%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL008-2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:43:11 EDT 2022
% Result : Unsatisfiable 97.18s 97.42s
% Output : CNFRefutation 97.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 70
% Number of leaves : 124
% Syntax : Number of clauses : 504 ( 258 unt; 0 nHn; 276 RR)
% Number of literals : 856 ( 855 equ; 358 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 697 ( 3 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_identity_6,axiom,
composition(A,one) = A ).
cnf(composition_distributivity_7,axiom,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).
cnf(converse_idempotence_8,axiom,
converse(converse(A)) = A ).
cnf(converse_additivity_9,axiom,
converse(join(A,B)) = join(converse(A),converse(B)) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(A,B)) = composition(converse(B),converse(A)) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).
cnf(def_top_12,axiom,
top = join(A,complement(A)) ).
cnf(def_zero_13,axiom,
zero = meet(A,complement(A)) ).
cnf(goals_14,negated_conjecture,
( join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ) ).
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( $equal(X,X) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
( join(A,join(B,C)) != join(join(A,B),C)
| join(join(A,B),C) = join(A,join(B,C)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).
cnf(refute_0_4,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(resolve,[$cnf( $equal(join(A,join(B,C)),join(join(A,B),C)) )],[maddux2_join_associativity_2,refute_0_3]) ).
cnf(refute_0_5,plain,
join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) = join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),
inference(subst,[],[refute_0_4:[bind(A,$fot(composition(sk1,sk2))),bind(B,$fot(composition(sk1,sk3))),bind(C,$fot(composition(sk1,join(sk2,sk3))))]]) ).
cnf(refute_0_6,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))),join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))) ),[1],$fot(composition(sk1,join(sk2,sk3)))]]) ).
cnf(refute_0_7,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))),join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_7,goals_14]) ).
cnf(refute_0_9,plain,
join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) = join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),
inference(subst,[],[refute_0_4:[bind(A,$fot(composition(sk1,join(sk2,sk3)))),bind(B,$fot(composition(sk1,sk2))),bind(C,$fot(composition(sk1,sk3)))]]) ).
cnf(refute_0_10,plain,
( join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3)))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3)))) ),[1],$fot(join(composition(sk1,sk2),composition(sk1,sk3)))]]) ).
cnf(refute_0_11,plain,
( join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) )],[refute_0_11,refute_0_8]) ).
cnf(refute_0_13,plain,
join(X_121,join(X_122,X_123)) = join(join(X_121,X_122),X_123),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_121)),bind(B,$fot(X_122)),bind(C,$fot(X_123))]]) ).
cnf(refute_0_14,plain,
join(X_122,X_121) = join(X_121,X_122),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_122)),bind(B,$fot(X_121))]]) ).
cnf(refute_0_15,plain,
( join(X_122,X_121) != join(X_121,X_122)
| join(X_121,X_122) = join(X_122,X_121) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_122,X_121))),bind(Y,$fot(join(X_121,X_122)))]]) ).
cnf(refute_0_16,plain,
join(X_121,X_122) = join(X_122,X_121),
inference(resolve,[$cnf( $equal(join(X_122,X_121),join(X_121,X_122)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
( join(X_121,X_122) != join(X_122,X_121)
| join(X_121,join(X_122,X_123)) != join(join(X_121,X_122),X_123)
| join(X_121,join(X_122,X_123)) = join(join(X_122,X_121),X_123) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_121,join(X_122,X_123)),join(join(X_121,X_122),X_123)) ),[1,0],$fot(join(X_122,X_121))]]) ).
cnf(refute_0_18,plain,
( join(X_121,join(X_122,X_123)) != join(join(X_121,X_122),X_123)
| join(X_121,join(X_122,X_123)) = join(join(X_122,X_121),X_123) ),
inference(resolve,[$cnf( $equal(join(X_121,X_122),join(X_122,X_121)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
join(X_121,join(X_122,X_123)) = join(join(X_122,X_121),X_123),
inference(resolve,[$cnf( $equal(join(X_121,join(X_122,X_123)),join(join(X_121,X_122),X_123)) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
join(join(X_122,X_121),X_123) = join(X_122,join(X_121,X_123)),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_122)),bind(B,$fot(X_121)),bind(C,$fot(X_123))]]) ).
cnf(refute_0_21,plain,
( join(X_121,join(X_122,X_123)) != join(join(X_122,X_121),X_123)
| join(join(X_122,X_121),X_123) != join(X_122,join(X_121,X_123))
| join(X_121,join(X_122,X_123)) = join(X_122,join(X_121,X_123)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_121,join(X_122,X_123)),join(X_122,join(X_121,X_123))) ),[0],$fot(join(join(X_122,X_121),X_123))]]) ).
cnf(refute_0_22,plain,
( join(X_121,join(X_122,X_123)) != join(join(X_122,X_121),X_123)
| join(X_121,join(X_122,X_123)) = join(X_122,join(X_121,X_123)) ),
inference(resolve,[$cnf( $equal(join(join(X_122,X_121),X_123),join(X_122,join(X_121,X_123))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
join(X_121,join(X_122,X_123)) = join(X_122,join(X_121,X_123)),
inference(resolve,[$cnf( $equal(join(X_121,join(X_122,X_123)),join(join(X_122,X_121),X_123)) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
join(X_203,join(X_204,X_205)) = join(X_204,join(X_203,X_205)),
inference(subst,[],[refute_0_23:[bind(X_121,$fot(X_203)),bind(X_122,$fot(X_204)),bind(X_123,$fot(X_205))]]) ).
cnf(refute_0_25,plain,
join(X_205,X_204) = join(X_204,X_205),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_205)),bind(B,$fot(X_204))]]) ).
cnf(refute_0_26,plain,
( join(X_205,X_204) != join(X_204,X_205)
| join(X_204,X_205) = join(X_205,X_204) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_205,X_204))),bind(Y,$fot(join(X_204,X_205)))]]) ).
cnf(refute_0_27,plain,
join(X_204,X_205) = join(X_205,X_204),
inference(resolve,[$cnf( $equal(join(X_205,X_204),join(X_204,X_205)) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( join(X_203,join(X_204,X_205)) != join(X_204,join(X_203,X_205))
| join(X_204,X_205) != join(X_205,X_204)
| join(X_203,join(X_205,X_204)) = join(X_204,join(X_203,X_205)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_203,join(X_204,X_205)),join(X_204,join(X_203,X_205))) ),[0,1],$fot(join(X_205,X_204))]]) ).
cnf(refute_0_29,plain,
( join(X_203,join(X_204,X_205)) != join(X_204,join(X_203,X_205))
| join(X_203,join(X_205,X_204)) = join(X_204,join(X_203,X_205)) ),
inference(resolve,[$cnf( $equal(join(X_204,X_205),join(X_205,X_204)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
join(X_203,join(X_205,X_204)) = join(X_204,join(X_203,X_205)),
inference(resolve,[$cnf( $equal(join(X_203,join(X_204,X_205)),join(X_204,join(X_203,X_205))) )],[refute_0_24,refute_0_29]) ).
cnf(refute_0_31,plain,
( join(X_203,join(X_205,X_204)) != join(X_204,join(X_203,X_205))
| join(X_204,join(X_203,X_205)) = join(X_203,join(X_205,X_204)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(X_203,join(X_205,X_204)))),bind(Y,$fot(join(X_204,join(X_203,X_205))))]]) ).
cnf(refute_0_32,plain,
join(X_204,join(X_203,X_205)) = join(X_203,join(X_205,X_204)),
inference(resolve,[$cnf( $equal(join(X_203,join(X_205,X_204)),join(X_204,join(X_203,X_205))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) = join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),
inference(subst,[],[refute_0_32:[bind(X_203,$fot(composition(sk1,sk2))),bind(X_204,$fot(composition(sk1,join(sk2,sk3)))),bind(X_205,$fot(composition(sk1,sk3)))]]) ).
cnf(refute_0_34,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_2,refute_0_34]) ).
cnf(refute_0_36,plain,
( join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) != join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))))),bind(Y,$fot(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))))),bind(Z,$fot(composition(sk1,join(sk2,sk3))))]]) ).
cnf(refute_0_37,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( composition(sk1,join(sk2,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),composition(sk1,join(sk2,sk3))) ),[1],$fot(join(composition(sk1,sk2),composition(sk1,sk3)))]]) ).
cnf(refute_0_39,plain,
( composition(sk1,join(sk2,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( composition(sk1,join(sk2,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))),join(composition(sk1,sk2),composition(sk1,sk3))) )],[refute_0_39,refute_0_12]) ).
cnf(refute_0_41,plain,
join(X_122,join(X_122,X_123)) = join(join(X_122,X_122),X_123),
inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_122)),bind(B,$fot(X_122)),bind(C,$fot(X_123))]]) ).
cnf(refute_0_42,plain,
composition(join(X_37,one),X_39) = join(composition(X_37,X_39),composition(one,X_39)),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(X_37)),bind(B,$fot(one)),bind(C,$fot(X_39))]]) ).
cnf(refute_0_43,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),converse(converse(A))),
inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_5))]]) ).
cnf(refute_0_44,plain,
( converse(composition(converse(A),X_5)) != composition(converse(X_5),converse(converse(A)))
| converse(converse(A)) != A
| converse(composition(converse(A),X_5)) = composition(converse(X_5),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_45,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_44]) ).
cnf(refute_0_46,plain,
converse(composition(converse(A),X_5)) = composition(converse(X_5),A),
inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_5)),composition(converse(X_5),converse(converse(A)))) )],[refute_0_43,refute_0_45]) ).
cnf(refute_0_47,plain,
converse(composition(converse(X_8),one)) = composition(converse(one),X_8),
inference(subst,[],[refute_0_46:[bind(A,$fot(X_8)),bind(X_5,$fot(one))]]) ).
cnf(refute_0_48,plain,
composition(converse(X_8),one) = converse(X_8),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_8)))]]) ).
cnf(refute_0_49,plain,
( composition(converse(X_8),one) != converse(X_8)
| converse(composition(converse(X_8),one)) != composition(converse(one),X_8)
| converse(converse(X_8)) = composition(converse(one),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_8),one)),composition(converse(one),X_8)) ),[0,0],$fot(converse(X_8))]]) ).
cnf(refute_0_50,plain,
( converse(composition(converse(X_8),one)) != composition(converse(one),X_8)
| converse(converse(X_8)) = composition(converse(one),X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(X_8),one),converse(X_8)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
converse(converse(X_8)) = composition(converse(one),X_8),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_8),one)),composition(converse(one),X_8)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
converse(converse(X_8)) = X_8,
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_8))]]) ).
cnf(refute_0_53,plain,
( converse(converse(X_8)) != X_8
| converse(converse(X_8)) != composition(converse(one),X_8)
| X_8 = composition(converse(one),X_8) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_8)),composition(converse(one),X_8)) ),[0],$fot(X_8)]]) ).
cnf(refute_0_54,plain,
( converse(converse(X_8)) != composition(converse(one),X_8)
| X_8 = composition(converse(one),X_8) ),
inference(resolve,[$cnf( $equal(converse(converse(X_8)),X_8) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
X_8 = composition(converse(one),X_8),
inference(resolve,[$cnf( $equal(converse(converse(X_8)),composition(converse(one),X_8)) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).
cnf(refute_0_57,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_55:[bind(X_8,$fot(one))]]) ).
cnf(refute_0_58,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_59,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_61,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_2:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_64,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
composition(converse(one),X_8) = composition(converse(one),X_8),
introduced(tautology,[refl,[$fot(composition(converse(one),X_8))]]) ).
cnf(refute_0_66,plain,
( composition(converse(one),X_8) != composition(converse(one),X_8)
| converse(one) != one
| composition(converse(one),X_8) = composition(one,X_8) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_8),composition(converse(one),X_8)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_67,plain,
( converse(one) != one
| composition(converse(one),X_8) = composition(one,X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_8),composition(converse(one),X_8)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
composition(converse(one),X_8) = composition(one,X_8),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( X_8 != composition(converse(one),X_8)
| composition(converse(one),X_8) != composition(one,X_8)
| X_8 = composition(one,X_8) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_8,composition(one,X_8)) ),[0],$fot(composition(converse(one),X_8))]]) ).
cnf(refute_0_70,plain,
( X_8 != composition(converse(one),X_8)
| X_8 = composition(one,X_8) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_8),composition(one,X_8)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
X_8 = composition(one,X_8),
inference(resolve,[$cnf( $equal(X_8,composition(converse(one),X_8)) )],[refute_0_55,refute_0_70]) ).
cnf(refute_0_72,plain,
X_39 = composition(one,X_39),
inference(subst,[],[refute_0_71:[bind(X_8,$fot(X_39))]]) ).
cnf(refute_0_73,plain,
( X_39 != composition(one,X_39)
| composition(one,X_39) = X_39 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_39)),bind(Y,$fot(composition(one,X_39)))]]) ).
cnf(refute_0_74,plain,
composition(one,X_39) = X_39,
inference(resolve,[$cnf( $equal(X_39,composition(one,X_39)) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
( composition(join(X_37,one),X_39) != join(composition(X_37,X_39),composition(one,X_39))
| composition(one,X_39) != X_39
| composition(join(X_37,one),X_39) = join(composition(X_37,X_39),X_39) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_37,one),X_39),join(composition(X_37,X_39),composition(one,X_39))) ),[1,1],$fot(X_39)]]) ).
cnf(refute_0_76,plain,
( composition(join(X_37,one),X_39) != join(composition(X_37,X_39),composition(one,X_39))
| composition(join(X_37,one),X_39) = join(composition(X_37,X_39),X_39) ),
inference(resolve,[$cnf( $equal(composition(one,X_39),X_39) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
composition(join(X_37,one),X_39) = join(composition(X_37,X_39),X_39),
inference(resolve,[$cnf( $equal(composition(join(X_37,one),X_39),join(composition(X_37,X_39),composition(one,X_39))) )],[refute_0_42,refute_0_76]) ).
cnf(refute_0_78,plain,
( join(A,B) != join(B,A)
| join(B,A) = join(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).
cnf(refute_0_79,plain,
join(B,A) = join(A,B),
inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_78]) ).
cnf(refute_0_80,plain,
join(composition(X_37,X_39),X_39) = join(X_39,composition(X_37,X_39)),
inference(subst,[],[refute_0_79:[bind(A,$fot(X_39)),bind(B,$fot(composition(X_37,X_39)))]]) ).
cnf(refute_0_81,plain,
( composition(join(X_37,one),X_39) != join(composition(X_37,X_39),X_39)
| join(composition(X_37,X_39),X_39) != join(X_39,composition(X_37,X_39))
| composition(join(X_37,one),X_39) = join(X_39,composition(X_37,X_39)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(X_37,one),X_39),join(X_39,composition(X_37,X_39))) ),[0],$fot(join(composition(X_37,X_39),X_39))]]) ).
cnf(refute_0_82,plain,
( composition(join(X_37,one),X_39) != join(composition(X_37,X_39),X_39)
| composition(join(X_37,one),X_39) = join(X_39,composition(X_37,X_39)) ),
inference(resolve,[$cnf( $equal(join(composition(X_37,X_39),X_39),join(X_39,composition(X_37,X_39))) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
composition(join(X_37,one),X_39) = join(X_39,composition(X_37,X_39)),
inference(resolve,[$cnf( $equal(composition(join(X_37,one),X_39),join(composition(X_37,X_39),X_39)) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
composition(join(one,one),X_41) = join(X_41,composition(one,X_41)),
inference(subst,[],[refute_0_83:[bind(X_37,$fot(one)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_85,plain,
X_41 = composition(one,X_41),
inference(subst,[],[refute_0_71:[bind(X_8,$fot(X_41))]]) ).
cnf(refute_0_86,plain,
( X_41 != composition(one,X_41)
| composition(one,X_41) = X_41 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_41)),bind(Y,$fot(composition(one,X_41)))]]) ).
cnf(refute_0_87,plain,
composition(one,X_41) = X_41,
inference(resolve,[$cnf( $equal(X_41,composition(one,X_41)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
( composition(join(one,one),X_41) != join(X_41,composition(one,X_41))
| composition(one,X_41) != X_41
| composition(join(one,one),X_41) = join(X_41,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_41),join(X_41,composition(one,X_41))) ),[1,1],$fot(X_41)]]) ).
cnf(refute_0_89,plain,
( composition(join(one,one),X_41) != join(X_41,composition(one,X_41))
| composition(join(one,one),X_41) = join(X_41,X_41) ),
inference(resolve,[$cnf( $equal(composition(one,X_41),X_41) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
composition(join(one,one),X_41) = join(X_41,X_41),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_41),join(X_41,composition(one,X_41))) )],[refute_0_84,refute_0_89]) ).
cnf(refute_0_91,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
inference(subst,[],[refute_0_79:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).
cnf(refute_0_92,plain,
( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
| join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
| join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
introduced(tautology,[equality,[$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_93,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( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_93]) ).
cnf(refute_0_95,plain,
join(complement(X_50),composition(converse(one),complement(composition(one,X_50)))) = complement(X_50),
inference(subst,[],[refute_0_94:[bind(A,$fot(one)),bind(B,$fot(X_50))]]) ).
cnf(refute_0_96,plain,
X_50 = composition(one,X_50),
inference(subst,[],[refute_0_71:[bind(X_8,$fot(X_50))]]) ).
cnf(refute_0_97,plain,
( X_50 != composition(one,X_50)
| composition(one,X_50) = X_50 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_50)),bind(Y,$fot(composition(one,X_50)))]]) ).
cnf(refute_0_98,plain,
composition(one,X_50) = X_50,
inference(resolve,[$cnf( $equal(X_50,composition(one,X_50)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( composition(one,X_50) != X_50
| join(complement(X_50),composition(converse(one),complement(composition(one,X_50)))) != complement(X_50)
| join(complement(X_50),composition(converse(one),complement(X_50))) = complement(X_50) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(composition(one,X_50)))),complement(X_50)) ),[0,1,1,0],$fot(X_50)]]) ).
cnf(refute_0_100,plain,
( join(complement(X_50),composition(converse(one),complement(composition(one,X_50)))) != complement(X_50)
| join(complement(X_50),composition(converse(one),complement(X_50))) = complement(X_50) ),
inference(resolve,[$cnf( $equal(composition(one,X_50),X_50) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
join(complement(X_50),composition(converse(one),complement(X_50))) = complement(X_50),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(composition(one,X_50)))),complement(X_50)) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
converse(join(X_12,one)) = join(converse(X_12),converse(one)),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_12)),bind(B,$fot(one))]]) ).
cnf(refute_0_103,plain,
( converse(join(X_12,one)) != join(converse(X_12),converse(one))
| converse(one) != one
| converse(join(X_12,one)) = join(converse(X_12),one) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,one)),join(converse(X_12),converse(one))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_104,plain,
( converse(join(X_12,one)) != join(converse(X_12),converse(one))
| converse(join(X_12,one)) = join(converse(X_12),one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_64,refute_0_103]) ).
cnf(refute_0_105,plain,
converse(join(X_12,one)) = join(converse(X_12),one),
inference(resolve,[$cnf( $equal(converse(join(X_12,one)),join(converse(X_12),converse(one))) )],[refute_0_102,refute_0_104]) ).
cnf(refute_0_106,plain,
join(converse(X_12),one) = join(one,converse(X_12)),
inference(subst,[],[refute_0_79:[bind(A,$fot(one)),bind(B,$fot(converse(X_12)))]]) ).
cnf(refute_0_107,plain,
( converse(join(X_12,one)) != join(converse(X_12),one)
| join(converse(X_12),one) != join(one,converse(X_12))
| converse(join(X_12,one)) = join(one,converse(X_12)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(join(X_12,one)),join(one,converse(X_12))) ),[0],$fot(join(converse(X_12),one))]]) ).
cnf(refute_0_108,plain,
( converse(join(X_12,one)) != join(converse(X_12),one)
| converse(join(X_12,one)) = join(one,converse(X_12)) ),
inference(resolve,[$cnf( $equal(join(converse(X_12),one),join(one,converse(X_12))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
converse(join(X_12,one)) = join(one,converse(X_12)),
inference(resolve,[$cnf( $equal(converse(join(X_12,one)),join(converse(X_12),one)) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
converse(join(one,one)) = join(one,converse(one)),
inference(subst,[],[refute_0_109:[bind(X_12,$fot(one))]]) ).
cnf(refute_0_111,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_112,plain,
( converse(join(one,one)) != join(one,converse(one))
| converse(join(one,one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_64,refute_0_111]) ).
cnf(refute_0_113,plain,
converse(join(one,one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,converse(one))) )],[refute_0_110,refute_0_112]) ).
cnf(refute_0_114,plain,
( converse(join(X_12,one)) != join(one,converse(X_12))
| join(one,converse(X_12)) = converse(join(X_12,one)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_12,one)))),bind(Y,$fot(join(one,converse(X_12))))]]) ).
cnf(refute_0_115,plain,
join(one,converse(X_12)) = converse(join(X_12,one)),
inference(resolve,[$cnf( $equal(converse(join(X_12,one)),join(one,converse(X_12))) )],[refute_0_109,refute_0_114]) ).
cnf(refute_0_116,plain,
join(one,converse(one)) = converse(join(one,one)),
inference(subst,[],[refute_0_115:[bind(X_12,$fot(one))]]) ).
cnf(refute_0_117,plain,
( converse(join(one,one)) != join(one,one)
| join(one,converse(one)) != converse(join(one,one))
| join(one,converse(one)) = join(one,one) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(one,converse(one)))),bind(Y,$fot(converse(join(one,one)))),bind(Z,$fot(join(one,one)))]]) ).
cnf(refute_0_118,plain,
( converse(join(one,one)) != join(one,one)
| join(one,converse(one)) = join(one,one) ),
inference(resolve,[$cnf( $equal(join(one,converse(one)),converse(join(one,one))) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
join(one,converse(one)) = join(one,one),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_113,refute_0_118]) ).
cnf(refute_0_120,plain,
composition(join(one,converse(one)),complement(X_50)) = composition(join(one,converse(one)),complement(X_50)),
introduced(tautology,[refl,[$fot(composition(join(one,converse(one)),complement(X_50)))]]) ).
cnf(refute_0_121,plain,
( composition(join(one,converse(one)),complement(X_50)) != composition(join(one,converse(one)),complement(X_50))
| join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_50)) = composition(join(one,one),complement(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,converse(one)),complement(X_50)),composition(join(one,converse(one)),complement(X_50))) ),[1,0],$fot(join(one,one))]]) ).
cnf(refute_0_122,plain,
( join(one,converse(one)) != join(one,one)
| composition(join(one,converse(one)),complement(X_50)) = composition(join(one,one),complement(X_50)) ),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_50)),composition(join(one,converse(one)),complement(X_50))) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
composition(join(one,converse(one)),complement(X_50)) = composition(join(one,one),complement(X_50)),
inference(resolve,[$cnf( $equal(join(one,converse(one)),join(one,one)) )],[refute_0_119,refute_0_122]) ).
cnf(refute_0_124,plain,
composition(join(X_40,one),X_41) = join(X_41,composition(X_40,X_41)),
inference(subst,[],[refute_0_83:[bind(X_37,$fot(X_40)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_125,plain,
join(one,X_40) = join(X_40,one),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(one)),bind(B,$fot(X_40))]]) ).
cnf(refute_0_126,plain,
( join(one,X_40) != join(X_40,one)
| join(X_40,one) = join(one,X_40) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(join(one,X_40))),bind(Y,$fot(join(X_40,one)))]]) ).
cnf(refute_0_127,plain,
join(X_40,one) = join(one,X_40),
inference(resolve,[$cnf( $equal(join(one,X_40),join(X_40,one)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( composition(join(X_40,one),X_41) != join(X_41,composition(X_40,X_41))
| join(X_40,one) != join(one,X_40)
| composition(join(one,X_40),X_41) = join(X_41,composition(X_40,X_41)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(X_40,one),X_41),join(X_41,composition(X_40,X_41))) ),[0,0],$fot(join(one,X_40))]]) ).
cnf(refute_0_129,plain,
( composition(join(X_40,one),X_41) != join(X_41,composition(X_40,X_41))
| composition(join(one,X_40),X_41) = join(X_41,composition(X_40,X_41)) ),
inference(resolve,[$cnf( $equal(join(X_40,one),join(one,X_40)) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
composition(join(one,X_40),X_41) = join(X_41,composition(X_40,X_41)),
inference(resolve,[$cnf( $equal(composition(join(X_40,one),X_41),join(X_41,composition(X_40,X_41))) )],[refute_0_124,refute_0_129]) ).
cnf(refute_0_131,plain,
( composition(join(X_37,one),X_39) != join(X_39,composition(X_37,X_39))
| join(X_39,composition(X_37,X_39)) = composition(join(X_37,one),X_39) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(X_37,one),X_39))),bind(Y,$fot(join(X_39,composition(X_37,X_39))))]]) ).
cnf(refute_0_132,plain,
join(X_39,composition(X_37,X_39)) = composition(join(X_37,one),X_39),
inference(resolve,[$cnf( $equal(composition(join(X_37,one),X_39),join(X_39,composition(X_37,X_39))) )],[refute_0_83,refute_0_131]) ).
cnf(refute_0_133,plain,
join(X_41,composition(X_40,X_41)) = composition(join(X_40,one),X_41),
inference(subst,[],[refute_0_132:[bind(X_37,$fot(X_40)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_134,plain,
( composition(join(one,X_40),X_41) != join(X_41,composition(X_40,X_41))
| join(X_41,composition(X_40,X_41)) != composition(join(X_40,one),X_41)
| composition(join(one,X_40),X_41) = composition(join(X_40,one),X_41) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(join(one,X_40),X_41),composition(join(X_40,one),X_41)) ),[0],$fot(join(X_41,composition(X_40,X_41)))]]) ).
cnf(refute_0_135,plain,
( composition(join(one,X_40),X_41) != join(X_41,composition(X_40,X_41))
| composition(join(one,X_40),X_41) = composition(join(X_40,one),X_41) ),
inference(resolve,[$cnf( $equal(join(X_41,composition(X_40,X_41)),composition(join(X_40,one),X_41)) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
composition(join(one,X_40),X_41) = composition(join(X_40,one),X_41),
inference(resolve,[$cnf( $equal(composition(join(one,X_40),X_41),join(X_41,composition(X_40,X_41))) )],[refute_0_130,refute_0_135]) ).
cnf(refute_0_137,plain,
( composition(join(one,X_40),X_41) != composition(join(X_40,one),X_41)
| composition(join(X_40,one),X_41) = composition(join(one,X_40),X_41) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,X_40),X_41))),bind(Y,$fot(composition(join(X_40,one),X_41)))]]) ).
cnf(refute_0_138,plain,
composition(join(X_40,one),X_41) = composition(join(one,X_40),X_41),
inference(resolve,[$cnf( $equal(composition(join(one,X_40),X_41),composition(join(X_40,one),X_41)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
composition(join(converse(one),one),complement(X_50)) = composition(join(one,converse(one)),complement(X_50)),
inference(subst,[],[refute_0_138:[bind(X_40,$fot(converse(one))),bind(X_41,$fot(complement(X_50)))]]) ).
cnf(refute_0_140,plain,
join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(converse(one),one),complement(X_50)),
inference(subst,[],[refute_0_132:[bind(X_37,$fot(converse(one))),bind(X_39,$fot(complement(X_50)))]]) ).
cnf(refute_0_141,plain,
( composition(join(converse(one),one),complement(X_50)) != composition(join(one,converse(one)),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) != composition(join(converse(one),one),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,converse(one)),complement(X_50)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(X_50),composition(converse(one),complement(X_50))))),bind(Y,$fot(composition(join(converse(one),one),complement(X_50)))),bind(Z,$fot(composition(join(one,converse(one)),complement(X_50))))]]) ).
cnf(refute_0_142,plain,
( composition(join(converse(one),one),complement(X_50)) != composition(join(one,converse(one)),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,converse(one)),complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(X_50))),composition(join(converse(one),one),complement(X_50))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,converse(one)),complement(X_50)),
inference(resolve,[$cnf( $equal(composition(join(converse(one),one),complement(X_50)),composition(join(one,converse(one)),complement(X_50))) )],[refute_0_139,refute_0_142]) ).
cnf(refute_0_144,plain,
( composition(join(one,converse(one)),complement(X_50)) != composition(join(one,one),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) != composition(join(one,converse(one)),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,one),complement(X_50)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(X_50),composition(converse(one),complement(X_50))))),bind(Y,$fot(composition(join(one,converse(one)),complement(X_50)))),bind(Z,$fot(composition(join(one,one),complement(X_50))))]]) ).
cnf(refute_0_145,plain,
( composition(join(one,converse(one)),complement(X_50)) != composition(join(one,one),complement(X_50))
| join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,one),complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(X_50))),composition(join(one,converse(one)),complement(X_50))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
join(complement(X_50),composition(converse(one),complement(X_50))) = composition(join(one,one),complement(X_50)),
inference(resolve,[$cnf( $equal(composition(join(one,converse(one)),complement(X_50)),composition(join(one,one),complement(X_50))) )],[refute_0_123,refute_0_145]) ).
cnf(refute_0_147,plain,
( join(complement(X_50),composition(converse(one),complement(X_50))) != complement(X_50)
| join(complement(X_50),composition(converse(one),complement(X_50))) != composition(join(one,one),complement(X_50))
| composition(join(one,one),complement(X_50)) = complement(X_50) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(X_50))),complement(X_50)) ),[0],$fot(composition(join(one,one),complement(X_50)))]]) ).
cnf(refute_0_148,plain,
( join(complement(X_50),composition(converse(one),complement(X_50))) != complement(X_50)
| composition(join(one,one),complement(X_50)) = complement(X_50) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(X_50))),composition(join(one,one),complement(X_50))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
composition(join(one,one),complement(X_50)) = complement(X_50),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(one),complement(X_50))),complement(X_50)) )],[refute_0_101,refute_0_148]) ).
cnf(refute_0_150,plain,
composition(join(one,one),complement(complement(X_88))) = complement(complement(X_88)),
inference(subst,[],[refute_0_149:[bind(X_50,$fot(complement(X_88)))]]) ).
cnf(refute_0_151,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_79:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_152,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_153,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( $equal(join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),complement(B))),complement(join(complement(A),B)))) )],[maddux3_a_kind_of_de_Morgan_3,refute_0_153]) ).
cnf(refute_0_155,plain,
join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
inference(subst,[],[refute_0_79:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).
cnf(refute_0_156,plain,
( meet(A,B) != complement(join(complement(A),complement(B)))
| complement(join(complement(A),complement(B))) = meet(A,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_157,plain,
complement(join(complement(A),complement(B))) = meet(A,B),
inference(resolve,[$cnf( $equal(meet(A,B),complement(join(complement(A),complement(B)))) )],[maddux4_definiton_of_meet_4,refute_0_156]) ).
cnf(refute_0_158,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))))]]) ).
cnf(refute_0_159,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_160,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(complement(join(complement(A),B)),meet(A,B)),
inference(resolve,[$cnf( $equal(complement(join(complement(A),complement(B))),meet(A,B)) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
( join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(complement(join(complement(A),B)),meet(A,B))
| join(complement(join(complement(A),B)),meet(A,B)) != join(meet(A,B),complement(join(complement(A),B)))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))) ),
inference(subst,[],[refute_0_35:[bind(X,$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_163,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(complement(join(complement(A),B)),meet(A,B))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(A),B)),meet(A,B)),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_155,refute_0_163]) ).
cnf(refute_0_165,plain,
( A != join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))
| join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) != join(meet(A,B),complement(join(complement(A),B)))
| A = join(meet(A,B),complement(join(complement(A),B))) ),
introduced(tautology,[equality,[$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_166,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( $equal(join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),join(meet(A,B),complement(join(complement(A),B)))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
A = join(meet(A,B),complement(join(complement(A),B))),
inference(resolve,[$cnf( $equal(A,join(complement(join(complement(A),B)),complement(join(complement(A),complement(B))))) )],[refute_0_154,refute_0_166]) ).
cnf(refute_0_168,plain,
X_69 = join(meet(X_69,complement(X_69)),complement(join(complement(X_69),complement(X_69)))),
inference(subst,[],[refute_0_167:[bind(A,$fot(X_69)),bind(B,$fot(complement(X_69)))]]) ).
cnf(refute_0_169,plain,
composition(join(one,one),complement(X_69)) = join(complement(X_69),complement(X_69)),
inference(subst,[],[refute_0_90:[bind(X_41,$fot(complement(X_69)))]]) ).
cnf(refute_0_170,plain,
( composition(join(one,one),complement(X_69)) != join(complement(X_69),complement(X_69))
| join(complement(X_69),complement(X_69)) = composition(join(one,one),complement(X_69)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(join(one,one),complement(X_69)))),bind(Y,$fot(join(complement(X_69),complement(X_69))))]]) ).
cnf(refute_0_171,plain,
join(complement(X_69),complement(X_69)) = composition(join(one,one),complement(X_69)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_69)),join(complement(X_69),complement(X_69))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
( X_69 != join(meet(X_69,complement(X_69)),complement(join(complement(X_69),complement(X_69))))
| join(complement(X_69),complement(X_69)) != composition(join(one,one),complement(X_69))
| X_69 = join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(X_69,join(meet(X_69,complement(X_69)),complement(join(complement(X_69),complement(X_69))))) ),[1,1,0],$fot(composition(join(one,one),complement(X_69)))]]) ).
cnf(refute_0_173,plain,
( X_69 != join(meet(X_69,complement(X_69)),complement(join(complement(X_69),complement(X_69))))
| X_69 = join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) ),
inference(resolve,[$cnf( $equal(join(complement(X_69),complement(X_69)),composition(join(one,one),complement(X_69))) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
X_69 = join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),
inference(resolve,[$cnf( $equal(X_69,join(meet(X_69,complement(X_69)),complement(join(complement(X_69),complement(X_69))))) )],[refute_0_168,refute_0_173]) ).
cnf(refute_0_175,plain,
composition(join(one,one),complement(X_69)) = complement(X_69),
inference(subst,[],[refute_0_149:[bind(X_50,$fot(X_69))]]) ).
cnf(refute_0_176,plain,
complement(composition(join(one,one),complement(X_69))) = complement(composition(join(one,one),complement(X_69))),
introduced(tautology,[refl,[$fot(complement(composition(join(one,one),complement(X_69))))]]) ).
cnf(refute_0_177,plain,
( complement(composition(join(one,one),complement(X_69))) != complement(composition(join(one,one),complement(X_69)))
| composition(join(one,one),complement(X_69)) != complement(X_69)
| complement(composition(join(one,one),complement(X_69))) = complement(complement(X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(composition(join(one,one),complement(X_69))),complement(composition(join(one,one),complement(X_69)))) ),[1,0],$fot(complement(X_69))]]) ).
cnf(refute_0_178,plain,
( composition(join(one,one),complement(X_69)) != complement(X_69)
| complement(composition(join(one,one),complement(X_69))) = complement(complement(X_69)) ),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_69))),complement(composition(join(one,one),complement(X_69)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
complement(composition(join(one,one),complement(X_69))) = complement(complement(X_69)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_69)),complement(X_69)) )],[refute_0_175,refute_0_178]) ).
cnf(refute_0_180,plain,
join(zero,complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(composition(join(one,one),complement(X_69)))),
introduced(tautology,[refl,[$fot(join(zero,complement(composition(join(one,one),complement(X_69)))))]]) ).
cnf(refute_0_181,plain,
( complement(composition(join(one,one),complement(X_69))) != complement(complement(X_69))
| join(zero,complement(composition(join(one,one),complement(X_69)))) != join(zero,complement(composition(join(one,one),complement(X_69))))
| join(zero,complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(composition(join(one,one),complement(X_69)))),join(zero,complement(composition(join(one,one),complement(X_69))))) ),[1,1],$fot(complement(complement(X_69)))]]) ).
cnf(refute_0_182,plain,
( complement(composition(join(one,one),complement(X_69))) != complement(complement(X_69))
| join(zero,complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,one),complement(X_69)))),join(zero,complement(composition(join(one,one),complement(X_69))))) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
join(zero,complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))),
inference(resolve,[$cnf( $equal(complement(composition(join(one,one),complement(X_69))),complement(complement(X_69))) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( zero != meet(A,complement(A))
| meet(A,complement(A)) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(meet(A,complement(A))))]]) ).
cnf(refute_0_185,plain,
meet(A,complement(A)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(A,complement(A))) )],[def_zero_13,refute_0_184]) ).
cnf(refute_0_186,plain,
meet(X_69,complement(X_69)) = zero,
inference(subst,[],[refute_0_185:[bind(A,$fot(X_69))]]) ).
cnf(refute_0_187,plain,
join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),
introduced(tautology,[refl,[$fot(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))))]]) ).
cnf(refute_0_188,plain,
( join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) != join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))
| meet(X_69,complement(X_69)) != zero
| join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(composition(join(one,one),complement(X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_189,plain,
( meet(X_69,complement(X_69)) != zero
| join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(composition(join(one,one),complement(X_69)))) ),
inference(resolve,[$cnf( $equal(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(composition(join(one,one),complement(X_69)))),
inference(resolve,[$cnf( $equal(meet(X_69,complement(X_69)),zero) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
( join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) != join(zero,complement(composition(join(one,one),complement(X_69))))
| join(zero,complement(composition(join(one,one),complement(X_69)))) != join(zero,complement(complement(X_69)))
| join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))))),bind(Y,$fot(join(zero,complement(composition(join(one,one),complement(X_69)))))),bind(Z,$fot(join(zero,complement(complement(X_69)))))]]) ).
cnf(refute_0_192,plain,
( join(zero,complement(composition(join(one,one),complement(X_69)))) != join(zero,complement(complement(X_69)))
| join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))) ),
inference(resolve,[$cnf( $equal(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),join(zero,complement(composition(join(one,one),complement(X_69))))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) = join(zero,complement(complement(X_69))),
inference(resolve,[$cnf( $equal(join(zero,complement(composition(join(one,one),complement(X_69)))),join(zero,complement(complement(X_69)))) )],[refute_0_183,refute_0_192]) ).
cnf(refute_0_194,plain,
( X_69 != join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))
| join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))) != join(zero,complement(complement(X_69)))
| X_69 = join(zero,complement(complement(X_69))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_69,join(zero,complement(complement(X_69)))) ),[0],$fot(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))))]]) ).
cnf(refute_0_195,plain,
( X_69 != join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))
| X_69 = join(zero,complement(complement(X_69))) ),
inference(resolve,[$cnf( $equal(join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69)))),join(zero,complement(complement(X_69)))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
X_69 = join(zero,complement(complement(X_69))),
inference(resolve,[$cnf( $equal(X_69,join(meet(X_69,complement(X_69)),complement(composition(join(one,one),complement(X_69))))) )],[refute_0_174,refute_0_195]) ).
cnf(refute_0_197,plain,
X_69 = join(meet(X_69,top),complement(join(complement(X_69),top))),
inference(subst,[],[refute_0_167:[bind(A,$fot(X_69)),bind(B,$fot(top))]]) ).
cnf(refute_0_198,plain,
meet(A,top) = complement(join(complement(A),complement(top))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(top))]]) ).
cnf(refute_0_199,plain,
zero = meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27)))),
inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_200,plain,
meet(X_26,X_27) = complement(join(complement(X_26),complement(X_27))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_26)),bind(B,$fot(X_27))]]) ).
cnf(refute_0_201,plain,
( meet(X_26,X_27) != complement(join(complement(X_26),complement(X_27)))
| complement(join(complement(X_26),complement(X_27))) = meet(X_26,X_27) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(X_26,X_27))),bind(Y,$fot(complement(join(complement(X_26),complement(X_27)))))]]) ).
cnf(refute_0_202,plain,
complement(join(complement(X_26),complement(X_27))) = meet(X_26,X_27),
inference(resolve,[$cnf( $equal(meet(X_26,X_27),complement(join(complement(X_26),complement(X_27)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| zero != meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) ),[1,1],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_204,plain,
( zero != meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
zero = meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) )],[refute_0_199,refute_0_204]) ).
cnf(refute_0_206,plain,
( top != join(A,complement(A))
| join(A,complement(A)) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).
cnf(refute_0_207,plain,
join(A,complement(A)) = top,
inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_206]) ).
cnf(refute_0_208,plain,
join(meet(X_26,X_27),complement(meet(X_26,X_27))) = top,
inference(subst,[],[refute_0_207:[bind(A,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_209,plain,
complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))))]]) ).
cnf(refute_0_210,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))
| join(meet(X_26,X_27),complement(meet(X_26,X_27))) != top
| complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_211,plain,
( join(meet(X_26,X_27),complement(meet(X_26,X_27))) != top
| complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) )],[refute_0_209,refute_0_210]) ).
cnf(refute_0_212,plain,
complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_26,X_27),complement(meet(X_26,X_27))),top) )],[refute_0_208,refute_0_211]) ).
cnf(refute_0_213,plain,
meet(join(complement(X_26),complement(X_27)),B) = complement(join(complement(join(complement(X_26),complement(X_27))),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_214,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| meet(join(complement(X_26),complement(X_27)),B) != complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))
| meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),B),complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))) ),[1,0,0],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_215,plain,
( meet(join(complement(X_26),complement(X_27)),B) != complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))
| meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_202,refute_0_214]) ).
cnf(refute_0_216,plain,
meet(join(complement(X_26),complement(X_27)),B) = complement(join(meet(X_26,X_27),complement(B))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),B),complement(join(complement(join(complement(X_26),complement(X_27))),complement(B)))) )],[refute_0_213,refute_0_215]) ).
cnf(refute_0_217,plain,
meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),
inference(subst,[],[refute_0_216:[bind(B,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_218,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(top)
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)))),bind(Y,$fot(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_219,plain,
( complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))) != complement(top)
| meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),complement(join(meet(X_26,X_27),complement(meet(X_26,X_27))))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_26,X_27),complement(meet(X_26,X_27)))),complement(top)) )],[refute_0_212,refute_0_219]) ).
cnf(refute_0_221,plain,
( meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != complement(top)
| zero != meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_222,plain,
( zero != meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),complement(top)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) )],[refute_0_205,refute_0_222]) ).
cnf(refute_0_224,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_2:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_225,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( complement(top) != zero
| meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) ),[1,0,1],$fot(zero)]]) ).
cnf(refute_0_227,plain,
( meet(A,top) != complement(join(complement(A),complement(top)))
| meet(A,top) = complement(join(complement(A),zero)) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_225,refute_0_226]) ).
cnf(refute_0_228,plain,
meet(A,top) = complement(join(complement(A),zero)),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),complement(top)))) )],[refute_0_198,refute_0_227]) ).
cnf(refute_0_229,plain,
meet(top,B) = complement(join(complement(top),complement(B))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(top))]]) ).
cnf(refute_0_230,plain,
( complement(top) != zero
| meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_231,plain,
( meet(top,B) != complement(join(complement(top),complement(B)))
| meet(top,B) = complement(join(zero,complement(B))) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_225,refute_0_230]) ).
cnf(refute_0_232,plain,
meet(top,B) = complement(join(zero,complement(B))),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(complement(top),complement(B)))) )],[refute_0_229,refute_0_231]) ).
cnf(refute_0_233,plain,
( meet(top,B) != complement(join(zero,complement(B)))
| complement(join(zero,complement(B))) = meet(top,B) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(meet(top,B))),bind(Y,$fot(complement(join(zero,complement(B)))))]]) ).
cnf(refute_0_234,plain,
complement(join(zero,complement(B))) = meet(top,B),
inference(resolve,[$cnf( $equal(meet(top,B),complement(join(zero,complement(B)))) )],[refute_0_232,refute_0_233]) ).
cnf(refute_0_235,plain,
complement(join(zero,complement(A))) = meet(top,A),
inference(subst,[],[refute_0_234:[bind(B,$fot(A))]]) ).
cnf(refute_0_236,plain,
join(complement(A),zero) = join(zero,complement(A)),
inference(subst,[],[refute_0_79:[bind(A,$fot(zero)),bind(B,$fot(complement(A)))]]) ).
cnf(refute_0_237,plain,
complement(join(complement(A),zero)) = complement(join(complement(A),zero)),
introduced(tautology,[refl,[$fot(complement(join(complement(A),zero)))]]) ).
cnf(refute_0_238,plain,
( complement(join(complement(A),zero)) != complement(join(complement(A),zero))
| join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) ),[1,0],$fot(join(zero,complement(A)))]]) ).
cnf(refute_0_239,plain,
( join(complement(A),zero) != join(zero,complement(A))
| complement(join(complement(A),zero)) = complement(join(zero,complement(A))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(complement(A),zero))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
complement(join(complement(A),zero)) = complement(join(zero,complement(A))),
inference(resolve,[$cnf( $equal(join(complement(A),zero),join(zero,complement(A))) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( complement(join(complement(A),zero)) != complement(join(zero,complement(A)))
| complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(complement(join(complement(A),zero)))),bind(Y,$fot(complement(join(zero,complement(A))))),bind(Z,$fot(meet(top,A)))]]) ).
cnf(refute_0_242,plain,
( complement(join(zero,complement(A))) != meet(top,A)
| complement(join(complement(A),zero)) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),complement(join(zero,complement(A)))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
complement(join(complement(A),zero)) = meet(top,A),
inference(resolve,[$cnf( $equal(complement(join(zero,complement(A))),meet(top,A)) )],[refute_0_235,refute_0_242]) ).
cnf(refute_0_244,plain,
( complement(join(complement(A),zero)) != meet(top,A)
| meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) ),[1],$fot(meet(top,A))]]) ).
cnf(refute_0_245,plain,
( meet(A,top) != complement(join(complement(A),zero))
| meet(A,top) = meet(top,A) ),
inference(resolve,[$cnf( $equal(complement(join(complement(A),zero)),meet(top,A)) )],[refute_0_243,refute_0_244]) ).
cnf(refute_0_246,plain,
meet(A,top) = meet(top,A),
inference(resolve,[$cnf( $equal(meet(A,top),complement(join(complement(A),zero))) )],[refute_0_228,refute_0_245]) ).
cnf(refute_0_247,plain,
meet(X_69,top) = meet(top,X_69),
inference(subst,[],[refute_0_246:[bind(A,$fot(X_69))]]) ).
cnf(refute_0_248,plain,
( X_69 != join(meet(X_69,top),complement(join(complement(X_69),top)))
| meet(X_69,top) != meet(top,X_69)
| X_69 = join(meet(top,X_69),complement(join(complement(X_69),top))) ),
introduced(tautology,[equality,[$cnf( $equal(X_69,join(meet(X_69,top),complement(join(complement(X_69),top)))) ),[1,0],$fot(meet(top,X_69))]]) ).
cnf(refute_0_249,plain,
( X_69 != join(meet(X_69,top),complement(join(complement(X_69),top)))
| X_69 = join(meet(top,X_69),complement(join(complement(X_69),top))) ),
inference(resolve,[$cnf( $equal(meet(X_69,top),meet(top,X_69)) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
X_69 = join(meet(top,X_69),complement(join(complement(X_69),top))),
inference(resolve,[$cnf( $equal(X_69,join(meet(X_69,top),complement(join(complement(X_69),top)))) )],[refute_0_197,refute_0_249]) ).
cnf(refute_0_251,plain,
join(complement(X_69),top) = join(top,complement(X_69)),
inference(subst,[],[refute_0_79:[bind(A,$fot(top)),bind(B,$fot(complement(X_69)))]]) ).
cnf(refute_0_252,plain,
complement(join(complement(X_69),top)) = complement(join(complement(X_69),top)),
introduced(tautology,[refl,[$fot(complement(join(complement(X_69),top)))]]) ).
cnf(refute_0_253,plain,
( complement(join(complement(X_69),top)) != complement(join(complement(X_69),top))
| join(complement(X_69),top) != join(top,complement(X_69))
| complement(join(complement(X_69),top)) = complement(join(top,complement(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(complement(X_69),top)),complement(join(complement(X_69),top))) ),[1,0],$fot(join(top,complement(X_69)))]]) ).
cnf(refute_0_254,plain,
( join(complement(X_69),top) != join(top,complement(X_69))
| complement(join(complement(X_69),top)) = complement(join(top,complement(X_69))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_69),top)),complement(join(complement(X_69),top))) )],[refute_0_252,refute_0_253]) ).
cnf(refute_0_255,plain,
complement(join(complement(X_69),top)) = complement(join(top,complement(X_69))),
inference(resolve,[$cnf( $equal(join(complement(X_69),top),join(top,complement(X_69))) )],[refute_0_251,refute_0_254]) ).
cnf(refute_0_256,plain,
join(meet(top,X_69),complement(join(complement(X_69),top))) = join(meet(top,X_69),complement(join(complement(X_69),top))),
introduced(tautology,[refl,[$fot(join(meet(top,X_69),complement(join(complement(X_69),top))))]]) ).
cnf(refute_0_257,plain,
( complement(join(complement(X_69),top)) != complement(join(top,complement(X_69)))
| join(meet(top,X_69),complement(join(complement(X_69),top))) != join(meet(top,X_69),complement(join(complement(X_69),top)))
| join(meet(top,X_69),complement(join(complement(X_69),top))) = join(meet(top,X_69),complement(join(top,complement(X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(top,X_69),complement(join(complement(X_69),top))),join(meet(top,X_69),complement(join(complement(X_69),top)))) ),[1,1],$fot(complement(join(top,complement(X_69))))]]) ).
cnf(refute_0_258,plain,
( complement(join(complement(X_69),top)) != complement(join(top,complement(X_69)))
| join(meet(top,X_69),complement(join(complement(X_69),top))) = join(meet(top,X_69),complement(join(top,complement(X_69)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_69),complement(join(complement(X_69),top))),join(meet(top,X_69),complement(join(complement(X_69),top)))) )],[refute_0_256,refute_0_257]) ).
cnf(refute_0_259,plain,
join(meet(top,X_69),complement(join(complement(X_69),top))) = join(meet(top,X_69),complement(join(top,complement(X_69)))),
inference(resolve,[$cnf( $equal(complement(join(complement(X_69),top)),complement(join(top,complement(X_69)))) )],[refute_0_255,refute_0_258]) ).
cnf(refute_0_260,plain,
( X_69 != join(meet(top,X_69),complement(join(complement(X_69),top)))
| join(meet(top,X_69),complement(join(complement(X_69),top))) != join(meet(top,X_69),complement(join(top,complement(X_69))))
| X_69 = join(meet(top,X_69),complement(join(top,complement(X_69)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_69,join(meet(top,X_69),complement(join(top,complement(X_69))))) ),[0],$fot(join(meet(top,X_69),complement(join(complement(X_69),top))))]]) ).
cnf(refute_0_261,plain,
( X_69 != join(meet(top,X_69),complement(join(complement(X_69),top)))
| X_69 = join(meet(top,X_69),complement(join(top,complement(X_69)))) ),
inference(resolve,[$cnf( $equal(join(meet(top,X_69),complement(join(complement(X_69),top))),join(meet(top,X_69),complement(join(top,complement(X_69))))) )],[refute_0_259,refute_0_260]) ).
cnf(refute_0_262,plain,
X_69 = join(meet(top,X_69),complement(join(top,complement(X_69)))),
inference(resolve,[$cnf( $equal(X_69,join(meet(top,X_69),complement(join(complement(X_69),top)))) )],[refute_0_250,refute_0_261]) ).
cnf(refute_0_263,plain,
complement(X_50) = join(meet(top,complement(X_50)),complement(join(top,complement(complement(X_50))))),
inference(subst,[],[refute_0_262:[bind(X_69,$fot(complement(X_50)))]]) ).
cnf(refute_0_264,plain,
join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = join(complement(X_32),join(complement(X_33),meet(X_32,X_33))),
inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(complement(X_33),meet(X_32,X_33)))),bind(B,$fot(complement(X_32)))]]) ).
cnf(refute_0_265,plain,
top = join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27)))),
inference(subst,[],[def_top_12:[bind(A,$fot(join(complement(X_26),complement(X_27))))]]) ).
cnf(refute_0_266,plain,
( complement(join(complement(X_26),complement(X_27))) != meet(X_26,X_27)
| top != join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) ),[1,1],$fot(meet(X_26,X_27))]]) ).
cnf(refute_0_267,plain,
( top != join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))
| top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_26),complement(X_27))),meet(X_26,X_27)) )],[refute_0_202,refute_0_266]) ).
cnf(refute_0_268,plain,
top = join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),complement(join(complement(X_26),complement(X_27))))) )],[refute_0_265,refute_0_267]) ).
cnf(refute_0_269,plain,
join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_26))),bind(B,$fot(complement(X_27))),bind(C,$fot(meet(X_26,X_27)))]]) ).
cnf(refute_0_270,plain,
( join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)) != join(complement(X_26),join(complement(X_27),meet(X_26,X_27)))
| top != join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))) ),
introduced(tautology,[equality,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) ),[1],$fot(join(complement(X_26),join(complement(X_27),meet(X_26,X_27))))]]) ).
cnf(refute_0_271,plain,
( top != join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))
| top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_26),complement(X_27)),meet(X_26,X_27)),join(complement(X_26),join(complement(X_27),meet(X_26,X_27)))) )],[refute_0_269,refute_0_270]) ).
cnf(refute_0_272,plain,
top = join(complement(X_26),join(complement(X_27),meet(X_26,X_27))),
inference(resolve,[$cnf( $equal(top,join(join(complement(X_26),complement(X_27)),meet(X_26,X_27))) )],[refute_0_268,refute_0_271]) ).
cnf(refute_0_273,plain,
top = join(complement(X_32),join(complement(X_33),meet(X_32,X_33))),
inference(subst,[],[refute_0_272:[bind(X_26,$fot(X_32)),bind(X_27,$fot(X_33))]]) ).
cnf(refute_0_274,plain,
( top != join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))
| join(complement(X_32),join(complement(X_33),meet(X_32,X_33))) = top ),
inference(subst,[],[refute_0_2:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))))]]) ).
cnf(refute_0_275,plain,
join(complement(X_32),join(complement(X_33),meet(X_32,X_33))) = top,
inference(resolve,[$cnf( $equal(top,join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
( join(complement(X_32),join(complement(X_33),meet(X_32,X_33))) != top
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))) ),[1],$fot(top)]]) ).
cnf(refute_0_277,plain,
( join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = top ),
inference(resolve,[$cnf( $equal(join(complement(X_32),join(complement(X_33),meet(X_32,X_33))),top) )],[refute_0_275,refute_0_276]) ).
cnf(refute_0_278,plain,
join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),join(complement(X_32),join(complement(X_33),meet(X_32,X_33)))) )],[refute_0_264,refute_0_277]) ).
cnf(refute_0_279,plain,
join(meet(X_32,X_33),complement(X_32)) = join(complement(X_32),meet(X_32,X_33)),
inference(subst,[],[refute_0_79:[bind(A,$fot(complement(X_32))),bind(B,$fot(meet(X_32,X_33)))]]) ).
cnf(refute_0_280,plain,
join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) = join(complement(X_33),join(meet(X_32,X_33),complement(X_32))),
introduced(tautology,[refl,[$fot(join(complement(X_33),join(meet(X_32,X_33),complement(X_32))))]]) ).
cnf(refute_0_281,plain,
( join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) != join(complement(X_33),join(meet(X_32,X_33),complement(X_32)))
| join(meet(X_32,X_33),complement(X_32)) != join(complement(X_32),meet(X_32,X_33))
| join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_33),join(meet(X_32,X_33),complement(X_32))),join(complement(X_33),join(meet(X_32,X_33),complement(X_32)))) ),[1,1],$fot(join(complement(X_32),meet(X_32,X_33)))]]) ).
cnf(refute_0_282,plain,
( join(meet(X_32,X_33),complement(X_32)) != join(complement(X_32),meet(X_32,X_33))
| join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) ),
inference(resolve,[$cnf( $equal(join(complement(X_33),join(meet(X_32,X_33),complement(X_32))),join(complement(X_33),join(meet(X_32,X_33),complement(X_32)))) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))),
inference(resolve,[$cnf( $equal(join(meet(X_32,X_33),complement(X_32)),join(complement(X_32),meet(X_32,X_33))) )],[refute_0_279,refute_0_282]) ).
cnf(refute_0_284,plain,
join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = join(complement(X_33),join(meet(X_32,X_33),complement(X_32))),
inference(subst,[],[refute_0_4:[bind(A,$fot(complement(X_33))),bind(B,$fot(meet(X_32,X_33))),bind(C,$fot(complement(X_32)))]]) ).
cnf(refute_0_285,plain,
( join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) != join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != join(complement(X_33),join(meet(X_32,X_33),complement(X_32)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)))),bind(Y,$fot(join(complement(X_33),join(meet(X_32,X_33),complement(X_32))))),bind(Z,$fot(join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))))]]) ).
cnf(refute_0_286,plain,
( join(complement(X_33),join(meet(X_32,X_33),complement(X_32))) != join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) ),
inference(resolve,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),join(complement(X_33),join(meet(X_32,X_33),complement(X_32)))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) = join(complement(X_33),join(complement(X_32),meet(X_32,X_33))),
inference(resolve,[$cnf( $equal(join(complement(X_33),join(meet(X_32,X_33),complement(X_32))),join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))) )],[refute_0_283,refute_0_286]) ).
cnf(refute_0_288,plain,
( join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))
| join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != top
| join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),top) ),[0],$fot(join(complement(X_33),join(complement(X_32),meet(X_32,X_33))))]]) ).
cnf(refute_0_289,plain,
( join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)) != top
| join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) = top ),
inference(resolve,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),join(complement(X_33),join(complement(X_32),meet(X_32,X_33)))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
join(complement(X_33),join(complement(X_32),meet(X_32,X_33))) = top,
inference(resolve,[$cnf( $equal(join(join(complement(X_33),meet(X_32,X_33)),complement(X_32)),top) )],[refute_0_278,refute_0_289]) ).
cnf(refute_0_291,plain,
join(complement(composition(join(one,one),X_62)),join(complement(X_62),meet(X_62,composition(join(one,one),X_62)))) = top,
inference(subst,[],[refute_0_290:[bind(X_32,$fot(X_62)),bind(X_33,$fot(composition(join(one,one),X_62)))]]) ).
cnf(refute_0_292,plain,
meet(A,composition(join(one,one),A)) = complement(join(complement(A),complement(composition(join(one,one),A)))),
inference(subst,[],[maddux4_definiton_of_meet_4:[bind(B,$fot(composition(join(one,one),A)))]]) ).
cnf(refute_0_293,plain,
join(complement(X_50),composition(converse(join(one,one)),complement(composition(join(one,one),X_50)))) = complement(X_50),
inference(subst,[],[refute_0_94:[bind(A,$fot(join(one,one))),bind(B,$fot(X_50))]]) ).
cnf(refute_0_294,plain,
( converse(join(one,one)) != join(one,one)
| join(complement(X_50),composition(converse(join(one,one)),complement(composition(join(one,one),X_50)))) != complement(X_50)
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = complement(X_50) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_50),composition(converse(join(one,one)),complement(composition(join(one,one),X_50)))),complement(X_50)) ),[0,1,0],$fot(join(one,one))]]) ).
cnf(refute_0_295,plain,
( join(complement(X_50),composition(converse(join(one,one)),complement(composition(join(one,one),X_50)))) != complement(X_50)
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = complement(X_50) ),
inference(resolve,[$cnf( $equal(converse(join(one,one)),join(one,one)) )],[refute_0_113,refute_0_294]) ).
cnf(refute_0_296,plain,
join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = complement(X_50),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(converse(join(one,one)),complement(composition(join(one,one),X_50)))),complement(X_50)) )],[refute_0_293,refute_0_295]) ).
cnf(refute_0_297,plain,
composition(join(one,one),complement(composition(join(one,one),X_50))) = complement(composition(join(one,one),X_50)),
inference(subst,[],[refute_0_149:[bind(X_50,$fot(composition(join(one,one),X_50)))]]) ).
cnf(refute_0_298,plain,
join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),
introduced(tautology,[refl,[$fot(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))))]]) ).
cnf(refute_0_299,plain,
( composition(join(one,one),complement(composition(join(one,one),X_50))) != complement(composition(join(one,one),X_50))
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) != join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50))))
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = join(complement(X_50),complement(composition(join(one,one),X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50))))) ),[1,1],$fot(complement(composition(join(one,one),X_50)))]]) ).
cnf(refute_0_300,plain,
( composition(join(one,one),complement(composition(join(one,one),X_50))) != complement(composition(join(one,one),X_50))
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = join(complement(X_50),complement(composition(join(one,one),X_50))) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) = join(complement(X_50),complement(composition(join(one,one),X_50))),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(composition(join(one,one),X_50))),complement(composition(join(one,one),X_50))) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
( join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) != complement(X_50)
| join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) != join(complement(X_50),complement(composition(join(one,one),X_50)))
| join(complement(X_50),complement(composition(join(one,one),X_50))) = complement(X_50) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),complement(X_50)) ),[0],$fot(join(complement(X_50),complement(composition(join(one,one),X_50))))]]) ).
cnf(refute_0_303,plain,
( join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))) != complement(X_50)
| join(complement(X_50),complement(composition(join(one,one),X_50))) = complement(X_50) ),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),join(complement(X_50),complement(composition(join(one,one),X_50)))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
join(complement(X_50),complement(composition(join(one,one),X_50))) = complement(X_50),
inference(resolve,[$cnf( $equal(join(complement(X_50),composition(join(one,one),complement(composition(join(one,one),X_50)))),complement(X_50)) )],[refute_0_296,refute_0_303]) ).
cnf(refute_0_305,plain,
join(complement(A),complement(composition(join(one,one),A))) = complement(A),
inference(subst,[],[refute_0_304:[bind(X_50,$fot(A))]]) ).
cnf(refute_0_306,plain,
( join(complement(A),complement(composition(join(one,one),A))) != complement(A)
| meet(A,composition(join(one,one),A)) != complement(join(complement(A),complement(composition(join(one,one),A))))
| meet(A,composition(join(one,one),A)) = complement(complement(A)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(A,composition(join(one,one),A)),complement(join(complement(A),complement(composition(join(one,one),A))))) ),[1,0],$fot(complement(A))]]) ).
cnf(refute_0_307,plain,
( meet(A,composition(join(one,one),A)) != complement(join(complement(A),complement(composition(join(one,one),A))))
| meet(A,composition(join(one,one),A)) = complement(complement(A)) ),
inference(resolve,[$cnf( $equal(join(complement(A),complement(composition(join(one,one),A))),complement(A)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
meet(A,composition(join(one,one),A)) = complement(complement(A)),
inference(resolve,[$cnf( $equal(meet(A,composition(join(one,one),A)),complement(join(complement(A),complement(composition(join(one,one),A))))) )],[refute_0_292,refute_0_307]) ).
cnf(refute_0_309,plain,
meet(X_62,composition(join(one,one),X_62)) = complement(complement(X_62)),
inference(subst,[],[refute_0_308:[bind(A,$fot(X_62))]]) ).
cnf(refute_0_310,plain,
( join(complement(composition(join(one,one),X_62)),join(complement(X_62),meet(X_62,composition(join(one,one),X_62)))) != top
| meet(X_62,composition(join(one,one),X_62)) != complement(complement(X_62))
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),meet(X_62,composition(join(one,one),X_62)))),top) ),[0,1,1],$fot(complement(complement(X_62)))]]) ).
cnf(refute_0_311,plain,
( join(complement(composition(join(one,one),X_62)),join(complement(X_62),meet(X_62,composition(join(one,one),X_62)))) != top
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = top ),
inference(resolve,[$cnf( $equal(meet(X_62,composition(join(one,one),X_62)),complement(complement(X_62))) )],[refute_0_309,refute_0_310]) ).
cnf(refute_0_312,plain,
join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = top,
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),meet(X_62,composition(join(one,one),X_62)))),top) )],[refute_0_291,refute_0_311]) ).
cnf(refute_0_313,plain,
join(complement(composition(join(one,one),X_62)),top) = join(top,complement(composition(join(one,one),X_62))),
inference(subst,[],[refute_0_79:[bind(A,$fot(top)),bind(B,$fot(complement(composition(join(one,one),X_62))))]]) ).
cnf(refute_0_314,plain,
join(complement(X_62),complement(complement(X_62))) = top,
inference(subst,[],[refute_0_207:[bind(A,$fot(complement(X_62)))]]) ).
cnf(refute_0_315,plain,
join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),
introduced(tautology,[refl,[$fot(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))))]]) ).
cnf(refute_0_316,plain,
( join(complement(X_62),complement(complement(X_62))) != top
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) != join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62))))
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(complement(composition(join(one,one),X_62)),top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62))))) ),[1,1],$fot(top)]]) ).
cnf(refute_0_317,plain,
( join(complement(X_62),complement(complement(X_62))) != top
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(complement(composition(join(one,one),X_62)),top) ),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62))))) )],[refute_0_315,refute_0_316]) ).
cnf(refute_0_318,plain,
join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(complement(composition(join(one,one),X_62)),top),
inference(resolve,[$cnf( $equal(join(complement(X_62),complement(complement(X_62))),top) )],[refute_0_314,refute_0_317]) ).
cnf(refute_0_319,plain,
( join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) != join(complement(composition(join(one,one),X_62)),top)
| join(complement(composition(join(one,one),X_62)),top) != join(top,complement(composition(join(one,one),X_62)))
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(top,complement(composition(join(one,one),X_62))) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))))),bind(Y,$fot(join(complement(composition(join(one,one),X_62)),top))),bind(Z,$fot(join(top,complement(composition(join(one,one),X_62)))))]]) ).
cnf(refute_0_320,plain,
( join(complement(composition(join(one,one),X_62)),top) != join(top,complement(composition(join(one,one),X_62)))
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(top,complement(composition(join(one,one),X_62))) ),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),join(complement(composition(join(one,one),X_62)),top)) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) = join(top,complement(composition(join(one,one),X_62))),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),top),join(top,complement(composition(join(one,one),X_62)))) )],[refute_0_313,refute_0_320]) ).
cnf(refute_0_322,plain,
( join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) != join(top,complement(composition(join(one,one),X_62)))
| join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) != top
| join(top,complement(composition(join(one,one),X_62))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),top) ),[0],$fot(join(top,complement(composition(join(one,one),X_62))))]]) ).
cnf(refute_0_323,plain,
( join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))) != top
| join(top,complement(composition(join(one,one),X_62))) = top ),
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),join(top,complement(composition(join(one,one),X_62)))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
join(top,complement(composition(join(one,one),X_62))) = top,
inference(resolve,[$cnf( $equal(join(complement(composition(join(one,one),X_62)),join(complement(X_62),complement(complement(X_62)))),top) )],[refute_0_312,refute_0_323]) ).
cnf(refute_0_325,plain,
join(top,complement(composition(join(one,one),complement(X_50)))) = top,
inference(subst,[],[refute_0_324:[bind(X_62,$fot(complement(X_50)))]]) ).
cnf(refute_0_326,plain,
( composition(join(one,one),complement(X_50)) != complement(X_50)
| join(top,complement(composition(join(one,one),complement(X_50)))) != top
| join(top,complement(complement(X_50))) = top ),
introduced(tautology,[equality,[$cnf( $equal(join(top,complement(composition(join(one,one),complement(X_50)))),top) ),[0,1,0],$fot(complement(X_50))]]) ).
cnf(refute_0_327,plain,
( join(top,complement(composition(join(one,one),complement(X_50)))) != top
| join(top,complement(complement(X_50))) = top ),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(X_50)),complement(X_50)) )],[refute_0_149,refute_0_326]) ).
cnf(refute_0_328,plain,
join(top,complement(complement(X_50))) = top,
inference(resolve,[$cnf( $equal(join(top,complement(composition(join(one,one),complement(X_50)))),top) )],[refute_0_325,refute_0_327]) ).
cnf(refute_0_329,plain,
( complement(X_50) != join(meet(top,complement(X_50)),complement(join(top,complement(complement(X_50)))))
| join(top,complement(complement(X_50))) != top
| complement(X_50) = join(meet(top,complement(X_50)),complement(top)) ),
introduced(tautology,[equality,[$cnf( $equal(complement(X_50),join(meet(top,complement(X_50)),complement(join(top,complement(complement(X_50)))))) ),[1,1,0],$fot(top)]]) ).
cnf(refute_0_330,plain,
( complement(X_50) != join(meet(top,complement(X_50)),complement(join(top,complement(complement(X_50)))))
| complement(X_50) = join(meet(top,complement(X_50)),complement(top)) ),
inference(resolve,[$cnf( $equal(join(top,complement(complement(X_50))),top) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
complement(X_50) = join(meet(top,complement(X_50)),complement(top)),
inference(resolve,[$cnf( $equal(complement(X_50),join(meet(top,complement(X_50)),complement(join(top,complement(complement(X_50)))))) )],[refute_0_263,refute_0_330]) ).
cnf(refute_0_332,plain,
meet(top,complement(X_71)) = complement(join(zero,complement(complement(X_71)))),
inference(subst,[],[refute_0_232:[bind(B,$fot(complement(X_71)))]]) ).
cnf(refute_0_333,plain,
X_71 = join(zero,complement(complement(X_71))),
inference(subst,[],[refute_0_196:[bind(X_69,$fot(X_71))]]) ).
cnf(refute_0_334,plain,
( X_71 != join(zero,complement(complement(X_71)))
| join(zero,complement(complement(X_71))) = X_71 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_71)),bind(Y,$fot(join(zero,complement(complement(X_71)))))]]) ).
cnf(refute_0_335,plain,
join(zero,complement(complement(X_71))) = X_71,
inference(resolve,[$cnf( $equal(X_71,join(zero,complement(complement(X_71)))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
( join(zero,complement(complement(X_71))) != X_71
| meet(top,complement(X_71)) != complement(join(zero,complement(complement(X_71))))
| meet(top,complement(X_71)) = complement(X_71) ),
introduced(tautology,[equality,[$cnf( $equal(meet(top,complement(X_71)),complement(join(zero,complement(complement(X_71))))) ),[1,0],$fot(X_71)]]) ).
cnf(refute_0_337,plain,
( meet(top,complement(X_71)) != complement(join(zero,complement(complement(X_71))))
| meet(top,complement(X_71)) = complement(X_71) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_71))),X_71) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
meet(top,complement(X_71)) = complement(X_71),
inference(resolve,[$cnf( $equal(meet(top,complement(X_71)),complement(join(zero,complement(complement(X_71))))) )],[refute_0_332,refute_0_337]) ).
cnf(refute_0_339,plain,
meet(top,complement(X_50)) = complement(X_50),
inference(subst,[],[refute_0_338:[bind(X_71,$fot(X_50))]]) ).
cnf(refute_0_340,plain,
join(zero,meet(top,complement(X_50))) = join(zero,meet(top,complement(X_50))),
introduced(tautology,[refl,[$fot(join(zero,meet(top,complement(X_50))))]]) ).
cnf(refute_0_341,plain,
( join(zero,meet(top,complement(X_50))) != join(zero,meet(top,complement(X_50)))
| meet(top,complement(X_50)) != complement(X_50)
| join(zero,meet(top,complement(X_50))) = join(zero,complement(X_50)) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,meet(top,complement(X_50))),join(zero,meet(top,complement(X_50)))) ),[1,1],$fot(complement(X_50))]]) ).
cnf(refute_0_342,plain,
( meet(top,complement(X_50)) != complement(X_50)
| join(zero,meet(top,complement(X_50))) = join(zero,complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(X_50))),join(zero,meet(top,complement(X_50)))) )],[refute_0_340,refute_0_341]) ).
cnf(refute_0_343,plain,
join(zero,meet(top,complement(X_50))) = join(zero,complement(X_50)),
inference(resolve,[$cnf( $equal(meet(top,complement(X_50)),complement(X_50)) )],[refute_0_339,refute_0_342]) ).
cnf(refute_0_344,plain,
join(complement(top),meet(top,complement(X_50))) = join(complement(top),meet(top,complement(X_50))),
introduced(tautology,[refl,[$fot(join(complement(top),meet(top,complement(X_50))))]]) ).
cnf(refute_0_345,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(X_50))) != join(complement(top),meet(top,complement(X_50)))
| join(complement(top),meet(top,complement(X_50))) = join(zero,meet(top,complement(X_50))) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(top,complement(X_50))),join(complement(top),meet(top,complement(X_50)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_346,plain,
( complement(top) != zero
| join(complement(top),meet(top,complement(X_50))) = join(zero,meet(top,complement(X_50))) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(X_50))),join(complement(top),meet(top,complement(X_50)))) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
join(complement(top),meet(top,complement(X_50))) = join(zero,meet(top,complement(X_50))),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_225,refute_0_346]) ).
cnf(refute_0_348,plain,
( join(complement(top),meet(top,complement(X_50))) != join(zero,meet(top,complement(X_50)))
| join(zero,meet(top,complement(X_50))) != join(zero,complement(X_50))
| join(complement(top),meet(top,complement(X_50))) = join(zero,complement(X_50)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(complement(top),meet(top,complement(X_50))))),bind(Y,$fot(join(zero,meet(top,complement(X_50))))),bind(Z,$fot(join(zero,complement(X_50))))]]) ).
cnf(refute_0_349,plain,
( join(zero,meet(top,complement(X_50))) != join(zero,complement(X_50))
| join(complement(top),meet(top,complement(X_50))) = join(zero,complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(X_50))),join(zero,meet(top,complement(X_50)))) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
join(complement(top),meet(top,complement(X_50))) = join(zero,complement(X_50)),
inference(resolve,[$cnf( $equal(join(zero,meet(top,complement(X_50))),join(zero,complement(X_50))) )],[refute_0_343,refute_0_349]) ).
cnf(refute_0_351,plain,
join(meet(top,complement(X_50)),complement(top)) = join(complement(top),meet(top,complement(X_50))),
inference(subst,[],[refute_0_79:[bind(A,$fot(complement(top))),bind(B,$fot(meet(top,complement(X_50))))]]) ).
cnf(refute_0_352,plain,
( join(complement(top),meet(top,complement(X_50))) != join(zero,complement(X_50))
| join(meet(top,complement(X_50)),complement(top)) != join(complement(top),meet(top,complement(X_50)))
| join(meet(top,complement(X_50)),complement(top)) = join(zero,complement(X_50)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(meet(top,complement(X_50)),complement(top)))),bind(Y,$fot(join(complement(top),meet(top,complement(X_50))))),bind(Z,$fot(join(zero,complement(X_50))))]]) ).
cnf(refute_0_353,plain,
( join(complement(top),meet(top,complement(X_50))) != join(zero,complement(X_50))
| join(meet(top,complement(X_50)),complement(top)) = join(zero,complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(X_50)),complement(top)),join(complement(top),meet(top,complement(X_50)))) )],[refute_0_351,refute_0_352]) ).
cnf(refute_0_354,plain,
join(meet(top,complement(X_50)),complement(top)) = join(zero,complement(X_50)),
inference(resolve,[$cnf( $equal(join(complement(top),meet(top,complement(X_50))),join(zero,complement(X_50))) )],[refute_0_350,refute_0_353]) ).
cnf(refute_0_355,plain,
( complement(X_50) != join(meet(top,complement(X_50)),complement(top))
| join(meet(top,complement(X_50)),complement(top)) != join(zero,complement(X_50))
| complement(X_50) = join(zero,complement(X_50)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(complement(X_50),join(zero,complement(X_50))) ),[0],$fot(join(meet(top,complement(X_50)),complement(top)))]]) ).
cnf(refute_0_356,plain,
( complement(X_50) != join(meet(top,complement(X_50)),complement(top))
| complement(X_50) = join(zero,complement(X_50)) ),
inference(resolve,[$cnf( $equal(join(meet(top,complement(X_50)),complement(top)),join(zero,complement(X_50))) )],[refute_0_354,refute_0_355]) ).
cnf(refute_0_357,plain,
complement(X_50) = join(zero,complement(X_50)),
inference(resolve,[$cnf( $equal(complement(X_50),join(meet(top,complement(X_50)),complement(top))) )],[refute_0_331,refute_0_356]) ).
cnf(refute_0_358,plain,
( complement(X_50) != join(zero,complement(X_50))
| join(zero,complement(X_50)) = complement(X_50) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(complement(X_50))),bind(Y,$fot(join(zero,complement(X_50))))]]) ).
cnf(refute_0_359,plain,
join(zero,complement(X_50)) = complement(X_50),
inference(resolve,[$cnf( $equal(complement(X_50),join(zero,complement(X_50))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
join(zero,complement(complement(X_69))) = complement(complement(X_69)),
inference(subst,[],[refute_0_359:[bind(X_50,$fot(complement(X_69)))]]) ).
cnf(refute_0_361,plain,
( X_69 != join(zero,complement(complement(X_69)))
| join(zero,complement(complement(X_69))) != complement(complement(X_69))
| X_69 = complement(complement(X_69)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_69,complement(complement(X_69))) ),[0],$fot(join(zero,complement(complement(X_69))))]]) ).
cnf(refute_0_362,plain,
( X_69 != join(zero,complement(complement(X_69)))
| X_69 = complement(complement(X_69)) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_69))),complement(complement(X_69))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
X_69 = complement(complement(X_69)),
inference(resolve,[$cnf( $equal(X_69,join(zero,complement(complement(X_69)))) )],[refute_0_196,refute_0_362]) ).
cnf(refute_0_364,plain,
X_88 = complement(complement(X_88)),
inference(subst,[],[refute_0_363:[bind(X_69,$fot(X_88))]]) ).
cnf(refute_0_365,plain,
( X_88 != complement(complement(X_88))
| complement(complement(X_88)) = X_88 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_88)),bind(Y,$fot(complement(complement(X_88))))]]) ).
cnf(refute_0_366,plain,
complement(complement(X_88)) = X_88,
inference(resolve,[$cnf( $equal(X_88,complement(complement(X_88))) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
( complement(complement(X_88)) != X_88
| composition(join(one,one),complement(complement(X_88))) != complement(complement(X_88))
| composition(join(one,one),X_88) = complement(complement(X_88)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),complement(complement(X_88))),complement(complement(X_88))) ),[0,1],$fot(X_88)]]) ).
cnf(refute_0_368,plain,
( composition(join(one,one),complement(complement(X_88))) != complement(complement(X_88))
| composition(join(one,one),X_88) = complement(complement(X_88)) ),
inference(resolve,[$cnf( $equal(complement(complement(X_88)),X_88) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
composition(join(one,one),X_88) = complement(complement(X_88)),
inference(resolve,[$cnf( $equal(composition(join(one,one),complement(complement(X_88))),complement(complement(X_88))) )],[refute_0_150,refute_0_368]) ).
cnf(refute_0_370,plain,
( complement(complement(X_88)) != X_88
| composition(join(one,one),X_88) != complement(complement(X_88))
| composition(join(one,one),X_88) = X_88 ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_88),complement(complement(X_88))) ),[1],$fot(X_88)]]) ).
cnf(refute_0_371,plain,
( composition(join(one,one),X_88) != complement(complement(X_88))
| composition(join(one,one),X_88) = X_88 ),
inference(resolve,[$cnf( $equal(complement(complement(X_88)),X_88) )],[refute_0_366,refute_0_370]) ).
cnf(refute_0_372,plain,
composition(join(one,one),X_88) = X_88,
inference(resolve,[$cnf( $equal(composition(join(one,one),X_88),complement(complement(X_88))) )],[refute_0_369,refute_0_371]) ).
cnf(refute_0_373,plain,
composition(join(one,one),X_41) = X_41,
inference(subst,[],[refute_0_372:[bind(X_88,$fot(X_41))]]) ).
cnf(refute_0_374,plain,
( composition(join(one,one),X_41) != X_41
| composition(join(one,one),X_41) != join(X_41,X_41)
| X_41 = join(X_41,X_41) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(one,one),X_41),join(X_41,X_41)) ),[0],$fot(X_41)]]) ).
cnf(refute_0_375,plain,
( composition(join(one,one),X_41) != join(X_41,X_41)
| X_41 = join(X_41,X_41) ),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_41),X_41) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
X_41 = join(X_41,X_41),
inference(resolve,[$cnf( $equal(composition(join(one,one),X_41),join(X_41,X_41)) )],[refute_0_90,refute_0_375]) ).
cnf(refute_0_377,plain,
X_122 = join(X_122,X_122),
inference(subst,[],[refute_0_376:[bind(X_41,$fot(X_122))]]) ).
cnf(refute_0_378,plain,
( X_122 != join(X_122,X_122)
| join(X_122,X_122) = X_122 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_122)),bind(Y,$fot(join(X_122,X_122)))]]) ).
cnf(refute_0_379,plain,
join(X_122,X_122) = X_122,
inference(resolve,[$cnf( $equal(X_122,join(X_122,X_122)) )],[refute_0_377,refute_0_378]) ).
cnf(refute_0_380,plain,
( join(X_122,X_122) != X_122
| join(X_122,join(X_122,X_123)) != join(join(X_122,X_122),X_123)
| join(X_122,join(X_122,X_123)) = join(X_122,X_123) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_122,join(X_122,X_123)),join(join(X_122,X_122),X_123)) ),[1,0],$fot(X_122)]]) ).
cnf(refute_0_381,plain,
( join(X_122,join(X_122,X_123)) != join(join(X_122,X_122),X_123)
| join(X_122,join(X_122,X_123)) = join(X_122,X_123) ),
inference(resolve,[$cnf( $equal(join(X_122,X_122),X_122) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
join(X_122,join(X_122,X_123)) = join(X_122,X_123),
inference(resolve,[$cnf( $equal(join(X_122,join(X_122,X_123)),join(join(X_122,X_122),X_123)) )],[refute_0_41,refute_0_381]) ).
cnf(refute_0_383,plain,
join(sk2,join(sk2,sk3)) = join(sk2,sk3),
inference(subst,[],[refute_0_382:[bind(X_122,$fot(sk2)),bind(X_123,$fot(sk3))]]) ).
cnf(refute_0_384,plain,
composition(sk1,join(sk2,join(sk2,sk3))) = composition(sk1,join(sk2,join(sk2,sk3))),
introduced(tautology,[refl,[$fot(composition(sk1,join(sk2,join(sk2,sk3))))]]) ).
cnf(refute_0_385,plain,
( composition(sk1,join(sk2,join(sk2,sk3))) != composition(sk1,join(sk2,join(sk2,sk3)))
| join(sk2,join(sk2,sk3)) != join(sk2,sk3)
| composition(sk1,join(sk2,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(sk1,join(sk2,join(sk2,sk3))),composition(sk1,join(sk2,join(sk2,sk3)))) ),[1,1],$fot(join(sk2,sk3))]]) ).
cnf(refute_0_386,plain,
( join(sk2,join(sk2,sk3)) != join(sk2,sk3)
| composition(sk1,join(sk2,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(sk1,join(sk2,join(sk2,sk3))),composition(sk1,join(sk2,join(sk2,sk3)))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
composition(sk1,join(sk2,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(sk2,join(sk2,sk3)),join(sk2,sk3)) )],[refute_0_383,refute_0_386]) ).
cnf(refute_0_388,plain,
converse(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(join(composition(X_251,X_252),composition(X_251,converse(X_253)))))]]) ).
cnf(refute_0_389,plain,
composition(join(converse(B),X_38),converse(A)) = join(composition(converse(B),converse(A)),composition(X_38,converse(A))),
inference(subst,[],[composition_distributivity_7:[bind(A,$fot(converse(B))),bind(B,$fot(X_38)),bind(C,$fot(converse(A)))]]) ).
cnf(refute_0_390,plain,
( converse(composition(A,B)) != composition(converse(B),converse(A))
| composition(converse(B),converse(A)) = converse(composition(A,B)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,B)))),bind(Y,$fot(composition(converse(B),converse(A))))]]) ).
cnf(refute_0_391,plain,
composition(converse(B),converse(A)) = converse(composition(A,B)),
inference(resolve,[$cnf( $equal(converse(composition(A,B)),composition(converse(B),converse(A))) )],[converse_multiplicativity_10,refute_0_390]) ).
cnf(refute_0_392,plain,
( composition(converse(B),converse(A)) != converse(composition(A,B))
| composition(join(converse(B),X_38),converse(A)) != join(composition(converse(B),converse(A)),composition(X_38,converse(A)))
| composition(join(converse(B),X_38),converse(A)) = join(converse(composition(A,B)),composition(X_38,converse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),X_38),converse(A)),join(composition(converse(B),converse(A)),composition(X_38,converse(A)))) ),[1,0],$fot(converse(composition(A,B)))]]) ).
cnf(refute_0_393,plain,
( composition(join(converse(B),X_38),converse(A)) != join(composition(converse(B),converse(A)),composition(X_38,converse(A)))
| composition(join(converse(B),X_38),converse(A)) = join(converse(composition(A,B)),composition(X_38,converse(A))) ),
inference(resolve,[$cnf( $equal(composition(converse(B),converse(A)),converse(composition(A,B))) )],[refute_0_391,refute_0_392]) ).
cnf(refute_0_394,plain,
composition(join(converse(B),X_38),converse(A)) = join(converse(composition(A,B)),composition(X_38,converse(A))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),X_38),converse(A)),join(composition(converse(B),converse(A)),composition(X_38,converse(A)))) )],[refute_0_389,refute_0_393]) ).
cnf(refute_0_395,plain,
converse(composition(A,join(X_16,converse(X_15)))) = composition(converse(join(X_16,converse(X_15))),converse(A)),
inference(subst,[],[converse_multiplicativity_10:[bind(B,$fot(join(X_16,converse(X_15))))]]) ).
cnf(refute_0_396,plain,
converse(join(X_12,converse(A))) = join(converse(X_12),converse(converse(A))),
inference(subst,[],[converse_additivity_9:[bind(A,$fot(X_12)),bind(B,$fot(converse(A)))]]) ).
cnf(refute_0_397,plain,
( converse(converse(A)) != A
| converse(join(X_12,converse(A))) != join(converse(X_12),converse(converse(A)))
| converse(join(X_12,converse(A))) = join(converse(X_12),A) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,converse(A))),join(converse(X_12),converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_398,plain,
( converse(join(X_12,converse(A))) != join(converse(X_12),converse(converse(A)))
| converse(join(X_12,converse(A))) = join(converse(X_12),A) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_397]) ).
cnf(refute_0_399,plain,
converse(join(X_12,converse(A))) = join(converse(X_12),A),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(A))),join(converse(X_12),converse(converse(A)))) )],[refute_0_396,refute_0_398]) ).
cnf(refute_0_400,plain,
converse(join(X_16,converse(X_15))) = join(converse(X_16),X_15),
inference(subst,[],[refute_0_399:[bind(A,$fot(X_15)),bind(X_12,$fot(X_16))]]) ).
cnf(refute_0_401,plain,
( converse(composition(A,join(X_16,converse(X_15)))) != composition(converse(join(X_16,converse(X_15))),converse(A))
| converse(join(X_16,converse(X_15))) != join(converse(X_16),X_15)
| converse(composition(A,join(X_16,converse(X_15)))) = composition(join(converse(X_16),X_15),converse(A)) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(A,join(X_16,converse(X_15)))),composition(converse(join(X_16,converse(X_15))),converse(A))) ),[1,0],$fot(join(converse(X_16),X_15))]]) ).
cnf(refute_0_402,plain,
( converse(composition(A,join(X_16,converse(X_15)))) != composition(converse(join(X_16,converse(X_15))),converse(A))
| converse(composition(A,join(X_16,converse(X_15)))) = composition(join(converse(X_16),X_15),converse(A)) ),
inference(resolve,[$cnf( $equal(converse(join(X_16,converse(X_15))),join(converse(X_16),X_15)) )],[refute_0_400,refute_0_401]) ).
cnf(refute_0_403,plain,
converse(composition(A,join(X_16,converse(X_15)))) = composition(join(converse(X_16),X_15),converse(A)),
inference(resolve,[$cnf( $equal(converse(composition(A,join(X_16,converse(X_15)))),composition(converse(join(X_16,converse(X_15))),converse(A))) )],[refute_0_395,refute_0_402]) ).
cnf(refute_0_404,plain,
( converse(composition(A,join(X_16,converse(X_15)))) != composition(join(converse(X_16),X_15),converse(A))
| composition(join(converse(X_16),X_15),converse(A)) = converse(composition(A,join(X_16,converse(X_15)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(A,join(X_16,converse(X_15)))))),bind(Y,$fot(composition(join(converse(X_16),X_15),converse(A))))]]) ).
cnf(refute_0_405,plain,
composition(join(converse(X_16),X_15),converse(A)) = converse(composition(A,join(X_16,converse(X_15)))),
inference(resolve,[$cnf( $equal(converse(composition(A,join(X_16,converse(X_15)))),composition(join(converse(X_16),X_15),converse(A))) )],[refute_0_403,refute_0_404]) ).
cnf(refute_0_406,plain,
composition(join(converse(B),X_38),converse(A)) = converse(composition(A,join(B,converse(X_38)))),
inference(subst,[],[refute_0_405:[bind(X_15,$fot(X_38)),bind(X_16,$fot(B))]]) ).
cnf(refute_0_407,plain,
( composition(join(converse(B),X_38),converse(A)) != converse(composition(A,join(B,converse(X_38))))
| composition(join(converse(B),X_38),converse(A)) != join(converse(composition(A,B)),composition(X_38,converse(A)))
| converse(composition(A,join(B,converse(X_38)))) = join(converse(composition(A,B)),composition(X_38,converse(A))) ),
introduced(tautology,[equality,[$cnf( $equal(composition(join(converse(B),X_38),converse(A)),join(converse(composition(A,B)),composition(X_38,converse(A)))) ),[0],$fot(converse(composition(A,join(B,converse(X_38)))))]]) ).
cnf(refute_0_408,plain,
( composition(join(converse(B),X_38),converse(A)) != join(converse(composition(A,B)),composition(X_38,converse(A)))
| converse(composition(A,join(B,converse(X_38)))) = join(converse(composition(A,B)),composition(X_38,converse(A))) ),
inference(resolve,[$cnf( $equal(composition(join(converse(B),X_38),converse(A)),converse(composition(A,join(B,converse(X_38))))) )],[refute_0_406,refute_0_407]) ).
cnf(refute_0_409,plain,
converse(join(X_12,converse(composition(X_25,converse(X_24))))) = join(converse(X_12),composition(X_25,converse(X_24))),
inference(subst,[],[refute_0_399:[bind(A,$fot(composition(X_25,converse(X_24))))]]) ).
cnf(refute_0_410,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_411,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_412,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( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_411]) ).
cnf(refute_0_413,plain,
converse(composition(X_4,converse(A))) = composition(A,converse(X_4)),
inference(resolve,[$cnf( $equal(converse(composition(X_4,converse(A))),composition(converse(converse(A)),converse(X_4))) )],[refute_0_410,refute_0_412]) ).
cnf(refute_0_414,plain,
converse(composition(X_25,converse(X_24))) = composition(X_24,converse(X_25)),
inference(subst,[],[refute_0_413:[bind(A,$fot(X_24)),bind(X_4,$fot(X_25))]]) ).
cnf(refute_0_415,plain,
( converse(composition(X_25,converse(X_24))) != composition(X_24,converse(X_25))
| converse(join(X_12,converse(composition(X_25,converse(X_24))))) != join(converse(X_12),composition(X_25,converse(X_24)))
| converse(join(X_12,composition(X_24,converse(X_25)))) = join(converse(X_12),composition(X_25,converse(X_24))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(join(X_12,converse(composition(X_25,converse(X_24))))),join(converse(X_12),composition(X_25,converse(X_24)))) ),[0,0,1],$fot(composition(X_24,converse(X_25)))]]) ).
cnf(refute_0_416,plain,
( converse(join(X_12,converse(composition(X_25,converse(X_24))))) != join(converse(X_12),composition(X_25,converse(X_24)))
| converse(join(X_12,composition(X_24,converse(X_25)))) = join(converse(X_12),composition(X_25,converse(X_24))) ),
inference(resolve,[$cnf( $equal(converse(composition(X_25,converse(X_24))),composition(X_24,converse(X_25))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
converse(join(X_12,composition(X_24,converse(X_25)))) = join(converse(X_12),composition(X_25,converse(X_24))),
inference(resolve,[$cnf( $equal(converse(join(X_12,converse(composition(X_25,converse(X_24))))),join(converse(X_12),composition(X_25,converse(X_24)))) )],[refute_0_409,refute_0_416]) ).
cnf(refute_0_418,plain,
( converse(join(X_12,composition(X_24,converse(X_25)))) != join(converse(X_12),composition(X_25,converse(X_24)))
| join(converse(X_12),composition(X_25,converse(X_24))) = converse(join(X_12,composition(X_24,converse(X_25)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(join(X_12,composition(X_24,converse(X_25)))))),bind(Y,$fot(join(converse(X_12),composition(X_25,converse(X_24)))))]]) ).
cnf(refute_0_419,plain,
join(converse(X_12),composition(X_25,converse(X_24))) = converse(join(X_12,composition(X_24,converse(X_25)))),
inference(resolve,[$cnf( $equal(converse(join(X_12,composition(X_24,converse(X_25)))),join(converse(X_12),composition(X_25,converse(X_24)))) )],[refute_0_417,refute_0_418]) ).
cnf(refute_0_420,plain,
join(converse(composition(A,B)),composition(X_38,converse(A))) = converse(join(composition(A,B),composition(A,converse(X_38)))),
inference(subst,[],[refute_0_419:[bind(X_12,$fot(composition(A,B))),bind(X_24,$fot(A)),bind(X_25,$fot(X_38))]]) ).
cnf(refute_0_421,plain,
( converse(composition(A,join(B,converse(X_38)))) != join(converse(composition(A,B)),composition(X_38,converse(A)))
| join(converse(composition(A,B)),composition(X_38,converse(A))) != converse(join(composition(A,B),composition(A,converse(X_38))))
| converse(composition(A,join(B,converse(X_38)))) = converse(join(composition(A,B),composition(A,converse(X_38)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(converse(composition(A,join(B,converse(X_38)))),converse(join(composition(A,B),composition(A,converse(X_38))))) ),[0],$fot(join(converse(composition(A,B)),composition(X_38,converse(A))))]]) ).
cnf(refute_0_422,plain,
( converse(composition(A,join(B,converse(X_38)))) != join(converse(composition(A,B)),composition(X_38,converse(A)))
| converse(composition(A,join(B,converse(X_38)))) = converse(join(composition(A,B),composition(A,converse(X_38)))) ),
inference(resolve,[$cnf( $equal(join(converse(composition(A,B)),composition(X_38,converse(A))),converse(join(composition(A,B),composition(A,converse(X_38))))) )],[refute_0_420,refute_0_421]) ).
cnf(refute_0_423,plain,
( composition(join(converse(B),X_38),converse(A)) != join(converse(composition(A,B)),composition(X_38,converse(A)))
| converse(composition(A,join(B,converse(X_38)))) = converse(join(composition(A,B),composition(A,converse(X_38)))) ),
inference(resolve,[$cnf( $equal(converse(composition(A,join(B,converse(X_38)))),join(converse(composition(A,B)),composition(X_38,converse(A)))) )],[refute_0_408,refute_0_422]) ).
cnf(refute_0_424,plain,
converse(composition(A,join(B,converse(X_38)))) = converse(join(composition(A,B),composition(A,converse(X_38)))),
inference(resolve,[$cnf( $equal(composition(join(converse(B),X_38),converse(A)),join(converse(composition(A,B)),composition(X_38,converse(A)))) )],[refute_0_394,refute_0_423]) ).
cnf(refute_0_425,plain,
converse(composition(X_251,join(X_252,converse(X_253)))) = converse(join(composition(X_251,X_252),composition(X_251,converse(X_253)))),
inference(subst,[],[refute_0_424:[bind(A,$fot(X_251)),bind(B,$fot(X_252)),bind(X_38,$fot(X_253))]]) ).
cnf(refute_0_426,plain,
( converse(composition(X_251,join(X_252,converse(X_253)))) != converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))
| converse(join(composition(X_251,X_252),composition(X_251,converse(X_253)))) = converse(composition(X_251,join(X_252,converse(X_253)))) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(converse(composition(X_251,join(X_252,converse(X_253)))))),bind(Y,$fot(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))))]]) ).
cnf(refute_0_427,plain,
converse(join(composition(X_251,X_252),composition(X_251,converse(X_253)))) = converse(composition(X_251,join(X_252,converse(X_253)))),
inference(resolve,[$cnf( $equal(converse(composition(X_251,join(X_252,converse(X_253)))),converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))) )],[refute_0_425,refute_0_426]) ).
cnf(refute_0_428,plain,
( converse(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))) != join(composition(X_251,X_252),composition(X_251,converse(X_253)))
| converse(join(composition(X_251,X_252),composition(X_251,converse(X_253)))) != converse(composition(X_251,join(X_252,converse(X_253))))
| converse(converse(composition(X_251,join(X_252,converse(X_253))))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))),join(composition(X_251,X_252),composition(X_251,converse(X_253)))) ),[0,0],$fot(converse(composition(X_251,join(X_252,converse(X_253)))))]]) ).
cnf(refute_0_429,plain,
( converse(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))) != join(composition(X_251,X_252),composition(X_251,converse(X_253)))
| converse(converse(composition(X_251,join(X_252,converse(X_253))))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))) ),
inference(resolve,[$cnf( $equal(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253)))),converse(composition(X_251,join(X_252,converse(X_253))))) )],[refute_0_427,refute_0_428]) ).
cnf(refute_0_430,plain,
converse(converse(composition(X_251,join(X_252,converse(X_253))))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))),
inference(resolve,[$cnf( $equal(converse(converse(join(composition(X_251,X_252),composition(X_251,converse(X_253))))),join(composition(X_251,X_252),composition(X_251,converse(X_253)))) )],[refute_0_388,refute_0_429]) ).
cnf(refute_0_431,plain,
converse(converse(composition(X_251,join(X_252,converse(X_253))))) = composition(X_251,join(X_252,converse(X_253))),
inference(subst,[],[converse_idempotence_8:[bind(A,$fot(composition(X_251,join(X_252,converse(X_253)))))]]) ).
cnf(refute_0_432,plain,
( converse(converse(composition(X_251,join(X_252,converse(X_253))))) != composition(X_251,join(X_252,converse(X_253)))
| converse(converse(composition(X_251,join(X_252,converse(X_253))))) != join(composition(X_251,X_252),composition(X_251,converse(X_253)))
| composition(X_251,join(X_252,converse(X_253))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(composition(X_251,join(X_252,converse(X_253))))),join(composition(X_251,X_252),composition(X_251,converse(X_253)))) ),[0],$fot(composition(X_251,join(X_252,converse(X_253))))]]) ).
cnf(refute_0_433,plain,
( converse(converse(composition(X_251,join(X_252,converse(X_253))))) != join(composition(X_251,X_252),composition(X_251,converse(X_253)))
| composition(X_251,join(X_252,converse(X_253))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))) ),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_251,join(X_252,converse(X_253))))),composition(X_251,join(X_252,converse(X_253)))) )],[refute_0_431,refute_0_432]) ).
cnf(refute_0_434,plain,
composition(X_251,join(X_252,converse(X_253))) = join(composition(X_251,X_252),composition(X_251,converse(X_253))),
inference(resolve,[$cnf( $equal(converse(converse(composition(X_251,join(X_252,converse(X_253))))),join(composition(X_251,X_252),composition(X_251,converse(X_253)))) )],[refute_0_430,refute_0_433]) ).
cnf(refute_0_435,plain,
composition(X_1405,join(X_1406,converse(converse(A)))) = join(composition(X_1405,X_1406),composition(X_1405,converse(converse(A)))),
inference(subst,[],[refute_0_434:[bind(X_251,$fot(X_1405)),bind(X_252,$fot(X_1406)),bind(X_253,$fot(converse(A)))]]) ).
cnf(refute_0_436,plain,
( composition(X_1405,join(X_1406,converse(converse(A)))) != join(composition(X_1405,X_1406),composition(X_1405,converse(converse(A))))
| converse(converse(A)) != A
| composition(X_1405,join(X_1406,converse(converse(A)))) = join(composition(X_1405,X_1406),composition(X_1405,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),join(composition(X_1405,X_1406),composition(X_1405,converse(converse(A))))) ),[1,1,1],$fot(A)]]) ).
cnf(refute_0_437,plain,
( composition(X_1405,join(X_1406,converse(converse(A)))) != join(composition(X_1405,X_1406),composition(X_1405,converse(converse(A))))
| composition(X_1405,join(X_1406,converse(converse(A)))) = join(composition(X_1405,X_1406),composition(X_1405,A)) ),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_436]) ).
cnf(refute_0_438,plain,
composition(X_1405,join(X_1406,converse(converse(A)))) = join(composition(X_1405,X_1406),composition(X_1405,A)),
inference(resolve,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),join(composition(X_1405,X_1406),composition(X_1405,converse(converse(A))))) )],[refute_0_435,refute_0_437]) ).
cnf(refute_0_439,plain,
join(X_1406,converse(converse(A))) = join(X_1406,converse(converse(A))),
introduced(tautology,[refl,[$fot(join(X_1406,converse(converse(A))))]]) ).
cnf(refute_0_440,plain,
( converse(converse(A)) != A
| join(X_1406,converse(converse(A))) != join(X_1406,converse(converse(A)))
| join(X_1406,converse(converse(A))) = join(X_1406,A) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_1406,converse(converse(A))),join(X_1406,converse(converse(A)))) ),[1,1],$fot(A)]]) ).
cnf(refute_0_441,plain,
( converse(converse(A)) != A
| join(X_1406,converse(converse(A))) = join(X_1406,A) ),
inference(resolve,[$cnf( $equal(join(X_1406,converse(converse(A))),join(X_1406,converse(converse(A)))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
join(X_1406,converse(converse(A))) = join(X_1406,A),
inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_441]) ).
cnf(refute_0_443,plain,
composition(X_1405,join(X_1406,converse(converse(A)))) = composition(X_1405,join(X_1406,converse(converse(A)))),
introduced(tautology,[refl,[$fot(composition(X_1405,join(X_1406,converse(converse(A)))))]]) ).
cnf(refute_0_444,plain,
( composition(X_1405,join(X_1406,converse(converse(A)))) != composition(X_1405,join(X_1406,converse(converse(A))))
| join(X_1406,converse(converse(A))) != join(X_1406,A)
| composition(X_1405,join(X_1406,converse(converse(A)))) = composition(X_1405,join(X_1406,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),composition(X_1405,join(X_1406,converse(converse(A))))) ),[1,1],$fot(join(X_1406,A))]]) ).
cnf(refute_0_445,plain,
( join(X_1406,converse(converse(A))) != join(X_1406,A)
| composition(X_1405,join(X_1406,converse(converse(A)))) = composition(X_1405,join(X_1406,A)) ),
inference(resolve,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),composition(X_1405,join(X_1406,converse(converse(A))))) )],[refute_0_443,refute_0_444]) ).
cnf(refute_0_446,plain,
composition(X_1405,join(X_1406,converse(converse(A)))) = composition(X_1405,join(X_1406,A)),
inference(resolve,[$cnf( $equal(join(X_1406,converse(converse(A))),join(X_1406,A)) )],[refute_0_442,refute_0_445]) ).
cnf(refute_0_447,plain,
( composition(X_1405,join(X_1406,converse(converse(A)))) != composition(X_1405,join(X_1406,A))
| composition(X_1405,join(X_1406,converse(converse(A)))) != join(composition(X_1405,X_1406),composition(X_1405,A))
| composition(X_1405,join(X_1406,A)) = join(composition(X_1405,X_1406),composition(X_1405,A)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),join(composition(X_1405,X_1406),composition(X_1405,A))) ),[0],$fot(composition(X_1405,join(X_1406,A)))]]) ).
cnf(refute_0_448,plain,
( composition(X_1405,join(X_1406,converse(converse(A)))) != join(composition(X_1405,X_1406),composition(X_1405,A))
| composition(X_1405,join(X_1406,A)) = join(composition(X_1405,X_1406),composition(X_1405,A)) ),
inference(resolve,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),composition(X_1405,join(X_1406,A))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
composition(X_1405,join(X_1406,A)) = join(composition(X_1405,X_1406),composition(X_1405,A)),
inference(resolve,[$cnf( $equal(composition(X_1405,join(X_1406,converse(converse(A)))),join(composition(X_1405,X_1406),composition(X_1405,A))) )],[refute_0_438,refute_0_448]) ).
cnf(refute_0_450,plain,
( composition(X_1405,join(X_1406,A)) != join(composition(X_1405,X_1406),composition(X_1405,A))
| join(composition(X_1405,X_1406),composition(X_1405,A)) = composition(X_1405,join(X_1406,A)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(composition(X_1405,join(X_1406,A)))),bind(Y,$fot(join(composition(X_1405,X_1406),composition(X_1405,A))))]]) ).
cnf(refute_0_451,plain,
join(composition(X_1405,X_1406),composition(X_1405,A)) = composition(X_1405,join(X_1406,A)),
inference(resolve,[$cnf( $equal(composition(X_1405,join(X_1406,A)),join(composition(X_1405,X_1406),composition(X_1405,A))) )],[refute_0_449,refute_0_450]) ).
cnf(refute_0_452,plain,
join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,join(sk2,sk3))),
inference(subst,[],[refute_0_451:[bind(A,$fot(join(sk2,sk3))),bind(X_1405,$fot(sk1)),bind(X_1406,$fot(sk2))]]) ).
cnf(refute_0_453,plain,
( composition(sk1,join(sk2,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,join(sk2,sk3)))
| join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))))),bind(Y,$fot(composition(sk1,join(sk2,join(sk2,sk3))))),bind(Z,$fot(composition(sk1,join(sk2,sk3))))]]) ).
cnf(refute_0_454,plain,
( composition(sk1,join(sk2,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,join(sk2,sk3)))) )],[refute_0_452,refute_0_453]) ).
cnf(refute_0_455,plain,
join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(sk1,join(sk2,join(sk2,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_387,refute_0_454]) ).
cnf(refute_0_456,plain,
( X_41 != join(X_41,X_41)
| join(X_41,X_41) = X_41 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(X_41)),bind(Y,$fot(join(X_41,X_41)))]]) ).
cnf(refute_0_457,plain,
join(X_41,X_41) = X_41,
inference(resolve,[$cnf( $equal(X_41,join(X_41,X_41)) )],[refute_0_376,refute_0_456]) ).
cnf(refute_0_458,plain,
join(sk3,sk3) = sk3,
inference(subst,[],[refute_0_457:[bind(X_41,$fot(sk3))]]) ).
cnf(refute_0_459,plain,
join(sk2,join(sk3,sk3)) = join(sk2,join(sk3,sk3)),
introduced(tautology,[refl,[$fot(join(sk2,join(sk3,sk3)))]]) ).
cnf(refute_0_460,plain,
( join(sk2,join(sk3,sk3)) != join(sk2,join(sk3,sk3))
| join(sk3,sk3) != sk3
| join(sk2,join(sk3,sk3)) = join(sk2,sk3) ),
introduced(tautology,[equality,[$cnf( $equal(join(sk2,join(sk3,sk3)),join(sk2,join(sk3,sk3))) ),[1,1],$fot(sk3)]]) ).
cnf(refute_0_461,plain,
( join(sk3,sk3) != sk3
| join(sk2,join(sk3,sk3)) = join(sk2,sk3) ),
inference(resolve,[$cnf( $equal(join(sk2,join(sk3,sk3)),join(sk2,join(sk3,sk3))) )],[refute_0_459,refute_0_460]) ).
cnf(refute_0_462,plain,
join(sk2,join(sk3,sk3)) = join(sk2,sk3),
inference(resolve,[$cnf( $equal(join(sk3,sk3),sk3) )],[refute_0_458,refute_0_461]) ).
cnf(refute_0_463,plain,
join(sk3,join(sk2,sk3)) = join(sk2,join(sk3,sk3)),
inference(subst,[],[refute_0_32:[bind(X_203,$fot(sk2)),bind(X_204,$fot(sk3)),bind(X_205,$fot(sk3))]]) ).
cnf(refute_0_464,plain,
( join(sk2,join(sk3,sk3)) != join(sk2,sk3)
| join(sk3,join(sk2,sk3)) != join(sk2,join(sk3,sk3))
| join(sk3,join(sk2,sk3)) = join(sk2,sk3) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(sk3,join(sk2,sk3)))),bind(Y,$fot(join(sk2,join(sk3,sk3)))),bind(Z,$fot(join(sk2,sk3)))]]) ).
cnf(refute_0_465,plain,
( join(sk2,join(sk3,sk3)) != join(sk2,sk3)
| join(sk3,join(sk2,sk3)) = join(sk2,sk3) ),
inference(resolve,[$cnf( $equal(join(sk3,join(sk2,sk3)),join(sk2,join(sk3,sk3))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
join(sk3,join(sk2,sk3)) = join(sk2,sk3),
inference(resolve,[$cnf( $equal(join(sk2,join(sk3,sk3)),join(sk2,sk3)) )],[refute_0_462,refute_0_465]) ).
cnf(refute_0_467,plain,
composition(sk1,join(sk3,join(sk2,sk3))) = composition(sk1,join(sk3,join(sk2,sk3))),
introduced(tautology,[refl,[$fot(composition(sk1,join(sk3,join(sk2,sk3))))]]) ).
cnf(refute_0_468,plain,
( composition(sk1,join(sk3,join(sk2,sk3))) != composition(sk1,join(sk3,join(sk2,sk3)))
| join(sk3,join(sk2,sk3)) != join(sk2,sk3)
| composition(sk1,join(sk3,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(sk1,join(sk3,join(sk2,sk3))),composition(sk1,join(sk3,join(sk2,sk3)))) ),[1,1],$fot(join(sk2,sk3))]]) ).
cnf(refute_0_469,plain,
( join(sk3,join(sk2,sk3)) != join(sk2,sk3)
| composition(sk1,join(sk3,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(composition(sk1,join(sk3,join(sk2,sk3))),composition(sk1,join(sk3,join(sk2,sk3)))) )],[refute_0_467,refute_0_468]) ).
cnf(refute_0_470,plain,
composition(sk1,join(sk3,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(sk3,join(sk2,sk3)),join(sk2,sk3)) )],[refute_0_466,refute_0_469]) ).
cnf(refute_0_471,plain,
join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk3,join(sk2,sk3))),
inference(subst,[],[refute_0_451:[bind(A,$fot(join(sk2,sk3))),bind(X_1405,$fot(sk1)),bind(X_1406,$fot(sk3))]]) ).
cnf(refute_0_472,plain,
( composition(sk1,join(sk3,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk3,join(sk2,sk3)))
| join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))),bind(Y,$fot(composition(sk1,join(sk3,join(sk2,sk3))))),bind(Z,$fot(composition(sk1,join(sk2,sk3))))]]) ).
cnf(refute_0_473,plain,
( composition(sk1,join(sk3,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk3,join(sk2,sk3)))) )],[refute_0_471,refute_0_472]) ).
cnf(refute_0_474,plain,
join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) = composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(sk1,join(sk3,join(sk2,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_470,refute_0_473]) ).
cnf(refute_0_475,plain,
join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),
introduced(tautology,[refl,[$fot(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))))]]) ).
cnf(refute_0_476,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))
| join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))) ),[1,1],$fot(composition(sk1,join(sk2,sk3)))]]) ).
cnf(refute_0_477,plain,
( join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))))) )],[refute_0_475,refute_0_476]) ).
cnf(refute_0_478,plain,
join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk3),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_474,refute_0_477]) ).
cnf(refute_0_479,plain,
( join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = composition(sk1,join(sk2,sk3)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))))),bind(Y,$fot(join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))))),bind(Z,$fot(composition(sk1,join(sk2,sk3))))]]) ).
cnf(refute_0_480,plain,
( join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))) )],[refute_0_478,refute_0_479]) ).
cnf(refute_0_481,plain,
join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))),composition(sk1,join(sk2,sk3))) )],[refute_0_455,refute_0_480]) ).
cnf(refute_0_482,plain,
( composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = composition(sk1,join(sk2,sk3)) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))) ),[0,1,1],$fot(composition(sk1,join(sk2,sk3)))]]) ).
cnf(refute_0_483,plain,
( composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) = composition(sk1,join(sk2,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))) )],[refute_0_481,refute_0_482]) ).
cnf(refute_0_484,plain,
( composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3))
| composition(sk1,join(sk2,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))),composition(sk1,join(sk2,sk3))) )],[refute_0_483,refute_0_40]) ).
cnf(refute_0_485,plain,
join(composition(sk1,sk2),composition(sk1,sk3)) = composition(sk1,join(sk2,sk3)),
inference(subst,[],[refute_0_451:[bind(A,$fot(sk3)),bind(X_1405,$fot(sk1)),bind(X_1406,$fot(sk2))]]) ).
cnf(refute_0_486,plain,
( composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != composition(sk1,join(sk2,sk3))
| composition(sk1,join(sk2,sk3)) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) ),[1],$fot(composition(sk1,join(sk2,sk3)))]]) ).
cnf(refute_0_487,plain,
( composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3))
| composition(sk1,join(sk2,sk3)) = join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) )],[refute_0_485,refute_0_486]) ).
cnf(refute_0_488,plain,
composition(sk1,join(sk2,sk3)) != composition(sk1,join(sk2,sk3)),
inference(resolve,[$cnf( $equal(composition(sk1,join(sk2,sk3)),join(composition(sk1,sk2),composition(sk1,sk3))) )],[refute_0_487,refute_0_484]) ).
cnf(refute_0_489,plain,
composition(sk1,join(sk2,sk3)) = composition(sk1,join(sk2,sk3)),
introduced(tautology,[refl,[$fot(composition(sk1,join(sk2,sk3)))]]) ).
cnf(refute_0_490,plain,
$false,
inference(resolve,[$cnf( $equal(composition(sk1,join(sk2,sk3)),composition(sk1,join(sk2,sk3))) )],[refute_0_489,refute_0_488]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : REL008-2 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n029.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Fri Jul 8 08:15:59 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 97.18/97.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 97.18/97.42
% 97.18/97.42 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 97.26/97.49
%------------------------------------------------------------------------------