y,$fot(join(X_34,X_35)))]]) ).
cnf(refute_0_352,plain,
join(X_34,X_35) = join(X_35,X_34),
inference(resolve,[$cnf( $equal(join(X_35,X_34),join(X_34,X_35)) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
( join(X_34,X_35) != join(X_35,X_34)
| join(X_34,join(X_35,X_36)) != join(join(X_34,X_35),X_36)
| join(X_34,join(X_35,X_36)) = join(join(X_35,X_34),X_36) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_34,join(X_35,X_36)),join(join(X_34,X_35),X_36)) ),[1,0],$fot(join(X_35,X_34))]]) ).
cnf(refute_0_354,plain,
( join(X_34,join(X_35,X_36)) != join(join(X_34,X_35),X_36)
| join(X_34,join(X_35,X_36)) = join(join(X_35,X_34),X_36) ),
inference(resolve,[$cnf( $equal(join(X_34,X_35),join(X_35,X_34)) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
join(X_34,join(X_35,X_36)) = join(join(X_35,X_34),X_36),
inference(resolve,[$cnf( $equal(join(X_34,join(X_35,X_36)),join(join(X_34,X_35),X_36)) )],[refute_0_349,refute_0_354]) ).
cnf(refute_0_356,plain,
join(join(X_35,X_34),X_36) = join(X_35,join(X_34,X_36)),
inference(subst,[],[refute_0_277:[bind(A,$fot(X_35)),bind(B,$fot(X_34)),bind(C,$fot(X_36))]]) ).
cnf(refute_0_357,plain,
( join(X_34,join(X_35,X_36)) != join(join(X_35,X_34),X_36)
| join(join(X_35,X_34),X_36) != join(X_35,join(X_34,X_36))
| join(X_34,join(X_35,X_36)) = join(X_35,join(X_34,X_36)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,join(X_35,X_36)),join(X_35,join(X_34,X_36))) ),[0],$fot(join(join(X_35,X_34),X_36))]]) ).
cnf(refute_0_358,plain,
( join(X_34,join(X_35,X_36)) != join(join(X_35,X_34),X_36)
| join(X_34,join(X_35,X_36)) = join(X_35,join(X_34,X_36)) ),
inference(resolve,[$cnf( $equal(join(join(X_35,X_34),X_36),join(X_35,join(X_34,X_36))) )],[refute_0_356,refute_0_357]) ).
cnf(refute_0_359,plain,
join(X_34,join(X_35,X_36)) = join(X_35,join(X_34,X_36)),
inference(resolve,[$cnf( $equal(join(X_34,join(X_35,X_36)),join(join(X_35,X_34),X_36)) )],[refute_0_355,refute_0_358]) ).
cnf(refute_0_360,plain,
( join(X_34,join(X_35,X_36)) != join(X_35,join(X_34,X_36))
| join(X_35,join(X_34,X_36)) = join(X_34,join(X_35,X_36)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_34,join(X_35,X_36)))),bind(Y,$fot(join(X_35,join(X_34,X_36))))]]) ).
cnf(refute_0_361,plain,
join(X_35,join(X_34,X_36)) = join(X_34,join(X_35,X_36)),
inference(resolve,[$cnf( $equal(join(X_34,join(X_35,X_36)),join(X_35,join(X_34,X_36))) )],[refute_0_359,refute_0_360]) ).
cnf(refute_0_362,plain,
join(zero,join(top,X_34)) = join(top,join(zero,X_34)),
inference(subst,[],[refute_0_361:[bind(X_34,$fot(top)),bind(X_35,$fot(zero)),bind(X_36,$fot(X_34))]]) ).
cnf(refute_0_363,plain,
( join(top,join(zero,X_34)) != join(top,X_34)
| join(zero,join(top,X_34)) != join(top,join(zero,X_34))
| join(zero,join(top,X_34)) = join(top,X_34) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(zero,join(top,X_34)))),bind(Y,$fot(join(top,join(zero,X_34)))),bind(Z,$fot(join(top,X_34)))]]) ).
cnf(refute_0_364,plain,
( join(top,join(zero,X_34)) != join(top,X_34)
| join(zero,join(top,X_34)) = join(top,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_34)),join(top,join(zero,X_34))) )],[refute_0_362,refute_0_363]) ).
cnf(refute_0_365,plain,
join(zero,join(top,X_34)) = join(top,X_34),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_34)),join(top,X_34)) )],[refute_0_348,refute_0_364]) ).
cnf(refute_0_366,plain,
join(zero,join(X_34,complement(zero))) = join(top,X_34),
inference(subst,[],[refute_0_194:[bind(X_41,$fot(zero)),bind(X_42,$fot(X_34))]]) ).
cnf(refute_0_367,plain,
join(zero,join(zero,join(X_34,complement(zero)))) = join(zero,join(zero,join(X_34,complement(zero)))),
introduced(tautology,[refl,[$fot(join(zero,join(zero,join(X_34,complement(zero)))))]]) ).
cnf(refute_0_368,plain,
( join(zero,join(X_34,complement(zero))) != join(top,X_34)
| join(zero,join(zero,join(X_34,complement(zero)))) != join(zero,join(zero,join(X_34,complement(zero))))
| join(zero,join(zero,join(X_34,complement(zero)))) = join(zero,join(top,X_34)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,join(X_34,complement(zero)))),join(zero,join(zero,join(X_34,complement(zero))))) ),[1,1],$fot(join(top,X_34))]]) ).
cnf(refute_0_369,plain,
( join(zero,join(X_34,complement(zero))) != join(top,X_34)
| join(zero,join(zero,join(X_34,complement(zero)))) = join(zero,join(top,X_34)) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(X_34,complement(zero)))),join(zero,join(zero,join(X_34,complement(zero))))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
join(zero,join(zero,join(X_34,complement(zero)))) = join(zero,join(top,X_34)),
inference(resolve,[$cnf( $equal(join(zero,join(X_34,complement(zero))),join(top,X_34)) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
( join(zero,join(top,X_34)) != join(top,X_34)
| join(zero,join(zero,join(X_34,complement(zero)))) != join(zero,join(top,X_34))
| join(zero,join(zero,join(X_34,complement(zero)))) = join(top,X_34) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(zero,join(zero,join(X_34,complement(zero)))))),bind(Y,$fot(join(zero,join(top,X_34)))),bind(Z,$fot(join(top,X_34)))]]) ).
cnf(refute_0_372,plain,
( join(zero,join(top,X_34)) != join(top,X_34)
| join(zero,join(zero,join(X_34,complement(zero)))) = join(top,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(X_34,complement(zero)))),join(zero,join(top,X_34))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
join(zero,join(zero,join(X_34,complement(zero)))) = join(top,X_34),
inference(resolve,[$cnf( $equal(join(zero,join(top,X_34)),join(top,X_34)) )],[refute_0_365,refute_0_372]) ).
cnf(refute_0_374,plain,
( join(X_34,top) != join(zero,join(zero,join(X_34,complement(zero))))
| join(zero,join(zero,join(X_34,complement(zero)))) != join(top,X_34)
| join(X_34,top) = join(top,X_34) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,top),join(top,X_34)) ),[0],$fot(join(zero,join(zero,join(X_34,complement(zero)))))]]) ).
cnf(refute_0_375,plain,
( join(X_34,top) != join(zero,join(zero,join(X_34,complement(zero))))
| join(X_34,top) = join(top,X_34) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,join(X_34,complement(zero)))),join(top,X_34)) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
join(X_34,top) = join(top,X_34),
inference(resolve,[$cnf( $equal(join(X_34,top),join(zero,join(zero,join(X_34,complement(zero))))) )],[refute_0_337,refute_0_375]) ).
cnf(refute_0_377,plain,
join(X_34,top) = top,
inference(subst,[],[refute_0_204:[bind(X_41,$fot(X_34))]]) ).
cnf(refute_0_378,plain,
( join(X_34,top) != join(top,X_34)
| join(X_34,top) != top
| top = join(top,X_34) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_34,top),join(top,X_34)) ),[0],$fot(top)]]) ).
cnf(refute_0_379,plain,
( join(X_34,top) != join(top,X_34)
| top = join(top,X_34) ),
inference(resolve,[$cnf( $equal(join(X_34,top),top) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
top = join(top,X_34),
inference(resolve,[$cnf( $equal(join(X_34,top),join(top,X_34)) )],[refute_0_376,refute_0_379]) ).
cnf(refute_0_381,plain,
( top != join(top,X_34)
| join(top,X_34) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(top,X_34)))]]) ).
cnf(refute_0_382,plain,
join(top,X_34) = top,
inference(resolve,[$cnf( $equal(top,join(top,X_34)) )],[refute_0_380,refute_0_381]) ).
cnf(refute_0_383,plain,
join(top,X_36) = top,
inference(subst,[],[refute_0_382:[bind(X_34,$fot(X_36))]]) ).
cnf(refute_0_384,plain,
( join(X_34,join(complement(X_34),X_36)) != join(top,X_36)
| join(top,X_36) != top
| join(X_34,join(complement(X_34),X_36)) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,join(complement(X_34),X_36)),top) ),[0],$fot(join(top,X_36))]]) ).
cnf(refute_0_385,plain,
( join(X_34,join(complement(X_34),X_36)) != join(top,X_36)
| join(X_34,join(complement(X_34),X_36)) = top ),
inference(resolve,[$cnf( $equal(join(top,X_36),top) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
join(X_34,join(complement(X_34),X_36)) = top,
inference(resolve,[$cnf( $equal(join(X_34,join(complement(X_34),X_36)),join(top,X_36)) )],[refute_0_146,refute_0_385]) ).
cnf(refute_0_387,plain,
join(complement(X_370),join(complement(complement(X_370)),X_36)) = top,
inference(subst,[],[refute_0_386:[bind(X_34,$fot(complement(X_370)))]]) ).
cnf(refute_0_388,plain,
( join(complement(X_370),join(complement(complement(X_370)),X_36)) != top
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) != complement(join(complement(X_370),join(complement(complement(X_370)),X_36)))
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),complement(join(complement(X_370),join(complement(complement(X_370)),X_36)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_389,plain,
( meet(X_370,complement(join(complement(complement(X_370)),X_36))) != complement(join(complement(X_370),join(complement(complement(X_370)),X_36)))
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) = complement(top) ),
inference(resolve,[$cnf( $equal(join(complement(X_370),join(complement(complement(X_370)),X_36)),top) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
meet(X_370,complement(join(complement(complement(X_370)),X_36))) = complement(top),
inference(resolve,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),complement(join(complement(X_370),join(complement(complement(X_370)),X_36)))) )],[refute_0_269,refute_0_389]) ).
cnf(refute_0_391,plain,
meet(join(zero,complement(X_16)),B) = complement(join(complement(join(zero,complement(X_16))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(zero,complement(X_16))))]]) ).
cnf(refute_0_392,plain,
( complement(join(zero,complement(X_16))) != meet(top,X_16)
| meet(join(zero,complement(X_16)),B) != complement(join(complement(join(zero,complement(X_16))),complement(B)))
| meet(join(zero,complement(X_16)),B) = complement(join(meet(top,X_16),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_16)),B),complement(join(complement(join(zero,complement(X_16))),complement(B)))) ),[1,0,0],$fot(meet(top,X_16))]]) ).
cnf(refute_0_393,plain,
( meet(join(zero,complement(X_16)),B) != complement(join(complement(join(zero,complement(X_16))),complement(B)))
| meet(join(zero,complement(X_16)),B) = complement(join(meet(top,X_16),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(X_16))),meet(top,X_16)) )],[refute_0_39,refute_0_392]) ).
cnf(refute_0_394,plain,
meet(join(zero,complement(X_16)),B) = complement(join(meet(top,X_16),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_16)),B),complement(join(complement(join(zero,complement(X_16))),complement(B)))) )],[refute_0_391,refute_0_393]) ).
cnf(refute_0_395,plain,
meet(join(zero,complement(X_16)),B) = meet(join(zero,complement(X_16)),B),
introduced(tautology,[refl,[$fot(meet(join(zero,complement(X_16)),B))]]) ).
cnf(refute_0_396,plain,
( join(zero,complement(X_16)) != complement(X_16)
| meet(join(zero,complement(X_16)),B) != meet(join(zero,complement(X_16)),B)
| meet(join(zero,complement(X_16)),B) = meet(complement(X_16),B) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_16)),B),meet(join(zero,complement(X_16)),B)) ),[1,0],$fot(complement(X_16))]]) ).
cnf(refute_0_397,plain,
( join(zero,complement(X_16)) != complement(X_16)
| meet(join(zero,complement(X_16)),B) = meet(complement(X_16),B) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_16)),B),meet(join(zero,complement(X_16)),B)) )],[refute_0_395,refute_0_396]) ).
cnf(refute_0_398,plain,
meet(join(zero,complement(X_16)),B) = meet(complement(X_16),B),
inference(resolve,[$cnf( $equal(join(zero,complement(X_16)),complement(X_16)) )],[refute_0_229,refute_0_397]) ).
cnf(refute_0_399,plain,
( meet(join(zero,complement(X_16)),B) != complement(join(meet(top,X_16),complement(B)))
| meet(join(zero,complement(X_16)),B) != meet(complement(X_16),B)
| meet(complement(X_16),B) = complement(join(meet(top,X_16),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(zero,complement(X_16)),B),complement(join(meet(top,X_16),complement(B)))) ),[0],$fot(meet(complement(X_16),B))]]) ).
cnf(refute_0_400,plain,
( meet(join(zero,complement(X_16)),B) != complement(join(meet(top,X_16),complement(B)))
| meet(complement(X_16),B) = complement(join(meet(top,X_16),complement(B))) ),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_16)),B),meet(complement(X_16),B)) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
join(meet(top,X_16),complement(B)) = join(meet(top,X_16),complement(B)),
introduced(tautology,[refl,[$fot(join(meet(top,X_16),complement(B)))]]) ).
cnf(refute_0_402,plain,
( join(meet(top,X_16),complement(B)) != join(meet(top,X_16),complement(B))
| meet(top,X_16) != X_16
| join(meet(top,X_16),complement(B)) = join(X_16,complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_16),complement(B)),join(meet(top,X_16),complement(B))) ),[1,0],$fot(X_16)]]) ).
cnf(refute_0_403,plain,
( meet(top,X_16) != X_16
| join(meet(top,X_16),complement(B)) = join(X_16,complement(B)) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_16),complement(B)),join(meet(top,X_16),complement(B))) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
join(meet(top,X_16),complement(B)) = join(X_16,complement(B)),
inference(resolve,[$cnf( $equal(meet(top,X_16),X_16) )],[refute_0_256,refute_0_403]) ).
cnf(refute_0_405,plain,
complement(join(meet(top,X_16),complement(B))) = complement(join(meet(top,X_16),complement(B))),
introduced(tautology,[refl,[$fot(complement(join(meet(top,X_16),complement(B))))]]) ).
cnf(refute_0_406,plain,
( complement(join(meet(top,X_16),complement(B))) != complement(join(meet(top,X_16),complement(B)))
| join(meet(top,X_16),complement(B)) != join(X_16,complement(B))
| complement(join(meet(top,X_16),complement(B))) = complement(join(X_16,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(top,X_16),complement(B))),complement(join(meet(top,X_16),complement(B)))) ),[1,0],$fot(join(X_16,complement(B)))]]) ).
cnf(refute_0_407,plain,
( join(meet(top,X_16),complement(B)) != join(X_16,complement(B))
| complement(join(meet(top,X_16),complement(B))) = complement(join(X_16,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_16),complement(B))),complement(join(meet(top,X_16),complement(B)))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
complement(join(meet(top,X_16),complement(B))) = complement(join(X_16,complement(B))),
inference(resolve,[$cnf( $equal(join(meet(top,X_16),complement(B)),join(X_16,complement(B))) )],[refute_0_404,refute_0_407]) ).
cnf(refute_0_409,plain,
( complement(join(meet(top,X_16),complement(B))) != complement(join(X_16,complement(B)))
| meet(complement(X_16),B) != complement(join(meet(top,X_16),complement(B)))
| meet(complement(X_16),B) = complement(join(X_16,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_16),B),complement(join(meet(top,X_16),complement(B)))) ),[1],$fot(complement(join(X_16,complement(B))))]]) ).
cnf(refute_0_410,plain,
( meet(complement(X_16),B) != complement(join(meet(top,X_16),complement(B)))
| meet(complement(X_16),B) = complement(join(X_16,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(meet(top,X_16),complement(B))),complement(join(X_16,complement(B)))) )],[refute_0_408,refute_0_409]) ).
cnf(refute_0_411,plain,
( meet(join(zero,complement(X_16)),B) != complement(join(meet(top,X_16),complement(B)))
| meet(complement(X_16),B) = complement(join(X_16,complement(B))) ),
inference(resolve,[$cnf( $equal(meet(complement(X_16),B),complement(join(meet(top,X_16),complement(B)))) )],[refute_0_400,refute_0_410]) ).
cnf(refute_0_412,plain,
meet(complement(X_16),B) = complement(join(X_16,complement(B))),
inference(resolve,[$cnf( $equal(meet(join(zero,complement(X_16)),B),complement(join(meet(top,X_16),complement(B)))) )],[refute_0_394,refute_0_411]) ).
cnf(refute_0_413,plain,
meet(complement(X_359),complement(B)) = complement(join(X_359,complement(complement(B)))),
inference(subst,[],[refute_0_412:[bind(B,$fot(complement(B))),bind(X_16,$fot(X_359))]]) ).
cnf(refute_0_414,plain,
meet(top,B) = B,
inference(subst,[],[refute_0_255:[bind(X_95,$fot(B))]]) ).
cnf(refute_0_415,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_416,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| B = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(meet(top,B),B) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
join(zero,complement(B)) = complement(B),
inference(subst,[],[refute_0_228:[bind(X_95,$fot(complement(B)))]]) ).
cnf(refute_0_418,plain,
complement(join(zero,complement(B))) = complement(join(zero,complement(B))),
introduced(tautology,[refl,[$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_419,plain,
( complement(join(zero,complement(B))) != complement(join(zero,complement(B)))
| join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) ),[1,0],$fot(complement(B))]]) ).
cnf(refute_0_420,plain,
( join(zero,complement(B)) != complement(B)
| complement(join(zero,complement(B))) = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(join(zero,complement(B)))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
complement(join(zero,complement(B))) = complement(complement(B)),
inference(resolve,[$cnf( $equal(join(zero,complement(B)),complement(B)) )],[refute_0_417,refute_0_420]) ).
cnf(refute_0_422,plain,
( B != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) != complement(complement(B))
| B = complement(complement(B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(B,complement(complement(B))) ),[0],$fot(complement(join(zero,complement(B))))]]) ).
cnf(refute_0_423,plain,
( B != complement(join(zero,complement(B)))
| B = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(B))),complement(complement(B))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| B = complement(complement(B)) ),
inference(resolve,[$cnf( $equal(B,complement(join(zero,complement(B)))) )],[refute_0_416,refute_0_423]) ).
cnf(refute_0_425,plain,
B = complement(complement(B)),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_36,refute_0_424]) ).
cnf(refute_0_426,plain,
( B != complement(complement(B))
| complement(complement(B)) = B ),
inference(subst,[],[refute_0_6:[bind(X,$fot(B)),bind(Y,$fot(complement(complement(B))))]]) ).
cnf(refute_0_427,plain,
complement(complement(B)) = B,
inference(resolve,[$cnf( $equal(B,complement(complement(B))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
( complement(complement(B)) != B
| meet(complement(X_359),complement(B)) != complement(join(X_359,complement(complement(B))))
| meet(complement(X_359),complement(B)) = complement(join(X_359,B)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(X_359),complement(B)),complement(join(X_359,complement(complement(B))))) ),[1,0,1],$fot(B)]]) ).
cnf(refute_0_429,plain,
( meet(complement(X_359),complement(B)) != complement(join(X_359,complement(complement(B))))
| meet(complement(X_359),complement(B)) = complement(join(X_359,B)) ),
inference(resolve,[$cnf( $equal(complement(complement(B)),B) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
meet(complement(X_359),complement(B)) = complement(join(X_359,B)),
inference(resolve,[$cnf( $equal(meet(complement(X_359),complement(B)),complement(join(X_359,complement(complement(B))))) )],[refute_0_413,refute_0_429]) ).
cnf(refute_0_431,plain,
meet(complement(X_370),complement(X_36)) = complement(join(X_370,X_36)),
inference(subst,[],[refute_0_430:[bind(B,$fot(X_36)),bind(X_359,$fot(X_370))]]) ).
cnf(refute_0_432,plain,
( meet(A,complement(X_16)) != complement(join(complement(A),X_16))
| complement(join(complement(A),X_16)) = meet(A,complement(X_16)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(A,complement(X_16)))),bind(Y,$fot(complement(join(complement(A),X_16))))]]) ).
cnf(refute_0_433,plain,
complement(join(complement(A),X_16)) = meet(A,complement(X_16)),
inference(resolve,[$cnf( $equal(meet(A,complement(X_16)),complement(join(complement(A),X_16))) )],[refute_0_268,refute_0_432]) ).
cnf(refute_0_434,plain,
complement(join(complement(complement(X_370)),X_36)) = meet(complement(X_370),complement(X_36)),
inference(subst,[],[refute_0_433:[bind(A,$fot(complement(X_370))),bind(X_16,$fot(X_36))]]) ).
cnf(refute_0_435,plain,
( complement(join(complement(complement(X_370)),X_36)) != meet(complement(X_370),complement(X_36))
| meet(complement(X_370),complement(X_36)) != complement(join(X_370,X_36))
| complement(join(complement(complement(X_370)),X_36)) = complement(join(X_370,X_36)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(complement(join(complement(complement(X_370)),X_36)))),bind(Y,$fot(meet(complement(X_370),complement(X_36)))),bind(Z,$fot(complement(join(X_370,X_36))))]]) ).
cnf(refute_0_436,plain,
( meet(complement(X_370),complement(X_36)) != complement(join(X_370,X_36))
| complement(join(complement(complement(X_370)),X_36)) = complement(join(X_370,X_36)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_370)),X_36)),meet(complement(X_370),complement(X_36))) )],[refute_0_434,refute_0_435]) ).
cnf(refute_0_437,plain,
complement(join(complement(complement(X_370)),X_36)) = complement(join(X_370,X_36)),
inference(resolve,[$cnf( $equal(meet(complement(X_370),complement(X_36)),complement(join(X_370,X_36))) )],[refute_0_431,refute_0_436]) ).
cnf(refute_0_438,plain,
meet(X_370,complement(join(complement(complement(X_370)),X_36))) = meet(X_370,complement(join(complement(complement(X_370)),X_36))),
introduced(tautology,[refl,[$fot(meet(X_370,complement(join(complement(complement(X_370)),X_36))))]]) ).
cnf(refute_0_439,plain,
( complement(join(complement(complement(X_370)),X_36)) != complement(join(X_370,X_36))
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) != meet(X_370,complement(join(complement(complement(X_370)),X_36)))
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) = meet(X_370,complement(join(X_370,X_36))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),meet(X_370,complement(join(complement(complement(X_370)),X_36)))) ),[1,1],$fot(complement(join(X_370,X_36)))]]) ).
cnf(refute_0_440,plain,
( complement(join(complement(complement(X_370)),X_36)) != complement(join(X_370,X_36))
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) = meet(X_370,complement(join(X_370,X_36))) ),
inference(resolve,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),meet(X_370,complement(join(complement(complement(X_370)),X_36)))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
meet(X_370,complement(join(complement(complement(X_370)),X_36))) = meet(X_370,complement(join(X_370,X_36))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_370)),X_36)),complement(join(X_370,X_36))) )],[refute_0_437,refute_0_440]) ).
cnf(refute_0_442,plain,
( meet(X_370,complement(join(complement(complement(X_370)),X_36))) != complement(top)
| meet(X_370,complement(join(complement(complement(X_370)),X_36))) != meet(X_370,complement(join(X_370,X_36)))
| meet(X_370,complement(join(X_370,X_36))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),complement(top)) ),[0],$fot(meet(X_370,complement(join(X_370,X_36))))]]) ).
cnf(refute_0_443,plain,
( meet(X_370,complement(join(complement(complement(X_370)),X_36))) != complement(top)
| meet(X_370,complement(join(X_370,X_36))) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),meet(X_370,complement(join(X_370,X_36)))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
( complement(top) != zero
| meet(X_370,complement(join(X_370,X_36))) != complement(top)
| meet(X_370,complement(join(X_370,X_36))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_370,complement(join(X_370,X_36))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_445,plain,
( meet(X_370,complement(join(X_370,X_36))) != complement(top)
| meet(X_370,complement(join(X_370,X_36))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_444]) ).
cnf(refute_0_446,plain,
( meet(X_370,complement(join(complement(complement(X_370)),X_36))) != complement(top)
| meet(X_370,complement(join(X_370,X_36))) = zero ),
inference(resolve,[$cnf( $equal(meet(X_370,complement(join(X_370,X_36))),complement(top)) )],[refute_0_443,refute_0_445]) ).
cnf(refute_0_447,plain,
meet(X_370,complement(join(X_370,X_36))) = zero,
inference(resolve,[$cnf( $equal(meet(X_370,complement(join(complement(complement(X_370)),X_36))),complement(top)) )],[refute_0_390,refute_0_446]) ).
cnf(refute_0_448,plain,
meet(sk2,complement(join(sk2,complement(converse(sk1))))) = zero,
inference(subst,[],[refute_0_447:[bind(X_36,$fot(complement(converse(sk1)))),bind(X_370,$fot(sk2))]]) ).
cnf(refute_0_449,plain,
converse(join(X_6,converse(A))) = join(converse(X_6),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_6)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_450,plain,
( converse(converse(A)) != A
| converse(join(X_6,converse(A))) != join(converse(X_6),converse(converse(A)))
| converse(join(X_6,converse(A))) = join(converse(X_6),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_6,converse(A))),join(converse(X_6),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_451,plain,
( converse(join(X_6,converse(A))) != join(converse(X_6),converse(converse(A)))
| converse(join(X_6,converse(A))) = join(converse(X_6),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_450]) ).
cnf(refute_0_452,plain,
converse(join(X_6,converse(A))) = join(converse(X_6),A),
inference(resolve,[$cnf( $equal(converse(join(X_6,converse(A))),join(converse(X_6),converse(converse(A)))) )],[refute_0_449,refute_0_451]) ).
cnf(refute_0_453,plain,
converse(join(X_6,converse(join(X_13,converse(X_12))))) = join(converse(X_6),join(X_13,converse(X_12))),
inference(subst,[],[refute_0_452:[bind(A,$fot(join(X_13,converse(X_12))))]]) ).
cnf(refute_0_454,plain,
converse(join(X_13,converse(X_12))) = join(converse(X_13),X_12),
inference(subst,[],[refute_0_452:[bind(A,$fot(X_12)),bind(X_6,$fot(X_13))]]) ).
cnf(refute_0_455,plain,
( converse(join(X_13,converse(X_12))) != join(converse(X_13),X_12)
| converse(join(X_6,converse(join(X_13,converse(X_12))))) != join(converse(X_6),join(X_13,converse(X_12)))
| converse(join(X_6,join(converse(X_13),X_12))) = join(converse(X_6),join(X_13,converse(X_12))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_6,converse(join(X_13,converse(X_12))))),join(converse(X_6),join(X_13,converse(X_12)))) ),[0,0,1],$fot(join(converse(X_13),X_12))]]) ).
cnf(refute_0_456,plain,
( converse(join(X_6,converse(join(X_13,converse(X_12))))) != join(converse(X_6),join(X_13,converse(X_12)))
| converse(join(X_6,join(converse(X_13),X_12))) = join(converse(X_6),join(X_13,converse(X_12))) ),
inference(resolve,[$cnf( $equal(converse(join(X_13,converse(X_12))),join(converse(X_13),X_12)) )],[refute_0_454,refute_0_455]) ).
cnf(refute_0_457,plain,
converse(join(X_6,join(converse(X_13),X_12))) = join(converse(X_6),join(X_13,converse(X_12))),
inference(resolve,[$cnf( $equal(converse(join(X_6,converse(join(X_13,converse(X_12))))),join(converse(X_6),join(X_13,converse(X_12)))) )],[refute_0_453,refute_0_456]) ).
cnf(refute_0_458,plain,
converse(join(X_143,join(converse(sk2),complement(sk1)))) = join(converse(X_143),join(sk2,converse(complement(sk1)))),
inference(subst,[],[refute_0_457:[bind(X_12,$fot(complement(sk1))),bind(X_13,$fot(sk2)),bind(X_6,$fot(X_143))]]) ).
cnf(refute_0_459,plain,
join(converse(A),converse(B)) = join(converse(B),converse(A)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(A))),bind(B,$fot(converse(B)))]]) ).
cnf(refute_0_460,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) != join(converse(B),converse(A))
| converse(join(A,B)) = join(converse(B),converse(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,B)),join(converse(B),converse(A))) ),[0],$fot(join(converse(A),converse(B)))]]) ).
cnf(refute_0_461,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| converse(join(A,B)) = join(converse(B),converse(A)) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(B)),join(converse(B),converse(A))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
converse(join(A,B)) = join(converse(B),converse(A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_461]) ).
cnf(refute_0_463,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_464,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_463]) ).
cnf(refute_0_465,plain,
join(converse(B),converse(A)) = converse(join(B,A)),
inference(subst,[],[refute_0_464:[bind(A,$fot(B)),bind(B,$fot(A))]]) ).
cnf(refute_0_466,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| join(converse(B),converse(A)) != converse(join(B,A))
| converse(join(A,B)) = converse(join(B,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(A,B)),converse(join(B,A))) ),[0],$fot(join(converse(B),converse(A)))]]) ).
cnf(refute_0_467,plain,
( converse(join(A,B)) != join(converse(B),converse(A))
| converse(join(A,B)) = converse(join(B,A)) ),
inference(resolve,[$cnf( $equal(join(converse(B),converse(A)),converse(join(B,A))) )],[refute_0_465,refute_0_466]) ).
cnf(refute_0_468,plain,
converse(join(A,B)) = converse(join(B,A)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(B),converse(A))) )],[refute_0_462,refute_0_467]) ).
cnf(refute_0_469,plain,
converse(join(converse(sk2),complement(sk1))) = converse(join(complement(sk1),converse(sk2))),
inference(subst,[],[refute_0_468:[bind(A,$fot(converse(sk2))),bind(B,$fot(complement(sk1)))]]) ).
cnf(refute_0_470,plain,
meet(top,join(complement(sk1),converse(sk2))) = complement(join(zero,complement(join(complement(sk1),converse(sk2))))),
inference(subst,[],[refute_0_36:[bind(B,$fot(join(complement(sk1),converse(sk2))))]]) ).
cnf(refute_0_471,plain,
sk1 = join(meet(sk1,converse(sk2)),complement(join(complement(sk1),converse(sk2)))),
inference(subst,[],[refute_0_138:[bind(A,$fot(sk1)),bind(B,$fot(converse(sk2)))]]) ).
cnf(refute_0_472,plain,
( meet(sk1,converse(sk2)) != zero
| sk1 != join(meet(sk1,converse(sk2)),complement(join(complement(sk1),converse(sk2))))
| sk1 = join(zero,complement(join(complement(sk1),converse(sk2)))) ),
introduced(tautology,[equality,[$cnf( $equal(sk1,join(meet(sk1,converse(sk2)),complement(join(complement(sk1),converse(sk2))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_473,plain,
( sk1 != join(meet(sk1,converse(sk2)),complement(join(complement(sk1),converse(sk2))))
| sk1 = join(zero,complement(join(complement(sk1),converse(sk2)))) ),
inference(resolve,[$cnf( $equal(meet(sk1,converse(sk2)),zero) )],[goals_14,refute_0_472]) ).
cnf(refute_0_474,plain,
sk1 = join(zero,complement(join(complement(sk1),converse(sk2)))),
inference(resolve,[$cnf( $equal(sk1,join(meet(sk1,converse(sk2)),complement(join(complement(sk1),converse(sk2))))) )],[refute_0_471,refute_0_473]) ).
cnf(refute_0_475,plain,
( sk1 != join(zero,complement(join(complement(sk1),converse(sk2))))
| join(zero,complement(join(complement(sk1),converse(sk2)))) = sk1 ),
inference(subst,[],[refute_0_6:[bind(X,$fot(sk1)),bind(Y,$fot(join(zero,complement(join(complement(sk1),converse(sk2))))))]]) ).
cnf(refute_0_476,plain,
join(zero,complement(join(complement(sk1),converse(sk2)))) = sk1,
inference(resolve,[$cnf( $equal(sk1,join(zero,complement(join(complement(sk1),converse(sk2))))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
( join(zero,complement(join(complement(sk1),converse(sk2)))) != sk1
| meet(top,join(complement(sk1),converse(sk2))) != complement(join(zero,complement(join(complement(sk1),converse(sk2)))))
| meet(top,join(complement(sk1),converse(sk2))) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(sk1),converse(sk2))),complement(join(zero,complement(join(complement(sk1),converse(sk2)))))) ),[1,0],$fot(sk1)]]) ).
cnf(refute_0_478,plain,
( meet(top,join(complement(sk1),converse(sk2))) != complement(join(zero,complement(join(complement(sk1),converse(sk2)))))
| meet(top,join(complement(sk1),converse(sk2))) = complement(sk1) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(sk1),converse(sk2)))),sk1) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
meet(top,join(complement(sk1),converse(sk2))) = complement(sk1),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),converse(sk2))),complement(join(zero,complement(join(complement(sk1),converse(sk2)))))) )],[refute_0_470,refute_0_478]) ).
cnf(refute_0_480,plain,
meet(top,join(complement(sk1),converse(sk2))) = join(complement(sk1),converse(sk2)),
inference(subst,[],[refute_0_255:[bind(X_95,$fot(join(complement(sk1),converse(sk2))))]]) ).
cnf(refute_0_481,plain,
( meet(top,join(complement(sk1),converse(sk2))) != complement(sk1)
| meet(top,join(complement(sk1),converse(sk2))) != join(complement(sk1),converse(sk2))
| join(complement(sk1),converse(sk2)) = complement(sk1) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,join(complement(sk1),converse(sk2))),complement(sk1)) ),[0],$fot(join(complement(sk1),converse(sk2)))]]) ).
cnf(refute_0_482,plain,
( meet(top,join(complement(sk1),converse(sk2))) != complement(sk1)
| join(complement(sk1),converse(sk2)) = complement(sk1) ),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),converse(sk2))),join(complement(sk1),converse(sk2))) )],[refute_0_480,refute_0_481]) ).
cnf(refute_0_483,plain,
join(complement(sk1),converse(sk2)) = complement(sk1),
inference(resolve,[$cnf( $equal(meet(top,join(complement(sk1),converse(sk2))),complement(sk1)) )],[refute_0_479,refute_0_482]) ).
cnf(refute_0_484,plain,
( converse(join(converse(sk2),complement(sk1))) != converse(join(complement(sk1),converse(sk2)))
| join(complement(sk1),converse(sk2)) != complement(sk1)
| converse(join(converse(sk2),complement(sk1))) = converse(complement(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),converse(join(complement(sk1),converse(sk2)))) ),[1,0],$fot(complement(sk1))]]) ).
cnf(refute_0_485,plain,
( converse(join(converse(sk2),complement(sk1))) != converse(join(complement(sk1),converse(sk2)))
| converse(join(converse(sk2),complement(sk1))) = converse(complement(sk1)) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),converse(sk2)),complement(sk1)) )],[refute_0_483,refute_0_484]) ).
cnf(refute_0_486,plain,
converse(join(converse(sk2),complement(sk1))) = converse(complement(sk1)),
inference(resolve,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),converse(join(complement(sk1),converse(sk2)))) )],[refute_0_469,refute_0_485]) ).
cnf(refute_0_487,plain,
join(converse(complement(sk1)),sk2) = join(sk2,converse(complement(sk1))),
inference(subst,[],[refute_0_45:[bind(A,$fot(sk2)),bind(B,$fot(converse(complement(sk1))))]]) ).
cnf(refute_0_488,plain,
converse(join(complement(sk1),converse(sk2))) = join(converse(complement(sk1)),sk2),
inference(subst,[],[refute_0_452:[bind(A,$fot(sk2)),bind(X_6,$fot(complement(sk1)))]]) ).
cnf(refute_0_489,plain,
( converse(join(complement(sk1),converse(sk2))) != join(converse(complement(sk1)),sk2)
| join(converse(complement(sk1)),sk2) != join(sk2,converse(complement(sk1)))
| converse(join(complement(sk1),converse(sk2))) = join(sk2,converse(complement(sk1))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(complement(sk1),converse(sk2))))),bind(Y,$fot(join(converse(complement(sk1)),sk2))),bind(Z,$fot(join(sk2,converse(complement(sk1)))))]]) ).
cnf(refute_0_490,plain,
( join(converse(complement(sk1)),sk2) != join(sk2,converse(complement(sk1)))
| converse(join(complement(sk1),converse(sk2))) = join(sk2,converse(complement(sk1))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(sk1),converse(sk2))),join(converse(complement(sk1)),sk2)) )],[refute_0_488,refute_0_489]) ).
cnf(refute_0_491,plain,
converse(join(complement(sk1),converse(sk2))) = join(sk2,converse(complement(sk1))),
inference(resolve,[$cnf( $equal(join(converse(complement(sk1)),sk2),join(sk2,converse(complement(sk1)))) )],[refute_0_487,refute_0_490]) ).
cnf(refute_0_492,plain,
( converse(join(complement(sk1),converse(sk2))) != join(sk2,converse(complement(sk1)))
| converse(join(converse(sk2),complement(sk1))) != converse(join(complement(sk1),converse(sk2)))
| converse(join(converse(sk2),complement(sk1))) = join(sk2,converse(complement(sk1))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(converse(sk2),complement(sk1))))),bind(Y,$fot(converse(join(complement(sk1),converse(sk2))))),bind(Z,$fot(join(sk2,converse(complement(sk1)))))]]) ).
cnf(refute_0_493,plain,
( converse(join(complement(sk1),converse(sk2))) != join(sk2,converse(complement(sk1)))
| converse(join(converse(sk2),complement(sk1))) = join(sk2,converse(complement(sk1))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),converse(join(complement(sk1),converse(sk2)))) )],[refute_0_469,refute_0_492]) ).
cnf(refute_0_494,plain,
converse(join(converse(sk2),complement(sk1))) = join(sk2,converse(complement(sk1))),
inference(resolve,[$cnf( $equal(converse(join(complement(sk1),converse(sk2))),join(sk2,converse(complement(sk1)))) )],[refute_0_491,refute_0_493]) ).
cnf(refute_0_495,plain,
( converse(join(converse(sk2),complement(sk1))) != converse(complement(sk1))
| converse(join(converse(sk2),complement(sk1))) != join(sk2,converse(complement(sk1)))
| join(sk2,converse(complement(sk1))) = converse(complement(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),converse(complement(sk1))) ),[0],$fot(join(sk2,converse(complement(sk1))))]]) ).
cnf(refute_0_496,plain,
( converse(join(converse(sk2),complement(sk1))) != converse(complement(sk1))
| join(sk2,converse(complement(sk1))) = converse(complement(sk1)) ),
inference(resolve,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),join(sk2,converse(complement(sk1)))) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
join(sk2,converse(complement(sk1))) = converse(complement(sk1)),
inference(resolve,[$cnf( $equal(converse(join(converse(sk2),complement(sk1))),converse(complement(sk1))) )],[refute_0_486,refute_0_496]) ).
cnf(refute_0_498,plain,
( converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(converse(X_143),join(sk2,converse(complement(sk1))))
| join(sk2,converse(complement(sk1))) != converse(complement(sk1))
| converse(join(X_143,join(converse(sk2),complement(sk1)))) = join(converse(X_143),converse(complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_143,join(converse(sk2),complement(sk1)))),join(converse(X_143),join(sk2,converse(complement(sk1))))) ),[1,1],$fot(converse(complement(sk1)))]]) ).
cnf(refute_0_499,plain,
( converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(converse(X_143),join(sk2,converse(complement(sk1))))
| converse(join(X_143,join(converse(sk2),complement(sk1)))) = join(converse(X_143),converse(complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(sk2,converse(complement(sk1))),converse(complement(sk1))) )],[refute_0_497,refute_0_498]) ).
cnf(refute_0_500,plain,
converse(join(X_143,join(converse(sk2),complement(sk1)))) = join(converse(X_143),converse(complement(sk1))),
inference(resolve,[$cnf( $equal(converse(join(X_143,join(converse(sk2),complement(sk1)))),join(converse(X_143),join(sk2,converse(complement(sk1))))) )],[refute_0_458,refute_0_499]) ).
cnf(refute_0_501,plain,
join(join(X_142,converse(X_141)),converse(X_143)) = join(converse(X_143),join(X_142,converse(X_141))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(X_142,converse(X_141)))),bind(B,$fot(converse(X_143)))]]) ).
cnf(refute_0_502,plain,
converse(join(X_143,join(converse(X_142),X_141))) = join(converse(X_143),join(X_142,converse(X_141))),
inference(subst,[],[refute_0_457:[bind(X_12,$fot(X_141)),bind(X_13,$fot(X_142)),bind(X_6,$fot(X_143))]]) ).
cnf(refute_0_503,plain,
( converse(join(X_143,join(converse(X_142),X_141))) != join(converse(X_143),join(X_142,converse(X_141)))
| join(converse(X_143),join(X_142,converse(X_141))) = converse(join(X_143,join(converse(X_142),X_141))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(converse(join(X_143,join(converse(X_142),X_141))))),bind(Y,$fot(join(converse(X_143),join(X_142,converse(X_141)))))]]) ).
cnf(refute_0_504,plain,
join(converse(X_143),join(X_142,converse(X_141))) = converse(join(X_143,join(converse(X_142),X_141))),
inference(resolve,[$cnf( $equal(converse(join(X_143,join(converse(X_142),X_141))),join(converse(X_143),join(X_142,converse(X_141)))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
( join(converse(X_143),join(X_142,converse(X_141))) != converse(join(X_143,join(converse(X_142),X_141)))
| join(join(X_142,converse(X_141)),converse(X_143)) != join(converse(X_143),join(X_142,converse(X_141)))
| join(join(X_142,converse(X_141)),converse(X_143)) = converse(join(X_143,join(converse(X_142),X_141))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),join(converse(X_143),join(X_142,converse(X_141)))) ),[1],$fot(converse(join(X_143,join(converse(X_142),X_141))))]]) ).
cnf(refute_0_506,plain,
( join(join(X_142,converse(X_141)),converse(X_143)) != join(converse(X_143),join(X_142,converse(X_141)))
| join(join(X_142,converse(X_141)),converse(X_143)) = converse(join(X_143,join(converse(X_142),X_141))) ),
inference(resolve,[$cnf( $equal(join(converse(X_143),join(X_142,converse(X_141))),converse(join(X_143,join(converse(X_142),X_141)))) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
join(join(X_142,converse(X_141)),converse(X_143)) = converse(join(X_143,join(converse(X_142),X_141))),
inference(resolve,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),join(converse(X_143),join(X_142,converse(X_141)))) )],[refute_0_501,refute_0_506]) ).
cnf(refute_0_508,plain,
join(converse(X_141),converse(X_143)) = converse(join(X_141,X_143)),
inference(subst,[],[refute_0_464:[bind(A,$fot(X_141)),bind(B,$fot(X_143))]]) ).
cnf(refute_0_509,plain,
join(X_142,join(converse(X_141),converse(X_143))) = join(X_142,join(converse(X_141),converse(X_143))),
introduced(tautology,[refl,[$fot(join(X_142,join(converse(X_141),converse(X_143))))]]) ).
cnf(refute_0_510,plain,
( join(X_142,join(converse(X_141),converse(X_143))) != join(X_142,join(converse(X_141),converse(X_143)))
| join(converse(X_141),converse(X_143)) != converse(join(X_141,X_143))
| join(X_142,join(converse(X_141),converse(X_143))) = join(X_142,converse(join(X_141,X_143))) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_142,join(converse(X_141),converse(X_143))),join(X_142,join(converse(X_141),converse(X_143)))) ),[1,1],$fot(converse(join(X_141,X_143)))]]) ).
cnf(refute_0_511,plain,
( join(converse(X_141),converse(X_143)) != converse(join(X_141,X_143))
| join(X_142,join(converse(X_141),converse(X_143))) = join(X_142,converse(join(X_141,X_143))) ),
inference(resolve,[$cnf( $equal(join(X_142,join(converse(X_141),converse(X_143))),join(X_142,join(converse(X_141),converse(X_143)))) )],[refute_0_509,refute_0_510]) ).
cnf(refute_0_512,plain,
join(X_142,join(converse(X_141),converse(X_143))) = join(X_142,converse(join(X_141,X_143))),
inference(resolve,[$cnf( $equal(join(converse(X_141),converse(X_143)),converse(join(X_141,X_143))) )],[refute_0_508,refute_0_511]) ).
cnf(refute_0_513,plain,
join(join(X_142,converse(X_141)),converse(X_143)) = join(X_142,join(converse(X_141),converse(X_143))),
inference(subst,[],[refute_0_277:[bind(A,$fot(X_142)),bind(B,$fot(converse(X_141))),bind(C,$fot(converse(X_143)))]]) ).
cnf(refute_0_514,plain,
( join(X_142,join(converse(X_141),converse(X_143))) != join(X_142,converse(join(X_141,X_143)))
| join(join(X_142,converse(X_141)),converse(X_143)) != join(X_142,join(converse(X_141),converse(X_143)))
| join(join(X_142,converse(X_141)),converse(X_143)) = join(X_142,converse(join(X_141,X_143))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(join(X_142,converse(X_141)),converse(X_143)))),bind(Y,$fot(join(X_142,join(converse(X_141),converse(X_143))))),bind(Z,$fot(join(X_142,converse(join(X_141,X_143)))))]]) ).
cnf(refute_0_515,plain,
( join(X_142,join(converse(X_141),converse(X_143))) != join(X_142,converse(join(X_141,X_143)))
| join(join(X_142,converse(X_141)),converse(X_143)) = join(X_142,converse(join(X_141,X_143))) ),
inference(resolve,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),join(X_142,join(converse(X_141),converse(X_143)))) )],[refute_0_513,refute_0_514]) ).
cnf(refute_0_516,plain,
join(join(X_142,converse(X_141)),converse(X_143)) = join(X_142,converse(join(X_141,X_143))),
inference(resolve,[$cnf( $equal(join(X_142,join(converse(X_141),converse(X_143))),join(X_142,converse(join(X_141,X_143)))) )],[refute_0_512,refute_0_515]) ).
cnf(refute_0_517,plain,
( join(join(X_142,converse(X_141)),converse(X_143)) != converse(join(X_143,join(converse(X_142),X_141)))
| join(join(X_142,converse(X_141)),converse(X_143)) != join(X_142,converse(join(X_141,X_143)))
| join(X_142,converse(join(X_141,X_143))) = converse(join(X_143,join(converse(X_142),X_141))) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),converse(join(X_143,join(converse(X_142),X_141)))) ),[0],$fot(join(X_142,converse(join(X_141,X_143))))]]) ).
cnf(refute_0_518,plain,
( join(join(X_142,converse(X_141)),converse(X_143)) != converse(join(X_143,join(converse(X_142),X_141)))
| join(X_142,converse(join(X_141,X_143))) = converse(join(X_143,join(converse(X_142),X_141))) ),
inference(resolve,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),join(X_142,converse(join(X_141,X_143)))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
join(X_142,converse(join(X_141,X_143))) = converse(join(X_143,join(converse(X_142),X_141))),
inference(resolve,[$cnf( $equal(join(join(X_142,converse(X_141)),converse(X_143)),converse(join(X_143,join(converse(X_142),X_141)))) )],[refute_0_507,refute_0_518]) ).
cnf(refute_0_520,plain,
( join(X_142,converse(join(X_141,X_143))) != converse(join(X_143,join(converse(X_142),X_141)))
| converse(join(X_143,join(converse(X_142),X_141))) = join(X_142,converse(join(X_141,X_143))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_142,converse(join(X_141,X_143))))),bind(Y,$fot(converse(join(X_143,join(converse(X_142),X_141)))))]]) ).
cnf(refute_0_521,plain,
converse(join(X_143,join(converse(X_142),X_141))) = join(X_142,converse(join(X_141,X_143))),
inference(resolve,[$cnf( $equal(join(X_142,converse(join(X_141,X_143))),converse(join(X_143,join(converse(X_142),X_141)))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
converse(join(X_143,join(converse(sk2),complement(sk1)))) = join(sk2,converse(join(complement(sk1),X_143))),
inference(subst,[],[refute_0_521:[bind(X_141,$fot(complement(sk1))),bind(X_142,$fot(sk2))]]) ).
cnf(refute_0_523,plain,
( converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(converse(X_143),converse(complement(sk1)))
| converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(sk2,converse(join(complement(sk1),X_143)))
| join(sk2,converse(join(complement(sk1),X_143))) = join(converse(X_143),converse(complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_143,join(converse(sk2),complement(sk1)))),join(converse(X_143),converse(complement(sk1)))) ),[0],$fot(join(sk2,converse(join(complement(sk1),X_143))))]]) ).
cnf(refute_0_524,plain,
( converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(converse(X_143),converse(complement(sk1)))
| join(sk2,converse(join(complement(sk1),X_143))) = join(converse(X_143),converse(complement(sk1))) ),
inference(resolve,[$cnf( $equal(converse(join(X_143,join(converse(sk2),complement(sk1)))),join(sk2,converse(join(complement(sk1),X_143)))) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
join(converse(X_143),converse(complement(sk1))) = converse(join(X_143,complement(sk1))),
inference(subst,[],[refute_0_464:[bind(A,$fot(X_143)),bind(B,$fot(complement(sk1)))]]) ).
cnf(refute_0_526,plain,
( join(converse(X_143),converse(complement(sk1))) != converse(join(X_143,complement(sk1)))
| join(sk2,converse(join(complement(sk1),X_143))) != join(converse(X_143),converse(complement(sk1)))
| join(sk2,converse(join(complement(sk1),X_143))) = converse(join(X_143,complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,converse(join(complement(sk1),X_143))),join(converse(X_143),converse(complement(sk1)))) ),[1],$fot(converse(join(X_143,complement(sk1))))]]) ).
cnf(refute_0_527,plain,
( join(sk2,converse(join(complement(sk1),X_143))) != join(converse(X_143),converse(complement(sk1)))
| join(sk2,converse(join(complement(sk1),X_143))) = converse(join(X_143,complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(converse(X_143),converse(complement(sk1))),converse(join(X_143,complement(sk1)))) )],[refute_0_525,refute_0_526]) ).
cnf(refute_0_528,plain,
( converse(join(X_143,join(converse(sk2),complement(sk1)))) != join(converse(X_143),converse(complement(sk1)))
| join(sk2,converse(join(complement(sk1),X_143))) = converse(join(X_143,complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(sk2,converse(join(complement(sk1),X_143))),join(converse(X_143),converse(complement(sk1)))) )],[refute_0_524,refute_0_527]) ).
cnf(refute_0_529,plain,
join(sk2,converse(join(complement(sk1),X_143))) = converse(join(X_143,complement(sk1))),
inference(resolve,[$cnf( $equal(converse(join(X_143,join(converse(sk2),complement(sk1)))),join(converse(X_143),converse(complement(sk1)))) )],[refute_0_500,refute_0_528]) ).
cnf(refute_0_530,plain,
join(sk2,converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))),
inference(subst,[],[refute_0_529:[bind(X_143,$fot(meet(sk1,converse(complement(converse(sk1))))))]]) ).
cnf(refute_0_531,plain,
X_93 = join(meet(X_93,X_94),complement(join(complement(X_93),X_94))),
inference(subst,[],[refute_0_138:[bind(A,$fot(X_93)),bind(B,$fot(X_94))]]) ).
cnf(refute_0_532,plain,
join(X_94,complement(X_93)) = join(complement(X_93),X_94),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_94)),bind(B,$fot(complement(X_93)))]]) ).
cnf(refute_0_533,plain,
( join(X_94,complement(X_93)) != join(complement(X_93),X_94)
| join(complement(X_93),X_94) = join(X_94,complement(X_93)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(X_94,complement(X_93)))),bind(Y,$fot(join(complement(X_93),X_94)))]]) ).
cnf(refute_0_534,plain,
join(complement(X_93),X_94) = join(X_94,complement(X_93)),
inference(resolve,[$cnf( $equal(join(X_94,complement(X_93)),join(complement(X_93),X_94)) )],[refute_0_532,refute_0_533]) ).
cnf(refute_0_535,plain,
( X_93 != join(meet(X_93,X_94),complement(join(complement(X_93),X_94)))
| join(complement(X_93),X_94) != join(X_94,complement(X_93))
| X_93 = join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_93,join(meet(X_93,X_94),complement(join(complement(X_93),X_94)))) ),[1,1,0],$fot(join(X_94,complement(X_93)))]]) ).
cnf(refute_0_536,plain,
( X_93 != join(meet(X_93,X_94),complement(join(complement(X_93),X_94)))
| X_93 = join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_93),X_94),join(X_94,complement(X_93))) )],[refute_0_534,refute_0_535]) ).
cnf(refute_0_537,plain,
X_93 = join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,X_94),complement(join(complement(X_93),X_94)))) )],[refute_0_531,refute_0_536]) ).
cnf(refute_0_538,plain,
( meet(complement(X_16),B) != complement(join(X_16,complement(B)))
| complement(join(X_16,complement(B))) = meet(complement(X_16),B) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(complement(X_16),B))),bind(Y,$fot(complement(join(X_16,complement(B)))))]]) ).
cnf(refute_0_539,plain,
complement(join(X_16,complement(B))) = meet(complement(X_16),B),
inference(resolve,[$cnf( $equal(meet(complement(X_16),B),complement(join(X_16,complement(B)))) )],[refute_0_412,refute_0_538]) ).
cnf(refute_0_540,plain,
complement(join(X_94,complement(X_93))) = meet(complement(X_94),X_93),
inference(subst,[],[refute_0_539:[bind(B,$fot(X_93)),bind(X_16,$fot(X_94))]]) ).
cnf(refute_0_541,plain,
join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) = join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))),
introduced(tautology,[refl,[$fot(join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))))]]) ).
cnf(refute_0_542,plain,
( complement(join(X_94,complement(X_93))) != meet(complement(X_94),X_93)
| join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) != join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))
| join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) = join(meet(X_93,X_94),meet(complement(X_94),X_93)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))),join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))) ),[1,1],$fot(meet(complement(X_94),X_93))]]) ).
cnf(refute_0_543,plain,
( complement(join(X_94,complement(X_93))) != meet(complement(X_94),X_93)
| join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) = join(meet(X_93,X_94),meet(complement(X_94),X_93)) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))),join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))) )],[refute_0_541,refute_0_542]) ).
cnf(refute_0_544,plain,
join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) = join(meet(X_93,X_94),meet(complement(X_94),X_93)),
inference(resolve,[$cnf( $equal(complement(join(X_94,complement(X_93))),meet(complement(X_94),X_93)) )],[refute_0_540,refute_0_543]) ).
cnf(refute_0_545,plain,
( X_93 != join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))
| join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))) != join(meet(X_93,X_94),meet(complement(X_94),X_93))
| X_93 = join(meet(X_93,X_94),meet(complement(X_94),X_93)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_93,join(meet(X_93,X_94),meet(complement(X_94),X_93))) ),[0],$fot(join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))))]]) ).
cnf(refute_0_546,plain,
( X_93 != join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))
| X_93 = join(meet(X_93,X_94),meet(complement(X_94),X_93)) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,X_94),complement(join(X_94,complement(X_93)))),join(meet(X_93,X_94),meet(complement(X_94),X_93))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
X_93 = join(meet(X_93,X_94),meet(complement(X_94),X_93)),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,X_94),complement(join(X_94,complement(X_93))))) )],[refute_0_537,refute_0_546]) ).
cnf(refute_0_548,plain,
converse(complement(converse(complement(complement(X_117))))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117))))))),
inference(subst,[],[refute_0_547:[bind(X_93,$fot(converse(complement(converse(complement(complement(X_117))))))),bind(X_94,$fot(X_117))]]) ).
cnf(refute_0_549,plain,
X_93 = join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(join(complement(X_93),converse(complement(converse(complement(X_93))))))),
inference(subst,[],[refute_0_138:[bind(A,$fot(X_93)),bind(B,$fot(converse(complement(converse(complement(X_93))))))]]) ).
cnf(refute_0_550,plain,
converse(join(converse(A),X_7)) = join(converse(converse(A)),converse(X_7)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).
cnf(refute_0_551,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_7)) != join(converse(converse(A)),converse(X_7))
| converse(join(converse(A),X_7)) = join(A,converse(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_7)),join(converse(converse(A)),converse(X_7))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_552,plain,
( converse(join(converse(A),X_7)) != join(converse(converse(A)),converse(X_7))
| converse(join(converse(A),X_7)) = join(A,converse(X_7)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_551]) ).
cnf(refute_0_553,plain,
converse(join(converse(A),X_7)) = join(A,converse(X_7)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_7)),join(converse(converse(A)),converse(X_7))) )],[refute_0_550,refute_0_552]) ).
cnf(refute_0_554,plain,
converse(join(converse(X_28),complement(converse(X_28)))) = join(X_28,converse(complement(converse(X_28)))),
inference(subst,[],[refute_0_553:[bind(A,$fot(X_28)),bind(X_7,$fot(complement(converse(X_28))))]]) ).
cnf(refute_0_555,plain,
top = join(converse(X_28),complement(converse(X_28))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_28)))]]) ).
cnf(refute_0_556,plain,
( top != join(converse(X_28),complement(converse(X_28)))
| join(converse(X_28),complement(converse(X_28))) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_28),complement(converse(X_28)))))]]) ).
cnf(refute_0_557,plain,
join(converse(X_28),complement(converse(X_28))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_28),complement(converse(X_28)))) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
( converse(join(converse(X_28),complement(converse(X_28)))) != join(X_28,converse(complement(converse(X_28))))
| join(converse(X_28),complement(converse(X_28))) != top
| converse(top) = join(X_28,converse(complement(converse(X_28)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_28),complement(converse(X_28)))),join(X_28,converse(complement(converse(X_28))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_559,plain,
( converse(join(converse(X_28),complement(converse(X_28)))) != join(X_28,converse(complement(converse(X_28))))
| converse(top) = join(X_28,converse(complement(converse(X_28)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_28),complement(converse(X_28))),top) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
converse(top) = join(X_28,converse(complement(converse(X_28)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_28),complement(converse(X_28)))),join(X_28,converse(complement(converse(X_28))))) )],[refute_0_554,refute_0_559]) ).
cnf(refute_0_561,plain,
converse(join(converse(top),complement(converse(zero)))) = join(converse(converse(top)),converse(complement(converse(zero)))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(top))),bind(B,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_562,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(top)),bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_563,plain,
join(top,join(zero,converse(complement(converse(zero))))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_347:[bind(X_36,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_564,plain,
converse(top) = join(zero,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_560:[bind(X_28,$fot(zero))]]) ).
cnf(refute_0_565,plain,
( converse(top) != join(zero,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) = converse(top) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(converse(top))),bind(Y,$fot(join(zero,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_566,plain,
join(zero,converse(complement(converse(zero)))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(zero,converse(complement(converse(zero))))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
( join(top,join(zero,converse(complement(converse(zero))))) != join(top,converse(complement(converse(zero))))
| join(zero,converse(complement(converse(zero)))) != converse(top)
| join(top,converse(top)) = join(top,converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) ),[0,1],$fot(converse(top))]]) ).
cnf(refute_0_568,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( $equal(join(zero,converse(complement(converse(zero)))),converse(top)) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
join(top,converse(top)) = join(top,converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(join(top,join(zero,converse(complement(converse(zero))))),join(top,converse(complement(converse(zero))))) )],[refute_0_563,refute_0_568]) ).
cnf(refute_0_570,plain,
( join(top,converse(top)) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(join(top,converse(top)))),bind(Y,$fot(join(top,converse(complement(converse(zero))))))]]) ).
cnf(refute_0_571,plain,
join(top,converse(complement(converse(zero)))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(top,converse(complement(converse(zero))))) )],[refute_0_569,refute_0_570]) ).
cnf(refute_0_572,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(complement(converse(zero)))) != join(top,converse(top))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0,0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_573,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),join(top,converse(top))) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
converse(join(top,converse(top))) = join(converse(top),converse(converse(complement(converse(zero))))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_562,refute_0_573]) ).
cnf(refute_0_575,plain,
join(converse(top),top) = join(top,converse(top)),
inference(subst,[],[refute_0_45:[bind(A,$fot(top)),bind(B,$fot(converse(top)))]]) ).
cnf(refute_0_576,plain,
converse(join(top,converse(top))) = join(converse(top),top),
inference(subst,[],[refute_0_452:[bind(A,$fot(top)),bind(X_6,$fot(top))]]) ).
cnf(refute_0_577,plain,
( converse(join(top,converse(top))) != join(converse(top),top)
| join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(top,converse(top))))),bind(Y,$fot(join(converse(top),top))),bind(Z,$fot(join(top,converse(top))))]]) ).
cnf(refute_0_578,plain,
( join(converse(top),top) != join(top,converse(top))
| converse(join(top,converse(top))) = join(top,converse(top)) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),top)) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
converse(join(top,converse(top))) = join(top,converse(top)),
inference(resolve,[$cnf( $equal(join(converse(top),top),join(top,converse(top))) )],[refute_0_575,refute_0_578]) ).
cnf(refute_0_580,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| converse(join(top,converse(top))) != join(top,converse(top))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) ),[0],$fot(join(top,converse(top)))]]) ).
cnf(refute_0_581,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),converse(converse(complement(converse(zero))))) ),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(top,converse(top))) )],[refute_0_579,refute_0_580]) ).
cnf(refute_0_582,plain,
converse(join(top,converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(subst,[],[refute_0_452:[bind(A,$fot(complement(converse(zero)))),bind(X_6,$fot(top))]]) ).
cnf(refute_0_583,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = converse(join(top,converse(complement(converse(zero))))),
inference(subst,[],[refute_0_464:[bind(A,$fot(top)),bind(B,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_584,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) != converse(join(top,converse(complement(converse(zero)))))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(converse(top),converse(converse(complement(converse(zero))))))),bind(Y,$fot(converse(join(top,converse(complement(converse(zero))))))),bind(Z,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_585,plain,
( converse(join(top,converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),converse(join(top,converse(complement(converse(zero)))))) )],[refute_0_583,refute_0_584]) ).
cnf(refute_0_586,plain,
join(converse(top),converse(converse(complement(converse(zero))))) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_582,refute_0_585]) ).
cnf(refute_0_587,plain,
( join(converse(top),converse(converse(complement(converse(zero))))) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) ),[1],$fot(join(converse(top),complement(converse(zero))))]]) ).
cnf(refute_0_588,plain,
( join(top,converse(top)) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(converse(top),converse(converse(complement(converse(zero))))),join(converse(top),complement(converse(zero)))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
( converse(join(top,converse(top))) != join(converse(top),converse(converse(complement(converse(zero)))))
| join(top,converse(top)) = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_581,refute_0_588]) ).
cnf(refute_0_590,plain,
join(top,converse(top)) = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(converse(join(top,converse(top))),join(converse(top),converse(converse(complement(converse(zero)))))) )],[refute_0_574,refute_0_589]) ).
cnf(refute_0_591,plain,
join(top,converse(top)) = top,
inference(subst,[],[refute_0_382:[bind(X_34,$fot(converse(top)))]]) ).
cnf(refute_0_592,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| join(top,converse(top)) != top
| top = join(converse(top),complement(converse(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) ),[0],$fot(top)]]) ).
cnf(refute_0_593,plain,
( join(top,converse(top)) != join(converse(top),complement(converse(zero)))
| top = join(converse(top),complement(converse(zero))) ),
inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_591,refute_0_592]) ).
cnf(refute_0_594,plain,
top = join(converse(top),complement(converse(zero))),
inference(resolve,[$cnf( $equal(join(top,converse(top)),join(converse(top),complement(converse(zero)))) )],[refute_0_590,refute_0_593]) ).
cnf(refute_0_595,plain,
( top != join(converse(top),complement(converse(zero)))
| join(converse(top),complement(converse(zero))) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(converse(top),complement(converse(zero)))))]]) ).
cnf(refute_0_596,plain,
join(converse(top),complement(converse(zero))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(top),complement(converse(zero)))) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(converse(converse(top)),converse(complement(converse(zero))))
| join(converse(top),complement(converse(zero))) != top
| converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(converse(converse(top)),converse(complement(converse(zero))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_598,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(converse(converse(top)),converse(complement(converse(zero))))
| converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(zero))),top) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
converse(top) = join(converse(converse(top)),converse(complement(converse(zero)))),
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(converse(converse(top)),converse(complement(converse(zero))))) )],[refute_0_561,refute_0_598]) ).
cnf(refute_0_600,plain,
join(top,converse(complement(converse(zero)))) = top,
inference(subst,[],[refute_0_382:[bind(X_34,$fot(converse(complement(converse(zero)))))]]) ).
cnf(refute_0_601,plain,
converse(join(converse(top),complement(converse(zero)))) = join(top,converse(complement(converse(zero)))),
inference(subst,[],[refute_0_553:[bind(A,$fot(top)),bind(X_7,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_602,plain,
( converse(join(converse(top),complement(converse(zero)))) != join(top,converse(complement(converse(zero))))
| join(top,converse(complement(converse(zero)))) != top
| converse(join(converse(top),complement(converse(zero)))) = top ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(converse(top),complement(converse(zero)))))),bind(Y,$fot(join(top,converse(complement(converse(zero)))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_603,plain,
( join(top,converse(complement(converse(zero)))) != top
| converse(join(converse(top),complement(converse(zero)))) = top ),
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),join(top,converse(complement(converse(zero))))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
converse(join(converse(top),complement(converse(zero)))) = top,
inference(resolve,[$cnf( $equal(join(top,converse(complement(converse(zero)))),top) )],[refute_0_600,refute_0_603]) ).
cnf(refute_0_605,plain,
join(converse(converse(top)),converse(complement(converse(zero)))) = converse(join(converse(top),complement(converse(zero)))),
inference(subst,[],[refute_0_464:[bind(A,$fot(converse(top))),bind(B,$fot(complement(converse(zero))))]]) ).
cnf(refute_0_606,plain,
( converse(join(converse(top),complement(converse(zero)))) != top
| join(converse(converse(top)),converse(complement(converse(zero)))) != converse(join(converse(top),complement(converse(zero))))
| join(converse(converse(top)),converse(complement(converse(zero)))) = top ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(converse(converse(top)),converse(complement(converse(zero)))))),bind(Y,$fot(converse(join(converse(top),complement(converse(zero)))))),bind(Z,$fot(top))]]) ).
cnf(refute_0_607,plain,
( converse(join(converse(top),complement(converse(zero)))) != top
| join(converse(converse(top)),converse(complement(converse(zero)))) = top ),
inference(resolve,[$cnf( $equal(join(converse(converse(top)),converse(complement(converse(zero)))),converse(join(converse(top),complement(converse(zero))))) )],[refute_0_605,refute_0_606]) ).
cnf(refute_0_608,plain,
join(converse(converse(top)),converse(complement(converse(zero)))) = top,
inference(resolve,[$cnf( $equal(converse(join(converse(top),complement(converse(zero)))),top) )],[refute_0_604,refute_0_607]) ).
cnf(refute_0_609,plain,
( converse(top) != join(converse(converse(top)),converse(complement(converse(zero))))
| join(converse(converse(top)),converse(complement(converse(zero)))) != top
| converse(top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(top),top) ),[0],$fot(join(converse(converse(top)),converse(complement(converse(zero)))))]]) ).
cnf(refute_0_610,plain,
( converse(top) != join(converse(converse(top)),converse(complement(converse(zero))))
| converse(top) = top ),
inference(resolve,[$cnf( $equal(join(converse(converse(top)),converse(complement(converse(zero)))),top) )],[refute_0_608,refute_0_609]) ).
cnf(refute_0_611,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(converse(top),join(converse(converse(top)),converse(complement(converse(zero))))) )],[refute_0_599,refute_0_610]) ).
cnf(refute_0_612,plain,
( converse(top) != join(X_28,converse(complement(converse(X_28))))
| converse(top) != top
| top = join(X_28,converse(complement(converse(X_28)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_28,converse(complement(converse(X_28))))) ),[0],$fot(top)]]) ).
cnf(refute_0_613,plain,
( converse(top) != join(X_28,converse(complement(converse(X_28))))
| top = join(X_28,converse(complement(converse(X_28)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_611,refute_0_612]) ).
cnf(refute_0_614,plain,
top = join(X_28,converse(complement(converse(X_28)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_28,converse(complement(converse(X_28))))) )],[refute_0_560,refute_0_613]) ).
cnf(refute_0_615,plain,
top = join(complement(X_93),converse(complement(converse(complement(X_93))))),
inference(subst,[],[refute_0_614:[bind(X_28,$fot(complement(X_93)))]]) ).
cnf(refute_0_616,plain,
( top != join(complement(X_93),converse(complement(converse(complement(X_93)))))
| join(complement(X_93),converse(complement(converse(complement(X_93))))) = top ),
inference(subst,[],[refute_0_6:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_93),converse(complement(converse(complement(X_93)))))))]]) ).
cnf(refute_0_617,plain,
join(complement(X_93),converse(complement(converse(complement(X_93))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_93),converse(complement(converse(complement(X_93)))))) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
( X_93 != join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(join(complement(X_93),converse(complement(converse(complement(X_93)))))))
| join(complement(X_93),converse(complement(converse(complement(X_93))))) != top
| X_93 = join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_93,join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(join(complement(X_93),converse(complement(converse(complement(X_93)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_619,plain,
( X_93 != join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(join(complement(X_93),converse(complement(converse(complement(X_93)))))))
| X_93 = join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_93),converse(complement(converse(complement(X_93))))),top) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
X_93 = join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(join(complement(X_93),converse(complement(converse(complement(X_93)))))))) )],[refute_0_549,refute_0_619]) ).
cnf(refute_0_621,plain,
join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) = join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))))]]) ).
cnf(refute_0_622,plain,
( complement(top) != zero
| join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) != join(complement(top),meet(X_93,converse(complement(converse(complement(X_93))))))
| join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))),join(complement(top),meet(X_93,converse(complement(converse(complement(X_93))))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_623,plain,
( complement(top) != zero
| join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))),join(complement(top),meet(X_93,converse(complement(converse(complement(X_93))))))) )],[refute_0_621,refute_0_622]) ).
cnf(refute_0_624,plain,
join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_33,refute_0_623]) ).
cnf(refute_0_625,plain,
join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) = join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))),
inference(subst,[],[refute_0_45:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_93,converse(complement(converse(complement(X_93)))))))]]) ).
cnf(refute_0_626,plain,
( join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) != join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))
| join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) != join(complement(top),meet(X_93,converse(complement(converse(complement(X_93))))))
| join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))))),bind(Z,$fot(join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))))]]) ).
cnf(refute_0_627,plain,
( join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))) != join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))
| join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)),join(complement(top),meet(X_93,converse(complement(converse(complement(X_93))))))) )],[refute_0_625,refute_0_626]) ).
cnf(refute_0_628,plain,
join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(X_93,converse(complement(converse(complement(X_93)))))),join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))) )],[refute_0_624,refute_0_627]) ).
cnf(refute_0_629,plain,
( X_93 != join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top))
| join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)) != join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))
| X_93 = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_93,join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))) ),[0],$fot(join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)))]]) ).
cnf(refute_0_630,plain,
( X_93 != join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top))
| X_93 = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) ),
inference(resolve,[$cnf( $equal(join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top)),join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
X_93 = join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))),
inference(resolve,[$cnf( $equal(X_93,join(meet(X_93,converse(complement(converse(complement(X_93))))),complement(top))) )],[refute_0_620,refute_0_630]) ).
cnf(refute_0_632,plain,
join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) = meet(X_93,converse(complement(converse(complement(X_93))))),
inference(subst,[],[refute_0_228:[bind(X_95,$fot(meet(X_93,converse(complement(converse(complement(X_93)))))))]]) ).
cnf(refute_0_633,plain,
( X_93 != join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))
| join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))) != meet(X_93,converse(complement(converse(complement(X_93)))))
| X_93 = meet(X_93,converse(complement(converse(complement(X_93))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_93,meet(X_93,converse(complement(converse(complement(X_93)))))) ),[0],$fot(join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))))]]) ).
cnf(refute_0_634,plain,
( X_93 != join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))
| X_93 = meet(X_93,converse(complement(converse(complement(X_93))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(X_93,converse(complement(converse(complement(X_93)))))),meet(X_93,converse(complement(converse(complement(X_93)))))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
X_93 = meet(X_93,converse(complement(converse(complement(X_93))))),
inference(resolve,[$cnf( $equal(X_93,join(zero,meet(X_93,converse(complement(converse(complement(X_93))))))) )],[refute_0_631,refute_0_634]) ).
cnf(refute_0_636,plain,
complement(X_117) = meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))),
inference(subst,[],[refute_0_635:[bind(X_93,$fot(complement(X_117)))]]) ).
cnf(refute_0_637,plain,
( complement(X_117) != meet(complement(X_117),converse(complement(converse(complement(complement(X_117))))))
| meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))) = complement(X_117) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(complement(X_117))),bind(Y,$fot(meet(complement(X_117),converse(complement(converse(complement(complement(X_117))))))))]]) ).
cnf(refute_0_638,plain,
meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))) = complement(X_117),
inference(resolve,[$cnf( $equal(complement(X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117))))))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
( converse(complement(converse(complement(complement(X_117))))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))))
| meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))) != complement(X_117)
| converse(complement(converse(complement(complement(X_117))))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))))) ),[1,1],$fot(complement(X_117))]]) ).
cnf(refute_0_640,plain,
( converse(complement(converse(complement(complement(X_117))))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))))
| converse(complement(converse(complement(complement(X_117))))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))),complement(X_117)) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
converse(complement(converse(complement(complement(X_117))))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(complement(X_117),converse(complement(converse(complement(complement(X_117)))))))) )],[refute_0_548,refute_0_640]) ).
cnf(refute_0_642,plain,
complement(complement(X_117)) = X_117,
inference(subst,[],[refute_0_427:[bind(B,$fot(X_117))]]) ).
cnf(refute_0_643,plain,
converse(complement(complement(X_117))) = converse(complement(complement(X_117))),
introduced(tautology,[refl,[$fot(converse(complement(complement(X_117))))]]) ).
cnf(refute_0_644,plain,
( complement(complement(X_117)) != X_117
| converse(complement(complement(X_117))) != converse(complement(complement(X_117)))
| converse(complement(complement(X_117))) = converse(X_117) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(complement(X_117))),converse(complement(complement(X_117)))) ),[1,0],$fot(X_117)]]) ).
cnf(refute_0_645,plain,
( complement(complement(X_117)) != X_117
| converse(complement(complement(X_117))) = converse(X_117) ),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_117))),converse(complement(complement(X_117)))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
converse(complement(complement(X_117))) = converse(X_117),
inference(resolve,[$cnf( $equal(complement(complement(X_117)),X_117) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
complement(converse(complement(complement(X_117)))) = complement(converse(complement(complement(X_117)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(complement(X_117)))))]]) ).
cnf(refute_0_648,plain,
( complement(converse(complement(complement(X_117)))) != complement(converse(complement(complement(X_117))))
| converse(complement(complement(X_117))) != converse(X_117)
| complement(converse(complement(complement(X_117)))) = complement(converse(X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(complement(X_117)))),complement(converse(complement(complement(X_117))))) ),[1,0],$fot(converse(X_117))]]) ).
cnf(refute_0_649,plain,
( converse(complement(complement(X_117))) != converse(X_117)
| complement(converse(complement(complement(X_117)))) = complement(converse(X_117)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_117)))),complement(converse(complement(complement(X_117))))) )],[refute_0_647,refute_0_648]) ).
cnf(refute_0_650,plain,
complement(converse(complement(complement(X_117)))) = complement(converse(X_117)),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_117))),converse(X_117)) )],[refute_0_646,refute_0_649]) ).
cnf(refute_0_651,plain,
converse(complement(converse(complement(complement(X_117))))) = converse(complement(converse(complement(complement(X_117))))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(complement(X_117))))))]]) ).
cnf(refute_0_652,plain,
( complement(converse(complement(complement(X_117)))) != complement(converse(X_117))
| converse(complement(converse(complement(complement(X_117))))) != converse(complement(converse(complement(complement(X_117)))))
| converse(complement(converse(complement(complement(X_117))))) = converse(complement(converse(X_117))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),converse(complement(converse(complement(complement(X_117)))))) ),[1,0],$fot(complement(converse(X_117)))]]) ).
cnf(refute_0_653,plain,
( complement(converse(complement(complement(X_117)))) != complement(converse(X_117))
| converse(complement(converse(complement(complement(X_117))))) = converse(complement(converse(X_117))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),converse(complement(converse(complement(complement(X_117)))))) )],[refute_0_651,refute_0_652]) ).
cnf(refute_0_654,plain,
converse(complement(converse(complement(complement(X_117))))) = converse(complement(converse(X_117))),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_117)))),complement(converse(X_117))) )],[refute_0_650,refute_0_653]) ).
cnf(refute_0_655,plain,
( converse(complement(converse(complement(complement(X_117))))) != converse(complement(converse(X_117)))
| converse(complement(converse(complement(complement(X_117))))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))
| converse(complement(converse(X_117))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))) ),[0],$fot(converse(complement(converse(X_117))))]]) ).
cnf(refute_0_656,plain,
( converse(complement(converse(complement(complement(X_117))))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))
| converse(complement(converse(X_117))) = join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),converse(complement(converse(X_117)))) )],[refute_0_654,refute_0_655]) ).
cnf(refute_0_657,plain,
meet(X_117,converse(complement(converse(complement(complement(X_117)))))) = meet(X_117,converse(complement(converse(complement(complement(X_117)))))),
introduced(tautology,[refl,[$fot(meet(X_117,converse(complement(converse(complement(complement(X_117)))))))]]) ).
cnf(refute_0_658,plain,
( converse(complement(converse(complement(complement(X_117))))) != converse(complement(converse(X_117)))
| meet(X_117,converse(complement(converse(complement(complement(X_117)))))) != meet(X_117,converse(complement(converse(complement(complement(X_117))))))
| meet(X_117,converse(complement(converse(complement(complement(X_117)))))) = meet(X_117,converse(complement(converse(X_117)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_117,converse(complement(converse(complement(complement(X_117)))))),meet(X_117,converse(complement(converse(complement(complement(X_117))))))) ),[1,1],$fot(converse(complement(converse(X_117))))]]) ).
cnf(refute_0_659,plain,
( converse(complement(converse(complement(complement(X_117))))) != converse(complement(converse(X_117)))
| meet(X_117,converse(complement(converse(complement(complement(X_117)))))) = meet(X_117,converse(complement(converse(X_117)))) ),
inference(resolve,[$cnf( $equal(meet(X_117,converse(complement(converse(complement(complement(X_117)))))),meet(X_117,converse(complement(converse(complement(complement(X_117))))))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
meet(X_117,converse(complement(converse(complement(complement(X_117)))))) = meet(X_117,converse(complement(converse(X_117)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),converse(complement(converse(X_117)))) )],[refute_0_654,refute_0_659]) ).
cnf(refute_0_661,plain,
( meet(A,B) != meet(B,A)
| meet(B,A) = meet(A,B) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(meet(A,B))),bind(Y,$fot(meet(B,A)))]]) ).
cnf(refute_0_662,plain,
meet(B,A) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),meet(B,A)) )],[refute_0_243,refute_0_661]) ).
cnf(refute_0_663,plain,
meet(converse(complement(converse(complement(complement(X_117))))),X_117) = meet(X_117,converse(complement(converse(complement(complement(X_117)))))),
inference(subst,[],[refute_0_662:[bind(A,$fot(X_117)),bind(B,$fot(converse(complement(converse(complement(complement(X_117)))))))]]) ).
cnf(refute_0_664,plain,
( meet(X_117,converse(complement(converse(complement(complement(X_117)))))) != meet(X_117,converse(complement(converse(X_117))))
| meet(converse(complement(converse(complement(complement(X_117))))),X_117) != meet(X_117,converse(complement(converse(complement(complement(X_117))))))
| meet(converse(complement(converse(complement(complement(X_117))))),X_117) = meet(X_117,converse(complement(converse(X_117)))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(meet(converse(complement(converse(complement(complement(X_117))))),X_117))),bind(Y,$fot(meet(X_117,converse(complement(converse(complement(complement(X_117)))))))),bind(Z,$fot(meet(X_117,converse(complement(converse(X_117))))))]]) ).
cnf(refute_0_665,plain,
( meet(X_117,converse(complement(converse(complement(complement(X_117)))))) != meet(X_117,converse(complement(converse(X_117))))
| meet(converse(complement(converse(complement(complement(X_117))))),X_117) = meet(X_117,converse(complement(converse(X_117)))) ),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(X_117,converse(complement(converse(complement(complement(X_117))))))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
meet(converse(complement(converse(complement(complement(X_117))))),X_117) = meet(X_117,converse(complement(converse(X_117)))),
inference(resolve,[$cnf( $equal(meet(X_117,converse(complement(converse(complement(complement(X_117)))))),meet(X_117,converse(complement(converse(X_117))))) )],[refute_0_660,refute_0_665]) ).
cnf(refute_0_667,plain,
join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) = join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)),
introduced(tautology,[refl,[$fot(join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)))]]) ).
cnf(refute_0_668,plain,
( join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) != join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117))
| meet(converse(complement(converse(complement(complement(X_117))))),X_117) != meet(X_117,converse(complement(converse(X_117))))
| join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)),join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117))) ),[1,1],$fot(meet(X_117,converse(complement(converse(X_117)))))]]) ).
cnf(refute_0_669,plain,
( meet(converse(complement(converse(complement(complement(X_117))))),X_117) != meet(X_117,converse(complement(converse(X_117))))
| join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
inference(resolve,[$cnf( $equal(join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)),join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117))) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(complement(X_117))))),X_117),meet(X_117,converse(complement(converse(X_117))))) )],[refute_0_666,refute_0_669]) ).
cnf(refute_0_671,plain,
join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) = join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)),
inference(subst,[],[refute_0_45:[bind(A,$fot(complement(X_117))),bind(B,$fot(meet(converse(complement(converse(complement(complement(X_117))))),X_117)))]]) ).
cnf(refute_0_672,plain,
( join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) != join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))
| join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) != join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117))
| join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)))),bind(Y,$fot(join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)))),bind(Z,$fot(join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))))]]) ).
cnf(refute_0_673,plain,
( join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)) != join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))
| join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)),join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))),
inference(resolve,[$cnf( $equal(join(complement(X_117),meet(converse(complement(converse(complement(complement(X_117))))),X_117)),join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))) )],[refute_0_670,refute_0_673]) ).
cnf(refute_0_675,plain,
( converse(complement(converse(X_117))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))
| join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)) != join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))
| converse(complement(converse(X_117))) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(X_117))),join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))) ),[0],$fot(join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)))]]) ).
cnf(refute_0_676,plain,
( converse(complement(converse(X_117))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))
| converse(complement(converse(X_117))) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117)),join(complement(X_117),meet(X_117,converse(complement(converse(X_117)))))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
( converse(complement(converse(complement(complement(X_117))))) != join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))
| converse(complement(converse(X_117))) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_117))),join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))) )],[refute_0_656,refute_0_676]) ).
cnf(refute_0_678,plain,
converse(complement(converse(X_117))) = join(complement(X_117),meet(X_117,converse(complement(converse(X_117))))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_117))))),join(meet(converse(complement(converse(complement(complement(X_117))))),X_117),complement(X_117))) )],[refute_0_641,refute_0_677]) ).
cnf(refute_0_679,plain,
converse(complement(converse(sk1))) = join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))),
inference(subst,[],[refute_0_678:[bind(X_117,$fot(sk1))]]) ).
cnf(refute_0_680,plain,
( converse(complement(converse(sk1))) != join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))
| join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))) = converse(complement(converse(sk1))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(converse(complement(converse(sk1))))),bind(Y,$fot(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))))]]) ).
cnf(refute_0_681,plain,
join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))) = converse(complement(converse(sk1))),
inference(resolve,[$cnf( $equal(converse(complement(converse(sk1))),join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) )],[refute_0_679,refute_0_680]) ).
cnf(refute_0_682,plain,
( join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))) != converse(complement(converse(sk1)))
| join(sk2,converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,converse(converse(complement(converse(sk1))))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) ),[0,1,0],$fot(converse(complement(converse(sk1))))]]) ).
cnf(refute_0_683,plain,
( join(sk2,converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,converse(converse(complement(converse(sk1))))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))),converse(complement(converse(sk1)))) )],[refute_0_681,refute_0_682]) ).
cnf(refute_0_684,plain,
join(sk2,converse(converse(complement(converse(sk1))))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))),
inference(resolve,[$cnf( $equal(join(sk2,converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) )],[refute_0_530,refute_0_683]) ).
cnf(refute_0_685,plain,
converse(converse(complement(converse(sk1)))) = complement(converse(sk1)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(sk1))))]]) ).
cnf(refute_0_686,plain,
join(sk2,converse(converse(complement(converse(sk1))))) = join(sk2,converse(converse(complement(converse(sk1))))),
introduced(tautology,[refl,[$fot(join(sk2,converse(converse(complement(converse(sk1))))))]]) ).
cnf(refute_0_687,plain,
( converse(converse(complement(converse(sk1)))) != complement(converse(sk1))
| join(sk2,converse(converse(complement(converse(sk1))))) != join(sk2,converse(converse(complement(converse(sk1)))))
| join(sk2,converse(converse(complement(converse(sk1))))) = join(sk2,complement(converse(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,converse(converse(complement(converse(sk1))))),join(sk2,converse(converse(complement(converse(sk1)))))) ),[1,1],$fot(complement(converse(sk1)))]]) ).
cnf(refute_0_688,plain,
( converse(converse(complement(converse(sk1)))) != complement(converse(sk1))
| join(sk2,converse(converse(complement(converse(sk1))))) = join(sk2,complement(converse(sk1))) ),
inference(resolve,[$cnf( $equal(join(sk2,converse(converse(complement(converse(sk1))))),join(sk2,converse(converse(complement(converse(sk1)))))) )],[refute_0_686,refute_0_687]) ).
cnf(refute_0_689,plain,
join(sk2,converse(converse(complement(converse(sk1))))) = join(sk2,complement(converse(sk1))),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(sk1)))),complement(converse(sk1))) )],[refute_0_685,refute_0_688]) ).
cnf(refute_0_690,plain,
( join(sk2,converse(converse(complement(converse(sk1))))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,converse(converse(complement(converse(sk1))))) != join(sk2,complement(converse(sk1)))
| join(sk2,complement(converse(sk1))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,converse(converse(complement(converse(sk1))))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) ),[0],$fot(join(sk2,complement(converse(sk1))))]]) ).
cnf(refute_0_691,plain,
( join(sk2,converse(converse(complement(converse(sk1))))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,complement(converse(sk1))) = converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) ),
inference(resolve,[$cnf( $equal(join(sk2,converse(converse(complement(converse(sk1))))),join(sk2,complement(converse(sk1)))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),
introduced(tautology,[refl,[$fot(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))))]]) ).
cnf(refute_0_693,plain,
( converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) != converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))
| join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))) != converse(complement(converse(sk1)))
| converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = converse(converse(complement(converse(sk1)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) ),[1,0],$fot(converse(complement(converse(sk1))))]]) ).
cnf(refute_0_694,plain,
( join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))) != converse(complement(converse(sk1)))
| converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = converse(converse(complement(converse(sk1)))) ),
inference(resolve,[$cnf( $equal(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) )],[refute_0_692,refute_0_693]) ).
cnf(refute_0_695,plain,
converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = converse(converse(complement(converse(sk1)))),
inference(resolve,[$cnf( $equal(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))),converse(complement(converse(sk1)))) )],[refute_0_681,refute_0_694]) ).
cnf(refute_0_696,plain,
( converse(converse(complement(converse(sk1)))) != complement(converse(sk1))
| converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) != converse(converse(complement(converse(sk1))))
| converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = complement(converse(sk1)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))))),bind(Y,$fot(converse(converse(complement(converse(sk1)))))),bind(Z,$fot(complement(converse(sk1))))]]) ).
cnf(refute_0_697,plain,
( converse(converse(complement(converse(sk1)))) != complement(converse(sk1))
| converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = complement(converse(sk1)) ),
inference(resolve,[$cnf( $equal(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),converse(converse(complement(converse(sk1))))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) = complement(converse(sk1)),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(sk1)))),complement(converse(sk1))) )],[refute_0_685,refute_0_697]) ).
cnf(refute_0_699,plain,
( converse(join(A,B)) != converse(join(B,A))
| converse(join(B,A)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(converse(join(B,A))))]]) ).
cnf(refute_0_700,plain,
converse(join(B,A)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),converse(join(B,A))) )],[refute_0_468,refute_0_699]) ).
cnf(refute_0_701,plain,
converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) = converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),
inference(subst,[],[refute_0_700:[bind(A,$fot(complement(sk1))),bind(B,$fot(meet(sk1,converse(complement(converse(sk1))))))]]) ).
cnf(refute_0_702,plain,
( converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) != complement(converse(sk1))
| converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) != converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))
| converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) = complement(converse(sk1)) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))))),bind(Y,$fot(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))))),bind(Z,$fot(complement(converse(sk1))))]]) ).
cnf(refute_0_703,plain,
( converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))) != complement(converse(sk1))
| converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) = complement(converse(sk1)) ),
inference(resolve,[$cnf( $equal(converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))),converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1))))))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) = complement(converse(sk1)),
inference(resolve,[$cnf( $equal(converse(join(complement(sk1),meet(sk1,converse(complement(converse(sk1)))))),complement(converse(sk1))) )],[refute_0_698,refute_0_703]) ).
cnf(refute_0_705,plain,
( converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))) != complement(converse(sk1))
| join(sk2,complement(converse(sk1))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,complement(converse(sk1))) = complement(converse(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,complement(converse(sk1))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) ),[1],$fot(complement(converse(sk1)))]]) ).
cnf(refute_0_706,plain,
( join(sk2,complement(converse(sk1))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,complement(converse(sk1))) = complement(converse(sk1)) ),
inference(resolve,[$cnf( $equal(converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1))),complement(converse(sk1))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
( join(sk2,converse(converse(complement(converse(sk1))))) != converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))
| join(sk2,complement(converse(sk1))) = complement(converse(sk1)) ),
inference(resolve,[$cnf( $equal(join(sk2,complement(converse(sk1))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) )],[refute_0_691,refute_0_706]) ).
cnf(refute_0_708,plain,
join(sk2,complement(converse(sk1))) = complement(converse(sk1)),
inference(resolve,[$cnf( $equal(join(sk2,converse(converse(complement(converse(sk1))))),converse(join(meet(sk1,converse(complement(converse(sk1)))),complement(sk1)))) )],[refute_0_684,refute_0_707]) ).
cnf(refute_0_709,plain,
( join(sk2,complement(converse(sk1))) != complement(converse(sk1))
| meet(sk2,complement(join(sk2,complement(converse(sk1))))) != zero
| meet(sk2,complement(complement(converse(sk1)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(sk2,complement(join(sk2,complement(converse(sk1))))),zero) ),[0,1,0],$fot(complement(converse(sk1)))]]) ).
cnf(refute_0_710,plain,
( meet(sk2,complement(join(sk2,complement(converse(sk1))))) != zero
| meet(sk2,complement(complement(converse(sk1)))) = zero ),
inference(resolve,[$cnf( $equal(join(sk2,complement(converse(sk1))),complement(converse(sk1))) )],[refute_0_708,refute_0_709]) ).
cnf(refute_0_711,plain,
meet(sk2,complement(complement(converse(sk1)))) = zero,
inference(resolve,[$cnf( $equal(meet(sk2,complement(join(sk2,complement(converse(sk1))))),zero) )],[refute_0_448,refute_0_710]) ).
cnf(refute_0_712,plain,
complement(complement(converse(sk1))) = converse(sk1),
inference(subst,[],[refute_0_427:[bind(B,$fot(converse(sk1)))]]) ).
cnf(refute_0_713,plain,
meet(sk2,complement(complement(converse(sk1)))) = meet(sk2,complement(complement(converse(sk1)))),
introduced(tautology,[refl,[$fot(meet(sk2,complement(complement(converse(sk1)))))]]) ).
cnf(refute_0_714,plain,
( complement(complement(converse(sk1))) != converse(sk1)
| meet(sk2,complement(complement(converse(sk1)))) != meet(sk2,complement(complement(converse(sk1))))
| meet(sk2,complement(complement(converse(sk1)))) = meet(sk2,converse(sk1)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(sk2,complement(complement(converse(sk1)))),meet(sk2,complement(complement(converse(sk1))))) ),[1,1],$fot(converse(sk1))]]) ).
cnf(refute_0_715,plain,
( complement(complement(converse(sk1))) != converse(sk1)
| meet(sk2,complement(complement(converse(sk1)))) = meet(sk2,converse(sk1)) ),
inference(resolve,[$cnf( $equal(meet(sk2,complement(complement(converse(sk1)))),meet(sk2,complement(complement(converse(sk1))))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
meet(sk2,complement(complement(converse(sk1)))) = meet(sk2,converse(sk1)),
inference(resolve,[$cnf( $equal(complement(complement(converse(sk1))),converse(sk1)) )],[refute_0_712,refute_0_715]) ).
cnf(refute_0_717,plain,
( meet(sk2,complement(complement(converse(sk1)))) != meet(sk2,converse(sk1))
| meet(sk2,complement(complement(converse(sk1)))) != zero
| meet(sk2,converse(sk1)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(meet(sk2,complement(complement(converse(sk1)))),zero) ),[0],$fot(meet(sk2,converse(sk1)))]]) ).
cnf(refute_0_718,plain,
( meet(sk2,complement(complement(converse(sk1)))) != zero
| meet(sk2,converse(sk1)) = zero ),
inference(resolve,[$cnf( $equal(meet(sk2,complement(complement(converse(sk1)))),meet(sk2,converse(sk1))) )],[refute_0_716,refute_0_717]) ).
cnf(refute_0_719,plain,
meet(sk2,converse(sk1)) = zero,
inference(resolve,[$cnf( $equal(meet(sk2,complement(complement(converse(sk1)))),zero) )],[refute_0_711,refute_0_718]) ).
cnf(refute_0_720,plain,
meet(converse(sk1),sk2) = meet(sk2,converse(sk1)),
inference(subst,[],[refute_0_662:[bind(A,$fot(sk2)),bind(B,$fot(converse(sk1)))]]) ).
cnf(refute_0_721,plain,
( meet(converse(sk1),sk2) != meet(sk2,converse(sk1))
| meet(sk2,converse(sk1)) != zero
| meet(converse(sk1),sk2) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(converse(sk1),sk2),zero) ),[0],$fot(meet(sk2,converse(sk1)))]]) ).
cnf(refute_0_722,plain,
( meet(sk2,converse(sk1)) != zero
| meet(converse(sk1),sk2) = zero ),
inference(resolve,[$cnf( $equal(meet(converse(sk1),sk2),meet(sk2,converse(sk1))) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
meet(sk2,converse(sk1)) != zero,
inference(resolve,[$cnf( $equal(meet(converse(sk1),sk2),zero) )],[refute_0_722,goals_15]) ).
cnf(refute_0_724,plain,
$false,
inference(resolve,[$cnf( $equal(meet(sk2,converse(sk1)),zero) )],[refute_0_719,refute_0_723]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : REL007-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Fri Jul 8 11:55:59 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6.06/6.27 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.06/6.27
% 6.06/6.27 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.17/6.34
%------------------------------------------------------------------------------