TSTP Solution File: REL050-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL050-4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:46:28 EDT 2022
% Result : Unsatisfiable 13.25s 13.43s
% Output : CNFRefutation 13.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 120
% Number of leaves : 339
% Syntax : Number of clauses : 1446 ( 717 unt; 0 nHn; 901 RR)
% Number of literals : 2495 (2494 equ;1055 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 1534 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
join(A,B) = join(B,A) ).
cnf(maddux2_join_associativity_2,axiom,
join(A,join(B,C)) = join(join(A,B),C) ).
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(A,B) = complement(join(complement(A),complement(B))) ).
cnf(composition_associativity_5,axiom,
composition(A,composition(B,C)) = composition(composition(A,B),C) ).
cnf(composition_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_17,negated_conjecture,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != complement(composition(sk1,top)) ) ).
cnf(refute_0_0,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_1,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_2,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_4,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_3]) ).
cnf(refute_0_5,plain,
join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(composition(sk1,top)))),bind(B,$fot(composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_6,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))))),bind(Y,$fot(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)))),bind(Z,$fot(composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_9,plain,
( join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_11,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top)
| join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_11,goals_17]) ).
cnf(refute_0_13,plain,
join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),
introduced(tautology,[refl,[$fot(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)))]]) ).
cnf(refute_0_14,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),complement(composition(sk1,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) ),[1,1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_15,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = join(complement(composition(sk1,top)),complement(composition(sk1,top))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
( join(complement(composition(sk1,top)),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) != join(complement(composition(sk1,top)),complement(composition(sk1,top)))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),complement(composition(sk1,top)))) ),[1],$fot(composition(complement(composition(sk1,top)),top))]]) ).
cnf(refute_0_17,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != composition(complement(composition(sk1,top)),top)
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),join(complement(composition(sk1,top)),complement(composition(sk1,top)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = composition(complement(composition(sk1,top)),top) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) ),[1],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_19,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)) = composition(complement(composition(sk1,top)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),composition(complement(composition(sk1,top)),top)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
( composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),composition(complement(composition(sk1,top)),top)),composition(complement(composition(sk1,top)),top)) )],[refute_0_19,refute_0_12]) ).
cnf(refute_0_21,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_22,plain,
( A != join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))
| join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) ),
introduced(tautology,[equality,[$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_23,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_23]) ).
cnf(refute_0_25,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_26,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_27,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_26]) ).
cnf(refute_0_28,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_29,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_30,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$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_33,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_36,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_24,refute_0_36]) ).
cnf(refute_0_38,plain,
X_70 = join(meet(X_70,complement(X_70)),complement(join(complement(X_70),complement(X_70)))),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_70)),bind(B,$fot(complement(X_70)))]]) ).
cnf(refute_0_39,plain,
converse(composition(X_4,converse(A))) = composition(converse(converse(A)),converse(X_4)),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(X_4)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_40,plain,
( converse(composition(X_4,converse(A))) != composition(converse(converse(A)),converse(X_4))
| converse(converse(A)) != A
| converse(composition(X_4,converse(A))) = composition(A,converse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_4,converse(A))),composition(converse(converse(A)),converse(X_4))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_41,plain,
( converse(composition(X_4,converse(A))) != composition(converse(converse(A)),converse(X_4))
| converse(composition(X_4,converse(A))) = composition(A,converse(X_4)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_40]) ).
cnf(refute_0_42,plain,
converse(composition(X_4,converse(A))) = composition(A,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(A))),composition(converse(converse(A)),converse(X_4))) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
converse(composition(join(one,one),converse(A))) = composition(A,converse(join(one,one))),
inference(subst,[],[refute_0_42:[bind(X_4,$fot(join(one,one)))]]) ).
cnf(refute_0_44,plain,
composition(join(X_36,one),X_38) = join(composition(X_36,X_38),composition(one,X_38)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_36)),bind(B,$fot(one)),bind(C,$fot(X_38))]]) ).
cnf(refute_0_45,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_46,plain,
( converse(composition(converse(A),X_5)) != composition(converse(X_5),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_5)) = composition(converse(X_5),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_47,plain,
( converse(composition(converse(A),X_5)) != composition(converse(X_5),converse(converse(A)))
| converse(composition(converse(A),X_5)) = composition(converse(X_5),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_46]) ).
cnf(refute_0_48,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
converse(composition(converse(X_14),one)) = composition(converse(one),X_14),
inference(subst,[],[refute_0_48:[bind(A,$fot(X_14)),bind(X_5,$fot(one))]]) ).
cnf(refute_0_50,plain,
composition(converse(X_14),one) = converse(X_14),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_14)))]]) ).
cnf(refute_0_51,plain,
( composition(converse(X_14),one) != converse(X_14)
| converse(composition(converse(X_14),one)) != composition(converse(one),X_14)
| converse(converse(X_14)) = composition(converse(one),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_14),one)),composition(converse(one),X_14)) ),[0,0],$fot(converse(X_14))]]) ).
cnf(refute_0_52,plain,
( converse(composition(converse(X_14),one)) != composition(converse(one),X_14)
| converse(converse(X_14)) = composition(converse(one),X_14) ),
inference(resolve,[$cnf( $equal(composition(converse(X_14),one),converse(X_14)) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
converse(converse(X_14)) = composition(converse(one),X_14),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_14),one)),composition(converse(one),X_14)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
converse(converse(X_14)) = X_14,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_14))]]) ).
cnf(refute_0_55,plain,
( converse(converse(X_14)) != X_14
| converse(converse(X_14)) != composition(converse(one),X_14)
| X_14 = composition(converse(one),X_14) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_14)),composition(converse(one),X_14)) ),[0],$fot(X_14)]]) ).
cnf(refute_0_56,plain,
( converse(converse(X_14)) != composition(converse(one),X_14)
| X_14 = composition(converse(one),X_14) ),
inference(resolve,[$cnf( $equal(converse(converse(X_14)),X_14) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
X_14 = composition(converse(one),X_14),
inference(resolve,[$cnf( $equal(converse(converse(X_14)),composition(converse(one),X_14)) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_59,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_57:[bind(X_14,$fot(one))]]) ).
cnf(refute_0_60,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_61,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_63,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_58,refute_0_63]) ).
cnf(refute_0_65,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_66,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
composition(converse(one),X_14) = composition(converse(one),X_14),
introduced(tautology,[refl,[$fot(composition(converse(one),X_14))]]) ).
cnf(refute_0_68,plain,
( composition(converse(one),X_14) != composition(converse(one),X_14)
| converse(one) != one
| composition(converse(one),X_14) = composition(one,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_14),composition(converse(one),X_14)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_69,plain,
( converse(one) != one
| composition(converse(one),X_14) = composition(one,X_14) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_14),composition(converse(one),X_14)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
composition(converse(one),X_14) = composition(one,X_14),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_69]) ).
cnf(refute_0_71,plain,
( X_14 != composition(converse(one),X_14)
| composition(converse(one),X_14) != composition(one,X_14)
| X_14 = composition(one,X_14) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_14,composition(one,X_14)) ),[0],$fot(composition(converse(one),X_14))]]) ).
cnf(refute_0_72,plain,
( X_14 != composition(converse(one),X_14)
| X_14 = composition(one,X_14) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_14),composition(one,X_14)) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
X_14 = composition(one,X_14),
inference(resolve,[$cnf( $equal(X_14,composition(converse(one),X_14)) )],[refute_0_57,refute_0_72]) ).
cnf(refute_0_74,plain,
X_38 = composition(one,X_38),
inference(subst,[],[refute_0_73:[bind(X_14,$fot(X_38))]]) ).
cnf(refute_0_75,plain,
( X_38 != composition(one,X_38)
| composition(one,X_38) = X_38 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_38)),bind(Y,$fot(composition(one,X_38)))]]) ).
cnf(refute_0_76,plain,
composition(one,X_38) = X_38,
inference(resolve,[$cnf( $equal(X_38,composition(one,X_38)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( composition(join(X_36,one),X_38) != join(composition(X_36,X_38),composition(one,X_38))
| composition(one,X_38) != X_38
| composition(join(X_36,one),X_38) = join(composition(X_36,X_38),X_38) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_36,one),X_38),join(composition(X_36,X_38),composition(one,X_38))) ),[1,1],$fot(X_38)]]) ).
cnf(refute_0_78,plain,
( composition(join(X_36,one),X_38) != join(composition(X_36,X_38),composition(one,X_38))
| composition(join(X_36,one),X_38) = join(composition(X_36,X_38),X_38) ),
inference(resolve,[$cnf( $equal(composition(one,X_38),X_38) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
composition(join(X_36,one),X_38) = join(composition(X_36,X_38),X_38),
inference(resolve,[$cnf( $equal(composition(join(X_36,one),X_38),join(composition(X_36,X_38),composition(one,X_38))) )],[refute_0_44,refute_0_78]) ).
cnf(refute_0_80,plain,
join(composition(X_36,X_38),X_38) = join(X_38,composition(X_36,X_38)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_38)),bind(B,$fot(composition(X_36,X_38)))]]) ).
cnf(refute_0_81,plain,
( composition(join(X_36,one),X_38) != join(composition(X_36,X_38),X_38)
| join(composition(X_36,X_38),X_38) != join(X_38,composition(X_36,X_38))
| composition(join(X_36,one),X_38) = join(X_38,composition(X_36,X_38)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_36,one),X_38),join(X_38,composition(X_36,X_38))) ),[0],$fot(join(composition(X_36,X_38),X_38))]]) ).
cnf(refute_0_82,plain,
( composition(join(X_36,one),X_38) != join(composition(X_36,X_38),X_38)
| composition(join(X_36,one),X_38) = join(X_38,composition(X_36,X_38)) ),
inference(resolve,[$cnf( $equal(join(composition(X_36,X_38),X_38),join(X_38,composition(X_36,X_38))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
composition(join(X_36,one),X_38) = join(X_38,composition(X_36,X_38)),
inference(resolve,[$cnf( $equal(composition(join(X_36,one),X_38),join(composition(X_36,X_38),X_38)) )],[refute_0_79,refute_0_82]) ).
cnf(refute_0_84,plain,
composition(join(one,one),X_40) = join(X_40,composition(one,X_40)),
inference(subst,[],[refute_0_83:[bind(X_36,$fot(one)),bind(X_38,$fot(X_40))]]) ).
cnf(refute_0_85,plain,
X_40 = composition(one,X_40),
inference(subst,[],[refute_0_73:[bind(X_14,$fot(X_40))]]) ).
cnf(refute_0_86,plain,
( X_40 != composition(one,X_40)
| composition(one,X_40) = X_40 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_40)),bind(Y,$fot(composition(one,X_40)))]]) ).
cnf(refute_0_87,plain,
composition(one,X_40) = X_40,
inference(resolve,[$cnf( $equal(X_40,composition(one,X_40)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( composition(join(one,one),X_40) != join(X_40,composition(one,X_40))
| composition(one,X_40) != X_40
| composition(join(one,one),X_40) = join(X_40,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_40),join(X_40,composition(one,X_40))) ),[1,1],$fot(X_40)]]) ).
cnf(refute_0_89,plain,
( composition(join(one,one),X_40) != join(X_40,composition(one,X_40))
| composition(join(one,one),X_40) = join(X_40,X_40) ),
inference(resolve,[$cnf( $equal(composition(one,X_40),X_40) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
composition(join(one,one),X_40) = join(X_40,X_40),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_40),join(X_40,composition(one,X_40))) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
composition(join(one,one),converse(A)) = join(converse(A),converse(A)),
inference(subst,[],[refute_0_90:[bind(X_40,$fot(converse(A)))]]) ).
cnf(refute_0_92,plain,
( composition(join(one,one),converse(A)) != join(converse(A),converse(A))
| converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) ),[0,0],$fot(join(converse(A),converse(A)))]]) ).
cnf(refute_0_93,plain,
( converse(composition(join(one,one),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),converse(A)),join(converse(A),converse(A))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
converse(join(converse(A),converse(A))) = composition(A,converse(join(one,one))),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_43,refute_0_93]) ).
cnf(refute_0_95,plain,
join(A,converse(converse(A))) = join(A,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(A,converse(converse(A))))]]) ).
cnf(refute_0_96,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) != join(A,converse(converse(A)))
| join(A,converse(converse(A))) = join(A,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_97,plain,
( converse(converse(A)) != A
| join(A,converse(converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,converse(converse(A)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
join(A,converse(converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_97]) ).
cnf(refute_0_99,plain,
converse(join(converse(A),X_11)) = join(converse(converse(A)),converse(X_11)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_11))]]) ).
cnf(refute_0_100,plain,
( converse(converse(A)) != A
| converse(join(converse(A),X_11)) != join(converse(converse(A)),converse(X_11))
| converse(join(converse(A),X_11)) = join(A,converse(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_11)),join(converse(converse(A)),converse(X_11))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_101,plain,
( converse(join(converse(A),X_11)) != join(converse(converse(A)),converse(X_11))
| converse(join(converse(A),X_11)) = join(A,converse(X_11)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_100]) ).
cnf(refute_0_102,plain,
converse(join(converse(A),X_11)) = join(A,converse(X_11)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),X_11)),join(converse(converse(A)),converse(X_11))) )],[refute_0_99,refute_0_101]) ).
cnf(refute_0_103,plain,
converse(join(converse(A),converse(A))) = join(A,converse(converse(A))),
inference(subst,[],[refute_0_102:[bind(X_11,$fot(converse(A)))]]) ).
cnf(refute_0_104,plain,
( converse(join(converse(A),converse(A))) != join(A,converse(converse(A)))
| join(A,converse(converse(A))) != join(A,A)
| converse(join(converse(A),converse(A))) = join(A,A) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(A),converse(A))))),bind(Y,$fot(join(A,converse(converse(A))))),bind(Z,$fot(join(A,A)))]]) ).
cnf(refute_0_105,plain,
( join(A,converse(converse(A))) != join(A,A)
| converse(join(converse(A),converse(A))) = join(A,A) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(A,converse(converse(A)))) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
converse(join(converse(A),converse(A))) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,converse(converse(A))),join(A,A)) )],[refute_0_98,refute_0_105]) ).
cnf(refute_0_107,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| converse(join(converse(A),converse(A))) != join(A,A)
| join(A,A) = composition(A,converse(join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) ),[0],$fot(join(A,A))]]) ).
cnf(refute_0_108,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,converse(join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),join(A,A)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
converse(join(X_10,converse(A))) = join(converse(X_10),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_10)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_110,plain,
( converse(converse(A)) != A
| converse(join(X_10,converse(A))) != join(converse(X_10),converse(converse(A)))
| converse(join(X_10,converse(A))) = join(converse(X_10),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_10,converse(A))),join(converse(X_10),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_111,plain,
( converse(join(X_10,converse(A))) != join(converse(X_10),converse(converse(A)))
| converse(join(X_10,converse(A))) = join(converse(X_10),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_110]) ).
cnf(refute_0_112,plain,
converse(join(X_10,converse(A))) = join(converse(X_10),A),
inference(resolve,[$cnf( $equal(converse(join(X_10,converse(A))),join(converse(X_10),converse(converse(A)))) )],[refute_0_109,refute_0_111]) ).
cnf(refute_0_113,plain,
converse(join(X_10,converse(one))) = join(converse(X_10),one),
inference(subst,[],[refute_0_112:[bind(A,$fot(one))]]) ).
cnf(refute_0_114,plain,
( converse(join(X_10,converse(one))) != join(converse(X_10),one)
| converse(one) != one
| converse(join(X_10,one)) = join(converse(X_10),one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_10,converse(one))),join(converse(X_10),one)) ),[0,0,1],$fot(one)]]) ).
cnf(refute_0_115,plain,
( converse(join(X_10,converse(one))) != join(converse(X_10),one)
| converse(join(X_10,one)) = join(converse(X_10),one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_114]) ).
cnf(refute_0_116,plain,
converse(join(X_10,one)) = join(converse(X_10),one),
inference(resolve,[$cnf( $equal(converse(join(X_10,converse(one))),join(converse(X_10),one)) )],[refute_0_113,refute_0_115]) ).
cnf(refute_0_117,plain,
join(converse(X_10),one) = join(one,converse(X_10)),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(converse(X_10)))]]) ).
cnf(refute_0_118,plain,
( converse(join(X_10,one)) != join(converse(X_10),one)
| join(converse(X_10),one) != join(one,converse(X_10))
| converse(join(X_10,one)) = join(one,converse(X_10)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_10,one)),join(one,converse(X_10))) ),[0],$fot(join(converse(X_10),one))]]) ).
cnf(refute_0_119,plain,
( converse(join(X_10,one)) != join(converse(X_10),one)
| converse(join(X_10,one)) = join(one,converse(X_10)) ),
inference(resolve,[$cnf( $equal(join(converse(X_10),one),join(one,converse(X_10))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
converse(join(X_10,one)) = join(one,converse(X_10)),
inference(resolve,[$cnf( $equal(converse(join(X_10,one)),join(converse(X_10),one)) )],[refute_0_116,refute_0_119]) ).
cnf(refute_0_121,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_120:[bind(X_10,$fot(one))]]) ).
cnf(refute_0_122,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(one) != one
| converse(join(one,one)) = join(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_123,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_122]) ).
cnf(refute_0_124,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_121,refute_0_123]) ).
cnf(refute_0_125,plain,
composition(A,converse(join(one,one))) = composition(A,converse(join(one,one))),
introduced(tautology,[refl,[$fot(composition(A,converse(join(one,one))))]]) ).
cnf(refute_0_126,plain,
( composition(A,converse(join(one,one))) != composition(A,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_127,plain,
( converse(join(one,one)) != join(one,one)
| composition(A,converse(join(one,one))) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,converse(join(one,one)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
composition(A,converse(join(one,one))) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
( composition(A,converse(join(one,one))) != composition(A,join(one,one))
| join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) ),[1],$fot(composition(A,join(one,one)))]]) ).
cnf(refute_0_130,plain,
( join(A,A) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(composition(A,converse(join(one,one))),composition(A,join(one,one))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( converse(join(converse(A),converse(A))) != composition(A,converse(join(one,one)))
| join(A,A) = composition(A,join(one,one)) ),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,converse(join(one,one)))) )],[refute_0_108,refute_0_130]) ).
cnf(refute_0_132,plain,
join(A,A) = composition(A,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(converse(A),converse(A))),composition(A,converse(join(one,one)))) )],[refute_0_94,refute_0_131]) ).
cnf(refute_0_133,plain,
join(complement(X_70),complement(X_70)) = composition(complement(X_70),join(one,one)),
inference(subst,[],[refute_0_132:[bind(A,$fot(complement(X_70)))]]) ).
cnf(refute_0_134,plain,
( X_70 != join(meet(X_70,complement(X_70)),complement(join(complement(X_70),complement(X_70))))
| join(complement(X_70),complement(X_70)) != composition(complement(X_70),join(one,one))
| X_70 = join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,join(meet(X_70,complement(X_70)),complement(join(complement(X_70),complement(X_70))))) ),[1,1,0],$fot(composition(complement(X_70),join(one,one)))]]) ).
cnf(refute_0_135,plain,
( X_70 != join(meet(X_70,complement(X_70)),complement(join(complement(X_70),complement(X_70))))
| X_70 = join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_70),complement(X_70)),composition(complement(X_70),join(one,one))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
X_70 = join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),
inference(resolve,[$cnf( $equal(X_70,join(meet(X_70,complement(X_70)),complement(join(complement(X_70),complement(X_70))))) )],[refute_0_38,refute_0_135]) ).
cnf(refute_0_137,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_138,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_139,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_139]) ).
cnf(refute_0_141,plain,
join(complement(X_20),composition(converse(one),complement(composition(one,X_20)))) = complement(X_20),
inference(subst,[],[refute_0_140:[bind(A,$fot(one)),bind(B,$fot(X_20))]]) ).
cnf(refute_0_142,plain,
X_20 = composition(one,X_20),
inference(subst,[],[refute_0_73:[bind(X_14,$fot(X_20))]]) ).
cnf(refute_0_143,plain,
( X_20 != composition(one,X_20)
| composition(one,X_20) = X_20 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_20)),bind(Y,$fot(composition(one,X_20)))]]) ).
cnf(refute_0_144,plain,
composition(one,X_20) = X_20,
inference(resolve,[$cnf( $equal(X_20,composition(one,X_20)) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
( composition(one,X_20) != X_20
| join(complement(X_20),composition(converse(one),complement(composition(one,X_20)))) != complement(X_20)
| join(complement(X_20),composition(converse(one),complement(X_20))) = complement(X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(composition(one,X_20)))),complement(X_20)) ),[0,1,1,0],$fot(X_20)]]) ).
cnf(refute_0_146,plain,
( join(complement(X_20),composition(converse(one),complement(composition(one,X_20)))) != complement(X_20)
| join(complement(X_20),composition(converse(one),complement(X_20))) = complement(X_20) ),
inference(resolve,[$cnf( $equal(composition(one,X_20),X_20) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
join(complement(X_20),composition(converse(one),complement(X_20))) = complement(X_20),
inference(resolve,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(composition(one,X_20)))),complement(X_20)) )],[refute_0_141,refute_0_146]) ).
cnf(refute_0_148,plain,
( X_14 != composition(one,X_14)
| composition(one,X_14) = X_14 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_14)),bind(Y,$fot(composition(one,X_14)))]]) ).
cnf(refute_0_149,plain,
composition(one,X_14) = X_14,
inference(resolve,[$cnf( $equal(X_14,composition(one,X_14)) )],[refute_0_73,refute_0_148]) ).
cnf(refute_0_150,plain,
composition(one,complement(X_20)) = complement(X_20),
inference(subst,[],[refute_0_149:[bind(X_14,$fot(complement(X_20)))]]) ).
cnf(refute_0_151,plain,
composition(converse(one),complement(X_20)) = composition(converse(one),complement(X_20)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_20)))]]) ).
cnf(refute_0_152,plain,
( composition(converse(one),complement(X_20)) != composition(converse(one),complement(X_20))
| converse(one) != one
| composition(converse(one),complement(X_20)) = composition(one,complement(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_20)),composition(converse(one),complement(X_20))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_153,plain,
( converse(one) != one
| composition(converse(one),complement(X_20)) = composition(one,complement(X_20)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_20)),composition(converse(one),complement(X_20))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
composition(converse(one),complement(X_20)) = composition(one,complement(X_20)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_153]) ).
cnf(refute_0_155,plain,
( composition(converse(one),complement(X_20)) != composition(one,complement(X_20))
| composition(one,complement(X_20)) != complement(X_20)
| composition(converse(one),complement(X_20)) = complement(X_20) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(converse(one),complement(X_20)))),bind(Y,$fot(composition(one,complement(X_20)))),bind(Z,$fot(complement(X_20)))]]) ).
cnf(refute_0_156,plain,
( composition(one,complement(X_20)) != complement(X_20)
| composition(converse(one),complement(X_20)) = complement(X_20) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_20)),composition(one,complement(X_20))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
composition(converse(one),complement(X_20)) = complement(X_20),
inference(resolve,[$cnf( $equal(composition(one,complement(X_20)),complement(X_20)) )],[refute_0_150,refute_0_156]) ).
cnf(refute_0_158,plain,
join(complement(X_20),composition(converse(one),complement(X_20))) = join(complement(X_20),composition(converse(one),complement(X_20))),
introduced(tautology,[refl,[$fot(join(complement(X_20),composition(converse(one),complement(X_20))))]]) ).
cnf(refute_0_159,plain,
( composition(converse(one),complement(X_20)) != complement(X_20)
| join(complement(X_20),composition(converse(one),complement(X_20))) != join(complement(X_20),composition(converse(one),complement(X_20)))
| join(complement(X_20),composition(converse(one),complement(X_20))) = join(complement(X_20),complement(X_20)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(X_20))),join(complement(X_20),composition(converse(one),complement(X_20)))) ),[1,1],$fot(complement(X_20))]]) ).
cnf(refute_0_160,plain,
( composition(converse(one),complement(X_20)) != complement(X_20)
| join(complement(X_20),composition(converse(one),complement(X_20))) = join(complement(X_20),complement(X_20)) ),
inference(resolve,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(X_20))),join(complement(X_20),composition(converse(one),complement(X_20)))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
join(complement(X_20),composition(converse(one),complement(X_20))) = join(complement(X_20),complement(X_20)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_20)),complement(X_20)) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
( join(complement(X_20),composition(converse(one),complement(X_20))) != complement(X_20)
| join(complement(X_20),composition(converse(one),complement(X_20))) != join(complement(X_20),complement(X_20))
| join(complement(X_20),complement(X_20)) = complement(X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(X_20))),complement(X_20)) ),[0],$fot(join(complement(X_20),complement(X_20)))]]) ).
cnf(refute_0_163,plain,
( join(complement(X_20),composition(converse(one),complement(X_20))) != complement(X_20)
| join(complement(X_20),complement(X_20)) = complement(X_20) ),
inference(resolve,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(X_20))),join(complement(X_20),complement(X_20))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
join(complement(X_20),complement(X_20)) = complement(X_20),
inference(resolve,[$cnf( $equal(join(complement(X_20),composition(converse(one),complement(X_20))),complement(X_20)) )],[refute_0_147,refute_0_163]) ).
cnf(refute_0_165,plain,
join(complement(X_20),complement(X_20)) = composition(complement(X_20),join(one,one)),
inference(subst,[],[refute_0_132:[bind(A,$fot(complement(X_20)))]]) ).
cnf(refute_0_166,plain,
( join(complement(X_20),complement(X_20)) != complement(X_20)
| join(complement(X_20),complement(X_20)) != composition(complement(X_20),join(one,one))
| composition(complement(X_20),join(one,one)) = complement(X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_20),complement(X_20)),complement(X_20)) ),[0],$fot(composition(complement(X_20),join(one,one)))]]) ).
cnf(refute_0_167,plain,
( join(complement(X_20),complement(X_20)) != complement(X_20)
| composition(complement(X_20),join(one,one)) = complement(X_20) ),
inference(resolve,[$cnf( $equal(join(complement(X_20),complement(X_20)),composition(complement(X_20),join(one,one))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
composition(complement(X_20),join(one,one)) = complement(X_20),
inference(resolve,[$cnf( $equal(join(complement(X_20),complement(X_20)),complement(X_20)) )],[refute_0_164,refute_0_167]) ).
cnf(refute_0_169,plain,
composition(complement(X_70),join(one,one)) = complement(X_70),
inference(subst,[],[refute_0_168:[bind(X_20,$fot(X_70))]]) ).
cnf(refute_0_170,plain,
complement(composition(complement(X_70),join(one,one))) = complement(composition(complement(X_70),join(one,one))),
introduced(tautology,[refl,[$fot(complement(composition(complement(X_70),join(one,one))))]]) ).
cnf(refute_0_171,plain,
( complement(composition(complement(X_70),join(one,one))) != complement(composition(complement(X_70),join(one,one)))
| composition(complement(X_70),join(one,one)) != complement(X_70)
| complement(composition(complement(X_70),join(one,one))) = complement(complement(X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(complement(X_70),join(one,one))),complement(composition(complement(X_70),join(one,one)))) ),[1,0],$fot(complement(X_70))]]) ).
cnf(refute_0_172,plain,
( composition(complement(X_70),join(one,one)) != complement(X_70)
| complement(composition(complement(X_70),join(one,one))) = complement(complement(X_70)) ),
inference(resolve,[$cnf( $equal(complement(composition(complement(X_70),join(one,one))),complement(composition(complement(X_70),join(one,one)))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
complement(composition(complement(X_70),join(one,one))) = complement(complement(X_70)),
inference(resolve,[$cnf( $equal(composition(complement(X_70),join(one,one)),complement(X_70)) )],[refute_0_169,refute_0_172]) ).
cnf(refute_0_174,plain,
join(zero,complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(composition(complement(X_70),join(one,one)))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(complement(X_70),join(one,one)))))]]) ).
cnf(refute_0_175,plain,
( complement(composition(complement(X_70),join(one,one))) != complement(complement(X_70))
| join(zero,complement(composition(complement(X_70),join(one,one)))) != join(zero,complement(composition(complement(X_70),join(one,one))))
| join(zero,complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(complement(X_70),join(one,one)))),join(zero,complement(composition(complement(X_70),join(one,one))))) ),[1,1],$fot(complement(complement(X_70)))]]) ).
cnf(refute_0_176,plain,
( complement(composition(complement(X_70),join(one,one))) != complement(complement(X_70))
| join(zero,complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(complement(X_70),join(one,one)))),join(zero,complement(composition(complement(X_70),join(one,one))))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
join(zero,complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))),
inference(resolve,[$cnf( $equal(complement(composition(complement(X_70),join(one,one))),complement(complement(X_70))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_179,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_178]) ).
cnf(refute_0_180,plain,
meet(X_70,complement(X_70)) = zero,
inference(subst,[],[refute_0_179:[bind(A,$fot(X_70))]]) ).
cnf(refute_0_181,plain,
join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),
introduced(tautology,[refl,[$fot(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))))]]) ).
cnf(refute_0_182,plain,
( join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) != join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))
| meet(X_70,complement(X_70)) != zero
| join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(composition(complement(X_70),join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_183,plain,
( meet(X_70,complement(X_70)) != zero
| join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(composition(complement(X_70),join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(composition(complement(X_70),join(one,one)))),
inference(resolve,[$cnf( $equal(meet(X_70,complement(X_70)),zero) )],[refute_0_180,refute_0_183]) ).
cnf(refute_0_185,plain,
( join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) != join(zero,complement(composition(complement(X_70),join(one,one))))
| join(zero,complement(composition(complement(X_70),join(one,one)))) != join(zero,complement(complement(X_70)))
| join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))))),bind(Y,$fot(join(zero,complement(composition(complement(X_70),join(one,one)))))),bind(Z,$fot(join(zero,complement(complement(X_70)))))]]) ).
cnf(refute_0_186,plain,
( join(zero,complement(composition(complement(X_70),join(one,one)))) != join(zero,complement(complement(X_70)))
| join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))) ),
inference(resolve,[$cnf( $equal(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),join(zero,complement(composition(complement(X_70),join(one,one))))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) = join(zero,complement(complement(X_70))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(complement(X_70),join(one,one)))),join(zero,complement(complement(X_70)))) )],[refute_0_177,refute_0_186]) ).
cnf(refute_0_188,plain,
( X_70 != join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))
| join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))) != join(zero,complement(complement(X_70)))
| X_70 = join(zero,complement(complement(X_70))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,join(zero,complement(complement(X_70)))) ),[0],$fot(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))))]]) ).
cnf(refute_0_189,plain,
( X_70 != join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))
| X_70 = join(zero,complement(complement(X_70))) ),
inference(resolve,[$cnf( $equal(join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one)))),join(zero,complement(complement(X_70)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
X_70 = join(zero,complement(complement(X_70))),
inference(resolve,[$cnf( $equal(X_70,join(meet(X_70,complement(X_70)),complement(composition(complement(X_70),join(one,one))))) )],[refute_0_136,refute_0_189]) ).
cnf(refute_0_191,plain,
join(zero,join(zero,X_44)) = join(join(zero,zero),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_192,plain,
join(complement(top),complement(top)) = complement(top),
inference(subst,[],[refute_0_164:[bind(X_20,$fot(top))]]) ).
cnf(refute_0_193,plain,
zero = meet(join(complement(X_23),complement(X_24)),complement(join(complement(X_23),complement(X_24)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_23),complement(X_24))))]]) ).
cnf(refute_0_194,plain,
meet(X_23,X_24) = complement(join(complement(X_23),complement(X_24))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_23)),bind(B,$fot(X_24))]]) ).
cnf(refute_0_195,plain,
( meet(X_23,X_24) != complement(join(complement(X_23),complement(X_24)))
| complement(join(complement(X_23),complement(X_24))) = meet(X_23,X_24) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_23,X_24))),bind(Y,$fot(complement(join(complement(X_23),complement(X_24)))))]]) ).
cnf(refute_0_196,plain,
complement(join(complement(X_23),complement(X_24))) = meet(X_23,X_24),
inference(resolve,[$cnf( $equal(meet(X_23,X_24),complement(join(complement(X_23),complement(X_24)))) )],[refute_0_194,refute_0_195]) ).
cnf(refute_0_197,plain,
( complement(join(complement(X_23),complement(X_24))) != meet(X_23,X_24)
| zero != meet(join(complement(X_23),complement(X_24)),complement(join(complement(X_23),complement(X_24))))
| zero = meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_23),complement(X_24)),complement(join(complement(X_23),complement(X_24))))) ),[1,1],$fot(meet(X_23,X_24))]]) ).
cnf(refute_0_198,plain,
( zero != meet(join(complement(X_23),complement(X_24)),complement(join(complement(X_23),complement(X_24))))
| zero = meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_23),complement(X_24))),meet(X_23,X_24)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
zero = meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_23),complement(X_24)),complement(join(complement(X_23),complement(X_24))))) )],[refute_0_193,refute_0_198]) ).
cnf(refute_0_200,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_201,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_200]) ).
cnf(refute_0_202,plain,
join(meet(X_23,X_24),complement(meet(X_23,X_24))) = top,
inference(subst,[],[refute_0_201:[bind(A,$fot(meet(X_23,X_24)))]]) ).
cnf(refute_0_203,plain,
complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) = complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))))]]) ).
cnf(refute_0_204,plain,
( complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) != complement(join(meet(X_23,X_24),complement(meet(X_23,X_24))))
| join(meet(X_23,X_24),complement(meet(X_23,X_24))) != top
| complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))),complement(join(meet(X_23,X_24),complement(meet(X_23,X_24))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_205,plain,
( join(meet(X_23,X_24),complement(meet(X_23,X_24))) != top
| complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))),complement(join(meet(X_23,X_24),complement(meet(X_23,X_24))))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_23,X_24),complement(meet(X_23,X_24))),top) )],[refute_0_202,refute_0_205]) ).
cnf(refute_0_207,plain,
meet(join(complement(X_23),complement(X_24)),B) = complement(join(complement(join(complement(X_23),complement(X_24))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_23),complement(X_24))))]]) ).
cnf(refute_0_208,plain,
( complement(join(complement(X_23),complement(X_24))) != meet(X_23,X_24)
| meet(join(complement(X_23),complement(X_24)),B) != complement(join(complement(join(complement(X_23),complement(X_24))),complement(B)))
| meet(join(complement(X_23),complement(X_24)),B) = complement(join(meet(X_23,X_24),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_23),complement(X_24)),B),complement(join(complement(join(complement(X_23),complement(X_24))),complement(B)))) ),[1,0,0],$fot(meet(X_23,X_24))]]) ).
cnf(refute_0_209,plain,
( meet(join(complement(X_23),complement(X_24)),B) != complement(join(complement(join(complement(X_23),complement(X_24))),complement(B)))
| meet(join(complement(X_23),complement(X_24)),B) = complement(join(meet(X_23,X_24),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_23),complement(X_24))),meet(X_23,X_24)) )],[refute_0_196,refute_0_208]) ).
cnf(refute_0_210,plain,
meet(join(complement(X_23),complement(X_24)),B) = complement(join(meet(X_23,X_24),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_23),complement(X_24)),B),complement(join(complement(join(complement(X_23),complement(X_24))),complement(B)))) )],[refute_0_207,refute_0_209]) ).
cnf(refute_0_211,plain,
meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) = complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))),
inference(subst,[],[refute_0_210:[bind(B,$fot(meet(X_23,X_24)))]]) ).
cnf(refute_0_212,plain,
( complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) != complement(top)
| meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) != complement(join(meet(X_23,X_24),complement(meet(X_23,X_24))))
| meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) = complement(top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)))),bind(Y,$fot(complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_213,plain,
( complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))) != complement(top)
| meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)),complement(join(meet(X_23,X_24),complement(meet(X_23,X_24))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_23,X_24),complement(meet(X_23,X_24)))),complement(top)) )],[refute_0_206,refute_0_213]) ).
cnf(refute_0_215,plain,
( meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)) != complement(top)
| zero != meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_216,plain,
( zero != meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24)),complement(top)) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_23),complement(X_24)),meet(X_23,X_24))) )],[refute_0_199,refute_0_216]) ).
cnf(refute_0_218,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_219,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
( complement(top) != zero
| join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_221,plain,
( join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_220]) ).
cnf(refute_0_222,plain,
join(zero,complement(top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) )],[refute_0_192,refute_0_221]) ).
cnf(refute_0_223,plain,
join(zero,complement(top)) = join(zero,complement(top)),
introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).
cnf(refute_0_224,plain,
( complement(top) != zero
| join(zero,complement(top)) != join(zero,complement(top))
| join(zero,complement(top)) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_225,plain,
( complement(top) != zero
| join(zero,complement(top)) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
join(zero,complement(top)) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_225]) ).
cnf(refute_0_227,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,complement(top)) != join(zero,zero)
| join(zero,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),complement(top)) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_228,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
( complement(top) != zero
| join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_230,plain,
( join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_229]) ).
cnf(refute_0_231,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_228,refute_0_230]) ).
cnf(refute_0_232,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,complement(top)),complement(top)) )],[refute_0_222,refute_0_231]) ).
cnf(refute_0_233,plain,
( join(zero,join(zero,X_44)) != join(join(zero,zero),X_44)
| join(zero,zero) != zero
| join(zero,join(zero,X_44)) = join(zero,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X_44)),join(join(zero,zero),X_44)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_234,plain,
( join(zero,join(zero,X_44)) != join(join(zero,zero),X_44)
| join(zero,join(zero,X_44)) = join(zero,X_44) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
join(zero,join(zero,X_44)) = join(zero,X_44),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_44)),join(join(zero,zero),X_44)) )],[refute_0_191,refute_0_234]) ).
cnf(refute_0_236,plain,
join(zero,join(zero,complement(complement(X_72)))) = join(zero,complement(complement(X_72))),
inference(subst,[],[refute_0_235:[bind(X_44,$fot(complement(complement(X_72))))]]) ).
cnf(refute_0_237,plain,
X_72 = join(zero,complement(complement(X_72))),
inference(subst,[],[refute_0_190:[bind(X_70,$fot(X_72))]]) ).
cnf(refute_0_238,plain,
( X_72 != join(zero,complement(complement(X_72)))
| join(zero,complement(complement(X_72))) = X_72 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_72)),bind(Y,$fot(join(zero,complement(complement(X_72)))))]]) ).
cnf(refute_0_239,plain,
join(zero,complement(complement(X_72))) = X_72,
inference(resolve,[$cnf( $equal(X_72,join(zero,complement(complement(X_72)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
( join(zero,complement(complement(X_72))) != X_72
| join(zero,join(zero,complement(complement(X_72)))) != join(zero,complement(complement(X_72)))
| join(zero,X_72) = join(zero,complement(complement(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,complement(complement(X_72)))),join(zero,complement(complement(X_72)))) ),[0,1],$fot(X_72)]]) ).
cnf(refute_0_241,plain,
( join(zero,join(zero,complement(complement(X_72)))) != join(zero,complement(complement(X_72)))
| join(zero,X_72) = join(zero,complement(complement(X_72))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_72))),X_72) )],[refute_0_239,refute_0_240]) ).
cnf(refute_0_242,plain,
join(zero,X_72) = join(zero,complement(complement(X_72))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(complement(X_72)))),join(zero,complement(complement(X_72)))) )],[refute_0_236,refute_0_241]) ).
cnf(refute_0_243,plain,
( join(zero,X_72) != join(zero,complement(complement(X_72)))
| join(zero,complement(complement(X_72))) != X_72
| join(zero,X_72) = X_72 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_72),X_72) ),[0],$fot(join(zero,complement(complement(X_72))))]]) ).
cnf(refute_0_244,plain,
( join(zero,X_72) != join(zero,complement(complement(X_72)))
| join(zero,X_72) = X_72 ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_72))),X_72) )],[refute_0_239,refute_0_243]) ).
cnf(refute_0_245,plain,
join(zero,X_72) = X_72,
inference(resolve,[$cnf( $equal(join(zero,X_72),join(zero,complement(complement(X_72)))) )],[refute_0_242,refute_0_244]) ).
cnf(refute_0_246,plain,
join(zero,complement(complement(X_70))) = complement(complement(X_70)),
inference(subst,[],[refute_0_245:[bind(X_72,$fot(complement(complement(X_70))))]]) ).
cnf(refute_0_247,plain,
( X_70 != join(zero,complement(complement(X_70)))
| join(zero,complement(complement(X_70))) != complement(complement(X_70))
| X_70 = complement(complement(X_70)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,complement(complement(X_70))) ),[0],$fot(join(zero,complement(complement(X_70))))]]) ).
cnf(refute_0_248,plain,
( X_70 != join(zero,complement(complement(X_70)))
| X_70 = complement(complement(X_70)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_70))),complement(complement(X_70))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
X_70 = complement(complement(X_70)),
inference(resolve,[$cnf( $equal(X_70,join(zero,complement(complement(X_70)))) )],[refute_0_190,refute_0_248]) ).
cnf(refute_0_250,plain,
join(X_91,X_91) = complement(complement(join(X_91,X_91))),
inference(subst,[],[refute_0_249:[bind(X_70,$fot(join(X_91,X_91)))]]) ).
cnf(refute_0_251,plain,
X_70 = join(meet(X_70,X_71),complement(join(complement(X_70),X_71))),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_70)),bind(B,$fot(X_71))]]) ).
cnf(refute_0_252,plain,
join(complement(X_24),complement(X_23)) = join(complement(X_23),complement(X_24)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(complement(X_24))),bind(B,$fot(complement(X_23)))]]) ).
cnf(refute_0_253,plain,
( join(complement(X_24),complement(X_23)) != join(complement(X_23),complement(X_24))
| join(complement(X_23),complement(X_24)) = join(complement(X_24),complement(X_23)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(complement(X_24),complement(X_23)))),bind(Y,$fot(join(complement(X_23),complement(X_24))))]]) ).
cnf(refute_0_254,plain,
join(complement(X_23),complement(X_24)) = join(complement(X_24),complement(X_23)),
inference(resolve,[$cnf( $equal(join(complement(X_24),complement(X_23)),join(complement(X_23),complement(X_24))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
( join(complement(X_23),complement(X_24)) != join(complement(X_24),complement(X_23))
| meet(X_23,X_24) != complement(join(complement(X_23),complement(X_24)))
| meet(X_23,X_24) = complement(join(complement(X_24),complement(X_23))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_23,X_24),complement(join(complement(X_23),complement(X_24)))) ),[1,0],$fot(join(complement(X_24),complement(X_23)))]]) ).
cnf(refute_0_256,plain,
( meet(X_23,X_24) != complement(join(complement(X_23),complement(X_24)))
| meet(X_23,X_24) = complement(join(complement(X_24),complement(X_23))) ),
inference(resolve,[$cnf( $equal(join(complement(X_23),complement(X_24)),join(complement(X_24),complement(X_23))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
meet(X_23,X_24) = complement(join(complement(X_24),complement(X_23))),
inference(resolve,[$cnf( $equal(meet(X_23,X_24),complement(join(complement(X_23),complement(X_24)))) )],[refute_0_194,refute_0_256]) ).
cnf(refute_0_258,plain,
complement(join(complement(X_24),complement(X_23))) = meet(X_24,X_23),
inference(subst,[],[refute_0_27:[bind(A,$fot(X_24)),bind(B,$fot(X_23))]]) ).
cnf(refute_0_259,plain,
( complement(join(complement(X_24),complement(X_23))) != meet(X_24,X_23)
| meet(X_23,X_24) != complement(join(complement(X_24),complement(X_23)))
| meet(X_23,X_24) = meet(X_24,X_23) ),
introduced(tautology,[equality,[$cnf( $equal(meet(X_23,X_24),complement(join(complement(X_24),complement(X_23)))) ),[1],$fot(meet(X_24,X_23))]]) ).
cnf(refute_0_260,plain,
( meet(X_23,X_24) != complement(join(complement(X_24),complement(X_23)))
| meet(X_23,X_24) = meet(X_24,X_23) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_24),complement(X_23))),meet(X_24,X_23)) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
meet(X_23,X_24) = meet(X_24,X_23),
inference(resolve,[$cnf( $equal(meet(X_23,X_24),complement(join(complement(X_24),complement(X_23)))) )],[refute_0_257,refute_0_260]) ).
cnf(refute_0_262,plain,
meet(X_71,X_70) = meet(X_70,X_71),
inference(subst,[],[refute_0_261:[bind(X_23,$fot(X_71)),bind(X_24,$fot(X_70))]]) ).
cnf(refute_0_263,plain,
( meet(X_71,X_70) != meet(X_70,X_71)
| meet(X_70,X_71) = meet(X_71,X_70) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_71,X_70))),bind(Y,$fot(meet(X_70,X_71)))]]) ).
cnf(refute_0_264,plain,
meet(X_70,X_71) = meet(X_71,X_70),
inference(resolve,[$cnf( $equal(meet(X_71,X_70),meet(X_70,X_71)) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
( X_70 != join(meet(X_70,X_71),complement(join(complement(X_70),X_71)))
| meet(X_70,X_71) != meet(X_71,X_70)
| X_70 = join(meet(X_71,X_70),complement(join(complement(X_70),X_71))) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,join(meet(X_70,X_71),complement(join(complement(X_70),X_71)))) ),[1,0],$fot(meet(X_71,X_70))]]) ).
cnf(refute_0_266,plain,
( X_70 != join(meet(X_70,X_71),complement(join(complement(X_70),X_71)))
| X_70 = join(meet(X_71,X_70),complement(join(complement(X_70),X_71))) ),
inference(resolve,[$cnf( $equal(meet(X_70,X_71),meet(X_71,X_70)) )],[refute_0_264,refute_0_265]) ).
cnf(refute_0_267,plain,
X_70 = join(meet(X_71,X_70),complement(join(complement(X_70),X_71))),
inference(resolve,[$cnf( $equal(X_70,join(meet(X_70,X_71),complement(join(complement(X_70),X_71)))) )],[refute_0_251,refute_0_266]) ).
cnf(refute_0_268,plain,
complement(X_90) = join(meet(X_90,complement(X_90)),complement(join(complement(complement(X_90)),X_90))),
inference(subst,[],[refute_0_267:[bind(X_70,$fot(complement(X_90))),bind(X_71,$fot(X_90))]]) ).
cnf(refute_0_269,plain,
zero = meet(X_90,complement(X_90)),
inference(subst,[],[def_zero_13:[bind(A,$fot(X_90))]]) ).
cnf(refute_0_270,plain,
( zero != meet(X_90,complement(X_90))
| meet(X_90,complement(X_90)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(X_90,complement(X_90))))]]) ).
cnf(refute_0_271,plain,
meet(X_90,complement(X_90)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X_90,complement(X_90))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
( complement(X_90) != join(meet(X_90,complement(X_90)),complement(join(complement(complement(X_90)),X_90)))
| meet(X_90,complement(X_90)) != zero
| complement(X_90) = join(zero,complement(join(complement(complement(X_90)),X_90))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_90),join(meet(X_90,complement(X_90)),complement(join(complement(complement(X_90)),X_90)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_273,plain,
( complement(X_90) != join(meet(X_90,complement(X_90)),complement(join(complement(complement(X_90)),X_90)))
| complement(X_90) = join(zero,complement(join(complement(complement(X_90)),X_90))) ),
inference(resolve,[$cnf( $equal(meet(X_90,complement(X_90)),zero) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
complement(X_90) = join(zero,complement(join(complement(complement(X_90)),X_90))),
inference(resolve,[$cnf( $equal(complement(X_90),join(meet(X_90,complement(X_90)),complement(join(complement(complement(X_90)),X_90)))) )],[refute_0_268,refute_0_273]) ).
cnf(refute_0_275,plain,
( X_70 != complement(complement(X_70))
| complement(complement(X_70)) = X_70 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_70)),bind(Y,$fot(complement(complement(X_70))))]]) ).
cnf(refute_0_276,plain,
complement(complement(X_70)) = X_70,
inference(resolve,[$cnf( $equal(X_70,complement(complement(X_70))) )],[refute_0_249,refute_0_275]) ).
cnf(refute_0_277,plain,
complement(complement(X_90)) = X_90,
inference(subst,[],[refute_0_276:[bind(X_70,$fot(X_90))]]) ).
cnf(refute_0_278,plain,
join(X_90,complement(complement(X_90))) = join(X_90,complement(complement(X_90))),
introduced(tautology,[refl,[$fot(join(X_90,complement(complement(X_90))))]]) ).
cnf(refute_0_279,plain,
( complement(complement(X_90)) != X_90
| join(X_90,complement(complement(X_90))) != join(X_90,complement(complement(X_90)))
| join(X_90,complement(complement(X_90))) = join(X_90,X_90) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_90,complement(complement(X_90))),join(X_90,complement(complement(X_90)))) ),[1,1],$fot(X_90)]]) ).
cnf(refute_0_280,plain,
( complement(complement(X_90)) != X_90
| join(X_90,complement(complement(X_90))) = join(X_90,X_90) ),
inference(resolve,[$cnf( $equal(join(X_90,complement(complement(X_90))),join(X_90,complement(complement(X_90)))) )],[refute_0_278,refute_0_279]) ).
cnf(refute_0_281,plain,
join(X_90,complement(complement(X_90))) = join(X_90,X_90),
inference(resolve,[$cnf( $equal(complement(complement(X_90)),X_90) )],[refute_0_277,refute_0_280]) ).
cnf(refute_0_282,plain,
join(complement(complement(X_90)),X_90) = join(X_90,complement(complement(X_90))),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_90)),bind(B,$fot(complement(complement(X_90))))]]) ).
cnf(refute_0_283,plain,
( join(X_90,complement(complement(X_90))) != join(X_90,X_90)
| join(complement(complement(X_90)),X_90) != join(X_90,complement(complement(X_90)))
| join(complement(complement(X_90)),X_90) = join(X_90,X_90) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(X_90)),X_90))),bind(Y,$fot(join(X_90,complement(complement(X_90))))),bind(Z,$fot(join(X_90,X_90)))]]) ).
cnf(refute_0_284,plain,
( join(X_90,complement(complement(X_90))) != join(X_90,X_90)
| join(complement(complement(X_90)),X_90) = join(X_90,X_90) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_90)),X_90),join(X_90,complement(complement(X_90)))) )],[refute_0_282,refute_0_283]) ).
cnf(refute_0_285,plain,
join(complement(complement(X_90)),X_90) = join(X_90,X_90),
inference(resolve,[$cnf( $equal(join(X_90,complement(complement(X_90))),join(X_90,X_90)) )],[refute_0_281,refute_0_284]) ).
cnf(refute_0_286,plain,
complement(join(complement(complement(X_90)),X_90)) = complement(join(complement(complement(X_90)),X_90)),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(X_90)),X_90)))]]) ).
cnf(refute_0_287,plain,
( complement(join(complement(complement(X_90)),X_90)) != complement(join(complement(complement(X_90)),X_90))
| join(complement(complement(X_90)),X_90) != join(X_90,X_90)
| complement(join(complement(complement(X_90)),X_90)) = complement(join(X_90,X_90)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(X_90)),X_90)),complement(join(complement(complement(X_90)),X_90))) ),[1,0],$fot(join(X_90,X_90))]]) ).
cnf(refute_0_288,plain,
( join(complement(complement(X_90)),X_90) != join(X_90,X_90)
| complement(join(complement(complement(X_90)),X_90)) = complement(join(X_90,X_90)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_90)),X_90)),complement(join(complement(complement(X_90)),X_90))) )],[refute_0_286,refute_0_287]) ).
cnf(refute_0_289,plain,
complement(join(complement(complement(X_90)),X_90)) = complement(join(X_90,X_90)),
inference(resolve,[$cnf( $equal(join(complement(complement(X_90)),X_90),join(X_90,X_90)) )],[refute_0_285,refute_0_288]) ).
cnf(refute_0_290,plain,
join(zero,complement(join(complement(complement(X_90)),X_90))) = complement(join(complement(complement(X_90)),X_90)),
inference(subst,[],[refute_0_245:[bind(X_72,$fot(complement(join(complement(complement(X_90)),X_90))))]]) ).
cnf(refute_0_291,plain,
( complement(join(complement(complement(X_90)),X_90)) != complement(join(X_90,X_90))
| join(zero,complement(join(complement(complement(X_90)),X_90))) != complement(join(complement(complement(X_90)),X_90))
| join(zero,complement(join(complement(complement(X_90)),X_90))) = complement(join(X_90,X_90)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,complement(join(complement(complement(X_90)),X_90))))),bind(Y,$fot(complement(join(complement(complement(X_90)),X_90)))),bind(Z,$fot(complement(join(X_90,X_90))))]]) ).
cnf(refute_0_292,plain,
( complement(join(complement(complement(X_90)),X_90)) != complement(join(X_90,X_90))
| join(zero,complement(join(complement(complement(X_90)),X_90))) = complement(join(X_90,X_90)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_90)),X_90))),complement(join(complement(complement(X_90)),X_90))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
join(zero,complement(join(complement(complement(X_90)),X_90))) = complement(join(X_90,X_90)),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(X_90)),X_90)),complement(join(X_90,X_90))) )],[refute_0_289,refute_0_292]) ).
cnf(refute_0_294,plain,
( complement(X_90) != join(zero,complement(join(complement(complement(X_90)),X_90)))
| join(zero,complement(join(complement(complement(X_90)),X_90))) != complement(join(X_90,X_90))
| complement(X_90) = complement(join(X_90,X_90)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_90),complement(join(X_90,X_90))) ),[0],$fot(join(zero,complement(join(complement(complement(X_90)),X_90))))]]) ).
cnf(refute_0_295,plain,
( complement(X_90) != join(zero,complement(join(complement(complement(X_90)),X_90)))
| complement(X_90) = complement(join(X_90,X_90)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(complement(complement(X_90)),X_90))),complement(join(X_90,X_90))) )],[refute_0_293,refute_0_294]) ).
cnf(refute_0_296,plain,
complement(X_90) = complement(join(X_90,X_90)),
inference(resolve,[$cnf( $equal(complement(X_90),join(zero,complement(join(complement(complement(X_90)),X_90)))) )],[refute_0_274,refute_0_295]) ).
cnf(refute_0_297,plain,
complement(X_91) = complement(join(X_91,X_91)),
inference(subst,[],[refute_0_296:[bind(X_90,$fot(X_91))]]) ).
cnf(refute_0_298,plain,
( complement(X_91) != complement(join(X_91,X_91))
| complement(join(X_91,X_91)) = complement(X_91) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_91))),bind(Y,$fot(complement(join(X_91,X_91))))]]) ).
cnf(refute_0_299,plain,
complement(join(X_91,X_91)) = complement(X_91),
inference(resolve,[$cnf( $equal(complement(X_91),complement(join(X_91,X_91))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
( complement(join(X_91,X_91)) != complement(X_91)
| join(X_91,X_91) != complement(complement(join(X_91,X_91)))
| join(X_91,X_91) = complement(complement(X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_91,X_91),complement(complement(join(X_91,X_91)))) ),[1,0],$fot(complement(X_91))]]) ).
cnf(refute_0_301,plain,
( join(X_91,X_91) != complement(complement(join(X_91,X_91)))
| join(X_91,X_91) = complement(complement(X_91)) ),
inference(resolve,[$cnf( $equal(complement(join(X_91,X_91)),complement(X_91)) )],[refute_0_299,refute_0_300]) ).
cnf(refute_0_302,plain,
join(X_91,X_91) = complement(complement(X_91)),
inference(resolve,[$cnf( $equal(join(X_91,X_91),complement(complement(join(X_91,X_91)))) )],[refute_0_250,refute_0_301]) ).
cnf(refute_0_303,plain,
complement(complement(X_91)) = X_91,
inference(subst,[],[refute_0_276:[bind(X_70,$fot(X_91))]]) ).
cnf(refute_0_304,plain,
( complement(complement(X_91)) != X_91
| join(X_91,X_91) != complement(complement(X_91))
| join(X_91,X_91) = X_91 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_91,X_91),complement(complement(X_91))) ),[1],$fot(X_91)]]) ).
cnf(refute_0_305,plain,
( join(X_91,X_91) != complement(complement(X_91))
| join(X_91,X_91) = X_91 ),
inference(resolve,[$cnf( $equal(complement(complement(X_91)),X_91) )],[refute_0_303,refute_0_304]) ).
cnf(refute_0_306,plain,
join(X_91,X_91) = X_91,
inference(resolve,[$cnf( $equal(join(X_91,X_91),complement(complement(X_91))) )],[refute_0_302,refute_0_305]) ).
cnf(refute_0_307,plain,
join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)),
inference(subst,[],[refute_0_306:[bind(X_91,$fot(complement(composition(sk1,top))))]]) ).
cnf(refute_0_308,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) ),[0,0],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_309,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| join(complement(composition(sk1,top)),complement(composition(sk1,top))) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(sk1,top)),complement(composition(sk1,top))),complement(composition(sk1,top))) )],[refute_0_309,refute_0_20]) ).
cnf(refute_0_311,plain,
complement(composition(sk1,top)) = complement(composition(sk1,top)),
introduced(tautology,[refl,[$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_312,plain,
composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_311,refute_0_310]) ).
cnf(refute_0_313,plain,
converse(converse(composition(complement(composition(X_531,top)),top))) = composition(complement(composition(X_531,top)),top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(complement(composition(X_531,top)),top)))]]) ).
cnf(refute_0_314,plain,
join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,composition(top,X_108))))) = complement(composition(top,X_108)),
inference(subst,[],[refute_0_140:[bind(A,$fot(top)),bind(B,$fot(composition(top,X_108)))]]) ).
cnf(refute_0_315,plain,
composition(top,composition(top,C)) = composition(composition(top,top),C),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(top)),bind(B,$fot(top))]]) ).
cnf(refute_0_316,plain,
composition(join(X_36,one),top) = join(top,composition(X_36,top)),
inference(subst,[],[refute_0_83:[bind(X_38,$fot(top))]]) ).
cnf(refute_0_317,plain,
join(join(top,X_82),top) = join(top,join(top,X_82)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(top,X_82))),bind(B,$fot(top))]]) ).
cnf(refute_0_318,plain,
join(top,join(complement(zero),C)) = join(join(top,complement(zero)),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(complement(zero)))]]) ).
cnf(refute_0_319,plain,
join(top,join(zero,X_44)) = join(join(top,zero),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(top)),bind(B,$fot(zero)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_320,plain,
top = join(top,complement(top)),
inference(subst,[],[def_top_12:[bind(A,$fot(top))]]) ).
cnf(refute_0_321,plain,
( complement(top) != zero
| top != join(top,complement(top))
| top = join(top,zero) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(top,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_322,plain,
( top != join(top,complement(top))
| top = join(top,zero) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_321]) ).
cnf(refute_0_323,plain,
top = join(top,zero),
inference(resolve,[$cnf( $equal(top,join(top,complement(top))) )],[refute_0_320,refute_0_322]) ).
cnf(refute_0_324,plain,
( top != join(top,zero)
| join(top,zero) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,zero)))]]) ).
cnf(refute_0_325,plain,
join(top,zero) = top,
inference(resolve,[$cnf( $equal(top,join(top,zero)) )],[refute_0_323,refute_0_324]) ).
cnf(refute_0_326,plain,
( join(top,join(zero,X_44)) != join(join(top,zero),X_44)
| join(top,zero) != top
| join(top,join(zero,X_44)) = join(top,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,X_44)),join(join(top,zero),X_44)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_327,plain,
( join(top,join(zero,X_44)) != join(join(top,zero),X_44)
| join(top,join(zero,X_44)) = join(top,X_44) ),
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_325,refute_0_326]) ).
cnf(refute_0_328,plain,
join(top,join(zero,X_44)) = join(top,X_44),
inference(resolve,[$cnf( $equal(join(top,join(zero,X_44)),join(join(top,zero),X_44)) )],[refute_0_319,refute_0_327]) ).
cnf(refute_0_329,plain,
join(top,join(zero,complement(zero))) = join(top,complement(zero)),
inference(subst,[],[refute_0_328:[bind(X_44,$fot(complement(zero)))]]) ).
cnf(refute_0_330,plain,
top = join(zero,complement(zero)),
inference(subst,[],[def_top_12:[bind(A,$fot(zero))]]) ).
cnf(refute_0_331,plain,
( top != join(zero,complement(zero))
| join(zero,complement(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(zero,complement(zero))))]]) ).
cnf(refute_0_332,plain,
join(zero,complement(zero)) = top,
inference(resolve,[$cnf( $equal(top,join(zero,complement(zero))) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
( join(top,join(zero,complement(zero))) != join(top,complement(zero))
| join(zero,complement(zero)) != top
| join(top,top) = join(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,complement(zero))),join(top,complement(zero))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_334,plain,
( join(top,join(zero,complement(zero))) != join(top,complement(zero))
| join(top,top) = join(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(zero)),top) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
join(top,top) = join(top,complement(zero)),
inference(resolve,[$cnf( $equal(join(top,join(zero,complement(zero))),join(top,complement(zero))) )],[refute_0_329,refute_0_334]) ).
cnf(refute_0_336,plain,
join(zero,join(complement(join(top,top)),X_44)) = join(join(zero,complement(join(top,top))),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(complement(join(top,top)))),bind(C,$fot(X_44))]]) ).
cnf(refute_0_337,plain,
join(complement(top),composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(subst,[],[refute_0_140:[bind(B,$fot(top))]]) ).
cnf(refute_0_338,plain,
( complement(top) != zero
| join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_339,plain,
( join(complement(top),composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_338]) ).
cnf(refute_0_340,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_337,refute_0_339]) ).
cnf(refute_0_341,plain,
( complement(top) != zero
| join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_342,plain,
( join(zero,composition(converse(A),complement(composition(A,top)))) != complement(top)
| join(zero,composition(converse(A),complement(composition(A,top)))) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_341]) ).
cnf(refute_0_343,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(A),complement(composition(A,top)))),complement(top)) )],[refute_0_340,refute_0_342]) ).
cnf(refute_0_344,plain,
join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) = zero,
inference(subst,[],[refute_0_343:[bind(A,$fot(join(one,one)))]]) ).
cnf(refute_0_345,plain,
( converse(join(one,one)) != join(one,one)
| join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))),zero) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_346,plain,
( join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_124,refute_0_345]) ).
cnf(refute_0_347,plain,
join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(converse(join(one,one)),complement(composition(join(one,one),top)))),zero) )],[refute_0_344,refute_0_346]) ).
cnf(refute_0_348,plain,
composition(join(one,one),top) = join(top,top),
inference(subst,[],[refute_0_90:[bind(X_40,$fot(top))]]) ).
cnf(refute_0_349,plain,
complement(composition(join(one,one),top)) = complement(composition(join(one,one),top)),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),top)))]]) ).
cnf(refute_0_350,plain,
( complement(composition(join(one,one),top)) != complement(composition(join(one,one),top))
| composition(join(one,one),top) != join(top,top)
| complement(composition(join(one,one),top)) = complement(join(top,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),top)),complement(composition(join(one,one),top))) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_351,plain,
( composition(join(one,one),top) != join(top,top)
| complement(composition(join(one,one),top)) = complement(join(top,top)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),complement(composition(join(one,one),top))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
complement(composition(join(one,one),top)) = complement(join(top,top)),
inference(resolve,[$cnf( $equal(composition(join(one,one),top),join(top,top)) )],[refute_0_348,refute_0_351]) ).
cnf(refute_0_353,plain,
composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),complement(composition(join(one,one),top))),
introduced(tautology,[refl,[$fot(composition(join(one,one),complement(composition(join(one,one),top))))]]) ).
cnf(refute_0_354,plain,
( complement(composition(join(one,one),top)) != complement(join(top,top))
| composition(join(one,one),complement(composition(join(one,one),top))) != composition(join(one,one),complement(composition(join(one,one),top)))
| composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),complement(composition(join(one,one),top)))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_355,plain,
( complement(composition(join(one,one),top)) != complement(join(top,top))
| composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),complement(composition(join(one,one),top)))) )],[refute_0_353,refute_0_354]) ).
cnf(refute_0_356,plain,
composition(join(one,one),complement(composition(join(one,one),top))) = composition(join(one,one),complement(join(top,top))),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),top)),complement(join(top,top))) )],[refute_0_352,refute_0_355]) ).
cnf(refute_0_357,plain,
join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),
introduced(tautology,[refl,[$fot(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))))]]) ).
cnf(refute_0_358,plain,
( composition(join(one,one),complement(composition(join(one,one),top))) != composition(join(one,one),complement(join(top,top)))
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != join(zero,composition(join(one,one),complement(composition(join(one,one),top))))
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = join(zero,composition(join(one,one),complement(join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),join(zero,composition(join(one,one),complement(composition(join(one,one),top))))) ),[1,1],$fot(composition(join(one,one),complement(join(top,top))))]]) ).
cnf(refute_0_359,plain,
( composition(join(one,one),complement(composition(join(one,one),top))) != composition(join(one,one),complement(join(top,top)))
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = join(zero,composition(join(one,one),complement(join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),join(zero,composition(join(one,one),complement(composition(join(one,one),top))))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) = join(zero,composition(join(one,one),complement(join(top,top)))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),top))),composition(join(one,one),complement(join(top,top)))) )],[refute_0_356,refute_0_359]) ).
cnf(refute_0_361,plain,
( join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != join(zero,composition(join(one,one),complement(join(top,top))))
| join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(join(top,top)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),zero) ),[0],$fot(join(zero,composition(join(one,one),complement(join(top,top)))))]]) ).
cnf(refute_0_362,plain,
( join(zero,composition(join(one,one),complement(composition(join(one,one),top)))) != zero
| join(zero,composition(join(one,one),complement(join(top,top)))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),join(zero,composition(join(one,one),complement(join(top,top))))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
join(zero,composition(join(one,one),complement(join(top,top)))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(composition(join(one,one),top)))),zero) )],[refute_0_347,refute_0_362]) ).
cnf(refute_0_364,plain,
composition(join(one,one),complement(X_20)) = join(complement(X_20),complement(X_20)),
inference(subst,[],[refute_0_90:[bind(X_40,$fot(complement(X_20)))]]) ).
cnf(refute_0_365,plain,
( composition(join(one,one),complement(X_20)) != join(complement(X_20),complement(X_20))
| join(complement(X_20),complement(X_20)) = composition(join(one,one),complement(X_20)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),complement(X_20)))),bind(Y,$fot(join(complement(X_20),complement(X_20))))]]) ).
cnf(refute_0_366,plain,
join(complement(X_20),complement(X_20)) = composition(join(one,one),complement(X_20)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_20)),join(complement(X_20),complement(X_20))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
( join(complement(X_20),complement(X_20)) != complement(X_20)
| join(complement(X_20),complement(X_20)) != composition(join(one,one),complement(X_20))
| composition(join(one,one),complement(X_20)) = complement(X_20) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_20),complement(X_20)),complement(X_20)) ),[0],$fot(composition(join(one,one),complement(X_20)))]]) ).
cnf(refute_0_368,plain,
( join(complement(X_20),complement(X_20)) != complement(X_20)
| composition(join(one,one),complement(X_20)) = complement(X_20) ),
inference(resolve,[$cnf( $equal(join(complement(X_20),complement(X_20)),composition(join(one,one),complement(X_20))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
composition(join(one,one),complement(X_20)) = complement(X_20),
inference(resolve,[$cnf( $equal(join(complement(X_20),complement(X_20)),complement(X_20)) )],[refute_0_164,refute_0_368]) ).
cnf(refute_0_370,plain,
composition(join(one,one),complement(join(top,top))) = complement(join(top,top)),
inference(subst,[],[refute_0_369:[bind(X_20,$fot(join(top,top)))]]) ).
cnf(refute_0_371,plain,
join(zero,composition(join(one,one),complement(join(top,top)))) = join(zero,composition(join(one,one),complement(join(top,top)))),
introduced(tautology,[refl,[$fot(join(zero,composition(join(one,one),complement(join(top,top)))))]]) ).
cnf(refute_0_372,plain,
( composition(join(one,one),complement(join(top,top))) != complement(join(top,top))
| join(zero,composition(join(one,one),complement(join(top,top)))) != join(zero,composition(join(one,one),complement(join(top,top))))
| join(zero,composition(join(one,one),complement(join(top,top)))) = join(zero,complement(join(top,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(join(one,one),complement(join(top,top)))),join(zero,composition(join(one,one),complement(join(top,top))))) ),[1,1],$fot(complement(join(top,top)))]]) ).
cnf(refute_0_373,plain,
( composition(join(one,one),complement(join(top,top))) != complement(join(top,top))
| join(zero,composition(join(one,one),complement(join(top,top)))) = join(zero,complement(join(top,top))) ),
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(join(top,top)))),join(zero,composition(join(one,one),complement(join(top,top))))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
join(zero,composition(join(one,one),complement(join(top,top)))) = join(zero,complement(join(top,top))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(top,top))),complement(join(top,top))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
( join(zero,composition(join(one,one),complement(join(top,top)))) != join(zero,complement(join(top,top)))
| join(zero,composition(join(one,one),complement(join(top,top)))) != zero
| join(zero,complement(join(top,top))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(join(one,one),complement(join(top,top)))),zero) ),[0],$fot(join(zero,complement(join(top,top))))]]) ).
cnf(refute_0_376,plain,
( join(zero,composition(join(one,one),complement(join(top,top)))) != zero
| join(zero,complement(join(top,top))) = zero ),
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(join(top,top)))),join(zero,complement(join(top,top)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
join(zero,complement(join(top,top))) = zero,
inference(resolve,[$cnf( $equal(join(zero,composition(join(one,one),complement(join(top,top)))),zero) )],[refute_0_363,refute_0_376]) ).
cnf(refute_0_378,plain,
( join(zero,complement(join(top,top))) != zero
| join(zero,join(complement(join(top,top)),X_44)) != join(join(zero,complement(join(top,top))),X_44)
| join(zero,join(complement(join(top,top)),X_44)) = join(zero,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(join(top,top)),X_44)),join(join(zero,complement(join(top,top))),X_44)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_379,plain,
( join(zero,join(complement(join(top,top)),X_44)) != join(join(zero,complement(join(top,top))),X_44)
| join(zero,join(complement(join(top,top)),X_44)) = join(zero,X_44) ),
inference(resolve,[$cnf( $equal(join(zero,complement(join(top,top))),zero) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
join(zero,join(complement(join(top,top)),X_44)) = join(zero,X_44),
inference(resolve,[$cnf( $equal(join(zero,join(complement(join(top,top)),X_44)),join(join(zero,complement(join(top,top))),X_44)) )],[refute_0_336,refute_0_379]) ).
cnf(refute_0_381,plain,
join(zero,join(complement(join(top,top)),complement(complement(join(top,top))))) = join(zero,complement(complement(join(top,top)))),
inference(subst,[],[refute_0_380:[bind(X_44,$fot(complement(complement(join(top,top)))))]]) ).
cnf(refute_0_382,plain,
top = join(complement(join(top,top)),complement(complement(join(top,top)))),
inference(subst,[],[def_top_12:[bind(A,$fot(complement(join(top,top))))]]) ).
cnf(refute_0_383,plain,
( top != join(complement(join(top,top)),complement(complement(join(top,top))))
| join(complement(join(top,top)),complement(complement(join(top,top)))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(join(top,top)),complement(complement(join(top,top))))))]]) ).
cnf(refute_0_384,plain,
join(complement(join(top,top)),complement(complement(join(top,top)))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(join(top,top)),complement(complement(join(top,top))))) )],[refute_0_382,refute_0_383]) ).
cnf(refute_0_385,plain,
( join(complement(join(top,top)),complement(complement(join(top,top)))) != top
| join(zero,join(complement(join(top,top)),complement(complement(join(top,top))))) != join(zero,complement(complement(join(top,top))))
| join(zero,top) = join(zero,complement(complement(join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(complement(join(top,top)),complement(complement(join(top,top))))),join(zero,complement(complement(join(top,top))))) ),[0,1],$fot(top)]]) ).
cnf(refute_0_386,plain,
( join(zero,join(complement(join(top,top)),complement(complement(join(top,top))))) != join(zero,complement(complement(join(top,top))))
| join(zero,top) = join(zero,complement(complement(join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(top,top)),complement(complement(join(top,top)))),top) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
join(zero,top) = join(zero,complement(complement(join(top,top)))),
inference(resolve,[$cnf( $equal(join(zero,join(complement(join(top,top)),complement(complement(join(top,top))))),join(zero,complement(complement(join(top,top))))) )],[refute_0_381,refute_0_386]) ).
cnf(refute_0_388,plain,
join(zero,top) = join(top,zero),
inference(subst,[],[refute_0_4:[bind(A,$fot(top)),bind(B,$fot(zero))]]) ).
cnf(refute_0_389,plain,
( join(top,zero) != top
| join(zero,top) != join(top,zero)
| join(zero,top) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(zero,top))),bind(Y,$fot(join(top,zero))),bind(Z,$fot(top))]]) ).
cnf(refute_0_390,plain,
( join(top,zero) != top
| join(zero,top) = top ),
inference(resolve,[$cnf( $equal(join(zero,top),join(top,zero)) )],[refute_0_388,refute_0_389]) ).
cnf(refute_0_391,plain,
join(zero,top) = top,
inference(resolve,[$cnf( $equal(join(top,zero),top) )],[refute_0_325,refute_0_390]) ).
cnf(refute_0_392,plain,
( join(zero,top) != join(zero,complement(complement(join(top,top))))
| join(zero,top) != top
| top = join(zero,complement(complement(join(top,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,top),join(zero,complement(complement(join(top,top))))) ),[0],$fot(top)]]) ).
cnf(refute_0_393,plain,
( join(zero,top) != join(zero,complement(complement(join(top,top))))
| top = join(zero,complement(complement(join(top,top)))) ),
inference(resolve,[$cnf( $equal(join(zero,top),top) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
top = join(zero,complement(complement(join(top,top)))),
inference(resolve,[$cnf( $equal(join(zero,top),join(zero,complement(complement(join(top,top))))) )],[refute_0_387,refute_0_393]) ).
cnf(refute_0_395,plain,
( X_70 != join(zero,complement(complement(X_70)))
| join(zero,complement(complement(X_70))) = X_70 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_70)),bind(Y,$fot(join(zero,complement(complement(X_70)))))]]) ).
cnf(refute_0_396,plain,
join(zero,complement(complement(X_70))) = X_70,
inference(resolve,[$cnf( $equal(X_70,join(zero,complement(complement(X_70)))) )],[refute_0_190,refute_0_395]) ).
cnf(refute_0_397,plain,
join(zero,complement(complement(join(top,top)))) = join(top,top),
inference(subst,[],[refute_0_396:[bind(X_70,$fot(join(top,top)))]]) ).
cnf(refute_0_398,plain,
( join(zero,complement(complement(join(top,top)))) != join(top,top)
| top != join(zero,complement(complement(join(top,top))))
| top = join(top,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(zero,complement(complement(join(top,top))))) ),[1],$fot(join(top,top))]]) ).
cnf(refute_0_399,plain,
( top != join(zero,complement(complement(join(top,top))))
| top = join(top,top) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(join(top,top)))),join(top,top)) )],[refute_0_397,refute_0_398]) ).
cnf(refute_0_400,plain,
top = join(top,top),
inference(resolve,[$cnf( $equal(top,join(zero,complement(complement(join(top,top))))) )],[refute_0_394,refute_0_399]) ).
cnf(refute_0_401,plain,
( top != join(top,top)
| join(top,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,top)))]]) ).
cnf(refute_0_402,plain,
join(top,top) = top,
inference(resolve,[$cnf( $equal(top,join(top,top)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
( join(top,top) != join(top,complement(zero))
| join(top,top) != top
| top = join(top,complement(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,top),join(top,complement(zero))) ),[0],$fot(top)]]) ).
cnf(refute_0_404,plain,
( join(top,top) != join(top,complement(zero))
| top = join(top,complement(zero)) ),
inference(resolve,[$cnf( $equal(join(top,top),top) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
top = join(top,complement(zero)),
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(zero))) )],[refute_0_335,refute_0_404]) ).
cnf(refute_0_406,plain,
( top != join(top,complement(zero))
| join(top,complement(zero)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_407,plain,
join(top,complement(zero)) = top,
inference(resolve,[$cnf( $equal(top,join(top,complement(zero))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
( join(top,complement(zero)) != top
| join(top,join(complement(zero),C)) != join(join(top,complement(zero)),C)
| join(top,join(complement(zero),C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,complement(zero)),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_409,plain,
( join(top,join(complement(zero),C)) != join(join(top,complement(zero)),C)
| join(top,join(complement(zero),C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),top) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
join(top,join(complement(zero),C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,complement(zero)),C)) )],[refute_0_318,refute_0_409]) ).
cnf(refute_0_411,plain,
( join(top,top) != join(top,complement(zero))
| join(top,complement(zero)) = join(top,top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(top,top))),bind(Y,$fot(join(top,complement(zero))))]]) ).
cnf(refute_0_412,plain,
join(top,complement(zero)) = join(top,top),
inference(resolve,[$cnf( $equal(join(top,top),join(top,complement(zero))) )],[refute_0_335,refute_0_411]) ).
cnf(refute_0_413,plain,
( join(top,complement(zero)) != join(top,top)
| join(top,join(complement(zero),C)) != join(join(top,complement(zero)),C)
| join(top,join(complement(zero),C)) = join(join(top,top),C) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,complement(zero)),C)) ),[1,0],$fot(join(top,top))]]) ).
cnf(refute_0_414,plain,
( join(top,join(complement(zero),C)) != join(join(top,complement(zero)),C)
| join(top,join(complement(zero),C)) = join(join(top,top),C) ),
inference(resolve,[$cnf( $equal(join(top,complement(zero)),join(top,top)) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
join(top,join(complement(zero),C)) = join(join(top,top),C),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,complement(zero)),C)) )],[refute_0_318,refute_0_414]) ).
cnf(refute_0_416,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_417,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_416]) ).
cnf(refute_0_418,plain,
join(join(top,top),C) = join(top,join(top,C)),
inference(subst,[],[refute_0_417:[bind(A,$fot(top)),bind(B,$fot(top))]]) ).
cnf(refute_0_419,plain,
( join(join(top,top),C) != join(top,join(top,C))
| join(top,join(complement(zero),C)) != join(join(top,top),C)
| join(top,join(complement(zero),C)) = join(top,join(top,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,top),C)) ),[1],$fot(join(top,join(top,C)))]]) ).
cnf(refute_0_420,plain,
( join(top,join(complement(zero),C)) != join(join(top,top),C)
| join(top,join(complement(zero),C)) = join(top,join(top,C)) ),
inference(resolve,[$cnf( $equal(join(join(top,top),C),join(top,join(top,C))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
join(top,join(complement(zero),C)) = join(top,join(top,C)),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),C)),join(join(top,top),C)) )],[refute_0_415,refute_0_420]) ).
cnf(refute_0_422,plain,
( join(top,join(complement(zero),C)) != join(top,C)
| join(top,join(complement(zero),C)) != join(top,join(top,C))
| join(top,join(top,C)) = join(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(complement(zero),C)),join(top,C)) ),[0],$fot(join(top,join(top,C)))]]) ).
cnf(refute_0_423,plain,
( join(top,join(complement(zero),C)) != join(top,C)
| join(top,join(top,C)) = join(top,C) ),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),C)),join(top,join(top,C))) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
join(top,join(top,C)) = join(top,C),
inference(resolve,[$cnf( $equal(join(top,join(complement(zero),C)),join(top,C)) )],[refute_0_410,refute_0_423]) ).
cnf(refute_0_425,plain,
join(top,join(top,X_82)) = join(top,X_82),
inference(subst,[],[refute_0_424:[bind(C,$fot(X_82))]]) ).
cnf(refute_0_426,plain,
( join(join(top,X_82),top) != join(top,join(top,X_82))
| join(top,join(top,X_82)) != join(top,X_82)
| join(join(top,X_82),top) = join(top,X_82) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(top,X_82),top),join(top,X_82)) ),[0],$fot(join(top,join(top,X_82)))]]) ).
cnf(refute_0_427,plain,
( join(join(top,X_82),top) != join(top,join(top,X_82))
| join(join(top,X_82),top) = join(top,X_82) ),
inference(resolve,[$cnf( $equal(join(top,join(top,X_82)),join(top,X_82)) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
join(join(top,X_82),top) = join(top,X_82),
inference(resolve,[$cnf( $equal(join(join(top,X_82),top),join(top,join(top,X_82))) )],[refute_0_317,refute_0_427]) ).
cnf(refute_0_429,plain,
join(join(top,X_82),top) = join(top,join(X_82,top)),
inference(subst,[],[refute_0_417:[bind(A,$fot(top)),bind(B,$fot(X_82)),bind(C,$fot(top))]]) ).
cnf(refute_0_430,plain,
( join(join(top,X_82),top) != join(top,X_82)
| join(join(top,X_82),top) != join(top,join(X_82,top))
| join(top,join(X_82,top)) = join(top,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(top,X_82),top),join(top,X_82)) ),[0],$fot(join(top,join(X_82,top)))]]) ).
cnf(refute_0_431,plain,
( join(join(top,X_82),top) != join(top,X_82)
| join(top,join(X_82,top)) = join(top,X_82) ),
inference(resolve,[$cnf( $equal(join(join(top,X_82),top),join(top,join(X_82,top))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
join(top,join(X_82,top)) = join(top,X_82),
inference(resolve,[$cnf( $equal(join(join(top,X_82),top),join(top,X_82)) )],[refute_0_428,refute_0_431]) ).
cnf(refute_0_433,plain,
top = join(join(X_91,X_91),complement(join(X_91,X_91))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(X_91,X_91)))]]) ).
cnf(refute_0_434,plain,
( complement(join(X_91,X_91)) != complement(X_91)
| top != join(join(X_91,X_91),complement(join(X_91,X_91)))
| top = join(join(X_91,X_91),complement(X_91)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_91,X_91),complement(join(X_91,X_91)))) ),[1,1],$fot(complement(X_91))]]) ).
cnf(refute_0_435,plain,
( top != join(join(X_91,X_91),complement(join(X_91,X_91)))
| top = join(join(X_91,X_91),complement(X_91)) ),
inference(resolve,[$cnf( $equal(complement(join(X_91,X_91)),complement(X_91)) )],[refute_0_299,refute_0_434]) ).
cnf(refute_0_436,plain,
top = join(join(X_91,X_91),complement(X_91)),
inference(resolve,[$cnf( $equal(top,join(join(X_91,X_91),complement(join(X_91,X_91)))) )],[refute_0_433,refute_0_435]) ).
cnf(refute_0_437,plain,
join(X_91,complement(X_91)) = top,
inference(subst,[],[refute_0_201:[bind(A,$fot(X_91))]]) ).
cnf(refute_0_438,plain,
join(X_91,join(X_91,complement(X_91))) = join(X_91,join(X_91,complement(X_91))),
introduced(tautology,[refl,[$fot(join(X_91,join(X_91,complement(X_91))))]]) ).
cnf(refute_0_439,plain,
( join(X_91,complement(X_91)) != top
| join(X_91,join(X_91,complement(X_91))) != join(X_91,join(X_91,complement(X_91)))
| join(X_91,join(X_91,complement(X_91))) = join(X_91,top) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_91,join(X_91,complement(X_91))),join(X_91,join(X_91,complement(X_91)))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_440,plain,
( join(X_91,complement(X_91)) != top
| join(X_91,join(X_91,complement(X_91))) = join(X_91,top) ),
inference(resolve,[$cnf( $equal(join(X_91,join(X_91,complement(X_91))),join(X_91,join(X_91,complement(X_91)))) )],[refute_0_438,refute_0_439]) ).
cnf(refute_0_441,plain,
join(X_91,join(X_91,complement(X_91))) = join(X_91,top),
inference(resolve,[$cnf( $equal(join(X_91,complement(X_91)),top) )],[refute_0_437,refute_0_440]) ).
cnf(refute_0_442,plain,
join(join(X_91,X_91),complement(X_91)) = join(X_91,join(X_91,complement(X_91))),
inference(subst,[],[refute_0_417:[bind(A,$fot(X_91)),bind(B,$fot(X_91)),bind(C,$fot(complement(X_91)))]]) ).
cnf(refute_0_443,plain,
( join(X_91,join(X_91,complement(X_91))) != join(X_91,top)
| join(join(X_91,X_91),complement(X_91)) != join(X_91,join(X_91,complement(X_91)))
| join(join(X_91,X_91),complement(X_91)) = join(X_91,top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(X_91,X_91),complement(X_91)))),bind(Y,$fot(join(X_91,join(X_91,complement(X_91))))),bind(Z,$fot(join(X_91,top)))]]) ).
cnf(refute_0_444,plain,
( join(X_91,join(X_91,complement(X_91))) != join(X_91,top)
| join(join(X_91,X_91),complement(X_91)) = join(X_91,top) ),
inference(resolve,[$cnf( $equal(join(join(X_91,X_91),complement(X_91)),join(X_91,join(X_91,complement(X_91)))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
join(join(X_91,X_91),complement(X_91)) = join(X_91,top),
inference(resolve,[$cnf( $equal(join(X_91,join(X_91,complement(X_91))),join(X_91,top)) )],[refute_0_441,refute_0_444]) ).
cnf(refute_0_446,plain,
( join(join(X_91,X_91),complement(X_91)) != join(X_91,top)
| top != join(join(X_91,X_91),complement(X_91))
| top = join(X_91,top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_91,X_91),complement(X_91))) ),[1],$fot(join(X_91,top))]]) ).
cnf(refute_0_447,plain,
( top != join(join(X_91,X_91),complement(X_91))
| top = join(X_91,top) ),
inference(resolve,[$cnf( $equal(join(join(X_91,X_91),complement(X_91)),join(X_91,top)) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
top = join(X_91,top),
inference(resolve,[$cnf( $equal(top,join(join(X_91,X_91),complement(X_91))) )],[refute_0_436,refute_0_447]) ).
cnf(refute_0_449,plain,
( top != join(X_91,top)
| join(X_91,top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_91,top)))]]) ).
cnf(refute_0_450,plain,
join(X_91,top) = top,
inference(resolve,[$cnf( $equal(top,join(X_91,top)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
join(X_82,top) = top,
inference(subst,[],[refute_0_450:[bind(X_91,$fot(X_82))]]) ).
cnf(refute_0_452,plain,
join(join(X_43,X_44),join(X_43,X_44)) = join(join(join(X_43,X_44),X_43),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(join(X_43,X_44))),bind(B,$fot(X_43)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_453,plain,
composition(join(one,one),join(X_43,X_44)) = join(join(X_43,X_44),join(X_43,X_44)),
inference(subst,[],[refute_0_90:[bind(X_40,$fot(join(X_43,X_44)))]]) ).
cnf(refute_0_454,plain,
( composition(join(one,one),join(X_43,X_44)) != join(join(X_43,X_44),join(X_43,X_44))
| join(join(X_43,X_44),join(X_43,X_44)) = composition(join(one,one),join(X_43,X_44)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),join(X_43,X_44)))),bind(Y,$fot(join(join(X_43,X_44),join(X_43,X_44))))]]) ).
cnf(refute_0_455,plain,
join(join(X_43,X_44),join(X_43,X_44)) = composition(join(one,one),join(X_43,X_44)),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(join(X_43,X_44),join(X_43,X_44))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
( join(join(X_43,X_44),join(X_43,X_44)) != composition(join(one,one),join(X_43,X_44))
| join(join(X_43,X_44),join(X_43,X_44)) != join(join(join(X_43,X_44),X_43),X_44)
| composition(join(one,one),join(X_43,X_44)) = join(join(join(X_43,X_44),X_43),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_43,X_44),join(X_43,X_44)),join(join(join(X_43,X_44),X_43),X_44)) ),[0],$fot(composition(join(one,one),join(X_43,X_44)))]]) ).
cnf(refute_0_457,plain,
( join(join(X_43,X_44),join(X_43,X_44)) != join(join(join(X_43,X_44),X_43),X_44)
| composition(join(one,one),join(X_43,X_44)) = join(join(join(X_43,X_44),X_43),X_44) ),
inference(resolve,[$cnf( $equal(join(join(X_43,X_44),join(X_43,X_44)),composition(join(one,one),join(X_43,X_44))) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
composition(join(one,one),join(X_43,X_44)) = join(join(join(X_43,X_44),X_43),X_44),
inference(resolve,[$cnf( $equal(join(join(X_43,X_44),join(X_43,X_44)),join(join(join(X_43,X_44),X_43),X_44)) )],[refute_0_452,refute_0_457]) ).
cnf(refute_0_459,plain,
join(X_42,join(X_43,X_44)) = join(join(X_42,X_43),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_42)),bind(B,$fot(X_43)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_460,plain,
join(X_44,X_43) = join(X_43,X_44),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_44)),bind(B,$fot(X_43))]]) ).
cnf(refute_0_461,plain,
( join(X_44,X_43) != join(X_43,X_44)
| join(X_43,X_44) = join(X_44,X_43) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_44,X_43))),bind(Y,$fot(join(X_43,X_44)))]]) ).
cnf(refute_0_462,plain,
join(X_43,X_44) = join(X_44,X_43),
inference(resolve,[$cnf( $equal(join(X_44,X_43),join(X_43,X_44)) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
( join(X_42,join(X_43,X_44)) != join(join(X_42,X_43),X_44)
| join(X_43,X_44) != join(X_44,X_43)
| join(X_42,join(X_44,X_43)) = join(join(X_42,X_43),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(join(X_42,X_43),X_44)) ),[0,1],$fot(join(X_44,X_43))]]) ).
cnf(refute_0_464,plain,
( join(X_42,join(X_43,X_44)) != join(join(X_42,X_43),X_44)
| join(X_42,join(X_44,X_43)) = join(join(X_42,X_43),X_44) ),
inference(resolve,[$cnf( $equal(join(X_43,X_44),join(X_44,X_43)) )],[refute_0_462,refute_0_463]) ).
cnf(refute_0_465,plain,
join(X_42,join(X_44,X_43)) = join(join(X_42,X_43),X_44),
inference(resolve,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(join(X_42,X_43),X_44)) )],[refute_0_459,refute_0_464]) ).
cnf(refute_0_466,plain,
join(join(X_42,X_43),X_44) = join(X_42,join(X_43,X_44)),
inference(subst,[],[refute_0_417:[bind(A,$fot(X_42)),bind(B,$fot(X_43)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_467,plain,
( join(X_42,join(X_44,X_43)) != join(join(X_42,X_43),X_44)
| join(join(X_42,X_43),X_44) != join(X_42,join(X_43,X_44))
| join(X_42,join(X_44,X_43)) = join(X_42,join(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_42,join(X_44,X_43)),join(X_42,join(X_43,X_44))) ),[0],$fot(join(join(X_42,X_43),X_44))]]) ).
cnf(refute_0_468,plain,
( join(X_42,join(X_44,X_43)) != join(join(X_42,X_43),X_44)
| join(X_42,join(X_44,X_43)) = join(X_42,join(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(join(join(X_42,X_43),X_44),join(X_42,join(X_43,X_44))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
join(X_42,join(X_44,X_43)) = join(X_42,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(X_42,join(X_44,X_43)),join(join(X_42,X_43),X_44)) )],[refute_0_465,refute_0_468]) ).
cnf(refute_0_470,plain,
( join(X_42,join(X_44,X_43)) != join(X_42,join(X_43,X_44))
| join(X_42,join(X_43,X_44)) = join(X_42,join(X_44,X_43)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_42,join(X_44,X_43)))),bind(Y,$fot(join(X_42,join(X_43,X_44))))]]) ).
cnf(refute_0_471,plain,
join(X_42,join(X_43,X_44)) = join(X_42,join(X_44,X_43)),
inference(resolve,[$cnf( $equal(join(X_42,join(X_44,X_43)),join(X_42,join(X_43,X_44))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
join(X_44,join(join(X_43,X_44),X_43)) = join(X_44,join(X_43,join(X_43,X_44))),
inference(subst,[],[refute_0_471:[bind(X_42,$fot(X_44)),bind(X_43,$fot(join(X_43,X_44))),bind(X_44,$fot(X_43))]]) ).
cnf(refute_0_473,plain,
join(A,join(X_42,X_43)) = join(join(X_42,X_43),A),
inference(subst,[],[maddux1_join_commutativity_1:[bind(B,$fot(join(X_42,X_43)))]]) ).
cnf(refute_0_474,plain,
join(X_42,join(X_43,A)) = join(join(X_42,X_43),A),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_42)),bind(B,$fot(X_43)),bind(C,$fot(A))]]) ).
cnf(refute_0_475,plain,
( join(X_42,join(X_43,A)) != join(join(X_42,X_43),A)
| join(join(X_42,X_43),A) = join(X_42,join(X_43,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_42,join(X_43,A)))),bind(Y,$fot(join(join(X_42,X_43),A)))]]) ).
cnf(refute_0_476,plain,
join(join(X_42,X_43),A) = join(X_42,join(X_43,A)),
inference(resolve,[$cnf( $equal(join(X_42,join(X_43,A)),join(join(X_42,X_43),A)) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
( join(A,join(X_42,X_43)) != join(join(X_42,X_43),A)
| join(join(X_42,X_43),A) != join(X_42,join(X_43,A))
| join(A,join(X_42,X_43)) = join(X_42,join(X_43,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,join(X_42,X_43)),join(X_42,join(X_43,A))) ),[0],$fot(join(join(X_42,X_43),A))]]) ).
cnf(refute_0_478,plain,
( join(A,join(X_42,X_43)) != join(join(X_42,X_43),A)
| join(A,join(X_42,X_43)) = join(X_42,join(X_43,A)) ),
inference(resolve,[$cnf( $equal(join(join(X_42,X_43),A),join(X_42,join(X_43,A))) )],[refute_0_476,refute_0_477]) ).
cnf(refute_0_479,plain,
join(A,join(X_42,X_43)) = join(X_42,join(X_43,A)),
inference(resolve,[$cnf( $equal(join(A,join(X_42,X_43)),join(join(X_42,X_43),A)) )],[refute_0_473,refute_0_478]) ).
cnf(refute_0_480,plain,
( join(A,join(X_42,X_43)) != join(X_42,join(X_43,A))
| join(X_42,join(X_43,A)) = join(A,join(X_42,X_43)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(X_42,X_43)))),bind(Y,$fot(join(X_42,join(X_43,A))))]]) ).
cnf(refute_0_481,plain,
join(X_42,join(X_43,A)) = join(A,join(X_42,X_43)),
inference(resolve,[$cnf( $equal(join(A,join(X_42,X_43)),join(X_42,join(X_43,A))) )],[refute_0_479,refute_0_480]) ).
cnf(refute_0_482,plain,
join(join(X_43,X_44),join(X_43,X_44)) = join(X_44,join(join(X_43,X_44),X_43)),
inference(subst,[],[refute_0_481:[bind(A,$fot(X_44)),bind(X_42,$fot(join(X_43,X_44)))]]) ).
cnf(refute_0_483,plain,
( join(X_44,join(join(X_43,X_44),X_43)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(join(X_43,X_44),join(X_43,X_44)) != join(X_44,join(join(X_43,X_44),X_43))
| join(join(X_43,X_44),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(X_43,X_44),join(X_43,X_44)))),bind(Y,$fot(join(X_44,join(join(X_43,X_44),X_43)))),bind(Z,$fot(join(X_44,join(X_43,join(X_43,X_44)))))]]) ).
cnf(refute_0_484,plain,
( join(X_44,join(join(X_43,X_44),X_43)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(join(X_43,X_44),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(join(join(X_43,X_44),join(X_43,X_44)),join(X_44,join(join(X_43,X_44),X_43))) )],[refute_0_482,refute_0_483]) ).
cnf(refute_0_485,plain,
join(join(X_43,X_44),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))),
inference(resolve,[$cnf( $equal(join(X_44,join(join(X_43,X_44),X_43)),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_472,refute_0_484]) ).
cnf(refute_0_486,plain,
join(join(join(X_43,X_44),X_43),X_44) = join(join(X_43,X_44),join(X_43,X_44)),
inference(subst,[],[refute_0_417:[bind(A,$fot(join(X_43,X_44))),bind(B,$fot(X_43)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_487,plain,
( join(join(X_43,X_44),join(X_43,X_44)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(join(join(X_43,X_44),X_43),X_44) != join(join(X_43,X_44),join(X_43,X_44))
| join(join(join(X_43,X_44),X_43),X_44) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(join(X_43,X_44),X_43),X_44))),bind(Y,$fot(join(join(X_43,X_44),join(X_43,X_44)))),bind(Z,$fot(join(X_44,join(X_43,join(X_43,X_44)))))]]) ).
cnf(refute_0_488,plain,
( join(join(X_43,X_44),join(X_43,X_44)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(join(join(X_43,X_44),X_43),X_44) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_43,X_44),X_43),X_44),join(join(X_43,X_44),join(X_43,X_44))) )],[refute_0_486,refute_0_487]) ).
cnf(refute_0_489,plain,
join(join(join(X_43,X_44),X_43),X_44) = join(X_44,join(X_43,join(X_43,X_44))),
inference(resolve,[$cnf( $equal(join(join(X_43,X_44),join(X_43,X_44)),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
( composition(join(one,one),join(X_43,X_44)) != join(join(join(X_43,X_44),X_43),X_44)
| join(join(join(X_43,X_44),X_43),X_44) != join(X_44,join(X_43,join(X_43,X_44)))
| composition(join(one,one),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,one),join(X_43,X_44)),join(X_44,join(X_43,join(X_43,X_44)))) ),[0],$fot(join(join(join(X_43,X_44),X_43),X_44))]]) ).
cnf(refute_0_491,plain,
( composition(join(one,one),join(X_43,X_44)) != join(join(join(X_43,X_44),X_43),X_44)
| composition(join(one,one),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(join(join(join(X_43,X_44),X_43),X_44),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_489,refute_0_490]) ).
cnf(refute_0_492,plain,
composition(join(one,one),join(X_43,X_44)) = join(X_44,join(X_43,join(X_43,X_44))),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(join(join(X_43,X_44),X_43),X_44)) )],[refute_0_458,refute_0_491]) ).
cnf(refute_0_493,plain,
composition(one,join(X_43,X_44)) = join(X_43,X_44),
inference(subst,[],[refute_0_149:[bind(X_14,$fot(join(X_43,X_44)))]]) ).
cnf(refute_0_494,plain,
join(one,one) = one,
inference(subst,[],[refute_0_306:[bind(X_91,$fot(one))]]) ).
cnf(refute_0_495,plain,
composition(join(one,one),join(X_43,X_44)) = composition(join(one,one),join(X_43,X_44)),
introduced(tautology,[refl,[$fot(composition(join(one,one),join(X_43,X_44)))]]) ).
cnf(refute_0_496,plain,
( composition(join(one,one),join(X_43,X_44)) != composition(join(one,one),join(X_43,X_44))
| join(one,one) != one
| composition(join(one,one),join(X_43,X_44)) = composition(one,join(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),composition(join(one,one),join(X_43,X_44))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_497,plain,
( join(one,one) != one
| composition(join(one,one),join(X_43,X_44)) = composition(one,join(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),composition(join(one,one),join(X_43,X_44))) )],[refute_0_495,refute_0_496]) ).
cnf(refute_0_498,plain,
composition(join(one,one),join(X_43,X_44)) = composition(one,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_494,refute_0_497]) ).
cnf(refute_0_499,plain,
( composition(join(one,one),join(X_43,X_44)) != composition(one,join(X_43,X_44))
| composition(one,join(X_43,X_44)) != join(X_43,X_44)
| composition(join(one,one),join(X_43,X_44)) = join(X_43,X_44) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,one),join(X_43,X_44)))),bind(Y,$fot(composition(one,join(X_43,X_44)))),bind(Z,$fot(join(X_43,X_44)))]]) ).
cnf(refute_0_500,plain,
( composition(one,join(X_43,X_44)) != join(X_43,X_44)
| composition(join(one,one),join(X_43,X_44)) = join(X_43,X_44) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),composition(one,join(X_43,X_44))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
composition(join(one,one),join(X_43,X_44)) = join(X_43,X_44),
inference(resolve,[$cnf( $equal(composition(one,join(X_43,X_44)),join(X_43,X_44)) )],[refute_0_493,refute_0_500]) ).
cnf(refute_0_502,plain,
( composition(join(one,one),join(X_43,X_44)) != join(X_43,X_44)
| composition(join(one,one),join(X_43,X_44)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_43,X_44) = join(X_44,join(X_43,join(X_43,X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(X_44,join(X_43,join(X_43,X_44)))) ),[0],$fot(join(X_43,X_44))]]) ).
cnf(refute_0_503,plain,
( composition(join(one,one),join(X_43,X_44)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_43,X_44) = join(X_44,join(X_43,join(X_43,X_44))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(X_43,X_44)) )],[refute_0_501,refute_0_502]) ).
cnf(refute_0_504,plain,
join(X_43,X_44) = join(X_44,join(X_43,join(X_43,X_44))),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_492,refute_0_503]) ).
cnf(refute_0_505,plain,
composition(join(A,B),join(one,one)) = join(composition(A,join(one,one)),composition(B,join(one,one))),
inference(subst,[],[composition_distributivity_7:[bind(C,$fot(join(one,one)))]]) ).
cnf(refute_0_506,plain,
( join(A,A) != composition(A,join(one,one))
| composition(A,join(one,one)) = join(A,A) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,A))),bind(Y,$fot(composition(A,join(one,one))))]]) ).
cnf(refute_0_507,plain,
composition(A,join(one,one)) = join(A,A),
inference(resolve,[$cnf( $equal(join(A,A),composition(A,join(one,one))) )],[refute_0_132,refute_0_506]) ).
cnf(refute_0_508,plain,
( composition(A,join(one,one)) != join(A,A)
| composition(join(A,B),join(one,one)) != join(composition(A,join(one,one)),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),join(composition(A,join(one,one)),composition(B,join(one,one)))) ),[1,0],$fot(join(A,A))]]) ).
cnf(refute_0_509,plain,
( composition(join(A,B),join(one,one)) != join(composition(A,join(one,one)),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(A,join(one,one)),join(A,A)) )],[refute_0_507,refute_0_508]) ).
cnf(refute_0_510,plain,
composition(join(A,B),join(one,one)) = join(join(A,A),composition(B,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(composition(A,join(one,one)),composition(B,join(one,one)))) )],[refute_0_505,refute_0_509]) ).
cnf(refute_0_511,plain,
join(join(A,A),composition(B,join(one,one))) = join(A,join(A,composition(B,join(one,one)))),
inference(subst,[],[refute_0_417:[bind(B,$fot(A)),bind(C,$fot(composition(B,join(one,one))))]]) ).
cnf(refute_0_512,plain,
( composition(join(A,B),join(one,one)) != join(join(A,A),composition(B,join(one,one)))
| join(join(A,A),composition(B,join(one,one))) != join(A,join(A,composition(B,join(one,one))))
| composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) ),[0],$fot(join(join(A,A),composition(B,join(one,one))))]]) ).
cnf(refute_0_513,plain,
( composition(join(A,B),join(one,one)) != join(join(A,A),composition(B,join(one,one)))
| composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(join(A,A),composition(B,join(one,one))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
composition(join(A,B),join(one,one)) = join(A,join(A,composition(B,join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(join(A,A),composition(B,join(one,one)))) )],[refute_0_510,refute_0_513]) ).
cnf(refute_0_515,plain,
composition(join(A,B),one) = join(A,B),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(A,B)))]]) ).
cnf(refute_0_516,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),join(one,one)),
introduced(tautology,[refl,[$fot(composition(join(A,B),join(one,one)))]]) ).
cnf(refute_0_517,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),join(one,one))
| join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_518,plain,
( join(one,one) != one
| composition(join(A,B),join(one,one)) = composition(join(A,B),one) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),join(one,one))) )],[refute_0_516,refute_0_517]) ).
cnf(refute_0_519,plain,
composition(join(A,B),join(one,one)) = composition(join(A,B),one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_494,refute_0_518]) ).
cnf(refute_0_520,plain,
( composition(join(A,B),join(one,one)) != composition(join(A,B),one)
| composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(A,B),join(one,one)))),bind(Y,$fot(composition(join(A,B),one))),bind(Z,$fot(join(A,B)))]]) ).
cnf(refute_0_521,plain,
( composition(join(A,B),one) != join(A,B)
| composition(join(A,B),join(one,one)) = join(A,B) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),composition(join(A,B),one)) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
composition(join(A,B),join(one,one)) = join(A,B),
inference(resolve,[$cnf( $equal(composition(join(A,B),one),join(A,B)) )],[refute_0_515,refute_0_521]) ).
cnf(refute_0_523,plain,
( composition(join(A,B),join(one,one)) != join(A,B)
| composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,composition(B,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) ),[0],$fot(join(A,B))]]) ).
cnf(refute_0_524,plain,
( composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,composition(B,join(one,one)))) ),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,B)) )],[refute_0_522,refute_0_523]) ).
cnf(refute_0_525,plain,
composition(B,one) = B,
inference(subst,[],[composition_identity_6:[bind(A,$fot(B))]]) ).
cnf(refute_0_526,plain,
composition(B,join(one,one)) = composition(B,join(one,one)),
introduced(tautology,[refl,[$fot(composition(B,join(one,one)))]]) ).
cnf(refute_0_527,plain,
( composition(B,join(one,one)) != composition(B,join(one,one))
| join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_528,plain,
( join(one,one) != one
| composition(B,join(one,one)) = composition(B,one) ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,join(one,one))) )],[refute_0_526,refute_0_527]) ).
cnf(refute_0_529,plain,
composition(B,join(one,one)) = composition(B,one),
inference(resolve,[$cnf( $equal(join(one,one),one) )],[refute_0_494,refute_0_528]) ).
cnf(refute_0_530,plain,
( composition(B,join(one,one)) != composition(B,one)
| composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(B,join(one,one)))),bind(Y,$fot(composition(B,one))),bind(Z,$fot(B))]]) ).
cnf(refute_0_531,plain,
( composition(B,one) != B
| composition(B,join(one,one)) = B ),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),composition(B,one)) )],[refute_0_529,refute_0_530]) ).
cnf(refute_0_532,plain,
composition(B,join(one,one)) = B,
inference(resolve,[$cnf( $equal(composition(B,one),B) )],[refute_0_525,refute_0_531]) ).
cnf(refute_0_533,plain,
join(A,composition(B,join(one,one))) = join(A,composition(B,join(one,one))),
introduced(tautology,[refl,[$fot(join(A,composition(B,join(one,one))))]]) ).
cnf(refute_0_534,plain,
( composition(B,join(one,one)) != B
| join(A,composition(B,join(one,one))) != join(A,composition(B,join(one,one)))
| join(A,composition(B,join(one,one))) = join(A,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,composition(B,join(one,one)))) ),[1,1],$fot(B)]]) ).
cnf(refute_0_535,plain,
( composition(B,join(one,one)) != B
| join(A,composition(B,join(one,one))) = join(A,B) ),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,composition(B,join(one,one)))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
join(A,composition(B,join(one,one))) = join(A,B),
inference(resolve,[$cnf( $equal(composition(B,join(one,one)),B) )],[refute_0_532,refute_0_535]) ).
cnf(refute_0_537,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,composition(B,join(one,one)))),
introduced(tautology,[refl,[$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_538,plain,
( join(A,composition(B,join(one,one))) != join(A,B)
| join(A,join(A,composition(B,join(one,one)))) != join(A,join(A,composition(B,join(one,one))))
| join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,composition(B,join(one,one))))) ),[1,1],$fot(join(A,B))]]) ).
cnf(refute_0_539,plain,
( join(A,composition(B,join(one,one))) != join(A,B)
| join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
join(A,join(A,composition(B,join(one,one)))) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(join(A,composition(B,join(one,one))),join(A,B)) )],[refute_0_536,refute_0_539]) ).
cnf(refute_0_541,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,join(A,composition(B,join(one,one)))) != join(A,join(A,B))
| join(A,B) = join(A,join(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(A,B),join(A,join(A,B))) ),[0],$fot(join(A,join(A,composition(B,join(one,one)))))]]) ).
cnf(refute_0_542,plain,
( join(A,B) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,join(A,composition(B,join(one,one)))),join(A,join(A,B))) )],[refute_0_540,refute_0_541]) ).
cnf(refute_0_543,plain,
( composition(join(A,B),join(one,one)) != join(A,join(A,composition(B,join(one,one))))
| join(A,B) = join(A,join(A,B)) ),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_524,refute_0_542]) ).
cnf(refute_0_544,plain,
join(A,B) = join(A,join(A,B)),
inference(resolve,[$cnf( $equal(composition(join(A,B),join(one,one)),join(A,join(A,composition(B,join(one,one))))) )],[refute_0_514,refute_0_543]) ).
cnf(refute_0_545,plain,
( join(A,B) != join(A,join(A,B))
| join(A,join(A,B)) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(A,join(A,B))))]]) ).
cnf(refute_0_546,plain,
join(A,join(A,B)) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(A,join(A,B))) )],[refute_0_544,refute_0_545]) ).
cnf(refute_0_547,plain,
join(X_43,join(X_43,X_44)) = join(X_43,X_44),
inference(subst,[],[refute_0_546:[bind(A,$fot(X_43)),bind(B,$fot(X_44))]]) ).
cnf(refute_0_548,plain,
join(X_44,join(X_43,join(X_43,X_44))) = join(X_44,join(X_43,join(X_43,X_44))),
introduced(tautology,[refl,[$fot(join(X_44,join(X_43,join(X_43,X_44))))]]) ).
cnf(refute_0_549,plain,
( join(X_43,join(X_43,X_44)) != join(X_43,X_44)
| join(X_44,join(X_43,join(X_43,X_44))) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_44,join(X_43,join(X_43,X_44))) = join(X_44,join(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_44,join(X_43,join(X_43,X_44))),join(X_44,join(X_43,join(X_43,X_44)))) ),[1,1],$fot(join(X_43,X_44))]]) ).
cnf(refute_0_550,plain,
( join(X_43,join(X_43,X_44)) != join(X_43,X_44)
| join(X_44,join(X_43,join(X_43,X_44))) = join(X_44,join(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(join(X_44,join(X_43,join(X_43,X_44))),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
join(X_44,join(X_43,join(X_43,X_44))) = join(X_44,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(X_43,join(X_43,X_44)),join(X_43,X_44)) )],[refute_0_547,refute_0_550]) ).
cnf(refute_0_552,plain,
( join(X_43,X_44) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_44,join(X_43,join(X_43,X_44))) != join(X_44,join(X_43,X_44))
| join(X_43,X_44) = join(X_44,join(X_43,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_43,X_44),join(X_44,join(X_43,X_44))) ),[0],$fot(join(X_44,join(X_43,join(X_43,X_44))))]]) ).
cnf(refute_0_553,plain,
( join(X_43,X_44) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_43,X_44) = join(X_44,join(X_43,X_44)) ),
inference(resolve,[$cnf( $equal(join(X_44,join(X_43,join(X_43,X_44))),join(X_44,join(X_43,X_44))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
join(X_43,X_44) = join(X_44,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(X_43,X_44),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_504,refute_0_553]) ).
cnf(refute_0_555,plain,
( join(X_43,X_44) != join(X_44,join(X_43,X_44))
| join(X_44,join(X_43,X_44)) = join(X_43,X_44) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_43,X_44))),bind(Y,$fot(join(X_44,join(X_43,X_44))))]]) ).
cnf(refute_0_556,plain,
join(X_44,join(X_43,X_44)) = join(X_43,X_44),
inference(resolve,[$cnf( $equal(join(X_43,X_44),join(X_44,join(X_43,X_44))) )],[refute_0_554,refute_0_555]) ).
cnf(refute_0_557,plain,
join(top,join(X_82,top)) = join(X_82,top),
inference(subst,[],[refute_0_556:[bind(X_43,$fot(X_82)),bind(X_44,$fot(top))]]) ).
cnf(refute_0_558,plain,
( join(X_82,top) != top
| join(top,join(X_82,top)) != join(X_82,top)
| join(top,join(X_82,top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(top,join(X_82,top)))),bind(Y,$fot(join(X_82,top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_559,plain,
( join(X_82,top) != top
| join(top,join(X_82,top)) = top ),
inference(resolve,[$cnf( $equal(join(top,join(X_82,top)),join(X_82,top)) )],[refute_0_557,refute_0_558]) ).
cnf(refute_0_560,plain,
join(top,join(X_82,top)) = top,
inference(resolve,[$cnf( $equal(join(X_82,top),top) )],[refute_0_451,refute_0_559]) ).
cnf(refute_0_561,plain,
( join(top,join(X_82,top)) != join(top,X_82)
| join(top,join(X_82,top)) != top
| top = join(top,X_82) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(X_82,top)),join(top,X_82)) ),[0],$fot(top)]]) ).
cnf(refute_0_562,plain,
( join(top,join(X_82,top)) != join(top,X_82)
| top = join(top,X_82) ),
inference(resolve,[$cnf( $equal(join(top,join(X_82,top)),top) )],[refute_0_560,refute_0_561]) ).
cnf(refute_0_563,plain,
top = join(top,X_82),
inference(resolve,[$cnf( $equal(join(top,join(X_82,top)),join(top,X_82)) )],[refute_0_432,refute_0_562]) ).
cnf(refute_0_564,plain,
top = join(top,composition(X_36,top)),
inference(subst,[],[refute_0_563:[bind(X_82,$fot(composition(X_36,top)))]]) ).
cnf(refute_0_565,plain,
( top != join(top,composition(X_36,top))
| join(top,composition(X_36,top)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,composition(X_36,top))))]]) ).
cnf(refute_0_566,plain,
join(top,composition(X_36,top)) = top,
inference(resolve,[$cnf( $equal(top,join(top,composition(X_36,top))) )],[refute_0_564,refute_0_565]) ).
cnf(refute_0_567,plain,
( composition(join(X_36,one),top) != join(top,composition(X_36,top))
| join(top,composition(X_36,top)) != top
| composition(join(X_36,one),top) = top ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_36,one),top),top) ),[0],$fot(join(top,composition(X_36,top)))]]) ).
cnf(refute_0_568,plain,
( composition(join(X_36,one),top) != join(top,composition(X_36,top))
| composition(join(X_36,one),top) = top ),
inference(resolve,[$cnf( $equal(join(top,composition(X_36,top)),top) )],[refute_0_566,refute_0_567]) ).
cnf(refute_0_569,plain,
composition(join(X_36,one),top) = top,
inference(resolve,[$cnf( $equal(composition(join(X_36,one),top),join(top,composition(X_36,top))) )],[refute_0_316,refute_0_568]) ).
cnf(refute_0_570,plain,
composition(join(top,one),top) = top,
inference(subst,[],[refute_0_569:[bind(X_36,$fot(top))]]) ).
cnf(refute_0_571,plain,
top = join(top,one),
inference(subst,[],[refute_0_563:[bind(X_82,$fot(one))]]) ).
cnf(refute_0_572,plain,
( top != join(top,one)
| join(top,one) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,one)))]]) ).
cnf(refute_0_573,plain,
join(top,one) = top,
inference(resolve,[$cnf( $equal(top,join(top,one)) )],[refute_0_571,refute_0_572]) ).
cnf(refute_0_574,plain,
( composition(join(top,one),top) != top
| join(top,one) != top
| composition(top,top) = top ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(top,one),top),top) ),[0,0],$fot(top)]]) ).
cnf(refute_0_575,plain,
( composition(join(top,one),top) != top
| composition(top,top) = top ),
inference(resolve,[$cnf( $equal(join(top,one),top) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
composition(top,top) = top,
inference(resolve,[$cnf( $equal(composition(join(top,one),top),top) )],[refute_0_570,refute_0_575]) ).
cnf(refute_0_577,plain,
( composition(top,composition(top,C)) != composition(composition(top,top),C)
| composition(top,top) != top
| composition(top,composition(top,C)) = composition(top,C) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,composition(top,C)),composition(composition(top,top),C)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_578,plain,
( composition(top,composition(top,C)) != composition(composition(top,top),C)
| composition(top,composition(top,C)) = composition(top,C) ),
inference(resolve,[$cnf( $equal(composition(top,top),top) )],[refute_0_576,refute_0_577]) ).
cnf(refute_0_579,plain,
composition(top,composition(top,C)) = composition(top,C),
inference(resolve,[$cnf( $equal(composition(top,composition(top,C)),composition(composition(top,top),C)) )],[refute_0_315,refute_0_578]) ).
cnf(refute_0_580,plain,
composition(top,composition(top,X_108)) = composition(top,X_108),
inference(subst,[],[refute_0_579:[bind(C,$fot(X_108))]]) ).
cnf(refute_0_581,plain,
( composition(top,composition(top,X_108)) != composition(top,X_108)
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,composition(top,X_108))))) != complement(composition(top,X_108))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = complement(composition(top,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,composition(top,X_108))))),complement(composition(top,X_108))) ),[0,1,1,0],$fot(composition(top,X_108))]]) ).
cnf(refute_0_582,plain,
( join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,composition(top,X_108))))) != complement(composition(top,X_108))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = complement(composition(top,X_108)) ),
inference(resolve,[$cnf( $equal(composition(top,composition(top,X_108)),composition(top,X_108)) )],[refute_0_580,refute_0_581]) ).
cnf(refute_0_583,plain,
join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = complement(composition(top,X_108)),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,composition(top,X_108))))),complement(composition(top,X_108))) )],[refute_0_314,refute_0_582]) ).
cnf(refute_0_584,plain,
top = join(converse(top),complement(converse(top))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(top)))]]) ).
cnf(refute_0_585,plain,
converse(join(top,converse(A))) = join(converse(top),A),
inference(subst,[],[refute_0_112:[bind(X_10,$fot(top))]]) ).
cnf(refute_0_586,plain,
top = join(top,converse(A)),
inference(subst,[],[refute_0_563:[bind(X_82,$fot(converse(A)))]]) ).
cnf(refute_0_587,plain,
( top != join(top,converse(A))
| join(top,converse(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(top,converse(A))))]]) ).
cnf(refute_0_588,plain,
join(top,converse(A)) = top,
inference(resolve,[$cnf( $equal(top,join(top,converse(A))) )],[refute_0_586,refute_0_587]) ).
cnf(refute_0_589,plain,
( converse(join(top,converse(A))) != join(converse(top),A)
| join(top,converse(A)) != top
| converse(top) = join(converse(top),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(top,converse(A))),join(converse(top),A)) ),[0,0],$fot(top)]]) ).
cnf(refute_0_590,plain,
( converse(join(top,converse(A))) != join(converse(top),A)
| converse(top) = join(converse(top),A) ),
inference(resolve,[$cnf( $equal(join(top,converse(A)),top) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
converse(top) = join(converse(top),A),
inference(resolve,[$cnf( $equal(converse(join(top,converse(A))),join(converse(top),A)) )],[refute_0_585,refute_0_590]) ).
cnf(refute_0_592,plain,
converse(top) = join(converse(top),complement(converse(top))),
inference(subst,[],[refute_0_591:[bind(A,$fot(complement(converse(top))))]]) ).
cnf(refute_0_593,plain,
( converse(top) != join(converse(top),complement(converse(top)))
| join(converse(top),complement(converse(top))) = converse(top) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(top))),bind(Y,$fot(join(converse(top),complement(converse(top)))))]]) ).
cnf(refute_0_594,plain,
join(converse(top),complement(converse(top))) = converse(top),
inference(resolve,[$cnf( $equal(converse(top),join(converse(top),complement(converse(top)))) )],[refute_0_592,refute_0_593]) ).
cnf(refute_0_595,plain,
( join(converse(top),complement(converse(top))) != converse(top)
| top != join(converse(top),complement(converse(top)))
| top = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(converse(top),complement(converse(top)))) ),[1],$fot(converse(top))]]) ).
cnf(refute_0_596,plain,
( top != join(converse(top),complement(converse(top)))
| top = converse(top) ),
inference(resolve,[$cnf( $equal(join(converse(top),complement(converse(top))),converse(top)) )],[refute_0_594,refute_0_595]) ).
cnf(refute_0_597,plain,
top = converse(top),
inference(resolve,[$cnf( $equal(top,join(converse(top),complement(converse(top)))) )],[refute_0_584,refute_0_596]) ).
cnf(refute_0_598,plain,
( top != converse(top)
| converse(top) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(converse(top)))]]) ).
cnf(refute_0_599,plain,
converse(top) = top,
inference(resolve,[$cnf( $equal(top,converse(top)) )],[refute_0_597,refute_0_598]) ).
cnf(refute_0_600,plain,
join(one,top) = top,
inference(subst,[],[refute_0_450:[bind(X_91,$fot(one))]]) ).
cnf(refute_0_601,plain,
converse(join(one,top)) = converse(join(one,top)),
introduced(tautology,[refl,[$fot(converse(join(one,top)))]]) ).
cnf(refute_0_602,plain,
( converse(join(one,top)) != converse(join(one,top))
| join(one,top) != top
| converse(join(one,top)) = converse(top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_603,plain,
( join(one,top) != top
| converse(join(one,top)) = converse(top) ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(join(one,top))) )],[refute_0_601,refute_0_602]) ).
cnf(refute_0_604,plain,
converse(join(one,top)) = converse(top),
inference(resolve,[$cnf( $equal(join(one,top),top) )],[refute_0_600,refute_0_603]) ).
cnf(refute_0_605,plain,
( converse(join(one,top)) != converse(top)
| converse(top) != top
| converse(join(one,top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(one,top)))),bind(Y,$fot(converse(top))),bind(Z,$fot(top))]]) ).
cnf(refute_0_606,plain,
( converse(top) != top
| converse(join(one,top)) = top ),
inference(resolve,[$cnf( $equal(converse(join(one,top)),converse(top)) )],[refute_0_604,refute_0_605]) ).
cnf(refute_0_607,plain,
converse(join(one,top)) = top,
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_599,refute_0_606]) ).
cnf(refute_0_608,plain,
converse(join(composition(join(one,one),join(one,one)),B)) = join(converse(composition(join(one,one),join(one,one))),converse(B)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_609,plain,
converse(join(join(one,join(one,one)),one)) = join(one,converse(join(one,join(one,one)))),
inference(subst,[],[refute_0_120:[bind(X_10,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_610,plain,
converse(join(join(one,one),one)) = join(one,converse(join(one,one))),
inference(subst,[],[refute_0_120:[bind(X_10,$fot(join(one,one)))]]) ).
cnf(refute_0_611,plain,
( converse(join(join(one,one),one)) != join(one,converse(join(one,one)))
| converse(join(one,one)) != join(one,one)
| converse(join(join(one,one),one)) = join(one,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,one),one)),join(one,converse(join(one,one)))) ),[1,1],$fot(join(one,one))]]) ).
cnf(refute_0_612,plain,
( converse(join(join(one,one),one)) != join(one,converse(join(one,one)))
| converse(join(join(one,one),one)) = join(one,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_124,refute_0_611]) ).
cnf(refute_0_613,plain,
converse(join(join(one,one),one)) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(join(one,one),one)),join(one,converse(join(one,one)))) )],[refute_0_610,refute_0_612]) ).
cnf(refute_0_614,plain,
converse(join(X_18,one)) = join(one,converse(X_18)),
inference(subst,[],[refute_0_120:[bind(X_10,$fot(X_18))]]) ).
cnf(refute_0_615,plain,
join(one,X_18) = join(X_18,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_18))]]) ).
cnf(refute_0_616,plain,
( join(one,X_18) != join(X_18,one)
| join(X_18,one) = join(one,X_18) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_18))),bind(Y,$fot(join(X_18,one)))]]) ).
cnf(refute_0_617,plain,
join(X_18,one) = join(one,X_18),
inference(resolve,[$cnf( $equal(join(one,X_18),join(X_18,one)) )],[refute_0_615,refute_0_616]) ).
cnf(refute_0_618,plain,
( converse(join(X_18,one)) != join(one,converse(X_18))
| join(X_18,one) != join(one,X_18)
| converse(join(one,X_18)) = join(one,converse(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_18,one)),join(one,converse(X_18))) ),[0,0],$fot(join(one,X_18))]]) ).
cnf(refute_0_619,plain,
( converse(join(X_18,one)) != join(one,converse(X_18))
| converse(join(one,X_18)) = join(one,converse(X_18)) ),
inference(resolve,[$cnf( $equal(join(X_18,one),join(one,X_18)) )],[refute_0_617,refute_0_618]) ).
cnf(refute_0_620,plain,
converse(join(one,X_18)) = join(one,converse(X_18)),
inference(resolve,[$cnf( $equal(converse(join(X_18,one)),join(one,converse(X_18))) )],[refute_0_614,refute_0_619]) ).
cnf(refute_0_621,plain,
( converse(join(X_10,one)) != join(one,converse(X_10))
| join(one,converse(X_10)) = converse(join(X_10,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_10,one)))),bind(Y,$fot(join(one,converse(X_10))))]]) ).
cnf(refute_0_622,plain,
join(one,converse(X_10)) = converse(join(X_10,one)),
inference(resolve,[$cnf( $equal(converse(join(X_10,one)),join(one,converse(X_10))) )],[refute_0_120,refute_0_621]) ).
cnf(refute_0_623,plain,
join(one,converse(X_18)) = converse(join(X_18,one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(X_18))]]) ).
cnf(refute_0_624,plain,
( converse(join(one,X_18)) != join(one,converse(X_18))
| join(one,converse(X_18)) != converse(join(X_18,one))
| converse(join(one,X_18)) = converse(join(X_18,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(one,X_18)),converse(join(X_18,one))) ),[0],$fot(join(one,converse(X_18)))]]) ).
cnf(refute_0_625,plain,
( converse(join(one,X_18)) != join(one,converse(X_18))
| converse(join(one,X_18)) = converse(join(X_18,one)) ),
inference(resolve,[$cnf( $equal(join(one,converse(X_18)),converse(join(X_18,one))) )],[refute_0_623,refute_0_624]) ).
cnf(refute_0_626,plain,
converse(join(one,X_18)) = converse(join(X_18,one)),
inference(resolve,[$cnf( $equal(converse(join(one,X_18)),join(one,converse(X_18))) )],[refute_0_620,refute_0_625]) ).
cnf(refute_0_627,plain,
( converse(join(one,X_18)) != converse(join(X_18,one))
| converse(join(X_18,one)) = converse(join(one,X_18)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,X_18)))),bind(Y,$fot(converse(join(X_18,one))))]]) ).
cnf(refute_0_628,plain,
converse(join(X_18,one)) = converse(join(one,X_18)),
inference(resolve,[$cnf( $equal(converse(join(one,X_18)),converse(join(X_18,one))) )],[refute_0_626,refute_0_627]) ).
cnf(refute_0_629,plain,
converse(join(join(one,one),one)) = converse(join(one,join(one,one))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(join(one,one)))]]) ).
cnf(refute_0_630,plain,
( converse(join(join(one,one),one)) != converse(join(one,join(one,one)))
| converse(join(join(one,one),one)) != join(one,join(one,one))
| converse(join(one,join(one,one))) = join(one,join(one,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,one),one)),join(one,join(one,one))) ),[0],$fot(converse(join(one,join(one,one))))]]) ).
cnf(refute_0_631,plain,
( converse(join(join(one,one),one)) != join(one,join(one,one))
| converse(join(one,join(one,one))) = join(one,join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,one),one)),converse(join(one,join(one,one)))) )],[refute_0_629,refute_0_630]) ).
cnf(refute_0_632,plain,
converse(join(one,join(one,one))) = join(one,join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(join(one,one),one)),join(one,join(one,one))) )],[refute_0_613,refute_0_631]) ).
cnf(refute_0_633,plain,
( converse(join(join(one,join(one,one)),one)) != join(one,converse(join(one,join(one,one))))
| converse(join(one,join(one,one))) != join(one,join(one,one))
| converse(join(join(one,join(one,one)),one)) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,join(one,one)),one)),join(one,converse(join(one,join(one,one))))) ),[1,1],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_634,plain,
( converse(join(join(one,join(one,one)),one)) != join(one,converse(join(one,join(one,one))))
| converse(join(join(one,join(one,one)),one)) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
converse(join(join(one,join(one,one)),one)) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,one)),one)),join(one,converse(join(one,join(one,one))))) )],[refute_0_609,refute_0_634]) ).
cnf(refute_0_636,plain,
converse(join(join(one,join(one,one)),one)) = converse(join(one,join(one,join(one,one)))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_637,plain,
( converse(join(join(one,join(one,one)),one)) != converse(join(one,join(one,join(one,one))))
| converse(join(join(one,join(one,one)),one)) != join(one,join(one,join(one,one)))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(join(one,join(one,one)),one)),join(one,join(one,join(one,one)))) ),[0],$fot(converse(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_638,plain,
( converse(join(join(one,join(one,one)),one)) != join(one,join(one,join(one,one)))
| converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,one)),one)),converse(join(one,join(one,join(one,one))))) )],[refute_0_636,refute_0_637]) ).
cnf(refute_0_639,plain,
converse(join(one,join(one,join(one,one)))) = join(one,join(one,join(one,one))),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,one)),one)),join(one,join(one,join(one,one)))) )],[refute_0_635,refute_0_638]) ).
cnf(refute_0_640,plain,
( composition(join(one,one),join(X_43,X_44)) != join(X_44,join(X_43,join(X_43,X_44)))
| join(X_44,join(X_43,join(X_43,X_44))) = composition(join(one,one),join(X_43,X_44)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),join(X_43,X_44)))),bind(Y,$fot(join(X_44,join(X_43,join(X_43,X_44)))))]]) ).
cnf(refute_0_641,plain,
join(X_44,join(X_43,join(X_43,X_44))) = composition(join(one,one),join(X_43,X_44)),
inference(resolve,[$cnf( $equal(composition(join(one,one),join(X_43,X_44)),join(X_44,join(X_43,join(X_43,X_44)))) )],[refute_0_492,refute_0_640]) ).
cnf(refute_0_642,plain,
join(one,join(one,join(one,one))) = composition(join(one,one),join(one,one)),
inference(subst,[],[refute_0_641:[bind(X_43,$fot(one)),bind(X_44,$fot(one))]]) ).
cnf(refute_0_643,plain,
converse(join(one,join(one,join(one,one)))) = converse(join(one,join(one,join(one,one)))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(one,one)))))]]) ).
cnf(refute_0_644,plain,
( converse(join(one,join(one,join(one,one)))) != converse(join(one,join(one,join(one,one))))
| join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) ),[1,0],$fot(composition(join(one,one),join(one,one)))]]) ).
cnf(refute_0_645,plain,
( join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(join(one,join(one,join(one,one))))) )],[refute_0_643,refute_0_644]) ).
cnf(refute_0_646,plain,
converse(join(one,join(one,join(one,one)))) = converse(composition(join(one,one),join(one,one))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_642,refute_0_645]) ).
cnf(refute_0_647,plain,
( converse(join(one,join(one,join(one,one)))) != converse(composition(join(one,one),join(one,one)))
| converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = join(one,join(one,join(one,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) ),[0],$fot(converse(composition(join(one,one),join(one,one))))]]) ).
cnf(refute_0_648,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = join(one,join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),converse(composition(join(one,one),join(one,one)))) )],[refute_0_646,refute_0_647]) ).
cnf(refute_0_649,plain,
( converse(composition(join(one,one),join(one,one))) != join(one,join(one,join(one,one)))
| join(one,join(one,join(one,one))) != composition(join(one,one),join(one,one))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(join(one,one),join(one,one))),composition(join(one,one),join(one,one))) ),[0],$fot(join(one,join(one,join(one,one))))]]) ).
cnf(refute_0_650,plain,
( converse(composition(join(one,one),join(one,one))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_642,refute_0_649]) ).
cnf(refute_0_651,plain,
( converse(join(one,join(one,join(one,one)))) != join(one,join(one,join(one,one)))
| converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(one,one))),join(one,join(one,join(one,one)))) )],[refute_0_648,refute_0_650]) ).
cnf(refute_0_652,plain,
converse(composition(join(one,one),join(one,one))) = composition(join(one,one),join(one,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,one)))),join(one,join(one,join(one,one)))) )],[refute_0_639,refute_0_651]) ).
cnf(refute_0_653,plain,
( converse(composition(join(one,one),join(one,one))) != composition(join(one,one),join(one,one))
| converse(join(composition(join(one,one),join(one,one)),B)) != join(converse(composition(join(one,one),join(one,one))),converse(B))
| converse(join(composition(join(one,one),join(one,one)),B)) = join(composition(join(one,one),join(one,one)),converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),join(converse(composition(join(one,one),join(one,one))),converse(B))) ),[1,0],$fot(composition(join(one,one),join(one,one)))]]) ).
cnf(refute_0_654,plain,
( converse(join(composition(join(one,one),join(one,one)),B)) != join(converse(composition(join(one,one),join(one,one))),converse(B))
| converse(join(composition(join(one,one),join(one,one)),B)) = join(composition(join(one,one),join(one,one)),converse(B)) ),
inference(resolve,[$cnf( $equal(converse(composition(join(one,one),join(one,one))),composition(join(one,one),join(one,one))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
converse(join(composition(join(one,one),join(one,one)),B)) = join(composition(join(one,one),join(one,one)),converse(B)),
inference(resolve,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),join(converse(composition(join(one,one),join(one,one))),converse(B))) )],[refute_0_608,refute_0_654]) ).
cnf(refute_0_656,plain,
join(join(one,one),B) = join(one,join(one,B)),
inference(subst,[],[refute_0_417:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(B))]]) ).
cnf(refute_0_657,plain,
join(one,join(join(one,one),B)) = join(one,join(join(one,one),B)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,one),B)))]]) ).
cnf(refute_0_658,plain,
( join(join(one,one),B) != join(one,join(one,B))
| join(one,join(join(one,one),B)) != join(one,join(join(one,one),B))
| join(one,join(join(one,one),B)) = join(one,join(one,join(one,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,one),B)),join(one,join(join(one,one),B))) ),[1,1],$fot(join(one,join(one,B)))]]) ).
cnf(refute_0_659,plain,
( join(join(one,one),B) != join(one,join(one,B))
| join(one,join(join(one,one),B)) = join(one,join(one,join(one,B))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),B)),join(one,join(join(one,one),B))) )],[refute_0_657,refute_0_658]) ).
cnf(refute_0_660,plain,
join(one,join(join(one,one),B)) = join(one,join(one,join(one,B))),
inference(resolve,[$cnf( $equal(join(join(one,one),B),join(one,join(one,B))) )],[refute_0_656,refute_0_659]) ).
cnf(refute_0_661,plain,
join(one,join(one,join(join(one,one),B))) = join(one,join(one,join(join(one,one),B))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(join(one,one),B))))]]) ).
cnf(refute_0_662,plain,
( join(one,join(join(one,one),B)) != join(one,join(one,join(one,B)))
| join(one,join(one,join(join(one,one),B))) != join(one,join(one,join(join(one,one),B)))
| join(one,join(one,join(join(one,one),B))) = join(one,join(one,join(one,join(one,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(join(one,one),B))),join(one,join(one,join(join(one,one),B)))) ),[1,1],$fot(join(one,join(one,join(one,B))))]]) ).
cnf(refute_0_663,plain,
( join(one,join(join(one,one),B)) != join(one,join(one,join(one,B)))
| join(one,join(one,join(join(one,one),B))) = join(one,join(one,join(one,join(one,B)))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(one,one),B))),join(one,join(one,join(join(one,one),B)))) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
join(one,join(one,join(join(one,one),B))) = join(one,join(one,join(one,join(one,B)))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),B)),join(one,join(one,join(one,B)))) )],[refute_0_660,refute_0_663]) ).
cnf(refute_0_665,plain,
join(join(one,one),join(join(one,one),B)) = join(one,join(one,join(join(one,one),B))),
inference(subst,[],[refute_0_417:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(join(join(one,one),B)))]]) ).
cnf(refute_0_666,plain,
join(X_43,join(X_43,X_44)) = join(join(X_43,X_43),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_43)),bind(B,$fot(X_43)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_667,plain,
composition(join(one,one),X_43) = join(X_43,X_43),
inference(subst,[],[refute_0_90:[bind(X_40,$fot(X_43))]]) ).
cnf(refute_0_668,plain,
( composition(join(one,one),X_43) != join(X_43,X_43)
| join(X_43,X_43) = composition(join(one,one),X_43) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),X_43))),bind(Y,$fot(join(X_43,X_43)))]]) ).
cnf(refute_0_669,plain,
join(X_43,X_43) = composition(join(one,one),X_43),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_43),join(X_43,X_43)) )],[refute_0_667,refute_0_668]) ).
cnf(refute_0_670,plain,
( join(X_43,X_43) != composition(join(one,one),X_43)
| join(X_43,join(X_43,X_44)) != join(join(X_43,X_43),X_44)
| join(X_43,join(X_43,X_44)) = join(composition(join(one,one),X_43),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_43,join(X_43,X_44)),join(join(X_43,X_43),X_44)) ),[1,0],$fot(composition(join(one,one),X_43))]]) ).
cnf(refute_0_671,plain,
( join(X_43,join(X_43,X_44)) != join(join(X_43,X_43),X_44)
| join(X_43,join(X_43,X_44)) = join(composition(join(one,one),X_43),X_44) ),
inference(resolve,[$cnf( $equal(join(X_43,X_43),composition(join(one,one),X_43)) )],[refute_0_669,refute_0_670]) ).
cnf(refute_0_672,plain,
join(X_43,join(X_43,X_44)) = join(composition(join(one,one),X_43),X_44),
inference(resolve,[$cnf( $equal(join(X_43,join(X_43,X_44)),join(join(X_43,X_43),X_44)) )],[refute_0_666,refute_0_671]) ).
cnf(refute_0_673,plain,
( join(X_43,join(X_43,X_44)) != join(composition(join(one,one),X_43),X_44)
| join(composition(join(one,one),X_43),X_44) = join(X_43,join(X_43,X_44)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_43,join(X_43,X_44)))),bind(Y,$fot(join(composition(join(one,one),X_43),X_44)))]]) ).
cnf(refute_0_674,plain,
join(composition(join(one,one),X_43),X_44) = join(X_43,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(X_43,join(X_43,X_44)),join(composition(join(one,one),X_43),X_44)) )],[refute_0_672,refute_0_673]) ).
cnf(refute_0_675,plain,
join(composition(join(one,one),join(one,one)),B) = join(join(one,one),join(join(one,one),B)),
inference(subst,[],[refute_0_674:[bind(X_43,$fot(join(one,one))),bind(X_44,$fot(B))]]) ).
cnf(refute_0_676,plain,
( join(composition(join(one,one),join(one,one)),B) != join(join(one,one),join(join(one,one),B))
| join(join(one,one),join(join(one,one),B)) != join(one,join(one,join(join(one,one),B)))
| join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(join(one,one),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(join(one,one),join(one,one)),B))),bind(Y,$fot(join(join(one,one),join(join(one,one),B)))),bind(Z,$fot(join(one,join(one,join(join(one,one),B)))))]]) ).
cnf(refute_0_677,plain,
( join(join(one,one),join(join(one,one),B)) != join(one,join(one,join(join(one,one),B)))
| join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(join(one,one),B))) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),B),join(join(one,one),join(join(one,one),B))) )],[refute_0_675,refute_0_676]) ).
cnf(refute_0_678,plain,
join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(join(one,one),B))),
inference(resolve,[$cnf( $equal(join(join(one,one),join(join(one,one),B)),join(one,join(one,join(join(one,one),B)))) )],[refute_0_665,refute_0_677]) ).
cnf(refute_0_679,plain,
( join(composition(join(one,one),join(one,one)),B) != join(one,join(one,join(join(one,one),B)))
| join(one,join(one,join(join(one,one),B))) != join(one,join(one,join(one,join(one,B))))
| join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(one,join(one,B)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(join(one,one),join(one,one)),B))),bind(Y,$fot(join(one,join(one,join(join(one,one),B))))),bind(Z,$fot(join(one,join(one,join(one,join(one,B))))))]]) ).
cnf(refute_0_680,plain,
( join(one,join(one,join(join(one,one),B))) != join(one,join(one,join(one,join(one,B))))
| join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(one,join(one,B)))) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),B),join(one,join(one,join(join(one,one),B)))) )],[refute_0_678,refute_0_679]) ).
cnf(refute_0_681,plain,
join(composition(join(one,one),join(one,one)),B) = join(one,join(one,join(one,join(one,B)))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(one,one),B))),join(one,join(one,join(one,join(one,B))))) )],[refute_0_664,refute_0_680]) ).
cnf(refute_0_682,plain,
converse(join(composition(join(one,one),join(one,one)),B)) = converse(join(composition(join(one,one),join(one,one)),B)),
introduced(tautology,[refl,[$fot(converse(join(composition(join(one,one),join(one,one)),B)))]]) ).
cnf(refute_0_683,plain,
( converse(join(composition(join(one,one),join(one,one)),B)) != converse(join(composition(join(one,one),join(one,one)),B))
| join(composition(join(one,one),join(one,one)),B) != join(one,join(one,join(one,join(one,B))))
| converse(join(composition(join(one,one),join(one,one)),B)) = converse(join(one,join(one,join(one,join(one,B))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),converse(join(composition(join(one,one),join(one,one)),B))) ),[1,0],$fot(join(one,join(one,join(one,join(one,B)))))]]) ).
cnf(refute_0_684,plain,
( join(composition(join(one,one),join(one,one)),B) != join(one,join(one,join(one,join(one,B))))
| converse(join(composition(join(one,one),join(one,one)),B)) = converse(join(one,join(one,join(one,join(one,B))))) ),
inference(resolve,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),converse(join(composition(join(one,one),join(one,one)),B))) )],[refute_0_682,refute_0_683]) ).
cnf(refute_0_685,plain,
converse(join(composition(join(one,one),join(one,one)),B)) = converse(join(one,join(one,join(one,join(one,B))))),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),B),join(one,join(one,join(one,join(one,B))))) )],[refute_0_681,refute_0_684]) ).
cnf(refute_0_686,plain,
( converse(join(composition(join(one,one),join(one,one)),B)) != converse(join(one,join(one,join(one,join(one,B)))))
| converse(join(composition(join(one,one),join(one,one)),B)) != join(composition(join(one,one),join(one,one)),converse(B))
| converse(join(one,join(one,join(one,join(one,B))))) = join(composition(join(one,one),join(one,one)),converse(B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),join(composition(join(one,one),join(one,one)),converse(B))) ),[0],$fot(converse(join(one,join(one,join(one,join(one,B))))))]]) ).
cnf(refute_0_687,plain,
( converse(join(composition(join(one,one),join(one,one)),B)) != join(composition(join(one,one),join(one,one)),converse(B))
| converse(join(one,join(one,join(one,join(one,B))))) = join(composition(join(one,one),join(one,one)),converse(B)) ),
inference(resolve,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),converse(join(one,join(one,join(one,join(one,B)))))) )],[refute_0_685,refute_0_686]) ).
cnf(refute_0_688,plain,
converse(join(join(one,join(one,join(B,one))),one)) = converse(join(one,join(one,join(one,join(B,one))))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(join(one,join(one,join(B,one)))))]]) ).
cnf(refute_0_689,plain,
join(one,converse(join(one,join(one,join(B,one))))) = converse(join(join(one,join(one,join(B,one))),one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(join(one,join(one,join(B,one)))))]]) ).
cnf(refute_0_690,plain,
( converse(join(join(one,join(one,join(B,one))),one)) != converse(join(one,join(one,join(one,join(B,one)))))
| join(one,converse(join(one,join(one,join(B,one))))) != converse(join(join(one,join(one,join(B,one))),one))
| join(one,converse(join(one,join(one,join(B,one))))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(join(one,join(one,join(B,one))))))),bind(Y,$fot(converse(join(join(one,join(one,join(B,one))),one)))),bind(Z,$fot(converse(join(one,join(one,join(one,join(B,one)))))))]]) ).
cnf(refute_0_691,plain,
( converse(join(join(one,join(one,join(B,one))),one)) != converse(join(one,join(one,join(one,join(B,one)))))
| join(one,converse(join(one,join(one,join(B,one))))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,join(B,one))))),converse(join(join(one,join(one,join(B,one))),one))) )],[refute_0_689,refute_0_690]) ).
cnf(refute_0_692,plain,
join(one,converse(join(one,join(one,join(B,one))))) = converse(join(one,join(one,join(one,join(B,one))))),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(one,join(B,one))),one)),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_688,refute_0_691]) ).
cnf(refute_0_693,plain,
converse(join(join(one,join(B,one)),one)) = converse(join(one,join(one,join(B,one)))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(join(one,join(B,one))))]]) ).
cnf(refute_0_694,plain,
join(one,converse(join(one,join(B,one)))) = converse(join(join(one,join(B,one)),one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(join(one,join(B,one))))]]) ).
cnf(refute_0_695,plain,
( converse(join(join(one,join(B,one)),one)) != converse(join(one,join(one,join(B,one))))
| join(one,converse(join(one,join(B,one)))) != converse(join(join(one,join(B,one)),one))
| join(one,converse(join(one,join(B,one)))) = converse(join(one,join(one,join(B,one)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(join(one,join(B,one)))))),bind(Y,$fot(converse(join(join(one,join(B,one)),one)))),bind(Z,$fot(converse(join(one,join(one,join(B,one))))))]]) ).
cnf(refute_0_696,plain,
( converse(join(join(one,join(B,one)),one)) != converse(join(one,join(one,join(B,one))))
| join(one,converse(join(one,join(B,one)))) = converse(join(one,join(one,join(B,one)))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(B,one)))),converse(join(join(one,join(B,one)),one))) )],[refute_0_694,refute_0_695]) ).
cnf(refute_0_697,plain,
join(one,converse(join(one,join(B,one)))) = converse(join(one,join(one,join(B,one)))),
inference(resolve,[$cnf( $equal(converse(join(join(one,join(B,one)),one)),converse(join(one,join(one,join(B,one))))) )],[refute_0_693,refute_0_696]) ).
cnf(refute_0_698,plain,
converse(join(join(B,one),one)) = converse(join(one,join(B,one))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(join(B,one)))]]) ).
cnf(refute_0_699,plain,
join(one,converse(join(B,one))) = converse(join(join(B,one),one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(join(B,one)))]]) ).
cnf(refute_0_700,plain,
( converse(join(join(B,one),one)) != converse(join(one,join(B,one)))
| join(one,converse(join(B,one))) != converse(join(join(B,one),one))
| join(one,converse(join(B,one))) = converse(join(one,join(B,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(join(B,one))))),bind(Y,$fot(converse(join(join(B,one),one)))),bind(Z,$fot(converse(join(one,join(B,one)))))]]) ).
cnf(refute_0_701,plain,
( converse(join(join(B,one),one)) != converse(join(one,join(B,one)))
| join(one,converse(join(B,one))) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(join(one,converse(join(B,one))),converse(join(join(B,one),one))) )],[refute_0_699,refute_0_700]) ).
cnf(refute_0_702,plain,
join(one,converse(join(B,one))) = converse(join(one,join(B,one))),
inference(resolve,[$cnf( $equal(converse(join(join(B,one),one)),converse(join(one,join(B,one)))) )],[refute_0_698,refute_0_701]) ).
cnf(refute_0_703,plain,
join(one,converse(B)) = converse(join(B,one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(B))]]) ).
cnf(refute_0_704,plain,
join(one,join(one,converse(B))) = join(one,join(one,converse(B))),
introduced(tautology,[refl,[$fot(join(one,join(one,converse(B))))]]) ).
cnf(refute_0_705,plain,
( join(one,converse(B)) != converse(join(B,one))
| join(one,join(one,converse(B))) != join(one,join(one,converse(B)))
| join(one,join(one,converse(B))) = join(one,converse(join(B,one))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,converse(B))),join(one,join(one,converse(B)))) ),[1,1],$fot(converse(join(B,one)))]]) ).
cnf(refute_0_706,plain,
( join(one,converse(B)) != converse(join(B,one))
| join(one,join(one,converse(B))) = join(one,converse(join(B,one))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(B))),join(one,join(one,converse(B)))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
join(one,join(one,converse(B))) = join(one,converse(join(B,one))),
inference(resolve,[$cnf( $equal(join(one,converse(B)),converse(join(B,one))) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
( join(one,converse(join(B,one))) != converse(join(one,join(B,one)))
| join(one,join(one,converse(B))) != join(one,converse(join(B,one)))
| join(one,join(one,converse(B))) = converse(join(one,join(B,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,join(one,converse(B))))),bind(Y,$fot(join(one,converse(join(B,one))))),bind(Z,$fot(converse(join(one,join(B,one)))))]]) ).
cnf(refute_0_709,plain,
( join(one,converse(join(B,one))) != converse(join(one,join(B,one)))
| join(one,join(one,converse(B))) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(B))),join(one,converse(join(B,one)))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
join(one,join(one,converse(B))) = converse(join(one,join(B,one))),
inference(resolve,[$cnf( $equal(join(one,converse(join(B,one))),converse(join(one,join(B,one)))) )],[refute_0_702,refute_0_709]) ).
cnf(refute_0_711,plain,
join(join(one,one),converse(B)) = join(one,join(one,converse(B))),
inference(subst,[],[refute_0_417:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(converse(B)))]]) ).
cnf(refute_0_712,plain,
( join(join(one,one),converse(B)) != join(one,join(one,converse(B)))
| join(one,join(one,converse(B))) != converse(join(one,join(B,one)))
| join(join(one,one),converse(B)) = converse(join(one,join(B,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(join(one,one),converse(B)))),bind(Y,$fot(join(one,join(one,converse(B))))),bind(Z,$fot(converse(join(one,join(B,one)))))]]) ).
cnf(refute_0_713,plain,
( join(one,join(one,converse(B))) != converse(join(one,join(B,one)))
| join(join(one,one),converse(B)) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(B)),join(one,join(one,converse(B)))) )],[refute_0_711,refute_0_712]) ).
cnf(refute_0_714,plain,
join(join(one,one),converse(B)) = converse(join(one,join(B,one))),
inference(resolve,[$cnf( $equal(join(one,join(one,converse(B))),converse(join(one,join(B,one)))) )],[refute_0_710,refute_0_713]) ).
cnf(refute_0_715,plain,
join(one,join(join(one,one),converse(B))) = join(one,join(join(one,one),converse(B))),
introduced(tautology,[refl,[$fot(join(one,join(join(one,one),converse(B))))]]) ).
cnf(refute_0_716,plain,
( join(join(one,one),converse(B)) != converse(join(one,join(B,one)))
| join(one,join(join(one,one),converse(B))) != join(one,join(join(one,one),converse(B)))
| join(one,join(join(one,one),converse(B))) = join(one,converse(join(one,join(B,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,one),converse(B))),join(one,join(join(one,one),converse(B)))) ),[1,1],$fot(converse(join(one,join(B,one))))]]) ).
cnf(refute_0_717,plain,
( join(join(one,one),converse(B)) != converse(join(one,join(B,one)))
| join(one,join(join(one,one),converse(B))) = join(one,converse(join(one,join(B,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(B))),join(one,join(join(one,one),converse(B)))) )],[refute_0_715,refute_0_716]) ).
cnf(refute_0_718,plain,
join(one,join(join(one,one),converse(B))) = join(one,converse(join(one,join(B,one)))),
inference(resolve,[$cnf( $equal(join(join(one,one),converse(B)),converse(join(one,join(B,one)))) )],[refute_0_714,refute_0_717]) ).
cnf(refute_0_719,plain,
( join(one,converse(join(one,join(B,one)))) != converse(join(one,join(one,join(B,one))))
| join(one,join(join(one,one),converse(B))) != join(one,converse(join(one,join(B,one))))
| join(one,join(join(one,one),converse(B))) = converse(join(one,join(one,join(B,one)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,join(join(one,one),converse(B))))),bind(Y,$fot(join(one,converse(join(one,join(B,one)))))),bind(Z,$fot(converse(join(one,join(one,join(B,one))))))]]) ).
cnf(refute_0_720,plain,
( join(one,converse(join(one,join(B,one)))) != converse(join(one,join(one,join(B,one))))
| join(one,join(join(one,one),converse(B))) = converse(join(one,join(one,join(B,one)))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(B))),join(one,converse(join(one,join(B,one))))) )],[refute_0_718,refute_0_719]) ).
cnf(refute_0_721,plain,
join(one,join(join(one,one),converse(B))) = converse(join(one,join(one,join(B,one)))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(B,one)))),converse(join(one,join(one,join(B,one))))) )],[refute_0_697,refute_0_720]) ).
cnf(refute_0_722,plain,
join(one,join(one,join(join(one,one),converse(B)))) = join(one,join(one,join(join(one,one),converse(B)))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(join(one,one),converse(B)))))]]) ).
cnf(refute_0_723,plain,
( join(one,join(join(one,one),converse(B))) != converse(join(one,join(one,join(B,one))))
| join(one,join(one,join(join(one,one),converse(B)))) != join(one,join(one,join(join(one,one),converse(B))))
| join(one,join(one,join(join(one,one),converse(B)))) = join(one,converse(join(one,join(one,join(B,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(join(one,one),converse(B)))),join(one,join(one,join(join(one,one),converse(B))))) ),[1,1],$fot(converse(join(one,join(one,join(B,one)))))]]) ).
cnf(refute_0_724,plain,
( join(one,join(join(one,one),converse(B))) != converse(join(one,join(one,join(B,one))))
| join(one,join(one,join(join(one,one),converse(B)))) = join(one,converse(join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(one,one),converse(B)))),join(one,join(one,join(join(one,one),converse(B))))) )],[refute_0_722,refute_0_723]) ).
cnf(refute_0_725,plain,
join(one,join(one,join(join(one,one),converse(B)))) = join(one,converse(join(one,join(one,join(B,one))))),
inference(resolve,[$cnf( $equal(join(one,join(join(one,one),converse(B))),converse(join(one,join(one,join(B,one))))) )],[refute_0_721,refute_0_724]) ).
cnf(refute_0_726,plain,
( join(one,converse(join(one,join(one,join(B,one))))) != converse(join(one,join(one,join(one,join(B,one)))))
| join(one,join(one,join(join(one,one),converse(B)))) != join(one,converse(join(one,join(one,join(B,one)))))
| join(one,join(one,join(join(one,one),converse(B)))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,join(one,join(join(one,one),converse(B)))))),bind(Y,$fot(join(one,converse(join(one,join(one,join(B,one))))))),bind(Z,$fot(converse(join(one,join(one,join(one,join(B,one)))))))]]) ).
cnf(refute_0_727,plain,
( join(one,converse(join(one,join(one,join(B,one))))) != converse(join(one,join(one,join(one,join(B,one)))))
| join(one,join(one,join(join(one,one),converse(B)))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(one,one),converse(B)))),join(one,converse(join(one,join(one,join(B,one)))))) )],[refute_0_725,refute_0_726]) ).
cnf(refute_0_728,plain,
join(one,join(one,join(join(one,one),converse(B)))) = converse(join(one,join(one,join(one,join(B,one))))),
inference(resolve,[$cnf( $equal(join(one,converse(join(one,join(one,join(B,one))))),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_692,refute_0_727]) ).
cnf(refute_0_729,plain,
join(join(one,one),join(join(one,one),converse(B))) = join(one,join(one,join(join(one,one),converse(B)))),
inference(subst,[],[refute_0_417:[bind(A,$fot(one)),bind(B,$fot(one)),bind(C,$fot(join(join(one,one),converse(B))))]]) ).
cnf(refute_0_730,plain,
join(composition(join(one,one),join(one,one)),converse(B)) = join(join(one,one),join(join(one,one),converse(B))),
inference(subst,[],[refute_0_674:[bind(X_43,$fot(join(one,one))),bind(X_44,$fot(converse(B)))]]) ).
cnf(refute_0_731,plain,
( join(composition(join(one,one),join(one,one)),converse(B)) != join(join(one,one),join(join(one,one),converse(B)))
| join(join(one,one),join(join(one,one),converse(B))) != join(one,join(one,join(join(one,one),converse(B))))
| join(composition(join(one,one),join(one,one)),converse(B)) = join(one,join(one,join(join(one,one),converse(B)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(join(one,one),join(one,one)),converse(B)))),bind(Y,$fot(join(join(one,one),join(join(one,one),converse(B))))),bind(Z,$fot(join(one,join(one,join(join(one,one),converse(B))))))]]) ).
cnf(refute_0_732,plain,
( join(join(one,one),join(join(one,one),converse(B))) != join(one,join(one,join(join(one,one),converse(B))))
| join(composition(join(one,one),join(one,one)),converse(B)) = join(one,join(one,join(join(one,one),converse(B)))) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),converse(B)),join(join(one,one),join(join(one,one),converse(B)))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
join(composition(join(one,one),join(one,one)),converse(B)) = join(one,join(one,join(join(one,one),converse(B)))),
inference(resolve,[$cnf( $equal(join(join(one,one),join(join(one,one),converse(B))),join(one,join(one,join(join(one,one),converse(B))))) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
( join(composition(join(one,one),join(one,one)),converse(B)) != join(one,join(one,join(join(one,one),converse(B))))
| join(one,join(one,join(join(one,one),converse(B)))) != converse(join(one,join(one,join(one,join(B,one)))))
| join(composition(join(one,one),join(one,one)),converse(B)) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(join(one,one),join(one,one)),converse(B)))),bind(Y,$fot(join(one,join(one,join(join(one,one),converse(B)))))),bind(Z,$fot(converse(join(one,join(one,join(one,join(B,one)))))))]]) ).
cnf(refute_0_735,plain,
( join(one,join(one,join(join(one,one),converse(B)))) != converse(join(one,join(one,join(one,join(B,one)))))
| join(composition(join(one,one),join(one,one)),converse(B)) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),converse(B)),join(one,join(one,join(join(one,one),converse(B))))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
join(composition(join(one,one),join(one,one)),converse(B)) = converse(join(one,join(one,join(one,join(B,one))))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(join(one,one),converse(B)))),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_728,refute_0_735]) ).
cnf(refute_0_737,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != join(composition(join(one,one),join(one,one)),converse(B))
| join(composition(join(one,one),join(one,one)),converse(B)) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,join(one,join(B,one))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,join(one,join(B,one)))))) ),[0],$fot(join(composition(join(one,one),join(one,one)),converse(B)))]]) ).
cnf(refute_0_738,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != join(composition(join(one,one),join(one,one)),converse(B))
| converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(join(composition(join(one,one),join(one,one)),converse(B)),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
( converse(join(composition(join(one,one),join(one,one)),B)) != join(composition(join(one,one),join(one,one)),converse(B))
| converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),join(composition(join(one,one),join(one,one)),converse(B))) )],[refute_0_687,refute_0_738]) ).
cnf(refute_0_740,plain,
converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,join(one,join(B,one))))),
inference(resolve,[$cnf( $equal(converse(join(composition(join(one,one),join(one,one)),B)),join(composition(join(one,one),join(one,one)),converse(B))) )],[refute_0_655,refute_0_739]) ).
cnf(refute_0_741,plain,
join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),C),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(one)),bind(B,$fot(join(one,meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_742,plain,
join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))) = complement(complement(one)),
inference(subst,[],[refute_0_140:[bind(A,$fot(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),bind(B,$fot(complement(one)))]]) ).
cnf(refute_0_743,plain,
join(complement(one),composition(converse(X_19),complement(composition(X_19,one)))) = complement(one),
inference(subst,[],[refute_0_140:[bind(A,$fot(X_19)),bind(B,$fot(one))]]) ).
cnf(refute_0_744,plain,
composition(X_19,one) = X_19,
inference(subst,[],[composition_identity_6:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_745,plain,
( composition(X_19,one) != X_19
| join(complement(one),composition(converse(X_19),complement(composition(X_19,one)))) != complement(one)
| join(complement(one),composition(converse(X_19),complement(X_19))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(X_19),complement(composition(X_19,one)))),complement(one)) ),[0,1,1,0],$fot(X_19)]]) ).
cnf(refute_0_746,plain,
( join(complement(one),composition(converse(X_19),complement(composition(X_19,one)))) != complement(one)
| join(complement(one),composition(converse(X_19),complement(X_19))) = complement(one) ),
inference(resolve,[$cnf( $equal(composition(X_19,one),X_19) )],[refute_0_744,refute_0_745]) ).
cnf(refute_0_747,plain,
join(complement(one),composition(converse(X_19),complement(X_19))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(X_19),complement(composition(X_19,one)))),complement(one)) )],[refute_0_743,refute_0_746]) ).
cnf(refute_0_748,plain,
join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(meet(one,join(one,join(one,join(one,top))))))) = complement(one),
inference(subst,[],[refute_0_747:[bind(X_19,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_749,plain,
complement(one) = join(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),join(one,join(one,top))))),
inference(subst,[],[refute_0_37:[bind(A,$fot(complement(one))),bind(B,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_750,plain,
meet(complement(one),join(one,join(one,top))) = complement(join(complement(complement(one)),complement(join(one,join(one,top))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(complement(one))),bind(B,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_751,plain,
one = join(meet(one,join(one,join(one,one))),complement(join(complement(one),join(one,join(one,one))))),
inference(subst,[],[refute_0_37:[bind(A,$fot(one)),bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_752,plain,
meet(one,join(one,join(one,one))) = complement(join(complement(one),complement(join(one,join(one,one))))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(one)),bind(B,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_753,plain,
join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) = complement(one),
inference(subst,[],[refute_0_747:[bind(X_19,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_754,plain,
( converse(join(one,join(one,one))) != join(one,join(one,one))
| join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))),complement(one)) ),[0,1,0],$fot(join(one,join(one,one)))]]) ).
cnf(refute_0_755,plain,
( join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,one))),join(one,join(one,one))) )],[refute_0_632,refute_0_754]) ).
cnf(refute_0_756,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(join(one,join(one,one))),complement(join(one,join(one,one))))),complement(one)) )],[refute_0_753,refute_0_755]) ).
cnf(refute_0_757,plain,
composition(one,complement(join(one,join(one,one)))) = complement(join(one,join(one,one))),
inference(subst,[],[refute_0_149:[bind(X_14,$fot(complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_758,plain,
composition(X_53,composition(join(one,one),X_55)) = composition(composition(X_53,join(one,one)),X_55),
inference(subst,[],[composition_associativity_5:[bind(A,$fot(X_53)),bind(B,$fot(join(one,one))),bind(C,$fot(X_55))]]) ).
cnf(refute_0_759,plain,
join(X_53,X_53) = composition(X_53,join(one,one)),
inference(subst,[],[refute_0_132:[bind(A,$fot(X_53))]]) ).
cnf(refute_0_760,plain,
( join(X_53,X_53) != composition(X_53,join(one,one))
| composition(X_53,join(one,one)) = join(X_53,X_53) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_53,X_53))),bind(Y,$fot(composition(X_53,join(one,one))))]]) ).
cnf(refute_0_761,plain,
composition(X_53,join(one,one)) = join(X_53,X_53),
inference(resolve,[$cnf( $equal(join(X_53,X_53),composition(X_53,join(one,one))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
( composition(X_53,composition(join(one,one),X_55)) != composition(composition(X_53,join(one,one)),X_55)
| composition(X_53,join(one,one)) != join(X_53,X_53)
| composition(X_53,composition(join(one,one),X_55)) = composition(join(X_53,X_53),X_55) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_53,composition(join(one,one),X_55)),composition(composition(X_53,join(one,one)),X_55)) ),[1,0],$fot(join(X_53,X_53))]]) ).
cnf(refute_0_763,plain,
( composition(X_53,composition(join(one,one),X_55)) != composition(composition(X_53,join(one,one)),X_55)
| composition(X_53,composition(join(one,one),X_55)) = composition(join(X_53,X_53),X_55) ),
inference(resolve,[$cnf( $equal(composition(X_53,join(one,one)),join(X_53,X_53)) )],[refute_0_761,refute_0_762]) ).
cnf(refute_0_764,plain,
composition(X_53,composition(join(one,one),X_55)) = composition(join(X_53,X_53),X_55),
inference(resolve,[$cnf( $equal(composition(X_53,composition(join(one,one),X_55)),composition(composition(X_53,join(one,one)),X_55)) )],[refute_0_758,refute_0_763]) ).
cnf(refute_0_765,plain,
composition(X_53,composition(join(one,one),complement(X_58))) = composition(join(X_53,X_53),complement(X_58)),
inference(subst,[],[refute_0_764:[bind(X_55,$fot(complement(X_58)))]]) ).
cnf(refute_0_766,plain,
composition(join(one,one),complement(X_58)) = complement(X_58),
inference(subst,[],[refute_0_369:[bind(X_20,$fot(X_58))]]) ).
cnf(refute_0_767,plain,
( composition(X_53,composition(join(one,one),complement(X_58))) != composition(join(X_53,X_53),complement(X_58))
| composition(join(one,one),complement(X_58)) != complement(X_58)
| composition(X_53,complement(X_58)) = composition(join(X_53,X_53),complement(X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_53,composition(join(one,one),complement(X_58))),composition(join(X_53,X_53),complement(X_58))) ),[0,1],$fot(complement(X_58))]]) ).
cnf(refute_0_768,plain,
( composition(X_53,composition(join(one,one),complement(X_58))) != composition(join(X_53,X_53),complement(X_58))
| composition(X_53,complement(X_58)) = composition(join(X_53,X_53),complement(X_58)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_58)),complement(X_58)) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
composition(X_53,complement(X_58)) = composition(join(X_53,X_53),complement(X_58)),
inference(resolve,[$cnf( $equal(composition(X_53,composition(join(one,one),complement(X_58))),composition(join(X_53,X_53),complement(X_58))) )],[refute_0_765,refute_0_768]) ).
cnf(refute_0_770,plain,
( composition(X_53,complement(X_58)) != composition(join(X_53,X_53),complement(X_58))
| composition(join(X_53,X_53),complement(X_58)) = composition(X_53,complement(X_58)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(X_53,complement(X_58)))),bind(Y,$fot(composition(join(X_53,X_53),complement(X_58))))]]) ).
cnf(refute_0_771,plain,
composition(join(X_53,X_53),complement(X_58)) = composition(X_53,complement(X_58)),
inference(resolve,[$cnf( $equal(composition(X_53,complement(X_58)),composition(join(X_53,X_53),complement(X_58))) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
composition(join(one,one),complement(join(one,join(one,one)))) = composition(one,complement(join(one,join(one,one)))),
inference(subst,[],[refute_0_771:[bind(X_53,$fot(one)),bind(X_58,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_773,plain,
( composition(join(one,one),complement(join(one,join(one,one)))) != composition(one,complement(join(one,join(one,one))))
| composition(one,complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| composition(join(one,one),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,one),complement(join(one,join(one,one)))))),bind(Y,$fot(composition(one,complement(join(one,join(one,one)))))),bind(Z,$fot(complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_774,plain,
( composition(one,complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| composition(join(one,one),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,join(one,one)))),composition(one,complement(join(one,join(one,one))))) )],[refute_0_772,refute_0_773]) ).
cnf(refute_0_775,plain,
composition(join(one,one),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(one,complement(join(one,join(one,one)))),complement(join(one,join(one,one)))) )],[refute_0_757,refute_0_774]) ).
cnf(refute_0_776,plain,
composition(join(A,join(one,one)),complement(X_58)) = join(composition(A,complement(X_58)),composition(join(one,one),complement(X_58))),
inference(subst,[],[composition_distributivity_7:[bind(B,$fot(join(one,one))),bind(C,$fot(complement(X_58)))]]) ).
cnf(refute_0_777,plain,
( composition(join(A,join(one,one)),complement(X_58)) != join(composition(A,complement(X_58)),composition(join(one,one),complement(X_58)))
| composition(join(one,one),complement(X_58)) != complement(X_58)
| composition(join(A,join(one,one)),complement(X_58)) = join(composition(A,complement(X_58)),complement(X_58)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_58)),join(composition(A,complement(X_58)),composition(join(one,one),complement(X_58)))) ),[1,1],$fot(complement(X_58))]]) ).
cnf(refute_0_778,plain,
( composition(join(A,join(one,one)),complement(X_58)) != join(composition(A,complement(X_58)),composition(join(one,one),complement(X_58)))
| composition(join(A,join(one,one)),complement(X_58)) = join(composition(A,complement(X_58)),complement(X_58)) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_58)),complement(X_58)) )],[refute_0_766,refute_0_777]) ).
cnf(refute_0_779,plain,
composition(join(A,join(one,one)),complement(X_58)) = join(composition(A,complement(X_58)),complement(X_58)),
inference(resolve,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_58)),join(composition(A,complement(X_58)),composition(join(one,one),complement(X_58)))) )],[refute_0_776,refute_0_778]) ).
cnf(refute_0_780,plain,
( composition(join(X_36,one),X_38) != join(X_38,composition(X_36,X_38))
| join(X_38,composition(X_36,X_38)) = composition(join(X_36,one),X_38) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_36,one),X_38))),bind(Y,$fot(join(X_38,composition(X_36,X_38))))]]) ).
cnf(refute_0_781,plain,
join(X_38,composition(X_36,X_38)) = composition(join(X_36,one),X_38),
inference(resolve,[$cnf( $equal(composition(join(X_36,one),X_38),join(X_38,composition(X_36,X_38))) )],[refute_0_83,refute_0_780]) ).
cnf(refute_0_782,plain,
join(complement(X_58),composition(A,complement(X_58))) = composition(join(A,one),complement(X_58)),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(A)),bind(X_38,$fot(complement(X_58)))]]) ).
cnf(refute_0_783,plain,
join(composition(A,complement(X_58)),complement(X_58)) = join(complement(X_58),composition(A,complement(X_58))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_58))),bind(B,$fot(composition(A,complement(X_58))))]]) ).
cnf(refute_0_784,plain,
( join(complement(X_58),composition(A,complement(X_58))) != composition(join(A,one),complement(X_58))
| join(composition(A,complement(X_58)),complement(X_58)) != join(complement(X_58),composition(A,complement(X_58)))
| join(composition(A,complement(X_58)),complement(X_58)) = composition(join(A,one),complement(X_58)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(composition(A,complement(X_58)),complement(X_58)))),bind(Y,$fot(join(complement(X_58),composition(A,complement(X_58))))),bind(Z,$fot(composition(join(A,one),complement(X_58))))]]) ).
cnf(refute_0_785,plain,
( join(complement(X_58),composition(A,complement(X_58))) != composition(join(A,one),complement(X_58))
| join(composition(A,complement(X_58)),complement(X_58)) = composition(join(A,one),complement(X_58)) ),
inference(resolve,[$cnf( $equal(join(composition(A,complement(X_58)),complement(X_58)),join(complement(X_58),composition(A,complement(X_58)))) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
join(composition(A,complement(X_58)),complement(X_58)) = composition(join(A,one),complement(X_58)),
inference(resolve,[$cnf( $equal(join(complement(X_58),composition(A,complement(X_58))),composition(join(A,one),complement(X_58))) )],[refute_0_782,refute_0_785]) ).
cnf(refute_0_787,plain,
( composition(join(A,join(one,one)),complement(X_58)) != join(composition(A,complement(X_58)),complement(X_58))
| join(composition(A,complement(X_58)),complement(X_58)) != composition(join(A,one),complement(X_58))
| composition(join(A,join(one,one)),complement(X_58)) = composition(join(A,one),complement(X_58)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(A,join(one,one)),complement(X_58)),composition(join(A,one),complement(X_58))) ),[0],$fot(join(composition(A,complement(X_58)),complement(X_58)))]]) ).
cnf(refute_0_788,plain,
( composition(join(A,join(one,one)),complement(X_58)) != join(composition(A,complement(X_58)),complement(X_58))
| composition(join(A,join(one,one)),complement(X_58)) = composition(join(A,one),complement(X_58)) ),
inference(resolve,[$cnf( $equal(join(composition(A,complement(X_58)),complement(X_58)),composition(join(A,one),complement(X_58))) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
composition(join(A,join(one,one)),complement(X_58)) = composition(join(A,one),complement(X_58)),
inference(resolve,[$cnf( $equal(composition(join(A,join(one,one)),complement(X_58)),join(composition(A,complement(X_58)),complement(X_58))) )],[refute_0_779,refute_0_788]) ).
cnf(refute_0_790,plain,
composition(join(one,join(one,one)),complement(join(one,join(one,one)))) = composition(join(one,one),complement(join(one,join(one,one)))),
inference(subst,[],[refute_0_789:[bind(A,$fot(one)),bind(X_58,$fot(join(one,join(one,one))))]]) ).
cnf(refute_0_791,plain,
( composition(join(one,join(one,one)),complement(join(one,join(one,one)))) != composition(join(one,one),complement(join(one,join(one,one))))
| composition(join(one,one),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| composition(join(one,join(one,one)),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,join(one,one)),complement(join(one,join(one,one)))))),bind(Y,$fot(composition(join(one,one),complement(join(one,join(one,one)))))),bind(Z,$fot(complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_792,plain,
( composition(join(one,one),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| composition(join(one,join(one,one)),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(join(one,join(one,one)))),composition(join(one,one),complement(join(one,join(one,one))))) )],[refute_0_790,refute_0_791]) ).
cnf(refute_0_793,plain,
composition(join(one,join(one,one)),complement(join(one,join(one,one)))) = complement(join(one,join(one,one))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(join(one,join(one,one)))),complement(join(one,join(one,one)))) )],[refute_0_775,refute_0_792]) ).
cnf(refute_0_794,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),
introduced(tautology,[refl,[$fot(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))))]]) ).
cnf(refute_0_795,plain,
( composition(join(one,join(one,one)),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))) ),[1,1],$fot(complement(join(one,join(one,one))))]]) ).
cnf(refute_0_796,plain,
( composition(join(one,join(one,one)),complement(join(one,join(one,one)))) != complement(join(one,join(one,one)))
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one)))))) )],[refute_0_794,refute_0_795]) ).
cnf(refute_0_797,plain,
join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) = join(complement(one),complement(join(one,join(one,one)))),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,one)),complement(join(one,join(one,one)))),complement(join(one,join(one,one)))) )],[refute_0_793,refute_0_796]) ).
cnf(refute_0_798,plain,
( join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != join(complement(one),complement(join(one,join(one,one))))
| join(complement(one),complement(join(one,join(one,one)))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),complement(one)) ),[0],$fot(join(complement(one),complement(join(one,join(one,one)))))]]) ).
cnf(refute_0_799,plain,
( join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))) != complement(one)
| join(complement(one),complement(join(one,join(one,one)))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),join(complement(one),complement(join(one,join(one,one))))) )],[refute_0_797,refute_0_798]) ).
cnf(refute_0_800,plain,
join(complement(one),complement(join(one,join(one,one)))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(join(one,join(one,one)),complement(join(one,join(one,one))))),complement(one)) )],[refute_0_756,refute_0_799]) ).
cnf(refute_0_801,plain,
( join(complement(one),complement(join(one,join(one,one)))) != complement(one)
| meet(one,join(one,join(one,one))) != complement(join(complement(one),complement(join(one,join(one,one)))))
| meet(one,join(one,join(one,one))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(join(complement(one),complement(join(one,join(one,one)))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_802,plain,
( meet(one,join(one,join(one,one))) != complement(join(complement(one),complement(join(one,join(one,one)))))
| meet(one,join(one,join(one,one))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(one,join(one,one)))),complement(one)) )],[refute_0_800,refute_0_801]) ).
cnf(refute_0_803,plain,
meet(one,join(one,join(one,one))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(join(complement(one),complement(join(one,join(one,one)))))) )],[refute_0_752,refute_0_802]) ).
cnf(refute_0_804,plain,
( meet(one,join(one,join(one,one))) != complement(complement(one))
| one != join(meet(one,join(one,join(one,one))),complement(join(complement(one),join(one,join(one,one)))))
| one = join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(meet(one,join(one,join(one,one))),complement(join(complement(one),join(one,join(one,one)))))) ),[1,0],$fot(complement(complement(one)))]]) ).
cnf(refute_0_805,plain,
( one != join(meet(one,join(one,join(one,one))),complement(join(complement(one),join(one,join(one,one)))))
| one = join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) ),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,one))),complement(complement(one))) )],[refute_0_803,refute_0_804]) ).
cnf(refute_0_806,plain,
one = join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))),
inference(resolve,[$cnf( $equal(one,join(meet(one,join(one,join(one,one))),complement(join(complement(one),join(one,join(one,one)))))) )],[refute_0_751,refute_0_805]) ).
cnf(refute_0_807,plain,
join(one,join(top,one)) = join(one,join(one,top)),
inference(subst,[],[refute_0_471:[bind(X_42,$fot(one)),bind(X_43,$fot(top)),bind(X_44,$fot(one))]]) ).
cnf(refute_0_808,plain,
join(X_43,X_42) = join(X_42,X_43),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_43)),bind(B,$fot(X_42))]]) ).
cnf(refute_0_809,plain,
( join(X_43,X_42) != join(X_42,X_43)
| join(X_42,X_43) = join(X_43,X_42) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_43,X_42))),bind(Y,$fot(join(X_42,X_43)))]]) ).
cnf(refute_0_810,plain,
join(X_42,X_43) = join(X_43,X_42),
inference(resolve,[$cnf( $equal(join(X_43,X_42),join(X_42,X_43)) )],[refute_0_808,refute_0_809]) ).
cnf(refute_0_811,plain,
( join(X_42,X_43) != join(X_43,X_42)
| join(X_42,join(X_43,X_44)) != join(join(X_42,X_43),X_44)
| join(X_42,join(X_43,X_44)) = join(join(X_43,X_42),X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(join(X_42,X_43),X_44)) ),[1,0],$fot(join(X_43,X_42))]]) ).
cnf(refute_0_812,plain,
( join(X_42,join(X_43,X_44)) != join(join(X_42,X_43),X_44)
| join(X_42,join(X_43,X_44)) = join(join(X_43,X_42),X_44) ),
inference(resolve,[$cnf( $equal(join(X_42,X_43),join(X_43,X_42)) )],[refute_0_810,refute_0_811]) ).
cnf(refute_0_813,plain,
join(X_42,join(X_43,X_44)) = join(join(X_43,X_42),X_44),
inference(resolve,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(join(X_42,X_43),X_44)) )],[refute_0_459,refute_0_812]) ).
cnf(refute_0_814,plain,
join(join(X_43,X_42),X_44) = join(X_43,join(X_42,X_44)),
inference(subst,[],[refute_0_417:[bind(A,$fot(X_43)),bind(B,$fot(X_42)),bind(C,$fot(X_44))]]) ).
cnf(refute_0_815,plain,
( join(X_42,join(X_43,X_44)) != join(join(X_43,X_42),X_44)
| join(join(X_43,X_42),X_44) != join(X_43,join(X_42,X_44))
| join(X_42,join(X_43,X_44)) = join(X_43,join(X_42,X_44)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_42,join(X_43,X_44)),join(X_43,join(X_42,X_44))) ),[0],$fot(join(join(X_43,X_42),X_44))]]) ).
cnf(refute_0_816,plain,
( join(X_42,join(X_43,X_44)) != join(join(X_43,X_42),X_44)
| join(X_42,join(X_43,X_44)) = join(X_43,join(X_42,X_44)) ),
inference(resolve,[$cnf( $equal(join(join(X_43,X_42),X_44),join(X_43,join(X_42,X_44))) )],[refute_0_814,refute_0_815]) ).
cnf(refute_0_817,plain,
join(X_42,join(X_43,X_44)) = join(X_43,join(X_42,X_44)),
inference(resolve,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(join(X_43,X_42),X_44)) )],[refute_0_813,refute_0_816]) ).
cnf(refute_0_818,plain,
( join(X_42,join(X_43,X_44)) != join(X_43,join(X_42,X_44))
| join(X_43,join(X_42,X_44)) = join(X_42,join(X_43,X_44)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_42,join(X_43,X_44)))),bind(Y,$fot(join(X_43,join(X_42,X_44))))]]) ).
cnf(refute_0_819,plain,
join(X_43,join(X_42,X_44)) = join(X_42,join(X_43,X_44)),
inference(resolve,[$cnf( $equal(join(X_42,join(X_43,X_44)),join(X_43,join(X_42,X_44))) )],[refute_0_817,refute_0_818]) ).
cnf(refute_0_820,plain,
join(top,join(one,one)) = join(one,join(top,one)),
inference(subst,[],[refute_0_819:[bind(X_42,$fot(one)),bind(X_43,$fot(top)),bind(X_44,$fot(one))]]) ).
cnf(refute_0_821,plain,
( join(one,join(top,one)) != join(one,join(one,top))
| join(top,join(one,one)) != join(one,join(top,one))
| join(top,join(one,one)) = join(one,join(one,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(top,join(one,one)))),bind(Y,$fot(join(one,join(top,one)))),bind(Z,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_822,plain,
( join(one,join(top,one)) != join(one,join(one,top))
| join(top,join(one,one)) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(join(top,join(one,one)),join(one,join(top,one))) )],[refute_0_820,refute_0_821]) ).
cnf(refute_0_823,plain,
join(top,join(one,one)) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(join(one,join(top,one)),join(one,join(one,top))) )],[refute_0_807,refute_0_822]) ).
cnf(refute_0_824,plain,
join(X_42,join(complement(X_42),X_44)) = join(join(X_42,complement(X_42)),X_44),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_42)),bind(B,$fot(complement(X_42))),bind(C,$fot(X_44))]]) ).
cnf(refute_0_825,plain,
top = join(X_42,complement(X_42)),
inference(subst,[],[def_top_12:[bind(A,$fot(X_42))]]) ).
cnf(refute_0_826,plain,
( top != join(X_42,complement(X_42))
| join(X_42,complement(X_42)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(X_42,complement(X_42))))]]) ).
cnf(refute_0_827,plain,
join(X_42,complement(X_42)) = top,
inference(resolve,[$cnf( $equal(top,join(X_42,complement(X_42))) )],[refute_0_825,refute_0_826]) ).
cnf(refute_0_828,plain,
( join(X_42,complement(X_42)) != top
| join(X_42,join(complement(X_42),X_44)) != join(join(X_42,complement(X_42)),X_44)
| join(X_42,join(complement(X_42),X_44)) = join(top,X_44) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_42,join(complement(X_42),X_44)),join(join(X_42,complement(X_42)),X_44)) ),[1,0],$fot(top)]]) ).
cnf(refute_0_829,plain,
( join(X_42,join(complement(X_42),X_44)) != join(join(X_42,complement(X_42)),X_44)
| join(X_42,join(complement(X_42),X_44)) = join(top,X_44) ),
inference(resolve,[$cnf( $equal(join(X_42,complement(X_42)),top) )],[refute_0_827,refute_0_828]) ).
cnf(refute_0_830,plain,
join(X_42,join(complement(X_42),X_44)) = join(top,X_44),
inference(resolve,[$cnf( $equal(join(X_42,join(complement(X_42),X_44)),join(join(X_42,complement(X_42)),X_44)) )],[refute_0_824,refute_0_829]) ).
cnf(refute_0_831,plain,
join(one,join(complement(one),join(one,one))) = join(top,join(one,one)),
inference(subst,[],[refute_0_830:[bind(X_42,$fot(one)),bind(X_44,$fot(join(one,one)))]]) ).
cnf(refute_0_832,plain,
( join(one,join(complement(one),join(one,one))) != join(top,join(one,one))
| join(top,join(one,one)) != join(one,join(one,top))
| join(one,join(complement(one),join(one,one))) = join(one,join(one,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,join(complement(one),join(one,one))))),bind(Y,$fot(join(top,join(one,one)))),bind(Z,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_833,plain,
( join(top,join(one,one)) != join(one,join(one,top))
| join(one,join(complement(one),join(one,one))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(join(one,join(complement(one),join(one,one))),join(top,join(one,one))) )],[refute_0_831,refute_0_832]) ).
cnf(refute_0_834,plain,
join(one,join(complement(one),join(one,one))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(join(top,join(one,one)),join(one,join(one,top))) )],[refute_0_823,refute_0_833]) ).
cnf(refute_0_835,plain,
join(complement(one),join(one,join(one,one))) = join(one,join(complement(one),join(one,one))),
inference(subst,[],[refute_0_819:[bind(X_42,$fot(one)),bind(X_43,$fot(complement(one))),bind(X_44,$fot(join(one,one)))]]) ).
cnf(refute_0_836,plain,
( join(complement(one),join(one,join(one,one))) != join(one,join(complement(one),join(one,one)))
| join(one,join(complement(one),join(one,one))) != join(one,join(one,top))
| join(complement(one),join(one,join(one,one))) = join(one,join(one,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(one),join(one,join(one,one))))),bind(Y,$fot(join(one,join(complement(one),join(one,one))))),bind(Z,$fot(join(one,join(one,top))))]]) ).
cnf(refute_0_837,plain,
( join(one,join(complement(one),join(one,one))) != join(one,join(one,top))
| join(complement(one),join(one,join(one,one))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(join(complement(one),join(one,join(one,one))),join(one,join(complement(one),join(one,one)))) )],[refute_0_835,refute_0_836]) ).
cnf(refute_0_838,plain,
join(complement(one),join(one,join(one,one))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(join(one,join(complement(one),join(one,one))),join(one,join(one,top))) )],[refute_0_834,refute_0_837]) ).
cnf(refute_0_839,plain,
complement(join(complement(one),join(one,join(one,one)))) = complement(join(complement(one),join(one,join(one,one)))),
introduced(tautology,[refl,[$fot(complement(join(complement(one),join(one,join(one,one)))))]]) ).
cnf(refute_0_840,plain,
( complement(join(complement(one),join(one,join(one,one)))) != complement(join(complement(one),join(one,join(one,one))))
| join(complement(one),join(one,join(one,one))) != join(one,join(one,top))
| complement(join(complement(one),join(one,join(one,one)))) = complement(join(one,join(one,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(one),join(one,join(one,one)))),complement(join(complement(one),join(one,join(one,one))))) ),[1,0],$fot(join(one,join(one,top)))]]) ).
cnf(refute_0_841,plain,
( join(complement(one),join(one,join(one,one))) != join(one,join(one,top))
| complement(join(complement(one),join(one,join(one,one)))) = complement(join(one,join(one,top))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(one),join(one,join(one,one)))),complement(join(complement(one),join(one,join(one,one))))) )],[refute_0_839,refute_0_840]) ).
cnf(refute_0_842,plain,
complement(join(complement(one),join(one,join(one,one)))) = complement(join(one,join(one,top))),
inference(resolve,[$cnf( $equal(join(complement(one),join(one,join(one,one))),join(one,join(one,top))) )],[refute_0_838,refute_0_841]) ).
cnf(refute_0_843,plain,
join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) = join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))),
introduced(tautology,[refl,[$fot(join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))))]]) ).
cnf(refute_0_844,plain,
( complement(join(complement(one),join(one,join(one,one)))) != complement(join(one,join(one,top)))
| join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) != join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))
| join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) = join(complement(complement(one)),complement(join(one,join(one,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))),join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))) ),[1,1],$fot(complement(join(one,join(one,top))))]]) ).
cnf(refute_0_845,plain,
( complement(join(complement(one),join(one,join(one,one)))) != complement(join(one,join(one,top)))
| join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) = join(complement(complement(one)),complement(join(one,join(one,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))),join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))) )],[refute_0_843,refute_0_844]) ).
cnf(refute_0_846,plain,
join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) = join(complement(complement(one)),complement(join(one,join(one,top)))),
inference(resolve,[$cnf( $equal(complement(join(complement(one),join(one,join(one,one)))),complement(join(one,join(one,top)))) )],[refute_0_842,refute_0_845]) ).
cnf(refute_0_847,plain,
( join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))) != join(complement(complement(one)),complement(join(one,join(one,top))))
| one != join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))
| one = join(complement(complement(one)),complement(join(one,join(one,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(one,join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))) ),[1],$fot(join(complement(complement(one)),complement(join(one,join(one,top)))))]]) ).
cnf(refute_0_848,plain,
( one != join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))
| one = join(complement(complement(one)),complement(join(one,join(one,top)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one))))),join(complement(complement(one)),complement(join(one,join(one,top))))) )],[refute_0_846,refute_0_847]) ).
cnf(refute_0_849,plain,
one = join(complement(complement(one)),complement(join(one,join(one,top)))),
inference(resolve,[$cnf( $equal(one,join(complement(complement(one)),complement(join(complement(one),join(one,join(one,one)))))) )],[refute_0_806,refute_0_848]) ).
cnf(refute_0_850,plain,
( one != join(complement(complement(one)),complement(join(one,join(one,top))))
| join(complement(complement(one)),complement(join(one,join(one,top)))) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(join(complement(complement(one)),complement(join(one,join(one,top))))))]]) ).
cnf(refute_0_851,plain,
join(complement(complement(one)),complement(join(one,join(one,top)))) = one,
inference(resolve,[$cnf( $equal(one,join(complement(complement(one)),complement(join(one,join(one,top))))) )],[refute_0_849,refute_0_850]) ).
cnf(refute_0_852,plain,
( join(complement(complement(one)),complement(join(one,join(one,top)))) != one
| meet(complement(one),join(one,join(one,top))) != complement(join(complement(complement(one)),complement(join(one,join(one,top)))))
| meet(complement(one),join(one,join(one,top))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),complement(join(one,join(one,top)))))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_853,plain,
( meet(complement(one),join(one,join(one,top))) != complement(join(complement(complement(one)),complement(join(one,join(one,top)))))
| meet(complement(one),join(one,join(one,top))) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),complement(join(one,join(one,top)))),one) )],[refute_0_851,refute_0_852]) ).
cnf(refute_0_854,plain,
meet(complement(one),join(one,join(one,top))) = complement(one),
inference(resolve,[$cnf( $equal(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),complement(join(one,join(one,top)))))) )],[refute_0_750,refute_0_853]) ).
cnf(refute_0_855,plain,
( complement(one) != join(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),join(one,join(one,top)))))
| meet(complement(one),join(one,join(one,top))) != complement(one)
| complement(one) = join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(one),join(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),join(one,join(one,top)))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_856,plain,
( complement(one) != join(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),join(one,join(one,top)))))
| complement(one) = join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(meet(complement(one),join(one,join(one,top))),complement(one)) )],[refute_0_854,refute_0_855]) ).
cnf(refute_0_857,plain,
complement(one) = join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(complement(one),join(meet(complement(one),join(one,join(one,top))),complement(join(complement(complement(one)),join(one,join(one,top)))))) )],[refute_0_749,refute_0_856]) ).
cnf(refute_0_858,plain,
join(one,join(complement(complement(one)),top)) = join(one,join(top,complement(complement(one)))),
inference(subst,[],[refute_0_471:[bind(X_42,$fot(one)),bind(X_43,$fot(complement(complement(one)))),bind(X_44,$fot(top))]]) ).
cnf(refute_0_859,plain,
join(complement(complement(one)),join(one,top)) = join(one,join(complement(complement(one)),top)),
inference(subst,[],[refute_0_819:[bind(X_42,$fot(one)),bind(X_43,$fot(complement(complement(one)))),bind(X_44,$fot(top))]]) ).
cnf(refute_0_860,plain,
( join(complement(complement(one)),join(one,top)) != join(one,join(complement(complement(one)),top))
| join(one,join(complement(complement(one)),top)) != join(one,join(top,complement(complement(one))))
| join(complement(complement(one)),join(one,top)) = join(one,join(top,complement(complement(one)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(one)),join(one,top)))),bind(Y,$fot(join(one,join(complement(complement(one)),top)))),bind(Z,$fot(join(one,join(top,complement(complement(one))))))]]) ).
cnf(refute_0_861,plain,
( join(one,join(complement(complement(one)),top)) != join(one,join(top,complement(complement(one))))
| join(complement(complement(one)),join(one,top)) = join(one,join(top,complement(complement(one)))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),join(one,top)),join(one,join(complement(complement(one)),top))) )],[refute_0_859,refute_0_860]) ).
cnf(refute_0_862,plain,
join(complement(complement(one)),join(one,top)) = join(one,join(top,complement(complement(one)))),
inference(resolve,[$cnf( $equal(join(one,join(complement(complement(one)),top)),join(one,join(top,complement(complement(one))))) )],[refute_0_858,refute_0_861]) ).
cnf(refute_0_863,plain,
join(one,join(complement(complement(one)),join(one,top))) = join(one,join(complement(complement(one)),join(one,top))),
introduced(tautology,[refl,[$fot(join(one,join(complement(complement(one)),join(one,top))))]]) ).
cnf(refute_0_864,plain,
( join(complement(complement(one)),join(one,top)) != join(one,join(top,complement(complement(one))))
| join(one,join(complement(complement(one)),join(one,top))) != join(one,join(complement(complement(one)),join(one,top)))
| join(one,join(complement(complement(one)),join(one,top))) = join(one,join(one,join(top,complement(complement(one))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(complement(complement(one)),join(one,top))),join(one,join(complement(complement(one)),join(one,top)))) ),[1,1],$fot(join(one,join(top,complement(complement(one)))))]]) ).
cnf(refute_0_865,plain,
( join(complement(complement(one)),join(one,top)) != join(one,join(top,complement(complement(one))))
| join(one,join(complement(complement(one)),join(one,top))) = join(one,join(one,join(top,complement(complement(one))))) ),
inference(resolve,[$cnf( $equal(join(one,join(complement(complement(one)),join(one,top))),join(one,join(complement(complement(one)),join(one,top)))) )],[refute_0_863,refute_0_864]) ).
cnf(refute_0_866,plain,
join(one,join(complement(complement(one)),join(one,top))) = join(one,join(one,join(top,complement(complement(one))))),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),join(one,top)),join(one,join(top,complement(complement(one))))) )],[refute_0_862,refute_0_865]) ).
cnf(refute_0_867,plain,
join(complement(complement(one)),join(one,join(one,top))) = join(one,join(complement(complement(one)),join(one,top))),
inference(subst,[],[refute_0_819:[bind(X_42,$fot(one)),bind(X_43,$fot(complement(complement(one)))),bind(X_44,$fot(join(one,top)))]]) ).
cnf(refute_0_868,plain,
( join(complement(complement(one)),join(one,join(one,top))) != join(one,join(complement(complement(one)),join(one,top)))
| join(one,join(complement(complement(one)),join(one,top))) != join(one,join(one,join(top,complement(complement(one)))))
| join(complement(complement(one)),join(one,join(one,top))) = join(one,join(one,join(top,complement(complement(one))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(one)),join(one,join(one,top))))),bind(Y,$fot(join(one,join(complement(complement(one)),join(one,top))))),bind(Z,$fot(join(one,join(one,join(top,complement(complement(one)))))))]]) ).
cnf(refute_0_869,plain,
( join(one,join(complement(complement(one)),join(one,top))) != join(one,join(one,join(top,complement(complement(one)))))
| join(complement(complement(one)),join(one,join(one,top))) = join(one,join(one,join(top,complement(complement(one))))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),join(one,join(one,top))),join(one,join(complement(complement(one)),join(one,top)))) )],[refute_0_867,refute_0_868]) ).
cnf(refute_0_870,plain,
join(complement(complement(one)),join(one,join(one,top))) = join(one,join(one,join(top,complement(complement(one))))),
inference(resolve,[$cnf( $equal(join(one,join(complement(complement(one)),join(one,top))),join(one,join(one,join(top,complement(complement(one)))))) )],[refute_0_866,refute_0_869]) ).
cnf(refute_0_871,plain,
complement(join(complement(complement(one)),join(one,join(one,top)))) = complement(join(complement(complement(one)),join(one,join(one,top)))),
introduced(tautology,[refl,[$fot(complement(join(complement(complement(one)),join(one,join(one,top)))))]]) ).
cnf(refute_0_872,plain,
( complement(join(complement(complement(one)),join(one,join(one,top)))) != complement(join(complement(complement(one)),join(one,join(one,top))))
| join(complement(complement(one)),join(one,join(one,top))) != join(one,join(one,join(top,complement(complement(one)))))
| complement(join(complement(complement(one)),join(one,join(one,top)))) = complement(join(one,join(one,join(top,complement(complement(one)))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(complement(one)),join(one,join(one,top)))),complement(join(complement(complement(one)),join(one,join(one,top))))) ),[1,0],$fot(join(one,join(one,join(top,complement(complement(one))))))]]) ).
cnf(refute_0_873,plain,
( join(complement(complement(one)),join(one,join(one,top))) != join(one,join(one,join(top,complement(complement(one)))))
| complement(join(complement(complement(one)),join(one,join(one,top)))) = complement(join(one,join(one,join(top,complement(complement(one)))))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(one)),join(one,join(one,top)))),complement(join(complement(complement(one)),join(one,join(one,top))))) )],[refute_0_871,refute_0_872]) ).
cnf(refute_0_874,plain,
complement(join(complement(complement(one)),join(one,join(one,top)))) = complement(join(one,join(one,join(top,complement(complement(one)))))),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),join(one,join(one,top))),join(one,join(one,join(top,complement(complement(one)))))) )],[refute_0_870,refute_0_873]) ).
cnf(refute_0_875,plain,
join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) = join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))),
introduced(tautology,[refl,[$fot(join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))))]]) ).
cnf(refute_0_876,plain,
( complement(join(complement(complement(one)),join(one,join(one,top)))) != complement(join(one,join(one,join(top,complement(complement(one))))))
| join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) != join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))
| join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))),join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))) ),[1,1],$fot(complement(join(one,join(one,join(top,complement(complement(one)))))))]]) ).
cnf(refute_0_877,plain,
( complement(join(complement(complement(one)),join(one,join(one,top)))) != complement(join(one,join(one,join(top,complement(complement(one))))))
| join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))),join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))) )],[refute_0_875,refute_0_876]) ).
cnf(refute_0_878,plain,
join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))),
inference(resolve,[$cnf( $equal(complement(join(complement(complement(one)),join(one,join(one,top)))),complement(join(one,join(one,join(top,complement(complement(one))))))) )],[refute_0_874,refute_0_877]) ).
cnf(refute_0_879,plain,
( complement(one) != join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))
| join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))) != join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))
| complement(one) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(one),join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))) ),[0],$fot(join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))))]]) ).
cnf(refute_0_880,plain,
( complement(one) != join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))
| complement(one) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top))))),join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))) )],[refute_0_878,refute_0_879]) ).
cnf(refute_0_881,plain,
complement(one) = join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))),
inference(resolve,[$cnf( $equal(complement(one),join(complement(one),complement(join(complement(complement(one)),join(one,join(one,top)))))) )],[refute_0_857,refute_0_880]) ).
cnf(refute_0_882,plain,
join(top,one) = join(one,top),
inference(subst,[],[refute_0_4:[bind(A,$fot(one)),bind(B,$fot(top))]]) ).
cnf(refute_0_883,plain,
join(top,join(zero,complement(complement(X_72)))) = join(top,complement(complement(X_72))),
inference(subst,[],[refute_0_328:[bind(X_44,$fot(complement(complement(X_72))))]]) ).
cnf(refute_0_884,plain,
( join(top,join(zero,complement(complement(X_72)))) != join(top,complement(complement(X_72)))
| join(zero,complement(complement(X_72))) != X_72
| join(top,X_72) = join(top,complement(complement(X_72))) ),
introduced(tautology,[equality,[$cnf( $equal(join(top,join(zero,complement(complement(X_72)))),join(top,complement(complement(X_72)))) ),[0,1],$fot(X_72)]]) ).
cnf(refute_0_885,plain,
( join(top,join(zero,complement(complement(X_72)))) != join(top,complement(complement(X_72)))
| join(top,X_72) = join(top,complement(complement(X_72))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_72))),X_72) )],[refute_0_239,refute_0_884]) ).
cnf(refute_0_886,plain,
join(top,X_72) = join(top,complement(complement(X_72))),
inference(resolve,[$cnf( $equal(join(top,join(zero,complement(complement(X_72)))),join(top,complement(complement(X_72)))) )],[refute_0_883,refute_0_885]) ).
cnf(refute_0_887,plain,
( join(top,X_72) != join(top,complement(complement(X_72)))
| join(top,complement(complement(X_72))) = join(top,X_72) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(top,X_72))),bind(Y,$fot(join(top,complement(complement(X_72)))))]]) ).
cnf(refute_0_888,plain,
join(top,complement(complement(X_72))) = join(top,X_72),
inference(resolve,[$cnf( $equal(join(top,X_72),join(top,complement(complement(X_72)))) )],[refute_0_886,refute_0_887]) ).
cnf(refute_0_889,plain,
join(top,complement(complement(one))) = join(top,one),
inference(subst,[],[refute_0_888:[bind(X_72,$fot(one))]]) ).
cnf(refute_0_890,plain,
( join(top,complement(complement(one))) != join(top,one)
| join(top,one) != join(one,top)
| join(top,complement(complement(one))) = join(one,top) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(top,complement(complement(one))))),bind(Y,$fot(join(top,one))),bind(Z,$fot(join(one,top)))]]) ).
cnf(refute_0_891,plain,
( join(top,one) != join(one,top)
| join(top,complement(complement(one))) = join(one,top) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(one))),join(top,one)) )],[refute_0_889,refute_0_890]) ).
cnf(refute_0_892,plain,
join(top,complement(complement(one))) = join(one,top),
inference(resolve,[$cnf( $equal(join(top,one),join(one,top)) )],[refute_0_882,refute_0_891]) ).
cnf(refute_0_893,plain,
join(one,join(top,complement(complement(one)))) = join(one,join(top,complement(complement(one)))),
introduced(tautology,[refl,[$fot(join(one,join(top,complement(complement(one)))))]]) ).
cnf(refute_0_894,plain,
( join(one,join(top,complement(complement(one)))) != join(one,join(top,complement(complement(one))))
| join(top,complement(complement(one))) != join(one,top)
| join(one,join(top,complement(complement(one)))) = join(one,join(one,top)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(top,complement(complement(one)))),join(one,join(top,complement(complement(one))))) ),[1,1],$fot(join(one,top))]]) ).
cnf(refute_0_895,plain,
( join(top,complement(complement(one))) != join(one,top)
| join(one,join(top,complement(complement(one)))) = join(one,join(one,top)) ),
inference(resolve,[$cnf( $equal(join(one,join(top,complement(complement(one)))),join(one,join(top,complement(complement(one))))) )],[refute_0_893,refute_0_894]) ).
cnf(refute_0_896,plain,
join(one,join(top,complement(complement(one)))) = join(one,join(one,top)),
inference(resolve,[$cnf( $equal(join(top,complement(complement(one))),join(one,top)) )],[refute_0_892,refute_0_895]) ).
cnf(refute_0_897,plain,
join(one,join(one,join(top,complement(complement(one))))) = join(one,join(one,join(top,complement(complement(one))))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(top,complement(complement(one))))))]]) ).
cnf(refute_0_898,plain,
( join(one,join(one,join(top,complement(complement(one))))) != join(one,join(one,join(top,complement(complement(one)))))
| join(one,join(top,complement(complement(one)))) != join(one,join(one,top))
| join(one,join(one,join(top,complement(complement(one))))) = join(one,join(one,join(one,top))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(top,complement(complement(one))))),join(one,join(one,join(top,complement(complement(one)))))) ),[1,1],$fot(join(one,join(one,top)))]]) ).
cnf(refute_0_899,plain,
( join(one,join(top,complement(complement(one)))) != join(one,join(one,top))
| join(one,join(one,join(top,complement(complement(one))))) = join(one,join(one,join(one,top))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(top,complement(complement(one))))),join(one,join(one,join(top,complement(complement(one)))))) )],[refute_0_897,refute_0_898]) ).
cnf(refute_0_900,plain,
join(one,join(one,join(top,complement(complement(one))))) = join(one,join(one,join(one,top))),
inference(resolve,[$cnf( $equal(join(one,join(top,complement(complement(one)))),join(one,join(one,top))) )],[refute_0_896,refute_0_899]) ).
cnf(refute_0_901,plain,
meet(one,join(one,join(one,join(top,complement(complement(one)))))) = meet(one,join(one,join(one,join(top,complement(complement(one)))))),
introduced(tautology,[refl,[$fot(meet(one,join(one,join(one,join(top,complement(complement(one)))))))]]) ).
cnf(refute_0_902,plain,
( join(one,join(one,join(top,complement(complement(one))))) != join(one,join(one,join(one,top)))
| meet(one,join(one,join(one,join(top,complement(complement(one)))))) != meet(one,join(one,join(one,join(top,complement(complement(one))))))
| meet(one,join(one,join(one,join(top,complement(complement(one)))))) = meet(one,join(one,join(one,join(one,top)))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,join(top,complement(complement(one)))))),meet(one,join(one,join(one,join(top,complement(complement(one))))))) ),[1,1],$fot(join(one,join(one,join(one,top))))]]) ).
cnf(refute_0_903,plain,
( join(one,join(one,join(top,complement(complement(one))))) != join(one,join(one,join(one,top)))
| meet(one,join(one,join(one,join(top,complement(complement(one)))))) = meet(one,join(one,join(one,join(one,top)))) ),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,join(top,complement(complement(one)))))),meet(one,join(one,join(one,join(top,complement(complement(one))))))) )],[refute_0_901,refute_0_902]) ).
cnf(refute_0_904,plain,
meet(one,join(one,join(one,join(top,complement(complement(one)))))) = meet(one,join(one,join(one,join(one,top)))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(top,complement(complement(one))))),join(one,join(one,join(one,top)))) )],[refute_0_900,refute_0_903]) ).
cnf(refute_0_905,plain,
complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))),
introduced(tautology,[refl,[$fot(complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))))]]) ).
cnf(refute_0_906,plain,
( complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) != complement(meet(one,join(one,join(one,join(top,complement(complement(one)))))))
| meet(one,join(one,join(one,join(top,complement(complement(one)))))) != meet(one,join(one,join(one,join(one,top))))
| complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))),complement(meet(one,join(one,join(one,join(top,complement(complement(one)))))))) ),[1,0],$fot(meet(one,join(one,join(one,join(one,top)))))]]) ).
cnf(refute_0_907,plain,
( meet(one,join(one,join(one,join(top,complement(complement(one)))))) != meet(one,join(one,join(one,join(one,top))))
| complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))),complement(meet(one,join(one,join(one,join(top,complement(complement(one)))))))) )],[refute_0_905,refute_0_906]) ).
cnf(refute_0_908,plain,
complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,join(top,complement(complement(one)))))),meet(one,join(one,join(one,join(one,top))))) )],[refute_0_904,refute_0_907]) ).
cnf(refute_0_909,plain,
join(complement(A),complement(B)) = join(zero,complement(complement(join(complement(A),complement(B))))),
inference(subst,[],[refute_0_190:[bind(X_70,$fot(join(complement(A),complement(B))))]]) ).
cnf(refute_0_910,plain,
( complement(join(complement(A),complement(B))) != meet(A,B)
| join(complement(A),complement(B)) != join(zero,complement(complement(join(complement(A),complement(B)))))
| join(complement(A),complement(B)) = join(zero,complement(meet(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) ),[1,1,0],$fot(meet(A,B))]]) ).
cnf(refute_0_911,plain,
( join(complement(A),complement(B)) != join(zero,complement(complement(join(complement(A),complement(B)))))
| join(complement(A),complement(B)) = join(zero,complement(meet(A,B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_27,refute_0_910]) ).
cnf(refute_0_912,plain,
join(complement(A),complement(B)) = join(zero,complement(meet(A,B))),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(complement(join(complement(A),complement(B)))))) )],[refute_0_909,refute_0_911]) ).
cnf(refute_0_913,plain,
join(zero,complement(meet(A,B))) = complement(meet(A,B)),
inference(subst,[],[refute_0_245:[bind(X_72,$fot(complement(meet(A,B))))]]) ).
cnf(refute_0_914,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| join(zero,complement(meet(A,B))) != complement(meet(A,B))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(complement(A),complement(B)),complement(meet(A,B))) ),[0],$fot(join(zero,complement(meet(A,B))))]]) ).
cnf(refute_0_915,plain,
( join(complement(A),complement(B)) != join(zero,complement(meet(A,B)))
| join(complement(A),complement(B)) = complement(meet(A,B)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(meet(A,B))),complement(meet(A,B))) )],[refute_0_913,refute_0_914]) ).
cnf(refute_0_916,plain,
join(complement(A),complement(B)) = complement(meet(A,B)),
inference(resolve,[$cnf( $equal(join(complement(A),complement(B)),join(zero,complement(meet(A,B)))) )],[refute_0_912,refute_0_915]) ).
cnf(refute_0_917,plain,
join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))),
inference(subst,[],[refute_0_916:[bind(A,$fot(one)),bind(B,$fot(join(one,join(one,join(top,complement(complement(one)))))))]]) ).
cnf(refute_0_918,plain,
( complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) != complement(meet(one,join(one,join(one,join(one,top)))))
| join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) != complement(meet(one,join(one,join(one,join(top,complement(complement(one)))))))
| join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))))),bind(Y,$fot(complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))))),bind(Z,$fot(complement(meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_919,plain,
( complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))) != complement(meet(one,join(one,join(one,join(one,top)))))
| join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))),complement(meet(one,join(one,join(one,join(top,complement(complement(one)))))))) )],[refute_0_917,refute_0_918]) ).
cnf(refute_0_920,plain,
join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) = complement(meet(one,join(one,join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(complement(meet(one,join(one,join(one,join(top,complement(complement(one))))))),complement(meet(one,join(one,join(one,join(one,top)))))) )],[refute_0_908,refute_0_919]) ).
cnf(refute_0_921,plain,
( complement(one) != join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))
| join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))) != complement(meet(one,join(one,join(one,join(one,top)))))
| complement(one) = complement(meet(one,join(one,join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(one),complement(meet(one,join(one,join(one,join(one,top)))))) ),[0],$fot(join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))))]]) ).
cnf(refute_0_922,plain,
( complement(one) != join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))
| complement(one) = complement(meet(one,join(one,join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(join(complement(one),complement(join(one,join(one,join(top,complement(complement(one))))))),complement(meet(one,join(one,join(one,join(one,top)))))) )],[refute_0_920,refute_0_921]) ).
cnf(refute_0_923,plain,
complement(one) = complement(meet(one,join(one,join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(complement(one),join(complement(one),complement(join(one,join(one,join(top,complement(complement(one)))))))) )],[refute_0_881,refute_0_922]) ).
cnf(refute_0_924,plain,
( complement(one) != complement(meet(one,join(one,join(one,join(one,top)))))
| complement(meet(one,join(one,join(one,join(one,top))))) = complement(one) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(one))),bind(Y,$fot(complement(meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_925,plain,
complement(meet(one,join(one,join(one,join(one,top))))) = complement(one),
inference(resolve,[$cnf( $equal(complement(one),complement(meet(one,join(one,join(one,join(one,top)))))) )],[refute_0_923,refute_0_924]) ).
cnf(refute_0_926,plain,
( complement(meet(one,join(one,join(one,join(one,top))))) != complement(one)
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(meet(one,join(one,join(one,join(one,top))))))) != complement(one)
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(meet(one,join(one,join(one,join(one,top))))))),complement(one)) ),[0,1,1],$fot(complement(one))]]) ).
cnf(refute_0_927,plain,
( join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(meet(one,join(one,join(one,join(one,top))))))) != complement(one)
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = complement(one) ),
inference(resolve,[$cnf( $equal(complement(meet(one,join(one,join(one,join(one,top))))),complement(one)) )],[refute_0_925,refute_0_926]) ).
cnf(refute_0_928,plain,
join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(meet(one,join(one,join(one,join(one,top))))))),complement(one)) )],[refute_0_748,refute_0_927]) ).
cnf(refute_0_929,plain,
converse(join(meet(one,join(one,join(one,join(one,top)))),one)) = converse(join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_930,plain,
join(one,converse(meet(one,join(one,join(one,join(one,top)))))) = converse(join(meet(one,join(one,join(one,join(one,top)))),one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_931,plain,
( converse(join(meet(one,join(one,join(one,join(one,top)))),one)) != converse(join(one,meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(meet(one,join(one,join(one,join(one,top)))))) != converse(join(meet(one,join(one,join(one,join(one,top)))),one))
| join(one,converse(meet(one,join(one,join(one,join(one,top)))))) = converse(join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(meet(one,join(one,join(one,join(one,top)))))))),bind(Y,$fot(converse(join(meet(one,join(one,join(one,join(one,top)))),one)))),bind(Z,$fot(converse(join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_932,plain,
( converse(join(meet(one,join(one,join(one,join(one,top)))),one)) != converse(join(one,meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(meet(one,join(one,join(one,join(one,top)))))) = converse(join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),converse(join(meet(one,join(one,join(one,join(one,top)))),one))) )],[refute_0_930,refute_0_931]) ).
cnf(refute_0_933,plain,
join(one,converse(meet(one,join(one,join(one,join(one,top)))))) = converse(join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(converse(join(meet(one,join(one,join(one,join(one,top)))),one)),converse(join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_929,refute_0_932]) ).
cnf(refute_0_934,plain,
composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) = composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)))]]) ).
cnf(refute_0_935,plain,
( composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) != composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(one,converse(meet(one,join(one,join(one,join(one,top)))))) != converse(join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))) ),[1,0],$fot(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_936,plain,
( join(one,converse(meet(one,join(one,join(one,join(one,top)))))) != converse(join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))) )],[refute_0_934,refute_0_935]) ).
cnf(refute_0_937,plain,
composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)),
inference(resolve,[$cnf( $equal(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),converse(join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_933,refute_0_936]) ).
cnf(refute_0_938,plain,
composition(join(X_39,one),X_40) = join(X_40,composition(X_39,X_40)),
inference(subst,[],[refute_0_83:[bind(X_36,$fot(X_39)),bind(X_38,$fot(X_40))]]) ).
cnf(refute_0_939,plain,
join(one,X_39) = join(X_39,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_39))]]) ).
cnf(refute_0_940,plain,
( join(one,X_39) != join(X_39,one)
| join(X_39,one) = join(one,X_39) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_39))),bind(Y,$fot(join(X_39,one)))]]) ).
cnf(refute_0_941,plain,
join(X_39,one) = join(one,X_39),
inference(resolve,[$cnf( $equal(join(one,X_39),join(X_39,one)) )],[refute_0_939,refute_0_940]) ).
cnf(refute_0_942,plain,
( composition(join(X_39,one),X_40) != join(X_40,composition(X_39,X_40))
| join(X_39,one) != join(one,X_39)
| composition(join(one,X_39),X_40) = join(X_40,composition(X_39,X_40)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_39,one),X_40),join(X_40,composition(X_39,X_40))) ),[0,0],$fot(join(one,X_39))]]) ).
cnf(refute_0_943,plain,
( composition(join(X_39,one),X_40) != join(X_40,composition(X_39,X_40))
| composition(join(one,X_39),X_40) = join(X_40,composition(X_39,X_40)) ),
inference(resolve,[$cnf( $equal(join(X_39,one),join(one,X_39)) )],[refute_0_941,refute_0_942]) ).
cnf(refute_0_944,plain,
composition(join(one,X_39),X_40) = join(X_40,composition(X_39,X_40)),
inference(resolve,[$cnf( $equal(composition(join(X_39,one),X_40),join(X_40,composition(X_39,X_40))) )],[refute_0_938,refute_0_943]) ).
cnf(refute_0_945,plain,
join(X_40,composition(X_39,X_40)) = composition(join(X_39,one),X_40),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(X_39)),bind(X_38,$fot(X_40))]]) ).
cnf(refute_0_946,plain,
( composition(join(one,X_39),X_40) != join(X_40,composition(X_39,X_40))
| join(X_40,composition(X_39,X_40)) != composition(join(X_39,one),X_40)
| composition(join(one,X_39),X_40) = composition(join(X_39,one),X_40) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_39),X_40),composition(join(X_39,one),X_40)) ),[0],$fot(join(X_40,composition(X_39,X_40)))]]) ).
cnf(refute_0_947,plain,
( composition(join(one,X_39),X_40) != join(X_40,composition(X_39,X_40))
| composition(join(one,X_39),X_40) = composition(join(X_39,one),X_40) ),
inference(resolve,[$cnf( $equal(join(X_40,composition(X_39,X_40)),composition(join(X_39,one),X_40)) )],[refute_0_945,refute_0_946]) ).
cnf(refute_0_948,plain,
composition(join(one,X_39),X_40) = composition(join(X_39,one),X_40),
inference(resolve,[$cnf( $equal(composition(join(one,X_39),X_40),join(X_40,composition(X_39,X_40))) )],[refute_0_944,refute_0_947]) ).
cnf(refute_0_949,plain,
( composition(join(one,X_39),X_40) != composition(join(X_39,one),X_40)
| composition(join(X_39,one),X_40) = composition(join(one,X_39),X_40) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_39),X_40))),bind(Y,$fot(composition(join(X_39,one),X_40)))]]) ).
cnf(refute_0_950,plain,
composition(join(X_39,one),X_40) = composition(join(one,X_39),X_40),
inference(resolve,[$cnf( $equal(composition(join(one,X_39),X_40),composition(join(X_39,one),X_40)) )],[refute_0_948,refute_0_949]) ).
cnf(refute_0_951,plain,
composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)) = composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),
inference(subst,[],[refute_0_950:[bind(X_39,$fot(converse(meet(one,join(one,join(one,join(one,top))))))),bind(X_40,$fot(complement(one)))]]) ).
cnf(refute_0_952,plain,
join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(converse(meet(one,join(one,join(one,join(one,top))))))),bind(X_38,$fot(complement(one)))]]) ).
cnf(refute_0_953,plain,
( composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)) != composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) != composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))))),bind(Y,$fot(composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)))),bind(Z,$fot(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))))]]) ).
cnf(refute_0_954,plain,
( composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)) != composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))),composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one))) )],[refute_0_952,refute_0_953]) ).
cnf(refute_0_955,plain,
join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),
inference(resolve,[$cnf( $equal(composition(join(converse(meet(one,join(one,join(one,join(one,top))))),one),complement(one)),composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))) )],[refute_0_951,refute_0_954]) ).
cnf(refute_0_956,plain,
( composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) != composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) != composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))))),bind(Y,$fot(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)))),bind(Z,$fot(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))]]) ).
cnf(refute_0_957,plain,
( composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)) != composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))),composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one))) )],[refute_0_955,refute_0_956]) ).
cnf(refute_0_958,plain,
join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) = composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(meet(one,join(one,join(one,join(one,top)))))),complement(one)),composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))) )],[refute_0_937,refute_0_957]) ).
cnf(refute_0_959,plain,
( join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) != complement(one)
| join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) != composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))
| composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) = complement(one) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))),complement(one)) ),[0],$fot(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)))]]) ).
cnf(refute_0_960,plain,
( join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))) != complement(one)
| composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) = complement(one) ),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))),composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))) )],[refute_0_958,refute_0_959]) ).
cnf(refute_0_961,plain,
composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) = complement(one),
inference(resolve,[$cnf( $equal(join(complement(one),composition(converse(meet(one,join(one,join(one,join(one,top))))),complement(one))),complement(one)) )],[refute_0_928,refute_0_960]) ).
cnf(refute_0_962,plain,
( composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)) != complement(one)
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))),complement(complement(one))) ),[0,1,1,0],$fot(complement(one))]]) ).
cnf(refute_0_963,plain,
( join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one)),complement(one)) )],[refute_0_961,refute_0_962]) ).
cnf(refute_0_964,plain,
join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(composition(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),complement(one))))),complement(complement(one))) )],[refute_0_742,refute_0_963]) ).
cnf(refute_0_965,plain,
composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(subst,[],[composition_identity_6:[bind(A,$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_966,plain,
complement(complement(one)) = one,
inference(subst,[],[refute_0_276:[bind(X_70,$fot(one))]]) ).
cnf(refute_0_967,plain,
composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))))]]) ).
cnf(refute_0_968,plain,
( complement(complement(one)) != one
| composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) != composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one)))
| composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))),composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_969,plain,
( complement(complement(one)) != one
| composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) ),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))),composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one)))) )],[refute_0_967,refute_0_968]) ).
cnf(refute_0_970,plain,
composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_966,refute_0_969]) ).
cnf(refute_0_971,plain,
join(converse(one),meet(one,join(one,join(one,join(one,top))))) = join(converse(one),meet(one,join(one,join(one,join(one,top))))),
introduced(tautology,[refl,[$fot(join(converse(one),meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_972,plain,
( converse(one) != one
| join(converse(one),meet(one,join(one,join(one,join(one,top))))) != join(converse(one),meet(one,join(one,join(one,join(one,top)))))
| join(converse(one),meet(one,join(one,join(one,join(one,top))))) = join(one,meet(one,join(one,join(one,join(one,top))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),meet(one,join(one,join(one,join(one,top))))),join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_973,plain,
( converse(one) != one
| join(converse(one),meet(one,join(one,join(one,join(one,top))))) = join(one,meet(one,join(one,join(one,join(one,top))))) ),
inference(resolve,[$cnf( $equal(join(converse(one),meet(one,join(one,join(one,join(one,top))))),join(converse(one),meet(one,join(one,join(one,join(one,top)))))) )],[refute_0_971,refute_0_972]) ).
cnf(refute_0_974,plain,
join(converse(one),meet(one,join(one,join(one,join(one,top))))) = join(one,meet(one,join(one,join(one,join(one,top))))),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_973]) ).
cnf(refute_0_975,plain,
join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),
introduced(tautology,[refl,[$fot(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_976,plain,
( join(converse(one),meet(one,join(one,join(one,join(one,top))))) != join(one,meet(one,join(one,join(one,join(one,top)))))
| join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) ),[1,1],$fot(join(one,meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_977,plain,
( join(converse(one),meet(one,join(one,join(one,join(one,top))))) != join(one,meet(one,join(one,join(one,join(one,top)))))
| join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_975,refute_0_976]) ).
cnf(refute_0_978,plain,
join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(converse(one),meet(one,join(one,join(one,join(one,top))))),join(one,meet(one,join(one,join(one,join(one,top)))))) )],[refute_0_974,refute_0_977]) ).
cnf(refute_0_979,plain,
join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),
inference(subst,[],[refute_0_819:[bind(X_42,$fot(one)),bind(X_43,$fot(converse(one))),bind(X_44,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_980,plain,
converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(subst,[],[refute_0_112:[bind(A,$fot(join(one,meet(one,join(one,join(one,join(one,top))))))),bind(X_10,$fot(one))]]) ).
cnf(refute_0_981,plain,
( converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(converse(one),join(one,meet(one,join(one,join(one,join(one,top))))))
| join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))))),bind(Y,$fot(join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))))),bind(Z,$fot(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_982,plain,
( join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),join(converse(one),join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_980,refute_0_981]) ).
cnf(refute_0_983,plain,
converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(converse(one),join(one,meet(one,join(one,join(one,join(one,top)))))),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_979,refute_0_982]) ).
cnf(refute_0_984,plain,
converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) = converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),
inference(subst,[],[refute_0_628:[bind(X_18,$fot(converse(join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_985,plain,
( converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) != converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top))))))))
| converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)))),bind(Y,$fot(converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))))),bind(Z,$fot(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_986,plain,
( converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)),converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top))))))))) )],[refute_0_984,refute_0_985]) ).
cnf(refute_0_987,plain,
converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(converse(join(one,converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_983,refute_0_986]) ).
cnf(refute_0_988,plain,
join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(converse(join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_989,plain,
( converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))))),bind(Y,$fot(converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)))),bind(Z,$fot(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_990,plain,
( converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one))) )],[refute_0_988,refute_0_989]) ).
cnf(refute_0_991,plain,
join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(converse(join(converse(join(one,meet(one,join(one,join(one,join(one,top)))))),one)),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_987,refute_0_990]) ).
cnf(refute_0_992,plain,
( join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))
| join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))))),bind(Y,$fot(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))))),bind(Z,$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_993,plain,
( join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),join(one,join(converse(one),meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_991,refute_0_992]) ).
cnf(refute_0_994,plain,
join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(join(one,join(converse(one),meet(one,join(one,join(one,join(one,top)))))),join(one,join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_978,refute_0_993]) ).
cnf(refute_0_995,plain,
composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))))]]) ).
cnf(refute_0_996,plain,
( composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) != composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))
| join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))) ),[1,0],$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_997,plain,
( join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))) )],[refute_0_995,refute_0_996]) ).
cnf(refute_0_998,plain,
composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))),
inference(resolve,[$cnf( $equal(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),join(one,join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_994,refute_0_997]) ).
cnf(refute_0_999,plain,
( composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) != composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one)))
| composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) != composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))))),bind(Y,$fot(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))))),bind(Z,$fot(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)))]]) ).
cnf(refute_0_1000,plain,
( composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) != composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one)))) )],[refute_0_998,refute_0_999]) ).
cnf(refute_0_1001,plain,
composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))),composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)) )],[refute_0_970,refute_0_1000]) ).
cnf(refute_0_1002,plain,
( composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) != composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)
| composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))))),bind(Y,$fot(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one))),bind(Z,$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_1003,plain,
( composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one)) )],[refute_0_1001,refute_0_1002]) ).
cnf(refute_0_1004,plain,
composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(composition(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one),join(one,join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_965,refute_0_1003]) ).
cnf(refute_0_1005,plain,
composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))) = composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),
inference(subst,[],[refute_0_950:[bind(X_39,$fot(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))))),bind(X_40,$fot(complement(complement(one))))]]) ).
cnf(refute_0_1006,plain,
join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))))),bind(X_38,$fot(complement(complement(one))))]]) ).
cnf(refute_0_1007,plain,
( composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))) != composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one)))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))))),bind(Y,$fot(composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))))),bind(Z,$fot(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))))]]) ).
cnf(refute_0_1008,plain,
( composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))) != composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))),composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one)))) )],[refute_0_1006,refute_0_1007]) ).
cnf(refute_0_1009,plain,
join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),
inference(resolve,[$cnf( $equal(composition(join(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),one),complement(complement(one))),composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))) )],[refute_0_1005,refute_0_1008]) ).
cnf(refute_0_1010,plain,
( composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))))),bind(Y,$fot(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))))),bind(Z,$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top))))))))]]) ).
cnf(refute_0_1011,plain,
( composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))),composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one)))) )],[refute_0_1009,refute_0_1010]) ).
cnf(refute_0_1012,plain,
join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) = join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(converse(join(one,meet(one,join(one,join(one,join(one,top)))))))),complement(complement(one))),join(one,join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_1004,refute_0_1011]) ).
cnf(refute_0_1013,plain,
( join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != complement(complement(one))
| join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != join(one,join(one,meet(one,join(one,join(one,join(one,top))))))
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))),complement(complement(one))) ),[0],$fot(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))))]]) ).
cnf(refute_0_1014,plain,
( join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != complement(complement(one))
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))),join(one,join(one,meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_1012,refute_0_1013]) ).
cnf(refute_0_1015,plain,
( complement(complement(one)) != one
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) != complement(complement(one))
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = one ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1016,plain,
( join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) != complement(complement(one))
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_966,refute_0_1015]) ).
cnf(refute_0_1017,plain,
( join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))) != complement(complement(one))
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = one ),
inference(resolve,[$cnf( $equal(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),complement(complement(one))) )],[refute_0_1014,refute_0_1016]) ).
cnf(refute_0_1018,plain,
join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) = one,
inference(resolve,[$cnf( $equal(join(complement(complement(one)),composition(converse(converse(join(one,meet(one,join(one,join(one,join(one,top))))))),complement(complement(one)))),complement(complement(one))) )],[refute_0_964,refute_0_1017]) ).
cnf(refute_0_1019,plain,
( join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),C)
| join(one,join(one,meet(one,join(one,join(one,join(one,top)))))) != one
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),C)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1020,plain,
( join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),C)
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,C) ),
inference(resolve,[$cnf( $equal(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),one) )],[refute_0_1018,refute_0_1019]) ).
cnf(refute_0_1021,plain,
join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,C),
inference(resolve,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(join(one,join(one,meet(one,join(one,join(one,join(one,top)))))),C)) )],[refute_0_741,refute_0_1020]) ).
cnf(refute_0_1022,plain,
join(join(one,meet(one,join(one,join(one,join(one,top))))),C) = join(one,join(meet(one,join(one,join(one,join(one,top)))),C)),
inference(subst,[],[refute_0_417:[bind(A,$fot(one)),bind(B,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_1023,plain,
join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),
introduced(tautology,[refl,[$fot(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)))]]) ).
cnf(refute_0_1024,plain,
( join(join(one,meet(one,join(one,join(one,join(one,top))))),C) != join(one,join(meet(one,join(one,join(one,join(one,top)))),C))
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C))
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C))) ),[1,1],$fot(join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))]]) ).
cnf(refute_0_1025,plain,
( join(join(one,meet(one,join(one,join(one,join(one,top))))),C) != join(one,join(meet(one,join(one,join(one,join(one,top)))),C))
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C))) )],[refute_0_1023,refute_0_1024]) ).
cnf(refute_0_1026,plain,
join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) = join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),
inference(resolve,[$cnf( $equal(join(join(one,meet(one,join(one,join(one,join(one,top))))),C),join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) )],[refute_0_1022,refute_0_1025]) ).
cnf(refute_0_1027,plain,
( join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(one,C)
| join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(one,C)) ),[0],$fot(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))))]]) ).
cnf(refute_0_1028,plain,
( join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)) != join(one,C)
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,C) ),
inference(resolve,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))) )],[refute_0_1026,refute_0_1027]) ).
cnf(refute_0_1029,plain,
join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,C),
inference(resolve,[$cnf( $equal(join(one,join(join(one,meet(one,join(one,join(one,join(one,top))))),C)),join(one,C)) )],[refute_0_1021,refute_0_1028]) ).
cnf(refute_0_1030,plain,
meet(one,join(one,join(one,join(one,top)))) = complement(complement(meet(one,join(one,join(one,join(one,top)))))),
inference(subst,[],[refute_0_249:[bind(X_70,$fot(meet(one,join(one,join(one,join(one,top))))))]]) ).
cnf(refute_0_1031,plain,
( complement(meet(one,join(one,join(one,join(one,top))))) != complement(one)
| meet(one,join(one,join(one,join(one,top)))) != complement(complement(meet(one,join(one,join(one,join(one,top))))))
| meet(one,join(one,join(one,join(one,top)))) = complement(complement(one)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,join(one,top)))),complement(complement(meet(one,join(one,join(one,join(one,top))))))) ),[1,0],$fot(complement(one))]]) ).
cnf(refute_0_1032,plain,
( meet(one,join(one,join(one,join(one,top)))) != complement(complement(meet(one,join(one,join(one,join(one,top))))))
| meet(one,join(one,join(one,join(one,top)))) = complement(complement(one)) ),
inference(resolve,[$cnf( $equal(complement(meet(one,join(one,join(one,join(one,top))))),complement(one)) )],[refute_0_925,refute_0_1031]) ).
cnf(refute_0_1033,plain,
meet(one,join(one,join(one,join(one,top)))) = complement(complement(one)),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,join(one,top)))),complement(complement(meet(one,join(one,join(one,join(one,top))))))) )],[refute_0_1030,refute_0_1032]) ).
cnf(refute_0_1034,plain,
( complement(complement(one)) != one
| meet(one,join(one,join(one,join(one,top)))) != complement(complement(one))
| meet(one,join(one,join(one,join(one,top)))) = one ),
introduced(tautology,[equality,[$cnf( $equal(meet(one,join(one,join(one,join(one,top)))),complement(complement(one))) ),[1],$fot(one)]]) ).
cnf(refute_0_1035,plain,
( meet(one,join(one,join(one,join(one,top)))) != complement(complement(one))
| meet(one,join(one,join(one,join(one,top)))) = one ),
inference(resolve,[$cnf( $equal(complement(complement(one)),one) )],[refute_0_966,refute_0_1034]) ).
cnf(refute_0_1036,plain,
meet(one,join(one,join(one,join(one,top)))) = one,
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,join(one,top)))),complement(complement(one))) )],[refute_0_1033,refute_0_1035]) ).
cnf(refute_0_1037,plain,
join(meet(one,join(one,join(one,join(one,top)))),C) = join(meet(one,join(one,join(one,join(one,top)))),C),
introduced(tautology,[refl,[$fot(join(meet(one,join(one,join(one,join(one,top)))),C))]]) ).
cnf(refute_0_1038,plain,
( join(meet(one,join(one,join(one,join(one,top)))),C) != join(meet(one,join(one,join(one,join(one,top)))),C)
| meet(one,join(one,join(one,join(one,top)))) != one
| join(meet(one,join(one,join(one,join(one,top)))),C) = join(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(one,join(one,join(one,join(one,top)))),C),join(meet(one,join(one,join(one,join(one,top)))),C)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1039,plain,
( meet(one,join(one,join(one,join(one,top)))) != one
| join(meet(one,join(one,join(one,join(one,top)))),C) = join(one,C) ),
inference(resolve,[$cnf( $equal(join(meet(one,join(one,join(one,join(one,top)))),C),join(meet(one,join(one,join(one,join(one,top)))),C)) )],[refute_0_1037,refute_0_1038]) ).
cnf(refute_0_1040,plain,
join(meet(one,join(one,join(one,join(one,top)))),C) = join(one,C),
inference(resolve,[$cnf( $equal(meet(one,join(one,join(one,join(one,top)))),one) )],[refute_0_1036,refute_0_1039]) ).
cnf(refute_0_1041,plain,
join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) = join(one,join(meet(one,join(one,join(one,join(one,top)))),C)),
introduced(tautology,[refl,[$fot(join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))]]) ).
cnf(refute_0_1042,plain,
( join(meet(one,join(one,join(one,join(one,top)))),C) != join(one,C)
| join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) != join(one,join(meet(one,join(one,join(one,join(one,top)))),C))
| join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) = join(one,join(one,C)) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(meet(one,join(one,join(one,join(one,top)))),C)),join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) ),[1,1],$fot(join(one,C))]]) ).
cnf(refute_0_1043,plain,
( join(meet(one,join(one,join(one,join(one,top)))),C) != join(one,C)
| join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) = join(one,join(one,C)) ),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,join(one,join(one,join(one,top)))),C)),join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) )],[refute_0_1041,refute_0_1042]) ).
cnf(refute_0_1044,plain,
join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) = join(one,join(one,C)),
inference(resolve,[$cnf( $equal(join(meet(one,join(one,join(one,join(one,top)))),C),join(one,C)) )],[refute_0_1040,refute_0_1043]) ).
cnf(refute_0_1045,plain,
join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),
introduced(tautology,[refl,[$fot(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))))]]) ).
cnf(refute_0_1046,plain,
( join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) != join(one,join(one,C))
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) != join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,join(one,join(one,C))) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))) ),[1,1],$fot(join(one,join(one,C)))]]) ).
cnf(refute_0_1047,plain,
( join(one,join(meet(one,join(one,join(one,join(one,top)))),C)) != join(one,join(one,C))
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,join(one,join(one,C))) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C)))) )],[refute_0_1045,refute_0_1046]) ).
cnf(refute_0_1048,plain,
join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) = join(one,join(one,join(one,C))),
inference(resolve,[$cnf( $equal(join(one,join(meet(one,join(one,join(one,join(one,top)))),C)),join(one,join(one,C))) )],[refute_0_1044,refute_0_1047]) ).
cnf(refute_0_1049,plain,
( join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) != join(one,C)
| join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) != join(one,join(one,join(one,C)))
| join(one,join(one,join(one,C))) = join(one,C) ),
introduced(tautology,[equality,[$cnf( $equal(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),join(one,C)) ),[0],$fot(join(one,join(one,join(one,C))))]]) ).
cnf(refute_0_1050,plain,
( join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))) != join(one,C)
| join(one,join(one,join(one,C))) = join(one,C) ),
inference(resolve,[$cnf( $equal(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),join(one,join(one,join(one,C)))) )],[refute_0_1048,refute_0_1049]) ).
cnf(refute_0_1051,plain,
join(one,join(one,join(one,C))) = join(one,C),
inference(resolve,[$cnf( $equal(join(one,join(one,join(meet(one,join(one,join(one,join(one,top)))),C))),join(one,C)) )],[refute_0_1029,refute_0_1050]) ).
cnf(refute_0_1052,plain,
join(one,join(one,join(one,join(one,B)))) = join(one,join(one,B)),
inference(subst,[],[refute_0_1051:[bind(C,$fot(join(one,B)))]]) ).
cnf(refute_0_1053,plain,
converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,join(one,join(one,B))))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(one,join(one,B))))))]]) ).
cnf(refute_0_1054,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != converse(join(one,join(one,join(one,join(one,B)))))
| join(one,join(one,join(one,join(one,B)))) != join(one,join(one,B))
| converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,join(one,join(one,B)))))) ),[1,0],$fot(join(one,join(one,B)))]]) ).
cnf(refute_0_1055,plain,
( join(one,join(one,join(one,join(one,B)))) != join(one,join(one,B))
| converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,B))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,join(one,join(one,B)))))) )],[refute_0_1053,refute_0_1054]) ).
cnf(refute_0_1056,plain,
converse(join(one,join(one,join(one,join(one,B))))) = converse(join(one,join(one,B))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(one,B)))),join(one,join(one,B))) )],[refute_0_1052,refute_0_1055]) ).
cnf(refute_0_1057,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != converse(join(one,join(one,B)))
| converse(join(one,join(one,join(one,join(one,B))))) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,B))) = converse(join(one,join(one,join(one,join(B,one))))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,join(one,join(B,one)))))) ),[0],$fot(converse(join(one,join(one,B))))]]) ).
cnf(refute_0_1058,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,B))) = converse(join(one,join(one,join(one,join(B,one))))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,B)))) )],[refute_0_1056,refute_0_1057]) ).
cnf(refute_0_1059,plain,
join(one,join(one,join(one,join(B,one)))) = join(one,join(B,one)),
inference(subst,[],[refute_0_1051:[bind(C,$fot(join(B,one)))]]) ).
cnf(refute_0_1060,plain,
converse(join(one,join(one,join(one,join(B,one))))) = converse(join(one,join(one,join(one,join(B,one))))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,join(one,join(B,one))))))]]) ).
cnf(refute_0_1061,plain,
( converse(join(one,join(one,join(one,join(B,one))))) != converse(join(one,join(one,join(one,join(B,one)))))
| join(one,join(one,join(one,join(B,one)))) != join(one,join(B,one))
| converse(join(one,join(one,join(one,join(B,one))))) = converse(join(one,join(B,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,join(one,join(B,one))))),converse(join(one,join(one,join(one,join(B,one)))))) ),[1,0],$fot(join(one,join(B,one)))]]) ).
cnf(refute_0_1062,plain,
( join(one,join(one,join(one,join(B,one)))) != join(one,join(B,one))
| converse(join(one,join(one,join(one,join(B,one))))) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(B,one))))),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_1060,refute_0_1061]) ).
cnf(refute_0_1063,plain,
converse(join(one,join(one,join(one,join(B,one))))) = converse(join(one,join(B,one))),
inference(resolve,[$cnf( $equal(join(one,join(one,join(one,join(B,one)))),join(one,join(B,one))) )],[refute_0_1059,refute_0_1062]) ).
cnf(refute_0_1064,plain,
( converse(join(one,join(one,B))) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,join(one,join(B,one))))) != converse(join(one,join(B,one)))
| converse(join(one,join(one,B))) = converse(join(one,join(B,one))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(one,join(one,B))),converse(join(one,join(B,one)))) ),[0],$fot(converse(join(one,join(one,join(one,join(B,one))))))]]) ).
cnf(refute_0_1065,plain,
( converse(join(one,join(one,B))) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,B))) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(B,one))))),converse(join(one,join(B,one)))) )],[refute_0_1063,refute_0_1064]) ).
cnf(refute_0_1066,plain,
( converse(join(one,join(one,join(one,join(one,B))))) != converse(join(one,join(one,join(one,join(B,one)))))
| converse(join(one,join(one,B))) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_1058,refute_0_1065]) ).
cnf(refute_0_1067,plain,
converse(join(one,join(one,B))) = converse(join(one,join(B,one))),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,join(one,join(one,B))))),converse(join(one,join(one,join(one,join(B,one)))))) )],[refute_0_740,refute_0_1066]) ).
cnf(refute_0_1068,plain,
join(one,join(one,B)) = join(one,B),
inference(subst,[],[refute_0_546:[bind(A,$fot(one))]]) ).
cnf(refute_0_1069,plain,
converse(join(one,join(one,B))) = converse(join(one,join(one,B))),
introduced(tautology,[refl,[$fot(converse(join(one,join(one,B))))]]) ).
cnf(refute_0_1070,plain,
( converse(join(one,join(one,B))) != converse(join(one,join(one,B)))
| join(one,join(one,B)) != join(one,B)
| converse(join(one,join(one,B))) = converse(join(one,B)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,join(one,B)))) ),[1,0],$fot(join(one,B))]]) ).
cnf(refute_0_1071,plain,
( join(one,join(one,B)) != join(one,B)
| converse(join(one,join(one,B))) = converse(join(one,B)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,join(one,B)))) )],[refute_0_1069,refute_0_1070]) ).
cnf(refute_0_1072,plain,
converse(join(one,join(one,B))) = converse(join(one,B)),
inference(resolve,[$cnf( $equal(join(one,join(one,B)),join(one,B)) )],[refute_0_1068,refute_0_1071]) ).
cnf(refute_0_1073,plain,
( converse(join(one,join(one,B))) != converse(join(one,B))
| converse(join(one,join(one,B))) != converse(join(one,join(B,one)))
| converse(join(one,B)) = converse(join(one,join(B,one))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,join(B,one)))) ),[0],$fot(converse(join(one,B)))]]) ).
cnf(refute_0_1074,plain,
( converse(join(one,join(one,B))) != converse(join(one,join(B,one)))
| converse(join(one,B)) = converse(join(one,join(B,one))) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,B))) )],[refute_0_1072,refute_0_1073]) ).
cnf(refute_0_1075,plain,
join(one,join(B,one)) = join(B,one),
inference(subst,[],[refute_0_556:[bind(X_43,$fot(B)),bind(X_44,$fot(one))]]) ).
cnf(refute_0_1076,plain,
converse(join(one,join(B,one))) = converse(join(one,join(B,one))),
introduced(tautology,[refl,[$fot(converse(join(one,join(B,one))))]]) ).
cnf(refute_0_1077,plain,
( converse(join(one,join(B,one))) != converse(join(one,join(B,one)))
| join(one,join(B,one)) != join(B,one)
| converse(join(one,join(B,one))) = converse(join(B,one)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(one,join(B,one))),converse(join(one,join(B,one)))) ),[1,0],$fot(join(B,one))]]) ).
cnf(refute_0_1078,plain,
( join(one,join(B,one)) != join(B,one)
| converse(join(one,join(B,one))) = converse(join(B,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(B,one))),converse(join(one,join(B,one)))) )],[refute_0_1076,refute_0_1077]) ).
cnf(refute_0_1079,plain,
converse(join(one,join(B,one))) = converse(join(B,one)),
inference(resolve,[$cnf( $equal(join(one,join(B,one)),join(B,one)) )],[refute_0_1075,refute_0_1078]) ).
cnf(refute_0_1080,plain,
( converse(join(one,B)) != converse(join(one,join(B,one)))
| converse(join(one,join(B,one))) != converse(join(B,one))
| converse(join(one,B)) = converse(join(B,one)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(one,B)),converse(join(B,one))) ),[0],$fot(converse(join(one,join(B,one))))]]) ).
cnf(refute_0_1081,plain,
( converse(join(one,B)) != converse(join(one,join(B,one)))
| converse(join(one,B)) = converse(join(B,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,join(B,one))),converse(join(B,one))) )],[refute_0_1079,refute_0_1080]) ).
cnf(refute_0_1082,plain,
( converse(join(one,join(one,B))) != converse(join(one,join(B,one)))
| converse(join(one,B)) = converse(join(B,one)) ),
inference(resolve,[$cnf( $equal(converse(join(one,B)),converse(join(one,join(B,one)))) )],[refute_0_1074,refute_0_1081]) ).
cnf(refute_0_1083,plain,
converse(join(one,B)) = converse(join(B,one)),
inference(resolve,[$cnf( $equal(converse(join(one,join(one,B))),converse(join(one,join(B,one)))) )],[refute_0_1067,refute_0_1082]) ).
cnf(refute_0_1084,plain,
( converse(join(one,B)) != converse(join(B,one))
| converse(join(B,one)) = converse(join(one,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(one,B)))),bind(Y,$fot(converse(join(B,one))))]]) ).
cnf(refute_0_1085,plain,
converse(join(B,one)) = converse(join(one,B)),
inference(resolve,[$cnf( $equal(converse(join(one,B)),converse(join(B,one))) )],[refute_0_1083,refute_0_1084]) ).
cnf(refute_0_1086,plain,
converse(join(top,one)) = converse(join(one,top)),
inference(subst,[],[refute_0_1085:[bind(B,$fot(top))]]) ).
cnf(refute_0_1087,plain,
join(one,converse(top)) = converse(join(top,one)),
inference(subst,[],[refute_0_622:[bind(X_10,$fot(top))]]) ).
cnf(refute_0_1088,plain,
( converse(join(top,one)) != converse(join(one,top))
| join(one,converse(top)) != converse(join(top,one))
| join(one,converse(top)) = converse(join(one,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(top)))),bind(Y,$fot(converse(join(top,one)))),bind(Z,$fot(converse(join(one,top))))]]) ).
cnf(refute_0_1089,plain,
( converse(join(top,one)) != converse(join(one,top))
| join(one,converse(top)) = converse(join(one,top)) ),
inference(resolve,[$cnf( $equal(join(one,converse(top)),converse(join(top,one))) )],[refute_0_1087,refute_0_1088]) ).
cnf(refute_0_1090,plain,
join(one,converse(top)) = converse(join(one,top)),
inference(resolve,[$cnf( $equal(converse(join(top,one)),converse(join(one,top))) )],[refute_0_1086,refute_0_1089]) ).
cnf(refute_0_1091,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) != converse(join(one,top))
| join(one,converse(top)) = top ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(one,converse(top)))),bind(Y,$fot(converse(join(one,top)))),bind(Z,$fot(top))]]) ).
cnf(refute_0_1092,plain,
( converse(join(one,top)) != top
| join(one,converse(top)) = top ),
inference(resolve,[$cnf( $equal(join(one,converse(top)),converse(join(one,top))) )],[refute_0_1090,refute_0_1091]) ).
cnf(refute_0_1093,plain,
join(one,converse(top)) = top,
inference(resolve,[$cnf( $equal(converse(join(one,top)),top) )],[refute_0_607,refute_0_1092]) ).
cnf(refute_0_1094,plain,
composition(join(one,converse(top)),complement(composition(top,X_108))) = composition(join(one,converse(top)),complement(composition(top,X_108))),
introduced(tautology,[refl,[$fot(composition(join(one,converse(top)),complement(composition(top,X_108))))]]) ).
cnf(refute_0_1095,plain,
( composition(join(one,converse(top)),complement(composition(top,X_108))) != composition(join(one,converse(top)),complement(composition(top,X_108)))
| join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(composition(top,X_108))) = composition(top,complement(composition(top,X_108))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_108))),composition(join(one,converse(top)),complement(composition(top,X_108)))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_1096,plain,
( join(one,converse(top)) != top
| composition(join(one,converse(top)),complement(composition(top,X_108))) = composition(top,complement(composition(top,X_108))) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_108))),composition(join(one,converse(top)),complement(composition(top,X_108)))) )],[refute_0_1094,refute_0_1095]) ).
cnf(refute_0_1097,plain,
composition(join(one,converse(top)),complement(composition(top,X_108))) = composition(top,complement(composition(top,X_108))),
inference(resolve,[$cnf( $equal(join(one,converse(top)),top) )],[refute_0_1093,refute_0_1096]) ).
cnf(refute_0_1098,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),composition(converse(B),converse(A))),
inference(subst,[],[refute_0_83:[bind(X_36,$fot(converse(B))),bind(X_38,$fot(converse(A)))]]) ).
cnf(refute_0_1099,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_1100,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_1099]) ).
cnf(refute_0_1101,plain,
( composition(converse(B),converse(A)) != converse(composition(A,B))
| composition(join(converse(B),one),converse(A)) != join(converse(A),composition(converse(B),converse(A)))
| composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),composition(converse(B),converse(A)))) ),[1,1],$fot(converse(composition(A,B)))]]) ).
cnf(refute_0_1102,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),composition(converse(B),converse(A)))
| composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))) ),
inference(resolve,[$cnf( $equal(composition(converse(B),converse(A)),converse(composition(A,B))) )],[refute_0_1100,refute_0_1101]) ).
cnf(refute_0_1103,plain,
composition(join(converse(B),one),converse(A)) = join(converse(A),converse(composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),composition(converse(B),converse(A)))) )],[refute_0_1098,refute_0_1102]) ).
cnf(refute_0_1104,plain,
join(converse(one),B) = join(converse(one),B),
introduced(tautology,[refl,[$fot(join(converse(one),B))]]) ).
cnf(refute_0_1105,plain,
( converse(one) != one
| join(converse(one),B) != join(converse(one),B)
| join(converse(one),B) = join(one,B) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),B),join(converse(one),B)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1106,plain,
( converse(one) != one
| join(converse(one),B) = join(one,B) ),
inference(resolve,[$cnf( $equal(join(converse(one),B),join(converse(one),B)) )],[refute_0_1104,refute_0_1105]) ).
cnf(refute_0_1107,plain,
join(converse(one),B) = join(one,B),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_1106]) ).
cnf(refute_0_1108,plain,
composition(A,join(converse(one),B)) = composition(A,join(converse(one),B)),
introduced(tautology,[refl,[$fot(composition(A,join(converse(one),B)))]]) ).
cnf(refute_0_1109,plain,
( composition(A,join(converse(one),B)) != composition(A,join(converse(one),B))
| join(converse(one),B) != join(one,B)
| composition(A,join(converse(one),B)) = composition(A,join(one,B)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(converse(one),B))) ),[1,1],$fot(join(one,B))]]) ).
cnf(refute_0_1110,plain,
( join(converse(one),B) != join(one,B)
| composition(A,join(converse(one),B)) = composition(A,join(one,B)) ),
inference(resolve,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(converse(one),B))) )],[refute_0_1108,refute_0_1109]) ).
cnf(refute_0_1111,plain,
composition(A,join(converse(one),B)) = composition(A,join(one,B)),
inference(resolve,[$cnf( $equal(join(converse(one),B),join(one,B)) )],[refute_0_1107,refute_0_1110]) ).
cnf(refute_0_1112,plain,
converse(composition(A,join(converse(one),B))) = converse(composition(A,join(converse(one),B))),
introduced(tautology,[refl,[$fot(converse(composition(A,join(converse(one),B))))]]) ).
cnf(refute_0_1113,plain,
( composition(A,join(converse(one),B)) != composition(A,join(one,B))
| converse(composition(A,join(converse(one),B))) != converse(composition(A,join(converse(one),B)))
| converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(converse(one),B)))) ),[1,0],$fot(composition(A,join(one,B)))]]) ).
cnf(refute_0_1114,plain,
( composition(A,join(converse(one),B)) != composition(A,join(one,B))
| converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(converse(one),B)))) )],[refute_0_1112,refute_0_1113]) ).
cnf(refute_0_1115,plain,
converse(composition(A,join(converse(one),B))) = converse(composition(A,join(one,B))),
inference(resolve,[$cnf( $equal(composition(A,join(converse(one),B)),composition(A,join(one,B))) )],[refute_0_1111,refute_0_1114]) ).
cnf(refute_0_1116,plain,
converse(composition(X_4,converse(join(X_13,converse(X_12))))) = composition(join(X_13,converse(X_12)),converse(X_4)),
inference(subst,[],[refute_0_42:[bind(A,$fot(join(X_13,converse(X_12))))]]) ).
cnf(refute_0_1117,plain,
converse(join(X_13,converse(X_12))) = join(converse(X_13),X_12),
inference(subst,[],[refute_0_112:[bind(A,$fot(X_12)),bind(X_10,$fot(X_13))]]) ).
cnf(refute_0_1118,plain,
( converse(composition(X_4,converse(join(X_13,converse(X_12))))) != composition(join(X_13,converse(X_12)),converse(X_4))
| converse(join(X_13,converse(X_12))) != join(converse(X_13),X_12)
| converse(composition(X_4,join(converse(X_13),X_12))) = composition(join(X_13,converse(X_12)),converse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_4,converse(join(X_13,converse(X_12))))),composition(join(X_13,converse(X_12)),converse(X_4))) ),[0,0,1],$fot(join(converse(X_13),X_12))]]) ).
cnf(refute_0_1119,plain,
( converse(composition(X_4,converse(join(X_13,converse(X_12))))) != composition(join(X_13,converse(X_12)),converse(X_4))
| converse(composition(X_4,join(converse(X_13),X_12))) = composition(join(X_13,converse(X_12)),converse(X_4)) ),
inference(resolve,[$cnf( $equal(converse(join(X_13,converse(X_12))),join(converse(X_13),X_12)) )],[refute_0_1117,refute_0_1118]) ).
cnf(refute_0_1120,plain,
converse(composition(X_4,join(converse(X_13),X_12))) = composition(join(X_13,converse(X_12)),converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(join(X_13,converse(X_12))))),composition(join(X_13,converse(X_12)),converse(X_4))) )],[refute_0_1116,refute_0_1119]) ).
cnf(refute_0_1121,plain,
( converse(composition(X_4,join(converse(X_13),X_12))) != composition(join(X_13,converse(X_12)),converse(X_4))
| composition(join(X_13,converse(X_12)),converse(X_4)) = converse(composition(X_4,join(converse(X_13),X_12))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_4,join(converse(X_13),X_12))))),bind(Y,$fot(composition(join(X_13,converse(X_12)),converse(X_4))))]]) ).
cnf(refute_0_1122,plain,
composition(join(X_13,converse(X_12)),converse(X_4)) = converse(composition(X_4,join(converse(X_13),X_12))),
inference(resolve,[$cnf( $equal(converse(composition(X_4,join(converse(X_13),X_12))),composition(join(X_13,converse(X_12)),converse(X_4))) )],[refute_0_1120,refute_0_1121]) ).
cnf(refute_0_1123,plain,
composition(join(one,converse(B)),converse(A)) = converse(composition(A,join(converse(one),B))),
inference(subst,[],[refute_0_1122:[bind(X_12,$fot(B)),bind(X_13,$fot(one)),bind(X_4,$fot(A))]]) ).
cnf(refute_0_1124,plain,
composition(join(converse(B),one),converse(A)) = composition(join(one,converse(B)),converse(A)),
inference(subst,[],[refute_0_950:[bind(X_39,$fot(converse(B))),bind(X_40,$fot(converse(A)))]]) ).
cnf(refute_0_1125,plain,
( composition(join(converse(B),one),converse(A)) != composition(join(one,converse(B)),converse(A))
| composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(converse(one),B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(converse(B),one),converse(A)))),bind(Y,$fot(composition(join(one,converse(B)),converse(A)))),bind(Z,$fot(converse(composition(A,join(converse(one),B)))))]]) ).
cnf(refute_0_1126,plain,
( composition(join(one,converse(B)),converse(A)) != converse(composition(A,join(converse(one),B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),composition(join(one,converse(B)),converse(A))) )],[refute_0_1124,refute_0_1125]) ).
cnf(refute_0_1127,plain,
composition(join(converse(B),one),converse(A)) = converse(composition(A,join(converse(one),B))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(B)),converse(A)),converse(composition(A,join(converse(one),B)))) )],[refute_0_1123,refute_0_1126]) ).
cnf(refute_0_1128,plain,
( composition(join(converse(B),one),converse(A)) != converse(composition(A,join(converse(one),B)))
| converse(composition(A,join(converse(one),B))) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(composition(join(converse(B),one),converse(A)))),bind(Y,$fot(converse(composition(A,join(converse(one),B))))),bind(Z,$fot(converse(composition(A,join(one,B)))))]]) ).
cnf(refute_0_1129,plain,
( converse(composition(A,join(converse(one),B))) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),converse(composition(A,join(converse(one),B)))) )],[refute_0_1127,refute_0_1128]) ).
cnf(refute_0_1130,plain,
composition(join(converse(B),one),converse(A)) = converse(composition(A,join(one,B))),
inference(resolve,[$cnf( $equal(converse(composition(A,join(converse(one),B))),converse(composition(A,join(one,B)))) )],[refute_0_1115,refute_0_1129]) ).
cnf(refute_0_1131,plain,
( composition(join(converse(B),one),converse(A)) != converse(composition(A,join(one,B)))
| composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = join(converse(A),converse(composition(A,B))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) ),[0],$fot(converse(composition(A,join(one,B))))]]) ).
cnf(refute_0_1132,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = join(converse(A),converse(composition(A,B))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),converse(composition(A,join(one,B)))) )],[refute_0_1130,refute_0_1131]) ).
cnf(refute_0_1133,plain,
( converse(join(A,B)) != join(converse(A),converse(B))
| join(converse(A),converse(B)) = converse(join(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(A,B)))),bind(Y,$fot(join(converse(A),converse(B))))]]) ).
cnf(refute_0_1134,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(resolve,[$cnf( $equal(converse(join(A,B)),join(converse(A),converse(B))) )],[converse_additivity_9,refute_0_1133]) ).
cnf(refute_0_1135,plain,
join(converse(A),converse(composition(A,B))) = converse(join(A,composition(A,B))),
inference(subst,[],[refute_0_1134:[bind(B,$fot(composition(A,B)))]]) ).
cnf(refute_0_1136,plain,
( converse(composition(A,join(one,B))) != join(converse(A),converse(composition(A,B)))
| join(converse(A),converse(composition(A,B))) != converse(join(A,composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(A,join(one,B))),converse(join(A,composition(A,B)))) ),[0],$fot(join(converse(A),converse(composition(A,B))))]]) ).
cnf(refute_0_1137,plain,
( converse(composition(A,join(one,B))) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(join(converse(A),converse(composition(A,B))),converse(join(A,composition(A,B)))) )],[refute_0_1135,refute_0_1136]) ).
cnf(refute_0_1138,plain,
( composition(join(converse(B),one),converse(A)) != join(converse(A),converse(composition(A,B)))
| converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(one,B))),join(converse(A),converse(composition(A,B)))) )],[refute_0_1132,refute_0_1137]) ).
cnf(refute_0_1139,plain,
converse(composition(A,join(one,B))) = converse(join(A,composition(A,B))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),one),converse(A)),join(converse(A),converse(composition(A,B)))) )],[refute_0_1103,refute_0_1138]) ).
cnf(refute_0_1140,plain,
converse(composition(converse(B),join(one,converse(A)))) = converse(join(converse(B),composition(converse(B),converse(A)))),
inference(subst,[],[refute_0_1139:[bind(A,$fot(converse(B))),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_1141,plain,
( composition(converse(B),converse(A)) != converse(composition(A,B))
| converse(composition(converse(B),join(one,converse(A)))) != converse(join(converse(B),composition(converse(B),converse(A))))
| converse(composition(converse(B),join(one,converse(A)))) = converse(join(converse(B),converse(composition(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),converse(join(converse(B),composition(converse(B),converse(A))))) ),[1,0,1],$fot(converse(composition(A,B)))]]) ).
cnf(refute_0_1142,plain,
( converse(composition(converse(B),join(one,converse(A)))) != converse(join(converse(B),composition(converse(B),converse(A))))
| converse(composition(converse(B),join(one,converse(A)))) = converse(join(converse(B),converse(composition(A,B)))) ),
inference(resolve,[$cnf( $equal(composition(converse(B),converse(A)),converse(composition(A,B))) )],[refute_0_1100,refute_0_1141]) ).
cnf(refute_0_1143,plain,
converse(composition(converse(B),join(one,converse(A)))) = converse(join(converse(B),converse(composition(A,B)))),
inference(resolve,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),converse(join(converse(B),composition(converse(B),converse(A))))) )],[refute_0_1140,refute_0_1142]) ).
cnf(refute_0_1144,plain,
join(converse(one),A) = join(converse(one),A),
introduced(tautology,[refl,[$fot(join(converse(one),A))]]) ).
cnf(refute_0_1145,plain,
( converse(one) != one
| join(converse(one),A) != join(converse(one),A)
| join(converse(one),A) = join(one,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(one),A),join(converse(one),A)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_1146,plain,
( converse(one) != one
| join(converse(one),A) = join(one,A) ),
inference(resolve,[$cnf( $equal(join(converse(one),A),join(converse(one),A)) )],[refute_0_1144,refute_0_1145]) ).
cnf(refute_0_1147,plain,
join(converse(one),A) = join(one,A),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_66,refute_0_1146]) ).
cnf(refute_0_1148,plain,
converse(join(one,converse(A))) = join(converse(one),A),
inference(subst,[],[refute_0_112:[bind(X_10,$fot(one))]]) ).
cnf(refute_0_1149,plain,
( converse(join(one,converse(A))) != join(converse(one),A)
| join(converse(one),A) != join(one,A)
| converse(join(one,converse(A))) = join(one,A) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(one,converse(A))))),bind(Y,$fot(join(converse(one),A))),bind(Z,$fot(join(one,A)))]]) ).
cnf(refute_0_1150,plain,
( join(converse(one),A) != join(one,A)
| converse(join(one,converse(A))) = join(one,A) ),
inference(resolve,[$cnf( $equal(converse(join(one,converse(A))),join(converse(one),A)) )],[refute_0_1148,refute_0_1149]) ).
cnf(refute_0_1151,plain,
converse(join(one,converse(A))) = join(one,A),
inference(resolve,[$cnf( $equal(join(converse(one),A),join(one,A)) )],[refute_0_1147,refute_0_1150]) ).
cnf(refute_0_1152,plain,
composition(converse(join(one,converse(A))),B) = composition(converse(join(one,converse(A))),B),
introduced(tautology,[refl,[$fot(composition(converse(join(one,converse(A))),B))]]) ).
cnf(refute_0_1153,plain,
( composition(converse(join(one,converse(A))),B) != composition(converse(join(one,converse(A))),B)
| converse(join(one,converse(A))) != join(one,A)
| composition(converse(join(one,converse(A))),B) = composition(join(one,A),B) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(join(one,converse(A))),B),composition(converse(join(one,converse(A))),B)) ),[1,0],$fot(join(one,A))]]) ).
cnf(refute_0_1154,plain,
( converse(join(one,converse(A))) != join(one,A)
| composition(converse(join(one,converse(A))),B) = composition(join(one,A),B) ),
inference(resolve,[$cnf( $equal(composition(converse(join(one,converse(A))),B),composition(converse(join(one,converse(A))),B)) )],[refute_0_1152,refute_0_1153]) ).
cnf(refute_0_1155,plain,
composition(converse(join(one,converse(A))),B) = composition(join(one,A),B),
inference(resolve,[$cnf( $equal(converse(join(one,converse(A))),join(one,A)) )],[refute_0_1151,refute_0_1154]) ).
cnf(refute_0_1156,plain,
converse(composition(converse(B),join(one,converse(A)))) = composition(converse(join(one,converse(A))),B),
inference(subst,[],[refute_0_48:[bind(A,$fot(B)),bind(X_5,$fot(join(one,converse(A))))]]) ).
cnf(refute_0_1157,plain,
( composition(converse(join(one,converse(A))),B) != composition(join(one,A),B)
| converse(composition(converse(B),join(one,converse(A)))) != composition(converse(join(one,converse(A))),B)
| converse(composition(converse(B),join(one,converse(A)))) = composition(join(one,A),B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(composition(converse(B),join(one,converse(A)))))),bind(Y,$fot(composition(converse(join(one,converse(A))),B))),bind(Z,$fot(composition(join(one,A),B)))]]) ).
cnf(refute_0_1158,plain,
( composition(converse(join(one,converse(A))),B) != composition(join(one,A),B)
| converse(composition(converse(B),join(one,converse(A)))) = composition(join(one,A),B) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),composition(converse(join(one,converse(A))),B)) )],[refute_0_1156,refute_0_1157]) ).
cnf(refute_0_1159,plain,
converse(composition(converse(B),join(one,converse(A)))) = composition(join(one,A),B),
inference(resolve,[$cnf( $equal(composition(converse(join(one,converse(A))),B),composition(join(one,A),B)) )],[refute_0_1155,refute_0_1158]) ).
cnf(refute_0_1160,plain,
( converse(composition(converse(B),join(one,converse(A)))) != composition(join(one,A),B)
| converse(composition(converse(B),join(one,converse(A)))) != converse(join(converse(B),converse(composition(A,B))))
| composition(join(one,A),B) = converse(join(converse(B),converse(composition(A,B)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),converse(join(converse(B),converse(composition(A,B))))) ),[0],$fot(composition(join(one,A),B))]]) ).
cnf(refute_0_1161,plain,
( converse(composition(converse(B),join(one,converse(A)))) != converse(join(converse(B),converse(composition(A,B))))
| composition(join(one,A),B) = converse(join(converse(B),converse(composition(A,B)))) ),
inference(resolve,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),composition(join(one,A),B)) )],[refute_0_1159,refute_0_1160]) ).
cnf(refute_0_1162,plain,
join(B,composition(A,B)) = composition(join(A,one),B),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(A)),bind(X_38,$fot(B))]]) ).
cnf(refute_0_1163,plain,
converse(converse(composition(A,B))) = composition(A,B),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(A,B)))]]) ).
cnf(refute_0_1164,plain,
join(B,converse(converse(composition(A,B)))) = join(B,converse(converse(composition(A,B)))),
introduced(tautology,[refl,[$fot(join(B,converse(converse(composition(A,B)))))]]) ).
cnf(refute_0_1165,plain,
( converse(converse(composition(A,B))) != composition(A,B)
| join(B,converse(converse(composition(A,B)))) != join(B,converse(converse(composition(A,B))))
| join(B,converse(converse(composition(A,B)))) = join(B,composition(A,B)) ),
introduced(tautology,[equality,[$cnf( $equal(join(B,converse(converse(composition(A,B)))),join(B,converse(converse(composition(A,B))))) ),[1,1],$fot(composition(A,B))]]) ).
cnf(refute_0_1166,plain,
( converse(converse(composition(A,B))) != composition(A,B)
| join(B,converse(converse(composition(A,B)))) = join(B,composition(A,B)) ),
inference(resolve,[$cnf( $equal(join(B,converse(converse(composition(A,B)))),join(B,converse(converse(composition(A,B))))) )],[refute_0_1164,refute_0_1165]) ).
cnf(refute_0_1167,plain,
join(B,converse(converse(composition(A,B)))) = join(B,composition(A,B)),
inference(resolve,[$cnf( $equal(converse(converse(composition(A,B))),composition(A,B)) )],[refute_0_1163,refute_0_1166]) ).
cnf(refute_0_1168,plain,
( join(B,composition(A,B)) != composition(join(A,one),B)
| join(B,converse(converse(composition(A,B)))) != join(B,composition(A,B))
| join(B,converse(converse(composition(A,B)))) = composition(join(A,one),B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(B,converse(converse(composition(A,B)))))),bind(Y,$fot(join(B,composition(A,B)))),bind(Z,$fot(composition(join(A,one),B)))]]) ).
cnf(refute_0_1169,plain,
( join(B,composition(A,B)) != composition(join(A,one),B)
| join(B,converse(converse(composition(A,B)))) = composition(join(A,one),B) ),
inference(resolve,[$cnf( $equal(join(B,converse(converse(composition(A,B)))),join(B,composition(A,B))) )],[refute_0_1167,refute_0_1168]) ).
cnf(refute_0_1170,plain,
join(B,converse(converse(composition(A,B)))) = composition(join(A,one),B),
inference(resolve,[$cnf( $equal(join(B,composition(A,B)),composition(join(A,one),B)) )],[refute_0_1162,refute_0_1169]) ).
cnf(refute_0_1171,plain,
converse(join(converse(B),converse(composition(A,B)))) = join(B,converse(converse(composition(A,B)))),
inference(subst,[],[refute_0_102:[bind(A,$fot(B)),bind(X_11,$fot(converse(composition(A,B))))]]) ).
cnf(refute_0_1172,plain,
( converse(join(converse(B),converse(composition(A,B)))) != join(B,converse(converse(composition(A,B))))
| join(B,converse(converse(composition(A,B)))) != composition(join(A,one),B)
| converse(join(converse(B),converse(composition(A,B)))) = composition(join(A,one),B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(join(converse(B),converse(composition(A,B)))))),bind(Y,$fot(join(B,converse(converse(composition(A,B)))))),bind(Z,$fot(composition(join(A,one),B)))]]) ).
cnf(refute_0_1173,plain,
( join(B,converse(converse(composition(A,B)))) != composition(join(A,one),B)
| converse(join(converse(B),converse(composition(A,B)))) = composition(join(A,one),B) ),
inference(resolve,[$cnf( $equal(converse(join(converse(B),converse(composition(A,B)))),join(B,converse(converse(composition(A,B))))) )],[refute_0_1171,refute_0_1172]) ).
cnf(refute_0_1174,plain,
converse(join(converse(B),converse(composition(A,B)))) = composition(join(A,one),B),
inference(resolve,[$cnf( $equal(join(B,converse(converse(composition(A,B)))),composition(join(A,one),B)) )],[refute_0_1170,refute_0_1173]) ).
cnf(refute_0_1175,plain,
( composition(join(one,A),B) != converse(join(converse(B),converse(composition(A,B))))
| converse(join(converse(B),converse(composition(A,B)))) != composition(join(A,one),B)
| composition(join(one,A),B) = composition(join(A,one),B) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,A),B),composition(join(A,one),B)) ),[0],$fot(converse(join(converse(B),converse(composition(A,B)))))]]) ).
cnf(refute_0_1176,plain,
( composition(join(one,A),B) != converse(join(converse(B),converse(composition(A,B))))
| composition(join(one,A),B) = composition(join(A,one),B) ),
inference(resolve,[$cnf( $equal(converse(join(converse(B),converse(composition(A,B)))),composition(join(A,one),B)) )],[refute_0_1174,refute_0_1175]) ).
cnf(refute_0_1177,plain,
( converse(composition(converse(B),join(one,converse(A)))) != converse(join(converse(B),converse(composition(A,B))))
| composition(join(one,A),B) = composition(join(A,one),B) ),
inference(resolve,[$cnf( $equal(composition(join(one,A),B),converse(join(converse(B),converse(composition(A,B))))) )],[refute_0_1161,refute_0_1176]) ).
cnf(refute_0_1178,plain,
composition(join(one,A),B) = composition(join(A,one),B),
inference(resolve,[$cnf( $equal(converse(composition(converse(B),join(one,converse(A)))),converse(join(converse(B),converse(composition(A,B))))) )],[refute_0_1143,refute_0_1177]) ).
cnf(refute_0_1179,plain,
( composition(join(one,A),B) != composition(join(A,one),B)
| composition(join(A,one),B) = composition(join(one,A),B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,A),B))),bind(Y,$fot(composition(join(A,one),B)))]]) ).
cnf(refute_0_1180,plain,
composition(join(A,one),B) = composition(join(one,A),B),
inference(resolve,[$cnf( $equal(composition(join(one,A),B),composition(join(A,one),B)) )],[refute_0_1178,refute_0_1179]) ).
cnf(refute_0_1181,plain,
composition(join(converse(top),one),complement(composition(top,X_108))) = composition(join(one,converse(top)),complement(composition(top,X_108))),
inference(subst,[],[refute_0_1180:[bind(A,$fot(converse(top))),bind(B,$fot(complement(composition(top,X_108))))]]) ).
cnf(refute_0_1182,plain,
join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(join(converse(top),one),complement(composition(top,X_108))),
inference(subst,[],[refute_0_781:[bind(X_36,$fot(converse(top))),bind(X_38,$fot(complement(composition(top,X_108))))]]) ).
cnf(refute_0_1183,plain,
( composition(join(converse(top),one),complement(composition(top,X_108))) != composition(join(one,converse(top)),complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) != composition(join(converse(top),one),complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(join(one,converse(top)),complement(composition(top,X_108))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))))),bind(Y,$fot(composition(join(converse(top),one),complement(composition(top,X_108))))),bind(Z,$fot(composition(join(one,converse(top)),complement(composition(top,X_108)))))]]) ).
cnf(refute_0_1184,plain,
( composition(join(converse(top),one),complement(composition(top,X_108))) != composition(join(one,converse(top)),complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(join(one,converse(top)),complement(composition(top,X_108))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))),composition(join(converse(top),one),complement(composition(top,X_108)))) )],[refute_0_1182,refute_0_1183]) ).
cnf(refute_0_1185,plain,
join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(join(one,converse(top)),complement(composition(top,X_108))),
inference(resolve,[$cnf( $equal(composition(join(converse(top),one),complement(composition(top,X_108))),composition(join(one,converse(top)),complement(composition(top,X_108)))) )],[refute_0_1181,refute_0_1184]) ).
cnf(refute_0_1186,plain,
( composition(join(one,converse(top)),complement(composition(top,X_108))) != composition(top,complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) != composition(join(one,converse(top)),complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(top,complement(composition(top,X_108))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))))),bind(Y,$fot(composition(join(one,converse(top)),complement(composition(top,X_108))))),bind(Z,$fot(composition(top,complement(composition(top,X_108)))))]]) ).
cnf(refute_0_1187,plain,
( composition(join(one,converse(top)),complement(composition(top,X_108))) != composition(top,complement(composition(top,X_108)))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(top,complement(composition(top,X_108))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))),composition(join(one,converse(top)),complement(composition(top,X_108)))) )],[refute_0_1185,refute_0_1186]) ).
cnf(refute_0_1188,plain,
join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) = composition(top,complement(composition(top,X_108))),
inference(resolve,[$cnf( $equal(composition(join(one,converse(top)),complement(composition(top,X_108))),composition(top,complement(composition(top,X_108)))) )],[refute_0_1097,refute_0_1187]) ).
cnf(refute_0_1189,plain,
( join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) != complement(composition(top,X_108))
| join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) != composition(top,complement(composition(top,X_108)))
| composition(top,complement(composition(top,X_108))) = complement(composition(top,X_108)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))),complement(composition(top,X_108))) ),[0],$fot(composition(top,complement(composition(top,X_108))))]]) ).
cnf(refute_0_1190,plain,
( join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))) != complement(composition(top,X_108))
| composition(top,complement(composition(top,X_108))) = complement(composition(top,X_108)) ),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))),composition(top,complement(composition(top,X_108)))) )],[refute_0_1188,refute_0_1189]) ).
cnf(refute_0_1191,plain,
composition(top,complement(composition(top,X_108))) = complement(composition(top,X_108)),
inference(resolve,[$cnf( $equal(join(complement(composition(top,X_108)),composition(converse(top),complement(composition(top,X_108)))),complement(composition(top,X_108))) )],[refute_0_583,refute_0_1190]) ).
cnf(refute_0_1192,plain,
composition(top,complement(composition(top,converse(X_4)))) = complement(composition(top,converse(X_4))),
inference(subst,[],[refute_0_1191:[bind(X_108,$fot(converse(X_4)))]]) ).
cnf(refute_0_1193,plain,
converse(composition(X_4,converse(top))) = composition(top,converse(X_4)),
inference(subst,[],[refute_0_42:[bind(A,$fot(top))]]) ).
cnf(refute_0_1194,plain,
( converse(composition(X_4,converse(top))) != composition(top,converse(X_4))
| converse(top) != top
| converse(composition(X_4,top)) = composition(top,converse(X_4)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(X_4,converse(top))),composition(top,converse(X_4))) ),[0,0,1],$fot(top)]]) ).
cnf(refute_0_1195,plain,
( converse(composition(X_4,converse(top))) != composition(top,converse(X_4))
| converse(composition(X_4,top)) = composition(top,converse(X_4)) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_599,refute_0_1194]) ).
cnf(refute_0_1196,plain,
converse(composition(X_4,top)) = composition(top,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(top))),composition(top,converse(X_4))) )],[refute_0_1193,refute_0_1195]) ).
cnf(refute_0_1197,plain,
( converse(composition(X_4,top)) != composition(top,converse(X_4))
| composition(top,converse(X_4)) = converse(composition(X_4,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_4,top)))),bind(Y,$fot(composition(top,converse(X_4))))]]) ).
cnf(refute_0_1198,plain,
composition(top,converse(X_4)) = converse(composition(X_4,top)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,top)),composition(top,converse(X_4))) )],[refute_0_1196,refute_0_1197]) ).
cnf(refute_0_1199,plain,
( composition(top,complement(composition(top,converse(X_4)))) != complement(composition(top,converse(X_4)))
| composition(top,converse(X_4)) != converse(composition(X_4,top))
| composition(top,complement(converse(composition(X_4,top)))) = complement(composition(top,converse(X_4))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(composition(top,converse(X_4)))),complement(composition(top,converse(X_4)))) ),[0,1,0],$fot(converse(composition(X_4,top)))]]) ).
cnf(refute_0_1200,plain,
( composition(top,complement(composition(top,converse(X_4)))) != complement(composition(top,converse(X_4)))
| composition(top,complement(converse(composition(X_4,top)))) = complement(composition(top,converse(X_4))) ),
inference(resolve,[$cnf( $equal(composition(top,converse(X_4)),converse(composition(X_4,top))) )],[refute_0_1198,refute_0_1199]) ).
cnf(refute_0_1201,plain,
composition(top,complement(converse(composition(X_4,top)))) = complement(composition(top,converse(X_4))),
inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,converse(X_4)))),complement(composition(top,converse(X_4)))) )],[refute_0_1192,refute_0_1200]) ).
cnf(refute_0_1202,plain,
complement(composition(top,converse(X_4))) = complement(composition(top,converse(X_4))),
introduced(tautology,[refl,[$fot(complement(composition(top,converse(X_4))))]]) ).
cnf(refute_0_1203,plain,
( complement(composition(top,converse(X_4))) != complement(composition(top,converse(X_4)))
| composition(top,converse(X_4)) != converse(composition(X_4,top))
| complement(composition(top,converse(X_4))) = complement(converse(composition(X_4,top))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(top,converse(X_4))),complement(composition(top,converse(X_4)))) ),[1,0],$fot(converse(composition(X_4,top)))]]) ).
cnf(refute_0_1204,plain,
( composition(top,converse(X_4)) != converse(composition(X_4,top))
| complement(composition(top,converse(X_4))) = complement(converse(composition(X_4,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,converse(X_4))),complement(composition(top,converse(X_4)))) )],[refute_0_1202,refute_0_1203]) ).
cnf(refute_0_1205,plain,
complement(composition(top,converse(X_4))) = complement(converse(composition(X_4,top))),
inference(resolve,[$cnf( $equal(composition(top,converse(X_4)),converse(composition(X_4,top))) )],[refute_0_1198,refute_0_1204]) ).
cnf(refute_0_1206,plain,
( complement(composition(top,converse(X_4))) != complement(converse(composition(X_4,top)))
| composition(top,complement(converse(composition(X_4,top)))) != complement(composition(top,converse(X_4)))
| composition(top,complement(converse(composition(X_4,top)))) = complement(converse(composition(X_4,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(converse(composition(X_4,top)))),complement(composition(top,converse(X_4)))) ),[1],$fot(complement(converse(composition(X_4,top))))]]) ).
cnf(refute_0_1207,plain,
( composition(top,complement(converse(composition(X_4,top)))) != complement(composition(top,converse(X_4)))
| composition(top,complement(converse(composition(X_4,top)))) = complement(converse(composition(X_4,top))) ),
inference(resolve,[$cnf( $equal(complement(composition(top,converse(X_4))),complement(converse(composition(X_4,top)))) )],[refute_0_1205,refute_0_1206]) ).
cnf(refute_0_1208,plain,
composition(top,complement(converse(composition(X_4,top)))) = complement(converse(composition(X_4,top))),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_4,top)))),complement(composition(top,converse(X_4)))) )],[refute_0_1201,refute_0_1207]) ).
cnf(refute_0_1209,plain,
converse(composition(complement(X_234),top)) = composition(top,converse(complement(X_234))),
inference(subst,[],[refute_0_1196:[bind(X_4,$fot(complement(X_234)))]]) ).
cnf(refute_0_1210,plain,
join(meet(X_100,X_101),meet(complement(X_100),X_101)) = join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))),
inference(subst,[],[refute_0_554:[bind(X_43,$fot(meet(X_100,X_101))),bind(X_44,$fot(meet(complement(X_100),X_101)))]]) ).
cnf(refute_0_1211,plain,
X_70 = join(meet(X_70,complement(B)),complement(join(complement(X_70),complement(B)))),
inference(subst,[],[refute_0_37:[bind(A,$fot(X_70)),bind(B,$fot(complement(B)))]]) ).
cnf(refute_0_1212,plain,
meet(X_70,B) = complement(join(complement(X_70),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_70))]]) ).
cnf(refute_0_1213,plain,
( meet(X_70,B) != complement(join(complement(X_70),complement(B)))
| complement(join(complement(X_70),complement(B))) = meet(X_70,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_70,B))),bind(Y,$fot(complement(join(complement(X_70),complement(B)))))]]) ).
cnf(refute_0_1214,plain,
complement(join(complement(X_70),complement(B))) = meet(X_70,B),
inference(resolve,[$cnf( $equal(meet(X_70,B),complement(join(complement(X_70),complement(B)))) )],[refute_0_1212,refute_0_1213]) ).
cnf(refute_0_1215,plain,
( X_70 != join(meet(X_70,complement(B)),complement(join(complement(X_70),complement(B))))
| complement(join(complement(X_70),complement(B))) != meet(X_70,B)
| X_70 = join(meet(X_70,complement(B)),meet(X_70,B)) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,join(meet(X_70,complement(B)),complement(join(complement(X_70),complement(B))))) ),[1,1],$fot(meet(X_70,B))]]) ).
cnf(refute_0_1216,plain,
( X_70 != join(meet(X_70,complement(B)),complement(join(complement(X_70),complement(B))))
| X_70 = join(meet(X_70,complement(B)),meet(X_70,B)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_70),complement(B))),meet(X_70,B)) )],[refute_0_1214,refute_0_1215]) ).
cnf(refute_0_1217,plain,
X_70 = join(meet(X_70,complement(B)),meet(X_70,B)),
inference(resolve,[$cnf( $equal(X_70,join(meet(X_70,complement(B)),complement(join(complement(X_70),complement(B))))) )],[refute_0_1211,refute_0_1216]) ).
cnf(refute_0_1218,plain,
join(meet(X_70,complement(B)),meet(X_70,B)) = join(meet(X_70,B),meet(X_70,complement(B))),
inference(subst,[],[refute_0_4:[bind(A,$fot(meet(X_70,B))),bind(B,$fot(meet(X_70,complement(B))))]]) ).
cnf(refute_0_1219,plain,
( X_70 != join(meet(X_70,complement(B)),meet(X_70,B))
| join(meet(X_70,complement(B)),meet(X_70,B)) != join(meet(X_70,B),meet(X_70,complement(B)))
| X_70 = join(meet(X_70,B),meet(X_70,complement(B))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,join(meet(X_70,B),meet(X_70,complement(B)))) ),[0],$fot(join(meet(X_70,complement(B)),meet(X_70,B)))]]) ).
cnf(refute_0_1220,plain,
( X_70 != join(meet(X_70,complement(B)),meet(X_70,B))
| X_70 = join(meet(X_70,B),meet(X_70,complement(B))) ),
inference(resolve,[$cnf( $equal(join(meet(X_70,complement(B)),meet(X_70,B)),join(meet(X_70,B),meet(X_70,complement(B)))) )],[refute_0_1218,refute_0_1219]) ).
cnf(refute_0_1221,plain,
X_70 = join(meet(X_70,B),meet(X_70,complement(B))),
inference(resolve,[$cnf( $equal(X_70,join(meet(X_70,complement(B)),meet(X_70,B))) )],[refute_0_1217,refute_0_1220]) ).
cnf(refute_0_1222,plain,
X_88 = join(meet(X_88,X_87),meet(X_88,complement(X_87))),
inference(subst,[],[refute_0_1221:[bind(B,$fot(X_87)),bind(X_70,$fot(X_88))]]) ).
cnf(refute_0_1223,plain,
meet(complement(X_87),X_88) = meet(X_88,complement(X_87)),
inference(subst,[],[refute_0_261:[bind(X_23,$fot(complement(X_87))),bind(X_24,$fot(X_88))]]) ).
cnf(refute_0_1224,plain,
( meet(complement(X_87),X_88) != meet(X_88,complement(X_87))
| meet(X_88,complement(X_87)) = meet(complement(X_87),X_88) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(complement(X_87),X_88))),bind(Y,$fot(meet(X_88,complement(X_87))))]]) ).
cnf(refute_0_1225,plain,
meet(X_88,complement(X_87)) = meet(complement(X_87),X_88),
inference(resolve,[$cnf( $equal(meet(complement(X_87),X_88),meet(X_88,complement(X_87))) )],[refute_0_1223,refute_0_1224]) ).
cnf(refute_0_1226,plain,
( X_88 != join(meet(X_88,X_87),meet(X_88,complement(X_87)))
| meet(X_88,complement(X_87)) != meet(complement(X_87),X_88)
| X_88 = join(meet(X_88,X_87),meet(complement(X_87),X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(X_88,join(meet(X_88,X_87),meet(X_88,complement(X_87)))) ),[1,1],$fot(meet(complement(X_87),X_88))]]) ).
cnf(refute_0_1227,plain,
( X_88 != join(meet(X_88,X_87),meet(X_88,complement(X_87)))
| X_88 = join(meet(X_88,X_87),meet(complement(X_87),X_88)) ),
inference(resolve,[$cnf( $equal(meet(X_88,complement(X_87)),meet(complement(X_87),X_88)) )],[refute_0_1225,refute_0_1226]) ).
cnf(refute_0_1228,plain,
X_88 = join(meet(X_88,X_87),meet(complement(X_87),X_88)),
inference(resolve,[$cnf( $equal(X_88,join(meet(X_88,X_87),meet(X_88,complement(X_87)))) )],[refute_0_1222,refute_0_1227]) ).
cnf(refute_0_1229,plain,
X_101 = join(meet(X_101,X_100),meet(complement(X_100),X_101)),
inference(subst,[],[refute_0_1228:[bind(X_87,$fot(X_100)),bind(X_88,$fot(X_101))]]) ).
cnf(refute_0_1230,plain,
meet(X_100,X_101) = meet(X_101,X_100),
inference(subst,[],[refute_0_261:[bind(X_23,$fot(X_100)),bind(X_24,$fot(X_101))]]) ).
cnf(refute_0_1231,plain,
( meet(X_100,X_101) != meet(X_101,X_100)
| meet(X_101,X_100) = meet(X_100,X_101) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_100,X_101))),bind(Y,$fot(meet(X_101,X_100)))]]) ).
cnf(refute_0_1232,plain,
meet(X_101,X_100) = meet(X_100,X_101),
inference(resolve,[$cnf( $equal(meet(X_100,X_101),meet(X_101,X_100)) )],[refute_0_1230,refute_0_1231]) ).
cnf(refute_0_1233,plain,
( X_101 != join(meet(X_101,X_100),meet(complement(X_100),X_101))
| meet(X_101,X_100) != meet(X_100,X_101)
| X_101 = join(meet(X_100,X_101),meet(complement(X_100),X_101)) ),
introduced(tautology,[equality,[$cnf( $equal(X_101,join(meet(X_101,X_100),meet(complement(X_100),X_101))) ),[1,0],$fot(meet(X_100,X_101))]]) ).
cnf(refute_0_1234,plain,
( X_101 != join(meet(X_101,X_100),meet(complement(X_100),X_101))
| X_101 = join(meet(X_100,X_101),meet(complement(X_100),X_101)) ),
inference(resolve,[$cnf( $equal(meet(X_101,X_100),meet(X_100,X_101)) )],[refute_0_1232,refute_0_1233]) ).
cnf(refute_0_1235,plain,
X_101 = join(meet(X_100,X_101),meet(complement(X_100),X_101)),
inference(resolve,[$cnf( $equal(X_101,join(meet(X_101,X_100),meet(complement(X_100),X_101))) )],[refute_0_1229,refute_0_1234]) ).
cnf(refute_0_1236,plain,
( X_101 != join(meet(X_100,X_101),meet(complement(X_100),X_101))
| join(meet(X_100,X_101),meet(complement(X_100),X_101)) = X_101 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_101)),bind(Y,$fot(join(meet(X_100,X_101),meet(complement(X_100),X_101))))]]) ).
cnf(refute_0_1237,plain,
join(meet(X_100,X_101),meet(complement(X_100),X_101)) = X_101,
inference(resolve,[$cnf( $equal(X_101,join(meet(X_100,X_101),meet(complement(X_100),X_101))) )],[refute_0_1235,refute_0_1236]) ).
cnf(refute_0_1238,plain,
( join(meet(X_100,X_101),meet(complement(X_100),X_101)) != X_101
| join(meet(X_100,X_101),meet(complement(X_100),X_101)) != join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| X_101 = join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_100,X_101),meet(complement(X_100),X_101)),join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))) ),[0],$fot(X_101)]]) ).
cnf(refute_0_1239,plain,
( join(meet(X_100,X_101),meet(complement(X_100),X_101)) != join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| X_101 = join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) ),
inference(resolve,[$cnf( $equal(join(meet(X_100,X_101),meet(complement(X_100),X_101)),X_101) )],[refute_0_1237,refute_0_1238]) ).
cnf(refute_0_1240,plain,
X_101 = join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))),
inference(resolve,[$cnf( $equal(join(meet(X_100,X_101),meet(complement(X_100),X_101)),join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))) )],[refute_0_1210,refute_0_1239]) ).
cnf(refute_0_1241,plain,
join(meet(complement(X_100),X_101),X_101) = join(X_101,meet(complement(X_100),X_101)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_101)),bind(B,$fot(meet(complement(X_100),X_101)))]]) ).
cnf(refute_0_1242,plain,
join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) = join(X_155,join(meet(X_100,X_101),meet(complement(X_100),X_101))),
inference(subst,[],[refute_0_479:[bind(A,$fot(meet(complement(X_100),X_101))),bind(X_42,$fot(X_155)),bind(X_43,$fot(meet(X_100,X_101)))]]) ).
cnf(refute_0_1243,plain,
( join(meet(X_100,X_101),meet(complement(X_100),X_101)) != X_101
| join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) != join(X_155,join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) = join(X_155,X_101) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))),join(X_155,join(meet(X_100,X_101),meet(complement(X_100),X_101)))) ),[1,1],$fot(X_101)]]) ).
cnf(refute_0_1244,plain,
( join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) != join(X_155,join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) = join(X_155,X_101) ),
inference(resolve,[$cnf( $equal(join(meet(X_100,X_101),meet(complement(X_100),X_101)),X_101) )],[refute_0_1237,refute_0_1243]) ).
cnf(refute_0_1245,plain,
join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) = join(X_155,X_101),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))),join(X_155,join(meet(X_100,X_101),meet(complement(X_100),X_101)))) )],[refute_0_1242,refute_0_1244]) ).
cnf(refute_0_1246,plain,
join(X_154,join(X_155,X_156)) = join(X_155,join(X_156,X_154)),
inference(subst,[],[refute_0_479:[bind(A,$fot(X_154)),bind(X_42,$fot(X_155)),bind(X_43,$fot(X_156))]]) ).
cnf(refute_0_1247,plain,
join(X_156,X_155) = join(X_155,X_156),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_156)),bind(B,$fot(X_155))]]) ).
cnf(refute_0_1248,plain,
( join(X_156,X_155) != join(X_155,X_156)
| join(X_155,X_156) = join(X_156,X_155) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_156,X_155))),bind(Y,$fot(join(X_155,X_156)))]]) ).
cnf(refute_0_1249,plain,
join(X_155,X_156) = join(X_156,X_155),
inference(resolve,[$cnf( $equal(join(X_156,X_155),join(X_155,X_156)) )],[refute_0_1247,refute_0_1248]) ).
cnf(refute_0_1250,plain,
( join(X_154,join(X_155,X_156)) != join(X_155,join(X_156,X_154))
| join(X_155,X_156) != join(X_156,X_155)
| join(X_154,join(X_156,X_155)) = join(X_155,join(X_156,X_154)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_154,join(X_155,X_156)),join(X_155,join(X_156,X_154))) ),[0,1],$fot(join(X_156,X_155))]]) ).
cnf(refute_0_1251,plain,
( join(X_154,join(X_155,X_156)) != join(X_155,join(X_156,X_154))
| join(X_154,join(X_156,X_155)) = join(X_155,join(X_156,X_154)) ),
inference(resolve,[$cnf( $equal(join(X_155,X_156),join(X_156,X_155)) )],[refute_0_1249,refute_0_1250]) ).
cnf(refute_0_1252,plain,
join(X_154,join(X_156,X_155)) = join(X_155,join(X_156,X_154)),
inference(resolve,[$cnf( $equal(join(X_154,join(X_155,X_156)),join(X_155,join(X_156,X_154))) )],[refute_0_1246,refute_0_1251]) ).
cnf(refute_0_1253,plain,
( join(X_154,join(X_156,X_155)) != join(X_155,join(X_156,X_154))
| join(X_155,join(X_156,X_154)) = join(X_154,join(X_156,X_155)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_154,join(X_156,X_155)))),bind(Y,$fot(join(X_155,join(X_156,X_154))))]]) ).
cnf(refute_0_1254,plain,
join(X_155,join(X_156,X_154)) = join(X_154,join(X_156,X_155)),
inference(resolve,[$cnf( $equal(join(X_154,join(X_156,X_155)),join(X_155,join(X_156,X_154))) )],[refute_0_1252,refute_0_1253]) ).
cnf(refute_0_1255,plain,
join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) = join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101))),
inference(subst,[],[refute_0_1254:[bind(X_154,$fot(meet(X_100,X_101))),bind(X_155,$fot(meet(complement(X_100),X_101))),bind(X_156,$fot(X_155))]]) ).
cnf(refute_0_1256,plain,
( join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) != join(X_155,X_101)
| join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) != join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101)))
| join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101))) = join(X_155,X_101) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))),join(X_155,X_101)) ),[0],$fot(join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101))))]]) ).
cnf(refute_0_1257,plain,
( join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))) != join(X_155,X_101)
| join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101))) = join(X_155,X_101) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))),join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101)))) )],[refute_0_1255,refute_0_1256]) ).
cnf(refute_0_1258,plain,
join(meet(X_100,X_101),join(X_155,meet(complement(X_100),X_101))) = join(X_155,X_101),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),join(X_155,meet(X_100,X_101))),join(X_155,X_101)) )],[refute_0_1245,refute_0_1257]) ).
cnf(refute_0_1259,plain,
join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) = join(meet(complement(X_100),X_101),X_101),
inference(subst,[],[refute_0_1258:[bind(X_155,$fot(meet(complement(X_100),X_101)))]]) ).
cnf(refute_0_1260,plain,
( join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) != join(meet(complement(X_100),X_101),X_101)
| join(meet(complement(X_100),X_101),X_101) != join(X_101,meet(complement(X_100),X_101))
| join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))))),bind(Y,$fot(join(meet(complement(X_100),X_101),X_101))),bind(Z,$fot(join(X_101,meet(complement(X_100),X_101))))]]) ).
cnf(refute_0_1261,plain,
( join(meet(complement(X_100),X_101),X_101) != join(X_101,meet(complement(X_100),X_101))
| join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)) ),
inference(resolve,[$cnf( $equal(join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))),join(meet(complement(X_100),X_101),X_101)) )],[refute_0_1259,refute_0_1260]) ).
cnf(refute_0_1262,plain,
join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),X_101),join(X_101,meet(complement(X_100),X_101))) )],[refute_0_1241,refute_0_1261]) ).
cnf(refute_0_1263,plain,
join(X_154,X_156) = join(X_156,X_154),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_154)),bind(B,$fot(X_156))]]) ).
cnf(refute_0_1264,plain,
( join(X_154,X_156) != join(X_156,X_154)
| join(X_156,X_154) = join(X_154,X_156) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_154,X_156))),bind(Y,$fot(join(X_156,X_154)))]]) ).
cnf(refute_0_1265,plain,
join(X_156,X_154) = join(X_154,X_156),
inference(resolve,[$cnf( $equal(join(X_154,X_156),join(X_156,X_154)) )],[refute_0_1263,refute_0_1264]) ).
cnf(refute_0_1266,plain,
( join(X_154,join(X_155,X_156)) != join(X_155,join(X_156,X_154))
| join(X_156,X_154) != join(X_154,X_156)
| join(X_154,join(X_155,X_156)) = join(X_155,join(X_154,X_156)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_154,join(X_155,X_156)),join(X_155,join(X_156,X_154))) ),[1,1],$fot(join(X_154,X_156))]]) ).
cnf(refute_0_1267,plain,
( join(X_154,join(X_155,X_156)) != join(X_155,join(X_156,X_154))
| join(X_154,join(X_155,X_156)) = join(X_155,join(X_154,X_156)) ),
inference(resolve,[$cnf( $equal(join(X_156,X_154),join(X_154,X_156)) )],[refute_0_1265,refute_0_1266]) ).
cnf(refute_0_1268,plain,
join(X_154,join(X_155,X_156)) = join(X_155,join(X_154,X_156)),
inference(resolve,[$cnf( $equal(join(X_154,join(X_155,X_156)),join(X_155,join(X_156,X_154))) )],[refute_0_1246,refute_0_1267]) ).
cnf(refute_0_1269,plain,
( join(X_154,join(X_155,X_156)) != join(X_155,join(X_154,X_156))
| join(X_155,join(X_154,X_156)) = join(X_154,join(X_155,X_156)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_154,join(X_155,X_156)))),bind(Y,$fot(join(X_155,join(X_154,X_156))))]]) ).
cnf(refute_0_1270,plain,
join(X_155,join(X_154,X_156)) = join(X_154,join(X_155,X_156)),
inference(resolve,[$cnf( $equal(join(X_154,join(X_155,X_156)),join(X_155,join(X_154,X_156))) )],[refute_0_1268,refute_0_1269]) ).
cnf(refute_0_1271,plain,
join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) = join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))),
inference(subst,[],[refute_0_1270:[bind(X_154,$fot(meet(X_100,X_101))),bind(X_155,$fot(meet(complement(X_100),X_101))),bind(X_156,$fot(meet(complement(X_100),X_101)))]]) ).
cnf(refute_0_1272,plain,
( join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) != join(X_101,meet(complement(X_100),X_101))
| join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) != join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101)))
| join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))))),bind(Y,$fot(join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))))),bind(Z,$fot(join(X_101,meet(complement(X_100),X_101))))]]) ).
cnf(refute_0_1273,plain,
( join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))) != join(X_101,meet(complement(X_100),X_101))
| join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))),join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101)))) )],[refute_0_1271,refute_0_1272]) ).
cnf(refute_0_1274,plain,
join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) = join(X_101,meet(complement(X_100),X_101)),
inference(resolve,[$cnf( $equal(join(meet(X_100,X_101),join(meet(complement(X_100),X_101),meet(complement(X_100),X_101))),join(X_101,meet(complement(X_100),X_101))) )],[refute_0_1262,refute_0_1273]) ).
cnf(refute_0_1275,plain,
( X_101 != join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))) != join(X_101,meet(complement(X_100),X_101))
| X_101 = join(X_101,meet(complement(X_100),X_101)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_101,join(X_101,meet(complement(X_100),X_101))) ),[0],$fot(join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))))]]) ).
cnf(refute_0_1276,plain,
( X_101 != join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))
| X_101 = join(X_101,meet(complement(X_100),X_101)) ),
inference(resolve,[$cnf( $equal(join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101))),join(X_101,meet(complement(X_100),X_101))) )],[refute_0_1274,refute_0_1275]) ).
cnf(refute_0_1277,plain,
X_101 = join(X_101,meet(complement(X_100),X_101)),
inference(resolve,[$cnf( $equal(X_101,join(meet(complement(X_100),X_101),join(meet(X_100,X_101),meet(complement(X_100),X_101)))) )],[refute_0_1240,refute_0_1276]) ).
cnf(refute_0_1278,plain,
converse(complement(converse(complement(complement(X_229))))) = join(converse(complement(converse(complement(complement(X_229))))),meet(complement(X_229),converse(complement(converse(complement(complement(X_229))))))),
inference(subst,[],[refute_0_1277:[bind(X_100,$fot(X_229)),bind(X_101,$fot(converse(complement(converse(complement(complement(X_229)))))))]]) ).
cnf(refute_0_1279,plain,
X_70 = join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(join(complement(X_70),converse(complement(converse(complement(X_70))))))),
inference(subst,[],[refute_0_267:[bind(X_71,$fot(converse(complement(converse(complement(X_70))))))]]) ).
cnf(refute_0_1280,plain,
converse(join(converse(X_145),complement(converse(X_145)))) = join(X_145,converse(complement(converse(X_145)))),
inference(subst,[],[refute_0_102:[bind(A,$fot(X_145)),bind(X_11,$fot(complement(converse(X_145))))]]) ).
cnf(refute_0_1281,plain,
top = join(converse(X_145),complement(converse(X_145))),
inference(subst,[],[def_top_12:[bind(A,$fot(converse(X_145)))]]) ).
cnf(refute_0_1282,plain,
( top != join(converse(X_145),complement(converse(X_145)))
| join(converse(X_145),complement(converse(X_145))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(converse(X_145),complement(converse(X_145)))))]]) ).
cnf(refute_0_1283,plain,
join(converse(X_145),complement(converse(X_145))) = top,
inference(resolve,[$cnf( $equal(top,join(converse(X_145),complement(converse(X_145)))) )],[refute_0_1281,refute_0_1282]) ).
cnf(refute_0_1284,plain,
( converse(join(converse(X_145),complement(converse(X_145)))) != join(X_145,converse(complement(converse(X_145))))
| join(converse(X_145),complement(converse(X_145))) != top
| converse(top) = join(X_145,converse(complement(converse(X_145)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(X_145),complement(converse(X_145)))),join(X_145,converse(complement(converse(X_145))))) ),[0,0],$fot(top)]]) ).
cnf(refute_0_1285,plain,
( converse(join(converse(X_145),complement(converse(X_145)))) != join(X_145,converse(complement(converse(X_145))))
| converse(top) = join(X_145,converse(complement(converse(X_145)))) ),
inference(resolve,[$cnf( $equal(join(converse(X_145),complement(converse(X_145))),top) )],[refute_0_1283,refute_0_1284]) ).
cnf(refute_0_1286,plain,
converse(top) = join(X_145,converse(complement(converse(X_145)))),
inference(resolve,[$cnf( $equal(converse(join(converse(X_145),complement(converse(X_145)))),join(X_145,converse(complement(converse(X_145))))) )],[refute_0_1280,refute_0_1285]) ).
cnf(refute_0_1287,plain,
( converse(top) != join(X_145,converse(complement(converse(X_145))))
| converse(top) != top
| top = join(X_145,converse(complement(converse(X_145)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(top),join(X_145,converse(complement(converse(X_145))))) ),[0],$fot(top)]]) ).
cnf(refute_0_1288,plain,
( converse(top) != join(X_145,converse(complement(converse(X_145))))
| top = join(X_145,converse(complement(converse(X_145)))) ),
inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_599,refute_0_1287]) ).
cnf(refute_0_1289,plain,
top = join(X_145,converse(complement(converse(X_145)))),
inference(resolve,[$cnf( $equal(converse(top),join(X_145,converse(complement(converse(X_145))))) )],[refute_0_1286,refute_0_1288]) ).
cnf(refute_0_1290,plain,
top = join(complement(X_70),converse(complement(converse(complement(X_70))))),
inference(subst,[],[refute_0_1289:[bind(X_145,$fot(complement(X_70)))]]) ).
cnf(refute_0_1291,plain,
( top != join(complement(X_70),converse(complement(converse(complement(X_70)))))
| join(complement(X_70),converse(complement(converse(complement(X_70))))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_70),converse(complement(converse(complement(X_70)))))))]]) ).
cnf(refute_0_1292,plain,
join(complement(X_70),converse(complement(converse(complement(X_70))))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_70),converse(complement(converse(complement(X_70)))))) )],[refute_0_1290,refute_0_1291]) ).
cnf(refute_0_1293,plain,
( X_70 != join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(join(complement(X_70),converse(complement(converse(complement(X_70)))))))
| join(complement(X_70),converse(complement(converse(complement(X_70))))) != top
| X_70 = join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(X_70,join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(join(complement(X_70),converse(complement(converse(complement(X_70)))))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_1294,plain,
( X_70 != join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(join(complement(X_70),converse(complement(converse(complement(X_70)))))))
| X_70 = join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) ),
inference(resolve,[$cnf( $equal(join(complement(X_70),converse(complement(converse(complement(X_70))))),top) )],[refute_0_1292,refute_0_1293]) ).
cnf(refute_0_1295,plain,
X_70 = join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)),
inference(resolve,[$cnf( $equal(X_70,join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(join(complement(X_70),converse(complement(converse(complement(X_70)))))))) )],[refute_0_1279,refute_0_1294]) ).
cnf(refute_0_1296,plain,
join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) = meet(X_70,converse(complement(converse(complement(X_70))))),
inference(subst,[],[refute_0_245:[bind(X_72,$fot(meet(X_70,converse(complement(converse(complement(X_70)))))))]]) ).
cnf(refute_0_1297,plain,
( meet(X_23,X_24) != meet(X_24,X_23)
| meet(X_24,X_23) = meet(X_23,X_24) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_23,X_24))),bind(Y,$fot(meet(X_24,X_23)))]]) ).
cnf(refute_0_1298,plain,
meet(X_24,X_23) = meet(X_23,X_24),
inference(resolve,[$cnf( $equal(meet(X_23,X_24),meet(X_24,X_23)) )],[refute_0_261,refute_0_1297]) ).
cnf(refute_0_1299,plain,
meet(converse(complement(converse(complement(X_70)))),X_70) = meet(X_70,converse(complement(converse(complement(X_70))))),
inference(subst,[],[refute_0_1298:[bind(X_23,$fot(X_70)),bind(X_24,$fot(converse(complement(converse(complement(X_70))))))]]) ).
cnf(refute_0_1300,plain,
join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)),
introduced(tautology,[refl,[$fot(join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)))]]) ).
cnf(refute_0_1301,plain,
( join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) != join(zero,meet(converse(complement(converse(complement(X_70)))),X_70))
| meet(converse(complement(converse(complement(X_70)))),X_70) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)),join(zero,meet(converse(complement(converse(complement(X_70)))),X_70))) ),[1,1],$fot(meet(X_70,converse(complement(converse(complement(X_70))))))]]) ).
cnf(refute_0_1302,plain,
( meet(converse(complement(converse(complement(X_70)))),X_70) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) ),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)),join(zero,meet(converse(complement(converse(complement(X_70)))),X_70))) )],[refute_0_1300,refute_0_1301]) ).
cnf(refute_0_1303,plain,
join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))),
inference(resolve,[$cnf( $equal(meet(converse(complement(converse(complement(X_70)))),X_70),meet(X_70,converse(complement(converse(complement(X_70)))))) )],[refute_0_1299,refute_0_1302]) ).
cnf(refute_0_1304,plain,
join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),
introduced(tautology,[refl,[$fot(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)))]]) ).
cnf(refute_0_1305,plain,
( complement(top) != zero
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) != join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70))
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_1306,plain,
( complement(top) != zero
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70))) )],[refute_0_1304,refute_0_1305]) ).
cnf(refute_0_1307,plain,
join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_219,refute_0_1306]) ).
cnf(refute_0_1308,plain,
( join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) != join(zero,meet(converse(complement(converse(complement(X_70)))),X_70))
| join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) != join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)))),bind(Y,$fot(join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)))),bind(Z,$fot(join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))))]]) ).
cnf(refute_0_1309,plain,
( join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)) != join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),join(zero,meet(converse(complement(converse(complement(X_70)))),X_70))) )],[refute_0_1307,refute_0_1308]) ).
cnf(refute_0_1310,plain,
join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))),
inference(resolve,[$cnf( $equal(join(zero,meet(converse(complement(converse(complement(X_70)))),X_70)),join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))) )],[refute_0_1303,refute_0_1309]) ).
cnf(refute_0_1311,plain,
( join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) != join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))
| join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = meet(X_70,converse(complement(converse(complement(X_70))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)))),bind(Y,$fot(join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))))),bind(Z,$fot(meet(X_70,converse(complement(converse(complement(X_70)))))))]]) ).
cnf(refute_0_1312,plain,
( join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = meet(X_70,converse(complement(converse(complement(X_70))))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),join(zero,meet(X_70,converse(complement(converse(complement(X_70))))))) )],[refute_0_1310,refute_0_1311]) ).
cnf(refute_0_1313,plain,
join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) = meet(X_70,converse(complement(converse(complement(X_70))))),
inference(resolve,[$cnf( $equal(join(zero,meet(X_70,converse(complement(converse(complement(X_70)))))),meet(X_70,converse(complement(converse(complement(X_70)))))) )],[refute_0_1296,refute_0_1312]) ).
cnf(refute_0_1314,plain,
join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) = join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(top))),bind(B,$fot(meet(converse(complement(converse(complement(X_70)))),X_70)))]]) ).
cnf(refute_0_1315,plain,
( join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) != join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70))
| join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) = meet(X_70,converse(complement(converse(complement(X_70))))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)))),bind(Y,$fot(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)))),bind(Z,$fot(meet(X_70,converse(complement(converse(complement(X_70)))))))]]) ).
cnf(refute_0_1316,plain,
( join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)) != meet(X_70,converse(complement(converse(complement(X_70)))))
| join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) = meet(X_70,converse(complement(converse(complement(X_70))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)),join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70))) )],[refute_0_1314,refute_0_1315]) ).
cnf(refute_0_1317,plain,
join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) = meet(X_70,converse(complement(converse(complement(X_70))))),
inference(resolve,[$cnf( $equal(join(complement(top),meet(converse(complement(converse(complement(X_70)))),X_70)),meet(X_70,converse(complement(converse(complement(X_70)))))) )],[refute_0_1313,refute_0_1316]) ).
cnf(refute_0_1318,plain,
( X_70 != join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top))
| join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)) != meet(X_70,converse(complement(converse(complement(X_70)))))
| X_70 = meet(X_70,converse(complement(converse(complement(X_70))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_70,meet(X_70,converse(complement(converse(complement(X_70)))))) ),[0],$fot(join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)))]]) ).
cnf(refute_0_1319,plain,
( X_70 != join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top))
| X_70 = meet(X_70,converse(complement(converse(complement(X_70))))) ),
inference(resolve,[$cnf( $equal(join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top)),meet(X_70,converse(complement(converse(complement(X_70)))))) )],[refute_0_1317,refute_0_1318]) ).
cnf(refute_0_1320,plain,
X_70 = meet(X_70,converse(complement(converse(complement(X_70))))),
inference(resolve,[$cnf( $equal(X_70,join(meet(converse(complement(converse(complement(X_70)))),X_70),complement(top))) )],[refute_0_1295,refute_0_1319]) ).
cnf(refute_0_1321,plain,
complement(X_229) = meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),
inference(subst,[],[refute_0_1320:[bind(X_70,$fot(complement(X_229)))]]) ).
cnf(refute_0_1322,plain,
( complement(X_229) != meet(complement(X_229),converse(complement(converse(complement(complement(X_229))))))
| meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = complement(X_229) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_229))),bind(Y,$fot(meet(complement(X_229),converse(complement(converse(complement(complement(X_229))))))))]]) ).
cnf(refute_0_1323,plain,
meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = complement(X_229),
inference(resolve,[$cnf( $equal(complement(X_229),meet(complement(X_229),converse(complement(converse(complement(complement(X_229))))))) )],[refute_0_1321,refute_0_1322]) ).
cnf(refute_0_1324,plain,
( converse(complement(converse(complement(complement(X_229))))) != join(converse(complement(converse(complement(complement(X_229))))),meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))
| meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) != complement(X_229)
| converse(complement(converse(complement(complement(X_229))))) = join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),join(converse(complement(converse(complement(complement(X_229))))),meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))) ),[1,1],$fot(complement(X_229))]]) ).
cnf(refute_0_1325,plain,
( converse(complement(converse(complement(complement(X_229))))) != join(converse(complement(converse(complement(complement(X_229))))),meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))
| converse(complement(converse(complement(complement(X_229))))) = join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) ),
inference(resolve,[$cnf( $equal(meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),complement(X_229)) )],[refute_0_1323,refute_0_1324]) ).
cnf(refute_0_1326,plain,
converse(complement(converse(complement(complement(X_229))))) = join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),join(converse(complement(converse(complement(complement(X_229))))),meet(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))) )],[refute_0_1278,refute_0_1325]) ).
cnf(refute_0_1327,plain,
complement(complement(X_229)) = X_229,
inference(subst,[],[refute_0_276:[bind(X_70,$fot(X_229))]]) ).
cnf(refute_0_1328,plain,
converse(complement(complement(X_229))) = converse(complement(complement(X_229))),
introduced(tautology,[refl,[$fot(converse(complement(complement(X_229))))]]) ).
cnf(refute_0_1329,plain,
( complement(complement(X_229)) != X_229
| converse(complement(complement(X_229))) != converse(complement(complement(X_229)))
| converse(complement(complement(X_229))) = converse(X_229) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(complement(X_229))),converse(complement(complement(X_229)))) ),[1,0],$fot(X_229)]]) ).
cnf(refute_0_1330,plain,
( complement(complement(X_229)) != X_229
| converse(complement(complement(X_229))) = converse(X_229) ),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_229))),converse(complement(complement(X_229)))) )],[refute_0_1328,refute_0_1329]) ).
cnf(refute_0_1331,plain,
converse(complement(complement(X_229))) = converse(X_229),
inference(resolve,[$cnf( $equal(complement(complement(X_229)),X_229) )],[refute_0_1327,refute_0_1330]) ).
cnf(refute_0_1332,plain,
complement(converse(complement(complement(X_229)))) = complement(converse(complement(complement(X_229)))),
introduced(tautology,[refl,[$fot(complement(converse(complement(complement(X_229)))))]]) ).
cnf(refute_0_1333,plain,
( complement(converse(complement(complement(X_229)))) != complement(converse(complement(complement(X_229))))
| converse(complement(complement(X_229))) != converse(X_229)
| complement(converse(complement(complement(X_229)))) = complement(converse(X_229)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(complement(complement(X_229)))),complement(converse(complement(complement(X_229))))) ),[1,0],$fot(converse(X_229))]]) ).
cnf(refute_0_1334,plain,
( converse(complement(complement(X_229))) != converse(X_229)
| complement(converse(complement(complement(X_229)))) = complement(converse(X_229)) ),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_229)))),complement(converse(complement(complement(X_229))))) )],[refute_0_1332,refute_0_1333]) ).
cnf(refute_0_1335,plain,
complement(converse(complement(complement(X_229)))) = complement(converse(X_229)),
inference(resolve,[$cnf( $equal(converse(complement(complement(X_229))),converse(X_229)) )],[refute_0_1331,refute_0_1334]) ).
cnf(refute_0_1336,plain,
converse(complement(converse(complement(complement(X_229))))) = converse(complement(converse(complement(complement(X_229))))),
introduced(tautology,[refl,[$fot(converse(complement(converse(complement(complement(X_229))))))]]) ).
cnf(refute_0_1337,plain,
( complement(converse(complement(complement(X_229)))) != complement(converse(X_229))
| converse(complement(converse(complement(complement(X_229))))) != converse(complement(converse(complement(complement(X_229)))))
| converse(complement(converse(complement(complement(X_229))))) = converse(complement(converse(X_229))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),converse(complement(converse(complement(complement(X_229)))))) ),[1,0],$fot(complement(converse(X_229)))]]) ).
cnf(refute_0_1338,plain,
( complement(converse(complement(complement(X_229)))) != complement(converse(X_229))
| converse(complement(converse(complement(complement(X_229))))) = converse(complement(converse(X_229))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),converse(complement(converse(complement(complement(X_229)))))) )],[refute_0_1336,refute_0_1337]) ).
cnf(refute_0_1339,plain,
converse(complement(converse(complement(complement(X_229))))) = converse(complement(converse(X_229))),
inference(resolve,[$cnf( $equal(complement(converse(complement(complement(X_229)))),complement(converse(X_229))) )],[refute_0_1335,refute_0_1338]) ).
cnf(refute_0_1340,plain,
( converse(complement(converse(complement(complement(X_229))))) != converse(complement(converse(X_229)))
| converse(complement(converse(complement(complement(X_229))))) != join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))
| converse(complement(converse(X_229))) = join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))) ),[0],$fot(converse(complement(converse(X_229))))]]) ).
cnf(refute_0_1341,plain,
( converse(complement(converse(complement(complement(X_229))))) != join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))
| converse(complement(converse(X_229))) = join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),converse(complement(converse(X_229)))) )],[refute_0_1339,refute_0_1340]) ).
cnf(refute_0_1342,plain,
join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),
introduced(tautology,[refl,[$fot(join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))]]) ).
cnf(refute_0_1343,plain,
( converse(complement(converse(complement(complement(X_229))))) != converse(complement(converse(X_229)))
| join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) != join(complement(X_229),converse(complement(converse(complement(complement(X_229))))))
| join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = join(complement(X_229),converse(complement(converse(X_229)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),join(complement(X_229),converse(complement(converse(complement(complement(X_229))))))) ),[1,1],$fot(converse(complement(converse(X_229))))]]) ).
cnf(refute_0_1344,plain,
( converse(complement(converse(complement(complement(X_229))))) != converse(complement(converse(X_229)))
| join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = join(complement(X_229),converse(complement(converse(X_229)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),join(complement(X_229),converse(complement(converse(complement(complement(X_229))))))) )],[refute_0_1342,refute_0_1343]) ).
cnf(refute_0_1345,plain,
join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) = join(complement(X_229),converse(complement(converse(X_229)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),converse(complement(converse(X_229)))) )],[refute_0_1339,refute_0_1344]) ).
cnf(refute_0_1346,plain,
join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) = join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_229))),bind(B,$fot(converse(complement(converse(complement(complement(X_229)))))))]]) ).
cnf(refute_0_1347,plain,
( join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) != join(complement(X_229),converse(complement(converse(X_229))))
| join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) != join(complement(X_229),converse(complement(converse(complement(complement(X_229))))))
| join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) = join(complement(X_229),converse(complement(converse(X_229)))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)))),bind(Y,$fot(join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))))),bind(Z,$fot(join(complement(X_229),converse(complement(converse(X_229))))))]]) ).
cnf(refute_0_1348,plain,
( join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))) != join(complement(X_229),converse(complement(converse(X_229))))
| join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) = join(complement(X_229),converse(complement(converse(X_229)))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)),join(complement(X_229),converse(complement(converse(complement(complement(X_229))))))) )],[refute_0_1346,refute_0_1347]) ).
cnf(refute_0_1349,plain,
join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) = join(complement(X_229),converse(complement(converse(X_229)))),
inference(resolve,[$cnf( $equal(join(complement(X_229),converse(complement(converse(complement(complement(X_229)))))),join(complement(X_229),converse(complement(converse(X_229))))) )],[refute_0_1345,refute_0_1348]) ).
cnf(refute_0_1350,plain,
( converse(complement(converse(X_229))) != join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))
| join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)) != join(complement(X_229),converse(complement(converse(X_229))))
| converse(complement(converse(X_229))) = join(complement(X_229),converse(complement(converse(X_229)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(converse(X_229))),join(complement(X_229),converse(complement(converse(X_229))))) ),[0],$fot(join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)))]]) ).
cnf(refute_0_1351,plain,
( converse(complement(converse(X_229))) != join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))
| converse(complement(converse(X_229))) = join(complement(X_229),converse(complement(converse(X_229)))) ),
inference(resolve,[$cnf( $equal(join(converse(complement(converse(complement(complement(X_229))))),complement(X_229)),join(complement(X_229),converse(complement(converse(X_229))))) )],[refute_0_1349,refute_0_1350]) ).
cnf(refute_0_1352,plain,
( converse(complement(converse(complement(complement(X_229))))) != join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))
| converse(complement(converse(X_229))) = join(complement(X_229),converse(complement(converse(X_229)))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_229))),join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))) )],[refute_0_1341,refute_0_1351]) ).
cnf(refute_0_1353,plain,
converse(complement(converse(X_229))) = join(complement(X_229),converse(complement(converse(X_229)))),
inference(resolve,[$cnf( $equal(converse(complement(converse(complement(complement(X_229))))),join(converse(complement(converse(complement(complement(X_229))))),complement(X_229))) )],[refute_0_1326,refute_0_1352]) ).
cnf(refute_0_1354,plain,
converse(complement(converse(converse(A)))) = join(complement(converse(A)),converse(complement(converse(converse(A))))),
inference(subst,[],[refute_0_1353:[bind(X_229,$fot(converse(A)))]]) ).
cnf(refute_0_1355,plain,
( converse(complement(converse(converse(A)))) != join(complement(converse(A)),converse(complement(converse(converse(A)))))
| converse(converse(A)) != A
| converse(complement(converse(converse(A)))) = join(complement(converse(A)),converse(complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(converse(A)))),join(complement(converse(A)),converse(complement(converse(converse(A)))))) ),[1,1,0,0],$fot(A)]]) ).
cnf(refute_0_1356,plain,
( converse(complement(converse(converse(A)))) != join(complement(converse(A)),converse(complement(converse(converse(A)))))
| converse(complement(converse(converse(A)))) = join(complement(converse(A)),converse(complement(A))) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1355]) ).
cnf(refute_0_1357,plain,
converse(complement(converse(converse(A)))) = join(complement(converse(A)),converse(complement(A))),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),join(complement(converse(A)),converse(complement(converse(converse(A)))))) )],[refute_0_1354,refute_0_1356]) ).
cnf(refute_0_1358,plain,
complement(converse(converse(A))) = complement(converse(converse(A))),
introduced(tautology,[refl,[$fot(complement(converse(converse(A))))]]) ).
cnf(refute_0_1359,plain,
( complement(converse(converse(A))) != complement(converse(converse(A)))
| converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) ),[1,0],$fot(A)]]) ).
cnf(refute_0_1360,plain,
( converse(converse(A)) != A
| complement(converse(converse(A))) = complement(A) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(converse(converse(A)))) )],[refute_0_1358,refute_0_1359]) ).
cnf(refute_0_1361,plain,
complement(converse(converse(A))) = complement(A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_1360]) ).
cnf(refute_0_1362,plain,
converse(complement(converse(converse(A)))) = converse(complement(converse(converse(A)))),
introduced(tautology,[refl,[$fot(converse(complement(converse(converse(A)))))]]) ).
cnf(refute_0_1363,plain,
( complement(converse(converse(A))) != complement(A)
| converse(complement(converse(converse(A)))) != converse(complement(converse(converse(A))))
| converse(complement(converse(converse(A)))) = converse(complement(A)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(converse(converse(A))))) ),[1,0],$fot(complement(A))]]) ).
cnf(refute_0_1364,plain,
( complement(converse(converse(A))) != complement(A)
| converse(complement(converse(converse(A)))) = converse(complement(A)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(converse(converse(A))))) )],[refute_0_1362,refute_0_1363]) ).
cnf(refute_0_1365,plain,
converse(complement(converse(converse(A)))) = converse(complement(A)),
inference(resolve,[$cnf( $equal(complement(converse(converse(A))),complement(A)) )],[refute_0_1361,refute_0_1364]) ).
cnf(refute_0_1366,plain,
( converse(complement(converse(converse(A)))) != converse(complement(A))
| converse(complement(converse(converse(A)))) != join(complement(converse(A)),converse(complement(A)))
| converse(complement(A)) = join(complement(converse(A)),converse(complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(converse(A)))),join(complement(converse(A)),converse(complement(A)))) ),[0],$fot(converse(complement(A)))]]) ).
cnf(refute_0_1367,plain,
( converse(complement(converse(converse(A)))) != join(complement(converse(A)),converse(complement(A)))
| converse(complement(A)) = join(complement(converse(A)),converse(complement(A))) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),converse(complement(A))) )],[refute_0_1365,refute_0_1366]) ).
cnf(refute_0_1368,plain,
join(converse(X_11),converse(X_10)) = join(converse(X_10),converse(X_11)),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(converse(X_11))),bind(B,$fot(converse(X_10)))]]) ).
cnf(refute_0_1369,plain,
converse(join(X_10,X_11)) = join(converse(X_10),converse(X_11)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_10)),bind(B,$fot(X_11))]]) ).
cnf(refute_0_1370,plain,
( converse(join(X_10,X_11)) != join(converse(X_10),converse(X_11))
| join(converse(X_10),converse(X_11)) = converse(join(X_10,X_11)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_10,X_11)))),bind(Y,$fot(join(converse(X_10),converse(X_11))))]]) ).
cnf(refute_0_1371,plain,
join(converse(X_10),converse(X_11)) = converse(join(X_10,X_11)),
inference(resolve,[$cnf( $equal(converse(join(X_10,X_11)),join(converse(X_10),converse(X_11))) )],[refute_0_1369,refute_0_1370]) ).
cnf(refute_0_1372,plain,
( join(converse(X_10),converse(X_11)) != converse(join(X_10,X_11))
| join(converse(X_11),converse(X_10)) != join(converse(X_10),converse(X_11))
| join(converse(X_11),converse(X_10)) = converse(join(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_11),converse(X_10)),join(converse(X_10),converse(X_11))) ),[1],$fot(converse(join(X_10,X_11)))]]) ).
cnf(refute_0_1373,plain,
( join(converse(X_11),converse(X_10)) != join(converse(X_10),converse(X_11))
| join(converse(X_11),converse(X_10)) = converse(join(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(join(converse(X_10),converse(X_11)),converse(join(X_10,X_11))) )],[refute_0_1371,refute_0_1372]) ).
cnf(refute_0_1374,plain,
join(converse(X_11),converse(X_10)) = converse(join(X_10,X_11)),
inference(resolve,[$cnf( $equal(join(converse(X_11),converse(X_10)),join(converse(X_10),converse(X_11))) )],[refute_0_1368,refute_0_1373]) ).
cnf(refute_0_1375,plain,
join(converse(X_11),converse(X_10)) = converse(join(X_11,X_10)),
inference(subst,[],[refute_0_1134:[bind(A,$fot(X_11)),bind(B,$fot(X_10))]]) ).
cnf(refute_0_1376,plain,
( join(converse(X_11),converse(X_10)) != converse(join(X_10,X_11))
| join(converse(X_11),converse(X_10)) != converse(join(X_11,X_10))
| converse(join(X_11,X_10)) = converse(join(X_10,X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(join(converse(X_11),converse(X_10)),converse(join(X_10,X_11))) ),[0],$fot(converse(join(X_11,X_10)))]]) ).
cnf(refute_0_1377,plain,
( join(converse(X_11),converse(X_10)) != converse(join(X_10,X_11))
| converse(join(X_11,X_10)) = converse(join(X_10,X_11)) ),
inference(resolve,[$cnf( $equal(join(converse(X_11),converse(X_10)),converse(join(X_11,X_10))) )],[refute_0_1375,refute_0_1376]) ).
cnf(refute_0_1378,plain,
converse(join(X_11,X_10)) = converse(join(X_10,X_11)),
inference(resolve,[$cnf( $equal(join(converse(X_11),converse(X_10)),converse(join(X_10,X_11))) )],[refute_0_1374,refute_0_1377]) ).
cnf(refute_0_1379,plain,
converse(join(converse(complement(converse(X_233))),complement(X_233))) = converse(join(complement(X_233),converse(complement(converse(X_233))))),
inference(subst,[],[refute_0_1378:[bind(X_10,$fot(complement(X_233))),bind(X_11,$fot(converse(complement(converse(X_233)))))]]) ).
cnf(refute_0_1380,plain,
converse(complement(converse(X_233))) = join(complement(X_233),converse(complement(converse(X_233)))),
inference(subst,[],[refute_0_1353:[bind(X_229,$fot(X_233))]]) ).
cnf(refute_0_1381,plain,
( converse(complement(converse(X_233))) != join(complement(X_233),converse(complement(converse(X_233))))
| join(complement(X_233),converse(complement(converse(X_233)))) = converse(complement(converse(X_233))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(complement(converse(X_233))))),bind(Y,$fot(join(complement(X_233),converse(complement(converse(X_233))))))]]) ).
cnf(refute_0_1382,plain,
join(complement(X_233),converse(complement(converse(X_233)))) = converse(complement(converse(X_233))),
inference(resolve,[$cnf( $equal(converse(complement(converse(X_233))),join(complement(X_233),converse(complement(converse(X_233))))) )],[refute_0_1380,refute_0_1381]) ).
cnf(refute_0_1383,plain,
( converse(join(converse(complement(converse(X_233))),complement(X_233))) != converse(join(complement(X_233),converse(complement(converse(X_233)))))
| join(complement(X_233),converse(complement(converse(X_233)))) != converse(complement(converse(X_233)))
| converse(join(converse(complement(converse(X_233))),complement(X_233))) = converse(converse(complement(converse(X_233)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(X_233))),complement(X_233))),converse(join(complement(X_233),converse(complement(converse(X_233)))))) ),[1,0],$fot(converse(complement(converse(X_233))))]]) ).
cnf(refute_0_1384,plain,
( converse(join(converse(complement(converse(X_233))),complement(X_233))) != converse(join(complement(X_233),converse(complement(converse(X_233)))))
| converse(join(converse(complement(converse(X_233))),complement(X_233))) = converse(converse(complement(converse(X_233)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_233),converse(complement(converse(X_233)))),converse(complement(converse(X_233)))) )],[refute_0_1382,refute_0_1383]) ).
cnf(refute_0_1385,plain,
converse(join(converse(complement(converse(X_233))),complement(X_233))) = converse(converse(complement(converse(X_233)))),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_233))),complement(X_233))),converse(join(complement(X_233),converse(complement(converse(X_233)))))) )],[refute_0_1379,refute_0_1384]) ).
cnf(refute_0_1386,plain,
converse(join(converse(complement(converse(X_233))),complement(X_233))) = join(complement(converse(X_233)),converse(complement(X_233))),
inference(subst,[],[refute_0_102:[bind(A,$fot(complement(converse(X_233)))),bind(X_11,$fot(complement(X_233)))]]) ).
cnf(refute_0_1387,plain,
( converse(join(converse(complement(converse(X_233))),complement(X_233))) != converse(converse(complement(converse(X_233))))
| converse(join(converse(complement(converse(X_233))),complement(X_233))) != join(complement(converse(X_233)),converse(complement(X_233)))
| join(complement(converse(X_233)),converse(complement(X_233))) = converse(converse(complement(converse(X_233)))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(complement(converse(X_233))),complement(X_233))),converse(converse(complement(converse(X_233))))) ),[0],$fot(join(complement(converse(X_233)),converse(complement(X_233))))]]) ).
cnf(refute_0_1388,plain,
( converse(join(converse(complement(converse(X_233))),complement(X_233))) != converse(converse(complement(converse(X_233))))
| join(complement(converse(X_233)),converse(complement(X_233))) = converse(converse(complement(converse(X_233)))) ),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_233))),complement(X_233))),join(complement(converse(X_233)),converse(complement(X_233)))) )],[refute_0_1386,refute_0_1387]) ).
cnf(refute_0_1389,plain,
converse(converse(complement(converse(X_233)))) = complement(converse(X_233)),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(complement(converse(X_233))))]]) ).
cnf(refute_0_1390,plain,
( converse(converse(complement(converse(X_233)))) != complement(converse(X_233))
| join(complement(converse(X_233)),converse(complement(X_233))) != converse(converse(complement(converse(X_233))))
| join(complement(converse(X_233)),converse(complement(X_233))) = complement(converse(X_233)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(converse(X_233)),converse(complement(X_233))),converse(converse(complement(converse(X_233))))) ),[1],$fot(complement(converse(X_233)))]]) ).
cnf(refute_0_1391,plain,
( join(complement(converse(X_233)),converse(complement(X_233))) != converse(converse(complement(converse(X_233))))
| join(complement(converse(X_233)),converse(complement(X_233))) = complement(converse(X_233)) ),
inference(resolve,[$cnf( $equal(converse(converse(complement(converse(X_233)))),complement(converse(X_233))) )],[refute_0_1389,refute_0_1390]) ).
cnf(refute_0_1392,plain,
( converse(join(converse(complement(converse(X_233))),complement(X_233))) != converse(converse(complement(converse(X_233))))
| join(complement(converse(X_233)),converse(complement(X_233))) = complement(converse(X_233)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(X_233)),converse(complement(X_233))),converse(converse(complement(converse(X_233))))) )],[refute_0_1388,refute_0_1391]) ).
cnf(refute_0_1393,plain,
join(complement(converse(X_233)),converse(complement(X_233))) = complement(converse(X_233)),
inference(resolve,[$cnf( $equal(converse(join(converse(complement(converse(X_233))),complement(X_233))),converse(converse(complement(converse(X_233))))) )],[refute_0_1385,refute_0_1392]) ).
cnf(refute_0_1394,plain,
join(complement(converse(A)),converse(complement(A))) = complement(converse(A)),
inference(subst,[],[refute_0_1393:[bind(X_233,$fot(A))]]) ).
cnf(refute_0_1395,plain,
( converse(complement(A)) != join(complement(converse(A)),converse(complement(A)))
| join(complement(converse(A)),converse(complement(A))) != complement(converse(A))
| converse(complement(A)) = complement(converse(A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(complement(A)),complement(converse(A))) ),[0],$fot(join(complement(converse(A)),converse(complement(A))))]]) ).
cnf(refute_0_1396,plain,
( converse(complement(A)) != join(complement(converse(A)),converse(complement(A)))
| converse(complement(A)) = complement(converse(A)) ),
inference(resolve,[$cnf( $equal(join(complement(converse(A)),converse(complement(A))),complement(converse(A))) )],[refute_0_1394,refute_0_1395]) ).
cnf(refute_0_1397,plain,
( converse(complement(converse(converse(A)))) != join(complement(converse(A)),converse(complement(A)))
| converse(complement(A)) = complement(converse(A)) ),
inference(resolve,[$cnf( $equal(converse(complement(A)),join(complement(converse(A)),converse(complement(A)))) )],[refute_0_1367,refute_0_1396]) ).
cnf(refute_0_1398,plain,
converse(complement(A)) = complement(converse(A)),
inference(resolve,[$cnf( $equal(converse(complement(converse(converse(A)))),join(complement(converse(A)),converse(complement(A)))) )],[refute_0_1357,refute_0_1397]) ).
cnf(refute_0_1399,plain,
converse(complement(X_234)) = complement(converse(X_234)),
inference(subst,[],[refute_0_1398:[bind(A,$fot(X_234))]]) ).
cnf(refute_0_1400,plain,
( converse(complement(X_234)) != complement(converse(X_234))
| converse(composition(complement(X_234),top)) != composition(top,converse(complement(X_234)))
| converse(composition(complement(X_234),top)) = composition(top,complement(converse(X_234))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(complement(X_234),top)),composition(top,converse(complement(X_234)))) ),[1,1],$fot(complement(converse(X_234)))]]) ).
cnf(refute_0_1401,plain,
( converse(composition(complement(X_234),top)) != composition(top,converse(complement(X_234)))
| converse(composition(complement(X_234),top)) = composition(top,complement(converse(X_234))) ),
inference(resolve,[$cnf( $equal(converse(complement(X_234)),complement(converse(X_234))) )],[refute_0_1399,refute_0_1400]) ).
cnf(refute_0_1402,plain,
converse(composition(complement(X_234),top)) = composition(top,complement(converse(X_234))),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_234),top)),composition(top,converse(complement(X_234)))) )],[refute_0_1209,refute_0_1401]) ).
cnf(refute_0_1403,plain,
( converse(composition(complement(X_234),top)) != composition(top,complement(converse(X_234)))
| composition(top,complement(converse(X_234))) = converse(composition(complement(X_234),top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(complement(X_234),top)))),bind(Y,$fot(composition(top,complement(converse(X_234)))))]]) ).
cnf(refute_0_1404,plain,
composition(top,complement(converse(X_234))) = converse(composition(complement(X_234),top)),
inference(resolve,[$cnf( $equal(converse(composition(complement(X_234),top)),composition(top,complement(converse(X_234)))) )],[refute_0_1402,refute_0_1403]) ).
cnf(refute_0_1405,plain,
composition(top,complement(converse(composition(X_4,top)))) = converse(composition(complement(composition(X_4,top)),top)),
inference(subst,[],[refute_0_1404:[bind(X_234,$fot(composition(X_4,top)))]]) ).
cnf(refute_0_1406,plain,
( composition(top,complement(converse(composition(X_4,top)))) != complement(converse(composition(X_4,top)))
| composition(top,complement(converse(composition(X_4,top)))) != converse(composition(complement(composition(X_4,top)),top))
| converse(composition(complement(composition(X_4,top)),top)) = complement(converse(composition(X_4,top))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(top,complement(converse(composition(X_4,top)))),complement(converse(composition(X_4,top)))) ),[0],$fot(converse(composition(complement(composition(X_4,top)),top)))]]) ).
cnf(refute_0_1407,plain,
( composition(top,complement(converse(composition(X_4,top)))) != complement(converse(composition(X_4,top)))
| converse(composition(complement(composition(X_4,top)),top)) = complement(converse(composition(X_4,top))) ),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_4,top)))),converse(composition(complement(composition(X_4,top)),top))) )],[refute_0_1405,refute_0_1406]) ).
cnf(refute_0_1408,plain,
converse(composition(complement(composition(X_4,top)),top)) = complement(converse(composition(X_4,top))),
inference(resolve,[$cnf( $equal(composition(top,complement(converse(composition(X_4,top)))),complement(converse(composition(X_4,top)))) )],[refute_0_1208,refute_0_1407]) ).
cnf(refute_0_1409,plain,
converse(composition(complement(composition(X_531,top)),top)) = complement(converse(composition(X_531,top))),
inference(subst,[],[refute_0_1408:[bind(X_4,$fot(X_531))]]) ).
cnf(refute_0_1410,plain,
( converse(composition(complement(composition(X_531,top)),top)) != complement(converse(composition(X_531,top)))
| converse(converse(composition(complement(composition(X_531,top)),top))) != composition(complement(composition(X_531,top)),top)
| converse(complement(converse(composition(X_531,top)))) = composition(complement(composition(X_531,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(complement(composition(X_531,top)),top))),composition(complement(composition(X_531,top)),top)) ),[0,0],$fot(complement(converse(composition(X_531,top))))]]) ).
cnf(refute_0_1411,plain,
( converse(converse(composition(complement(composition(X_531,top)),top))) != composition(complement(composition(X_531,top)),top)
| converse(complement(converse(composition(X_531,top)))) = composition(complement(composition(X_531,top)),top) ),
inference(resolve,[$cnf( $equal(converse(composition(complement(composition(X_531,top)),top)),complement(converse(composition(X_531,top)))) )],[refute_0_1409,refute_0_1410]) ).
cnf(refute_0_1412,plain,
converse(complement(converse(composition(X_531,top)))) = composition(complement(composition(X_531,top)),top),
inference(resolve,[$cnf( $equal(converse(converse(composition(complement(composition(X_531,top)),top))),composition(complement(composition(X_531,top)),top)) )],[refute_0_313,refute_0_1411]) ).
cnf(refute_0_1413,plain,
converse(converse(composition(X_531,top))) = composition(X_531,top),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_531,top)))]]) ).
cnf(refute_0_1414,plain,
complement(converse(converse(composition(X_531,top)))) = complement(converse(converse(composition(X_531,top)))),
introduced(tautology,[refl,[$fot(complement(converse(converse(composition(X_531,top)))))]]) ).
cnf(refute_0_1415,plain,
( complement(converse(converse(composition(X_531,top)))) != complement(converse(converse(composition(X_531,top))))
| converse(converse(composition(X_531,top))) != composition(X_531,top)
| complement(converse(converse(composition(X_531,top)))) = complement(composition(X_531,top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(converse(converse(composition(X_531,top)))),complement(converse(converse(composition(X_531,top))))) ),[1,0],$fot(composition(X_531,top))]]) ).
cnf(refute_0_1416,plain,
( converse(converse(composition(X_531,top))) != composition(X_531,top)
| complement(converse(converse(composition(X_531,top)))) = complement(composition(X_531,top)) ),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(X_531,top)))),complement(converse(converse(composition(X_531,top))))) )],[refute_0_1414,refute_0_1415]) ).
cnf(refute_0_1417,plain,
complement(converse(converse(composition(X_531,top)))) = complement(composition(X_531,top)),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_531,top))),composition(X_531,top)) )],[refute_0_1413,refute_0_1416]) ).
cnf(refute_0_1418,plain,
converse(complement(converse(composition(X_531,top)))) = complement(converse(converse(composition(X_531,top)))),
inference(subst,[],[refute_0_1398:[bind(A,$fot(converse(composition(X_531,top))))]]) ).
cnf(refute_0_1419,plain,
( complement(converse(converse(composition(X_531,top)))) != complement(composition(X_531,top))
| converse(complement(converse(composition(X_531,top)))) != complement(converse(converse(composition(X_531,top))))
| converse(complement(converse(composition(X_531,top)))) = complement(composition(X_531,top)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(converse(complement(converse(composition(X_531,top)))))),bind(Y,$fot(complement(converse(converse(composition(X_531,top)))))),bind(Z,$fot(complement(composition(X_531,top))))]]) ).
cnf(refute_0_1420,plain,
( complement(converse(converse(composition(X_531,top)))) != complement(composition(X_531,top))
| converse(complement(converse(composition(X_531,top)))) = complement(composition(X_531,top)) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_531,top)))),complement(converse(converse(composition(X_531,top))))) )],[refute_0_1418,refute_0_1419]) ).
cnf(refute_0_1421,plain,
converse(complement(converse(composition(X_531,top)))) = complement(composition(X_531,top)),
inference(resolve,[$cnf( $equal(complement(converse(converse(composition(X_531,top)))),complement(composition(X_531,top))) )],[refute_0_1417,refute_0_1420]) ).
cnf(refute_0_1422,plain,
( converse(complement(converse(composition(X_531,top)))) != complement(composition(X_531,top))
| converse(complement(converse(composition(X_531,top)))) != composition(complement(composition(X_531,top)),top)
| complement(composition(X_531,top)) = composition(complement(composition(X_531,top)),top) ),
introduced(tautology,[equality,[$cnf( $equal(converse(complement(converse(composition(X_531,top)))),composition(complement(composition(X_531,top)),top)) ),[0],$fot(complement(composition(X_531,top)))]]) ).
cnf(refute_0_1423,plain,
( converse(complement(converse(composition(X_531,top)))) != composition(complement(composition(X_531,top)),top)
| complement(composition(X_531,top)) = composition(complement(composition(X_531,top)),top) ),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_531,top)))),complement(composition(X_531,top))) )],[refute_0_1421,refute_0_1422]) ).
cnf(refute_0_1424,plain,
complement(composition(X_531,top)) = composition(complement(composition(X_531,top)),top),
inference(resolve,[$cnf( $equal(converse(complement(converse(composition(X_531,top)))),composition(complement(composition(X_531,top)),top)) )],[refute_0_1412,refute_0_1423]) ).
cnf(refute_0_1425,plain,
( complement(composition(X_531,top)) != composition(complement(composition(X_531,top)),top)
| composition(complement(composition(X_531,top)),top) = complement(composition(X_531,top)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(composition(X_531,top)))),bind(Y,$fot(composition(complement(composition(X_531,top)),top)))]]) ).
cnf(refute_0_1426,plain,
composition(complement(composition(X_531,top)),top) = complement(composition(X_531,top)),
inference(resolve,[$cnf( $equal(complement(composition(X_531,top)),composition(complement(composition(X_531,top)),top)) )],[refute_0_1424,refute_0_1425]) ).
cnf(refute_0_1427,plain,
composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)),
inference(subst,[],[refute_0_1426:[bind(X_531,$fot(sk1))]]) ).
cnf(refute_0_1428,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) ),[0,0],$fot(complement(composition(sk1,top)))]]) ).
cnf(refute_0_1429,plain,
( complement(composition(sk1,top)) != complement(composition(sk1,top))
| composition(complement(composition(sk1,top)),top) = complement(composition(sk1,top)) ),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_1427,refute_0_1428]) ).
cnf(refute_0_1430,plain,
complement(composition(sk1,top)) != complement(composition(sk1,top)),
inference(resolve,[$cnf( $equal(composition(complement(composition(sk1,top)),top),complement(composition(sk1,top))) )],[refute_0_1429,refute_0_312]) ).
cnf(refute_0_1431,plain,
$false,
inference(resolve,[$cnf( $equal(complement(composition(sk1,top)),complement(composition(sk1,top))) )],[refute_0_311,refute_0_1430]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL050-4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 8 07:31:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.25/13.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.25/13.43
% 13.25/13.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.36/13.57
%------------------------------------------------------------------------------