%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : REL013-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n004.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 19:43:22 EDT 2022

% Result   : Unsatisfiable 0.54s 0.74s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   56
%            Number of leaves      :   95
% Syntax   : Number of clauses     :  371 ( 191 unt;   0 nHn; 208 RR)
%            Number of literals    :  629 ( 628 equ; 262 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    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :  446 (  20 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(maddux1_join_commutativity_1,axiom,
    join(A,B) = join(B,A) ).

cnf(maddux2_join_associativity_2,axiom,
    join(A,join(B,C)) = join(join(A,B),C) ).

cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
    A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) ).

cnf(maddux4_definiton_of_meet_4,axiom,
    meet(A,B) = complement(join(complement(A),complement(B))) ).

cnf(composition_associativity_5,axiom,
    composition(A,composition(B,C)) = composition(composition(A,B),C) ).

cnf(composition_identity_6,axiom,
    composition(A,one) = A ).

cnf(composition_distributivity_7,axiom,
    composition(join(A,B),C) = join(composition(A,C),composition(B,C)) ).

cnf(converse_idempotence_8,axiom,
    converse(converse(A)) = A ).

cnf(converse_additivity_9,axiom,
    converse(join(A,B)) = join(converse(A),converse(B)) ).

cnf(converse_multiplicativity_10,axiom,
    converse(composition(A,B)) = composition(converse(B),converse(A)) ).

cnf(converse_cancellativity_11,axiom,
    join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B) ).

cnf(def_top_12,axiom,
    top = join(A,complement(A)) ).

cnf(def_zero_13,axiom,
    zero = meet(A,complement(A)) ).

cnf(goals_14,negated_conjecture,
    ( composition(sk1,zero) != zero
    | composition(zero,sk1) != zero ) ).

cnf(refute_0_0,plain,
    composition(A,composition(top,complement(composition(top,top)))) = composition(composition(A,top),complement(composition(top,top))),
    inference(subst,[],[composition_associativity_5:[bind(B,$fot(top)),bind(C,$fot(complement(composition(top,top))))]]) ).

cnf(refute_0_1,plain,
    X = X,
    introduced(tautology,[refl,[$fot(X)]]) ).

cnf(refute_0_2,plain,
    ( X != X
    | X != Y
    | Y = X ),
    introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).

cnf(refute_0_3,plain,
    ( X != Y
    | Y = X ),
    inference(resolve,[$cnf( $equal(X,X) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( join(A,B) != join(B,A)
    | join(B,A) = join(A,B) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,B))),bind(Y,$fot(join(B,A)))]]) ).

cnf(refute_0_5,plain,
    join(B,A) = join(A,B),
    inference(resolve,[$cnf( $equal(join(A,B),join(B,A)) )],[maddux1_join_commutativity_1,refute_0_4]) ).

cnf(refute_0_6,plain,
    join(composition(converse(A),complement(composition(A,B))),complement(B)) = join(complement(B),composition(converse(A),complement(composition(A,B)))),
    inference(subst,[],[refute_0_5:[bind(A,$fot(complement(B))),bind(B,$fot(composition(converse(A),complement(composition(A,B)))))]]) ).

cnf(refute_0_7,plain,
    ( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
    | join(composition(converse(A),complement(composition(A,B))),complement(B)) != join(complement(B),composition(converse(A),complement(composition(A,B))))
    | join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
    introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) ),[0],$fot(join(complement(B),composition(converse(A),complement(composition(A,B)))))]]) ).

cnf(refute_0_8,plain,
    ( join(composition(converse(A),complement(composition(A,B))),complement(B)) != complement(B)
    | join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B) ),
    inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),join(complement(B),composition(converse(A),complement(composition(A,B))))) )],[refute_0_6,refute_0_7]) ).

cnf(refute_0_9,plain,
    join(complement(B),composition(converse(A),complement(composition(A,B)))) = complement(B),
    inference(resolve,[$cnf( $equal(join(composition(converse(A),complement(composition(A,B))),complement(B)),complement(B)) )],[converse_cancellativity_11,refute_0_8]) ).

cnf(refute_0_10,plain,
    join(complement(top),composition(converse(X_51),complement(composition(X_51,top)))) = complement(top),
    inference(subst,[],[refute_0_9:[bind(A,$fot(X_51)),bind(B,$fot(top))]]) ).

cnf(refute_0_11,plain,
    zero = meet(join(complement(X_25),complement(X_26)),complement(join(complement(X_25),complement(X_26)))),
    inference(subst,[],[def_zero_13:[bind(A,$fot(join(complement(X_25),complement(X_26))))]]) ).

cnf(refute_0_12,plain,
    meet(X_25,X_26) = complement(join(complement(X_25),complement(X_26))),
    inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(X_25)),bind(B,$fot(X_26))]]) ).

cnf(refute_0_13,plain,
    ( meet(X_25,X_26) != complement(join(complement(X_25),complement(X_26)))
    | complement(join(complement(X_25),complement(X_26))) = meet(X_25,X_26) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_25,X_26))),bind(Y,$fot(complement(join(complement(X_25),complement(X_26)))))]]) ).

cnf(refute_0_14,plain,
    complement(join(complement(X_25),complement(X_26))) = meet(X_25,X_26),
    inference(resolve,[$cnf( $equal(meet(X_25,X_26),complement(join(complement(X_25),complement(X_26)))) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( complement(join(complement(X_25),complement(X_26))) != meet(X_25,X_26)
    | zero != meet(join(complement(X_25),complement(X_26)),complement(join(complement(X_25),complement(X_26))))
    | zero = meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_25),complement(X_26)),complement(join(complement(X_25),complement(X_26))))) ),[1,1],$fot(meet(X_25,X_26))]]) ).

cnf(refute_0_16,plain,
    ( zero != meet(join(complement(X_25),complement(X_26)),complement(join(complement(X_25),complement(X_26))))
    | zero = meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) ),
    inference(resolve,[$cnf( $equal(complement(join(complement(X_25),complement(X_26))),meet(X_25,X_26)) )],[refute_0_14,refute_0_15]) ).

cnf(refute_0_17,plain,
    zero = meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)),
    inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_25),complement(X_26)),complement(join(complement(X_25),complement(X_26))))) )],[refute_0_11,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( top != join(A,complement(A))
    | join(A,complement(A)) = top ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(A,complement(A))))]]) ).

cnf(refute_0_19,plain,
    join(A,complement(A)) = top,
    inference(resolve,[$cnf( $equal(top,join(A,complement(A))) )],[def_top_12,refute_0_18]) ).

cnf(refute_0_20,plain,
    join(meet(X_25,X_26),complement(meet(X_25,X_26))) = top,
    inference(subst,[],[refute_0_19:[bind(A,$fot(meet(X_25,X_26)))]]) ).

cnf(refute_0_21,plain,
    complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) = complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))),
    introduced(tautology,[refl,[$fot(complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))))]]) ).

cnf(refute_0_22,plain,
    ( complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) != complement(join(meet(X_25,X_26),complement(meet(X_25,X_26))))
    | join(meet(X_25,X_26),complement(meet(X_25,X_26))) != top
    | complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) = complement(top) ),
    introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))),complement(join(meet(X_25,X_26),complement(meet(X_25,X_26))))) ),[1,0],$fot(top)]]) ).

cnf(refute_0_23,plain,
    ( join(meet(X_25,X_26),complement(meet(X_25,X_26))) != top
    | complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) = complement(top) ),
    inference(resolve,[$cnf( $equal(complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))),complement(join(meet(X_25,X_26),complement(meet(X_25,X_26))))) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) = complement(top),
    inference(resolve,[$cnf( $equal(join(meet(X_25,X_26),complement(meet(X_25,X_26))),top) )],[refute_0_20,refute_0_23]) ).

cnf(refute_0_25,plain,
    meet(join(complement(X_25),complement(X_26)),B) = complement(join(complement(join(complement(X_25),complement(X_26))),complement(B))),
    inference(subst,[],[maddux4_definiton_of_meet_4:[bind(A,$fot(join(complement(X_25),complement(X_26))))]]) ).

cnf(refute_0_26,plain,
    ( complement(join(complement(X_25),complement(X_26))) != meet(X_25,X_26)
    | meet(join(complement(X_25),complement(X_26)),B) != complement(join(complement(join(complement(X_25),complement(X_26))),complement(B)))
    | meet(join(complement(X_25),complement(X_26)),B) = complement(join(meet(X_25,X_26),complement(B))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_25),complement(X_26)),B),complement(join(complement(join(complement(X_25),complement(X_26))),complement(B)))) ),[1,0,0],$fot(meet(X_25,X_26))]]) ).

cnf(refute_0_27,plain,
    ( meet(join(complement(X_25),complement(X_26)),B) != complement(join(complement(join(complement(X_25),complement(X_26))),complement(B)))
    | meet(join(complement(X_25),complement(X_26)),B) = complement(join(meet(X_25,X_26),complement(B))) ),
    inference(resolve,[$cnf( $equal(complement(join(complement(X_25),complement(X_26))),meet(X_25,X_26)) )],[refute_0_14,refute_0_26]) ).

cnf(refute_0_28,plain,
    meet(join(complement(X_25),complement(X_26)),B) = complement(join(meet(X_25,X_26),complement(B))),
    inference(resolve,[$cnf( $equal(meet(join(complement(X_25),complement(X_26)),B),complement(join(complement(join(complement(X_25),complement(X_26))),complement(B)))) )],[refute_0_25,refute_0_27]) ).

cnf(refute_0_29,plain,
    meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) = complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))),
    inference(subst,[],[refute_0_28:[bind(B,$fot(meet(X_25,X_26)))]]) ).

cnf(refute_0_30,plain,
    ( Y != X
    | Y != Z
    | X = Z ),
    introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).

cnf(refute_0_31,plain,
    ( X != Y
    | Y != Z
    | X = Z ),
    inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_3,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) != complement(top)
    | meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) != complement(join(meet(X_25,X_26),complement(meet(X_25,X_26))))
    | meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) = complement(top) ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)))),bind(Y,$fot(complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))))),bind(Z,$fot(complement(top)))]]) ).

cnf(refute_0_33,plain,
    ( complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))) != complement(top)
    | meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) = complement(top) ),
    inference(resolve,[$cnf( $equal(meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)),complement(join(meet(X_25,X_26),complement(meet(X_25,X_26))))) )],[refute_0_29,refute_0_32]) ).

cnf(refute_0_34,plain,
    meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) = complement(top),
    inference(resolve,[$cnf( $equal(complement(join(meet(X_25,X_26),complement(meet(X_25,X_26)))),complement(top)) )],[refute_0_24,refute_0_33]) ).

cnf(refute_0_35,plain,
    ( meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)) != complement(top)
    | zero != meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26))
    | zero = complement(top) ),
    introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26))) ),[1],$fot(complement(top))]]) ).

cnf(refute_0_36,plain,
    ( zero != meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26))
    | zero = complement(top) ),
    inference(resolve,[$cnf( $equal(meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26)),complement(top)) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    zero = complement(top),
    inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_25),complement(X_26)),meet(X_25,X_26))) )],[refute_0_17,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( zero != complement(top)
    | complement(top) = zero ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).

cnf(refute_0_39,plain,
    complement(top) = zero,
    inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_37,refute_0_38]) ).

cnf(refute_0_40,plain,
    ( complement(top) != zero
    | join(complement(top),composition(converse(X_51),complement(composition(X_51,top)))) != complement(top)
    | join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = complement(top) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(top),composition(converse(X_51),complement(composition(X_51,top)))),complement(top)) ),[0,0],$fot(zero)]]) ).

cnf(refute_0_41,plain,
    ( join(complement(top),composition(converse(X_51),complement(composition(X_51,top)))) != complement(top)
    | join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = complement(top) ),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = complement(top),
    inference(resolve,[$cnf( $equal(join(complement(top),composition(converse(X_51),complement(composition(X_51,top)))),complement(top)) )],[refute_0_10,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( complement(top) != zero
    | join(zero,composition(converse(X_51),complement(composition(X_51,top)))) != complement(top)
    | join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(X_51),complement(composition(X_51,top)))),complement(top)) ),[1],$fot(zero)]]) ).

cnf(refute_0_44,plain,
    ( join(zero,composition(converse(X_51),complement(composition(X_51,top)))) != complement(top)
    | join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = zero ),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_43]) ).

cnf(refute_0_45,plain,
    join(zero,composition(converse(X_51),complement(composition(X_51,top)))) = zero,
    inference(resolve,[$cnf( $equal(join(zero,composition(converse(X_51),complement(composition(X_51,top)))),complement(top)) )],[refute_0_42,refute_0_44]) ).

cnf(refute_0_46,plain,
    join(zero,composition(converse(top),complement(composition(top,top)))) = zero,
    inference(subst,[],[refute_0_45:[bind(X_51,$fot(top))]]) ).

cnf(refute_0_47,plain,
    join(join(X_18,complement(join(B,X_18))),B) = join(B,join(X_18,complement(join(B,X_18)))),
    inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(X_18,complement(join(B,X_18)))))]]) ).

cnf(refute_0_48,plain,
    top = join(join(X_14,X_15),complement(join(X_14,X_15))),
    inference(subst,[],[def_top_12:[bind(A,$fot(join(X_14,X_15)))]]) ).

cnf(refute_0_49,plain,
    join(X_14,join(X_15,complement(join(X_14,X_15)))) = join(join(X_14,X_15),complement(join(X_14,X_15))),
    inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(complement(join(X_14,X_15))))]]) ).

cnf(refute_0_50,plain,
    ( join(X_14,join(X_15,complement(join(X_14,X_15)))) != join(join(X_14,X_15),complement(join(X_14,X_15)))
    | join(join(X_14,X_15),complement(join(X_14,X_15))) = join(X_14,join(X_15,complement(join(X_14,X_15)))) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_14,join(X_15,complement(join(X_14,X_15)))))),bind(Y,$fot(join(join(X_14,X_15),complement(join(X_14,X_15)))))]]) ).

cnf(refute_0_51,plain,
    join(join(X_14,X_15),complement(join(X_14,X_15))) = join(X_14,join(X_15,complement(join(X_14,X_15)))),
    inference(resolve,[$cnf( $equal(join(X_14,join(X_15,complement(join(X_14,X_15)))),join(join(X_14,X_15),complement(join(X_14,X_15)))) )],[refute_0_49,refute_0_50]) ).

cnf(refute_0_52,plain,
    ( join(join(X_14,X_15),complement(join(X_14,X_15))) != join(X_14,join(X_15,complement(join(X_14,X_15))))
    | top != join(join(X_14,X_15),complement(join(X_14,X_15)))
    | top = join(X_14,join(X_15,complement(join(X_14,X_15)))) ),
    introduced(tautology,[equality,[$cnf( $equal(top,join(join(X_14,X_15),complement(join(X_14,X_15)))) ),[1],$fot(join(X_14,join(X_15,complement(join(X_14,X_15)))))]]) ).

cnf(refute_0_53,plain,
    ( top != join(join(X_14,X_15),complement(join(X_14,X_15)))
    | top = join(X_14,join(X_15,complement(join(X_14,X_15)))) ),
    inference(resolve,[$cnf( $equal(join(join(X_14,X_15),complement(join(X_14,X_15))),join(X_14,join(X_15,complement(join(X_14,X_15))))) )],[refute_0_51,refute_0_52]) ).

cnf(refute_0_54,plain,
    top = join(X_14,join(X_15,complement(join(X_14,X_15)))),
    inference(resolve,[$cnf( $equal(top,join(join(X_14,X_15),complement(join(X_14,X_15)))) )],[refute_0_48,refute_0_53]) ).

cnf(refute_0_55,plain,
    top = join(B,join(X_18,complement(join(B,X_18)))),
    inference(subst,[],[refute_0_54:[bind(X_14,$fot(B)),bind(X_15,$fot(X_18))]]) ).

cnf(refute_0_56,plain,
    ( top != join(B,join(X_18,complement(join(B,X_18))))
    | join(B,join(X_18,complement(join(B,X_18)))) = top ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(B,join(X_18,complement(join(B,X_18))))))]]) ).

cnf(refute_0_57,plain,
    join(B,join(X_18,complement(join(B,X_18)))) = top,
    inference(resolve,[$cnf( $equal(top,join(B,join(X_18,complement(join(B,X_18))))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    ( join(B,join(X_18,complement(join(B,X_18)))) != top
    | join(join(X_18,complement(join(B,X_18))),B) != join(B,join(X_18,complement(join(B,X_18))))
    | join(join(X_18,complement(join(B,X_18))),B) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),join(B,join(X_18,complement(join(B,X_18))))) ),[1],$fot(top)]]) ).

cnf(refute_0_59,plain,
    ( join(join(X_18,complement(join(B,X_18))),B) != join(B,join(X_18,complement(join(B,X_18))))
    | join(join(X_18,complement(join(B,X_18))),B) = top ),
    inference(resolve,[$cnf( $equal(join(B,join(X_18,complement(join(B,X_18)))),top) )],[refute_0_57,refute_0_58]) ).

cnf(refute_0_60,plain,
    join(join(X_18,complement(join(B,X_18))),B) = top,
    inference(resolve,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),join(B,join(X_18,complement(join(B,X_18))))) )],[refute_0_47,refute_0_59]) ).

cnf(refute_0_61,plain,
    join(X_14,join(X_15,X_16)) = join(join(X_14,X_15),X_16),
    inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).

cnf(refute_0_62,plain,
    join(X_16,X_15) = join(X_15,X_16),
    inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_16)),bind(B,$fot(X_15))]]) ).

cnf(refute_0_63,plain,
    ( join(X_16,X_15) != join(X_15,X_16)
    | join(X_15,X_16) = join(X_16,X_15) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_16,X_15))),bind(Y,$fot(join(X_15,X_16)))]]) ).

cnf(refute_0_64,plain,
    join(X_15,X_16) = join(X_16,X_15),
    inference(resolve,[$cnf( $equal(join(X_16,X_15),join(X_15,X_16)) )],[refute_0_62,refute_0_63]) ).

cnf(refute_0_65,plain,
    ( join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
    | join(X_15,X_16) != join(X_16,X_15)
    | join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) ),[0,1],$fot(join(X_16,X_15))]]) ).

cnf(refute_0_66,plain,
    ( join(X_14,join(X_15,X_16)) != join(join(X_14,X_15),X_16)
    | join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16) ),
    inference(resolve,[$cnf( $equal(join(X_15,X_16),join(X_16,X_15)) )],[refute_0_64,refute_0_65]) ).

cnf(refute_0_67,plain,
    join(X_14,join(X_16,X_15)) = join(join(X_14,X_15),X_16),
    inference(resolve,[$cnf( $equal(join(X_14,join(X_15,X_16)),join(join(X_14,X_15),X_16)) )],[refute_0_61,refute_0_66]) ).

cnf(refute_0_68,plain,
    ( join(A,join(B,C)) != join(join(A,B),C)
    | join(join(A,B),C) = join(A,join(B,C)) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(A,join(B,C)))),bind(Y,$fot(join(join(A,B),C)))]]) ).

cnf(refute_0_69,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_68]) ).

cnf(refute_0_70,plain,
    join(join(X_14,X_15),X_16) = join(X_14,join(X_15,X_16)),
    inference(subst,[],[refute_0_69:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).

cnf(refute_0_71,plain,
    ( join(X_14,join(X_16,X_15)) != join(join(X_14,X_15),X_16)
    | join(join(X_14,X_15),X_16) != join(X_14,join(X_15,X_16))
    | join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_14,join(X_16,X_15)),join(X_14,join(X_15,X_16))) ),[0],$fot(join(join(X_14,X_15),X_16))]]) ).

cnf(refute_0_72,plain,
    ( join(X_14,join(X_16,X_15)) != join(join(X_14,X_15),X_16)
    | join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(join(join(X_14,X_15),X_16),join(X_14,join(X_15,X_16))) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    join(X_14,join(X_16,X_15)) = join(X_14,join(X_15,X_16)),
    inference(resolve,[$cnf( $equal(join(X_14,join(X_16,X_15)),join(join(X_14,X_15),X_16)) )],[refute_0_67,refute_0_72]) ).

cnf(refute_0_74,plain,
    ( join(X_14,join(X_16,X_15)) != join(X_14,join(X_15,X_16))
    | join(X_14,join(X_15,X_16)) = join(X_14,join(X_16,X_15)) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_14,join(X_16,X_15)))),bind(Y,$fot(join(X_14,join(X_15,X_16))))]]) ).

cnf(refute_0_75,plain,
    join(X_14,join(X_15,X_16)) = join(X_14,join(X_16,X_15)),
    inference(resolve,[$cnf( $equal(join(X_14,join(X_16,X_15)),join(X_14,join(X_15,X_16))) )],[refute_0_73,refute_0_74]) ).

cnf(refute_0_76,plain,
    join(X_18,join(complement(join(B,X_18)),B)) = join(X_18,join(B,complement(join(B,X_18)))),
    inference(subst,[],[refute_0_75:[bind(X_14,$fot(X_18)),bind(X_15,$fot(complement(join(B,X_18)))),bind(X_16,$fot(B))]]) ).

cnf(refute_0_77,plain,
    join(join(X_18,complement(join(B,X_18))),B) = join(X_18,join(complement(join(B,X_18)),B)),
    inference(subst,[],[refute_0_69:[bind(A,$fot(X_18)),bind(B,$fot(complement(join(B,X_18)))),bind(C,$fot(B))]]) ).

cnf(refute_0_78,plain,
    ( join(X_18,join(complement(join(B,X_18)),B)) != join(X_18,join(B,complement(join(B,X_18))))
    | join(join(X_18,complement(join(B,X_18))),B) != join(X_18,join(complement(join(B,X_18)),B))
    | join(join(X_18,complement(join(B,X_18))),B) = join(X_18,join(B,complement(join(B,X_18)))) ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(join(join(X_18,complement(join(B,X_18))),B))),bind(Y,$fot(join(X_18,join(complement(join(B,X_18)),B)))),bind(Z,$fot(join(X_18,join(B,complement(join(B,X_18))))))]]) ).

cnf(refute_0_79,plain,
    ( join(X_18,join(complement(join(B,X_18)),B)) != join(X_18,join(B,complement(join(B,X_18))))
    | join(join(X_18,complement(join(B,X_18))),B) = join(X_18,join(B,complement(join(B,X_18)))) ),
    inference(resolve,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),join(X_18,join(complement(join(B,X_18)),B))) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    join(join(X_18,complement(join(B,X_18))),B) = join(X_18,join(B,complement(join(B,X_18)))),
    inference(resolve,[$cnf( $equal(join(X_18,join(complement(join(B,X_18)),B)),join(X_18,join(B,complement(join(B,X_18))))) )],[refute_0_76,refute_0_79]) ).

cnf(refute_0_81,plain,
    ( join(join(X_18,complement(join(B,X_18))),B) != join(X_18,join(B,complement(join(B,X_18))))
    | join(join(X_18,complement(join(B,X_18))),B) != top
    | join(X_18,join(B,complement(join(B,X_18)))) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),top) ),[0],$fot(join(X_18,join(B,complement(join(B,X_18)))))]]) ).

cnf(refute_0_82,plain,
    ( join(join(X_18,complement(join(B,X_18))),B) != top
    | join(X_18,join(B,complement(join(B,X_18)))) = top ),
    inference(resolve,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),join(X_18,join(B,complement(join(B,X_18))))) )],[refute_0_80,refute_0_81]) ).

cnf(refute_0_83,plain,
    join(X_18,join(B,complement(join(B,X_18)))) = top,
    inference(resolve,[$cnf( $equal(join(join(X_18,complement(join(B,X_18))),B),top) )],[refute_0_60,refute_0_82]) ).

cnf(refute_0_84,plain,
    join(top,join(B,complement(join(B,top)))) = top,
    inference(subst,[],[refute_0_83:[bind(X_18,$fot(top))]]) ).

cnf(refute_0_85,plain,
    join(X_14,join(complement(X_14),X_16)) = join(join(X_14,complement(X_14)),X_16),
    inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(X_14)),bind(B,$fot(complement(X_14))),bind(C,$fot(X_16))]]) ).

cnf(refute_0_86,plain,
    top = join(X_14,complement(X_14)),
    inference(subst,[],[def_top_12:[bind(A,$fot(X_14))]]) ).

cnf(refute_0_87,plain,
    ( top != join(X_14,complement(X_14))
    | join(X_14,complement(X_14)) = top ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(X_14,complement(X_14))))]]) ).

cnf(refute_0_88,plain,
    join(X_14,complement(X_14)) = top,
    inference(resolve,[$cnf( $equal(top,join(X_14,complement(X_14))) )],[refute_0_86,refute_0_87]) ).

cnf(refute_0_89,plain,
    ( join(X_14,complement(X_14)) != top
    | join(X_14,join(complement(X_14),X_16)) != join(join(X_14,complement(X_14)),X_16)
    | join(X_14,join(complement(X_14),X_16)) = join(top,X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_14,join(complement(X_14),X_16)),join(join(X_14,complement(X_14)),X_16)) ),[1,0],$fot(top)]]) ).

cnf(refute_0_90,plain,
    ( join(X_14,join(complement(X_14),X_16)) != join(join(X_14,complement(X_14)),X_16)
    | join(X_14,join(complement(X_14),X_16)) = join(top,X_16) ),
    inference(resolve,[$cnf( $equal(join(X_14,complement(X_14)),top) )],[refute_0_88,refute_0_89]) ).

cnf(refute_0_91,plain,
    join(X_14,join(complement(X_14),X_16)) = join(top,X_16),
    inference(resolve,[$cnf( $equal(join(X_14,join(complement(X_14),X_16)),join(join(X_14,complement(X_14)),X_16)) )],[refute_0_85,refute_0_90]) ).

cnf(refute_0_92,plain,
    join(X_19,join(complement(X_19),complement(complement(X_19)))) = join(top,complement(complement(X_19))),
    inference(subst,[],[refute_0_91:[bind(X_14,$fot(X_19)),bind(X_16,$fot(complement(complement(X_19))))]]) ).

cnf(refute_0_93,plain,
    top = join(complement(X_19),complement(complement(X_19))),
    inference(subst,[],[def_top_12:[bind(A,$fot(complement(X_19)))]]) ).

cnf(refute_0_94,plain,
    ( top != join(complement(X_19),complement(complement(X_19)))
    | join(complement(X_19),complement(complement(X_19))) = top ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(top)),bind(Y,$fot(join(complement(X_19),complement(complement(X_19)))))]]) ).

cnf(refute_0_95,plain,
    join(complement(X_19),complement(complement(X_19))) = top,
    inference(resolve,[$cnf( $equal(top,join(complement(X_19),complement(complement(X_19)))) )],[refute_0_93,refute_0_94]) ).

cnf(refute_0_96,plain,
    ( join(X_19,join(complement(X_19),complement(complement(X_19)))) != join(top,complement(complement(X_19)))
    | join(complement(X_19),complement(complement(X_19))) != top
    | join(X_19,top) = join(top,complement(complement(X_19))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_19,join(complement(X_19),complement(complement(X_19)))),join(top,complement(complement(X_19)))) ),[0,1],$fot(top)]]) ).

cnf(refute_0_97,plain,
    ( join(X_19,join(complement(X_19),complement(complement(X_19)))) != join(top,complement(complement(X_19)))
    | join(X_19,top) = join(top,complement(complement(X_19))) ),
    inference(resolve,[$cnf( $equal(join(complement(X_19),complement(complement(X_19))),top) )],[refute_0_95,refute_0_96]) ).

cnf(refute_0_98,plain,
    join(X_19,top) = join(top,complement(complement(X_19))),
    inference(resolve,[$cnf( $equal(join(X_19,join(complement(X_19),complement(complement(X_19)))),join(top,complement(complement(X_19)))) )],[refute_0_92,refute_0_97]) ).

cnf(refute_0_99,plain,
    join(complement(X_53),join(complement(X_53),complement(join(complement(X_53),complement(X_53))))) = top,
    inference(subst,[],[refute_0_83:[bind(B,$fot(complement(X_53))),bind(X_18,$fot(complement(X_53)))]]) ).

cnf(refute_0_100,plain,
    join(complement(X_52),composition(converse(one),complement(composition(one,X_52)))) = complement(X_52),
    inference(subst,[],[refute_0_9:[bind(A,$fot(one)),bind(B,$fot(X_52))]]) ).

cnf(refute_0_101,plain,
    composition(converse(one),one) = converse(one),
    inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(one)))]]) ).

cnf(refute_0_102,plain,
    converse(composition(converse(A),X_7)) = composition(converse(X_7),converse(converse(A))),
    inference(subst,[],[converse_multiplicativity_10:[bind(A,$fot(converse(A))),bind(B,$fot(X_7))]]) ).

cnf(refute_0_103,plain,
    ( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
    | converse(converse(A)) != A
    | converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) ),[1,1],$fot(A)]]) ).

cnf(refute_0_104,plain,
    ( converse(composition(converse(A),X_7)) != composition(converse(X_7),converse(converse(A)))
    | converse(composition(converse(A),X_7)) = composition(converse(X_7),A) ),
    inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_103]) ).

cnf(refute_0_105,plain,
    converse(composition(converse(A),X_7)) = composition(converse(X_7),A),
    inference(resolve,[$cnf( $equal(converse(composition(converse(A),X_7)),composition(converse(X_7),converse(converse(A)))) )],[refute_0_102,refute_0_104]) ).

cnf(refute_0_106,plain,
    converse(composition(converse(X_8),one)) = composition(converse(one),X_8),
    inference(subst,[],[refute_0_105:[bind(A,$fot(X_8)),bind(X_7,$fot(one))]]) ).

cnf(refute_0_107,plain,
    composition(converse(X_8),one) = converse(X_8),
    inference(subst,[],[composition_identity_6:[bind(A,$fot(converse(X_8)))]]) ).

cnf(refute_0_108,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_109,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_107,refute_0_108]) ).

cnf(refute_0_110,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_106,refute_0_109]) ).

cnf(refute_0_111,plain,
    converse(converse(X_8)) = X_8,
    inference(subst,[],[converse_idempotence_8:[bind(A,$fot(X_8))]]) ).

cnf(refute_0_112,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_113,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_111,refute_0_112]) ).

cnf(refute_0_114,plain,
    X_8 = composition(converse(one),X_8),
    inference(resolve,[$cnf( $equal(converse(converse(X_8)),composition(converse(one),X_8)) )],[refute_0_110,refute_0_113]) ).

cnf(refute_0_115,plain,
    one = composition(converse(one),one),
    inference(subst,[],[refute_0_114:[bind(X_8,$fot(one))]]) ).

cnf(refute_0_116,plain,
    ( one != composition(converse(one),one)
    | composition(converse(one),one) = one ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).

cnf(refute_0_117,plain,
    composition(converse(one),one) = one,
    inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,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_119,plain,
    ( composition(converse(one),one) != converse(one)
    | one = converse(one) ),
    inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_117,refute_0_118]) ).

cnf(refute_0_120,plain,
    one = converse(one),
    inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_101,refute_0_119]) ).

cnf(refute_0_121,plain,
    ( one != converse(one)
    | converse(one) = one ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).

cnf(refute_0_122,plain,
    converse(one) = one,
    inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    ( converse(one) != one
    | join(complement(X_52),composition(converse(one),complement(composition(one,X_52)))) != complement(X_52)
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) = complement(X_52) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(X_52),composition(converse(one),complement(composition(one,X_52)))),complement(X_52)) ),[0,1,0],$fot(one)]]) ).

cnf(refute_0_124,plain,
    ( join(complement(X_52),composition(converse(one),complement(composition(one,X_52)))) != complement(X_52)
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) = complement(X_52) ),
    inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_122,refute_0_123]) ).

cnf(refute_0_125,plain,
    join(complement(X_52),composition(one,complement(composition(one,X_52)))) = complement(X_52),
    inference(resolve,[$cnf( $equal(join(complement(X_52),composition(converse(one),complement(composition(one,X_52)))),complement(X_52)) )],[refute_0_100,refute_0_124]) ).

cnf(refute_0_126,plain,
    composition(converse(one),X_8) = composition(converse(one),X_8),
    introduced(tautology,[refl,[$fot(composition(converse(one),X_8))]]) ).

cnf(refute_0_127,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_128,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_126,refute_0_127]) ).

cnf(refute_0_129,plain,
    composition(converse(one),X_8) = composition(one,X_8),
    inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_122,refute_0_128]) ).

cnf(refute_0_130,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_131,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_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    X_8 = composition(one,X_8),
    inference(resolve,[$cnf( $equal(X_8,composition(converse(one),X_8)) )],[refute_0_114,refute_0_131]) ).

cnf(refute_0_133,plain,
    ( X_8 != composition(one,X_8)
    | composition(one,X_8) = X_8 ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_8)),bind(Y,$fot(composition(one,X_8)))]]) ).

cnf(refute_0_134,plain,
    composition(one,X_8) = X_8,
    inference(resolve,[$cnf( $equal(X_8,composition(one,X_8)) )],[refute_0_132,refute_0_133]) ).

cnf(refute_0_135,plain,
    composition(one,X_52) = X_52,
    inference(subst,[],[refute_0_134:[bind(X_8,$fot(X_52))]]) ).

cnf(refute_0_136,plain,
    complement(composition(one,X_52)) = complement(composition(one,X_52)),
    introduced(tautology,[refl,[$fot(complement(composition(one,X_52)))]]) ).

cnf(refute_0_137,plain,
    ( complement(composition(one,X_52)) != complement(composition(one,X_52))
    | composition(one,X_52) != X_52
    | complement(composition(one,X_52)) = complement(X_52) ),
    introduced(tautology,[equality,[$cnf( $equal(complement(composition(one,X_52)),complement(composition(one,X_52))) ),[1,0],$fot(X_52)]]) ).

cnf(refute_0_138,plain,
    ( composition(one,X_52) != X_52
    | complement(composition(one,X_52)) = complement(X_52) ),
    inference(resolve,[$cnf( $equal(complement(composition(one,X_52)),complement(composition(one,X_52))) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    complement(composition(one,X_52)) = complement(X_52),
    inference(resolve,[$cnf( $equal(composition(one,X_52),X_52) )],[refute_0_135,refute_0_138]) ).

cnf(refute_0_140,plain,
    composition(one,complement(composition(one,X_52))) = complement(composition(one,X_52)),
    inference(subst,[],[refute_0_134:[bind(X_8,$fot(complement(composition(one,X_52))))]]) ).

cnf(refute_0_141,plain,
    ( complement(composition(one,X_52)) != complement(X_52)
    | composition(one,complement(composition(one,X_52))) != complement(composition(one,X_52))
    | composition(one,complement(composition(one,X_52))) = complement(X_52) ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(composition(one,complement(composition(one,X_52))))),bind(Y,$fot(complement(composition(one,X_52)))),bind(Z,$fot(complement(X_52)))]]) ).

cnf(refute_0_142,plain,
    ( complement(composition(one,X_52)) != complement(X_52)
    | composition(one,complement(composition(one,X_52))) = complement(X_52) ),
    inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_52))),complement(composition(one,X_52))) )],[refute_0_140,refute_0_141]) ).

cnf(refute_0_143,plain,
    composition(one,complement(composition(one,X_52))) = complement(X_52),
    inference(resolve,[$cnf( $equal(complement(composition(one,X_52)),complement(X_52)) )],[refute_0_139,refute_0_142]) ).

cnf(refute_0_144,plain,
    join(complement(X_52),composition(one,complement(composition(one,X_52)))) = join(complement(X_52),composition(one,complement(composition(one,X_52)))),
    introduced(tautology,[refl,[$fot(join(complement(X_52),composition(one,complement(composition(one,X_52)))))]]) ).

cnf(refute_0_145,plain,
    ( composition(one,complement(composition(one,X_52))) != complement(X_52)
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) != join(complement(X_52),composition(one,complement(composition(one,X_52))))
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) = join(complement(X_52),complement(X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(X_52),composition(one,complement(composition(one,X_52)))),join(complement(X_52),composition(one,complement(composition(one,X_52))))) ),[1,1],$fot(complement(X_52))]]) ).

cnf(refute_0_146,plain,
    ( composition(one,complement(composition(one,X_52))) != complement(X_52)
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) = join(complement(X_52),complement(X_52)) ),
    inference(resolve,[$cnf( $equal(join(complement(X_52),composition(one,complement(composition(one,X_52)))),join(complement(X_52),composition(one,complement(composition(one,X_52))))) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    join(complement(X_52),composition(one,complement(composition(one,X_52)))) = join(complement(X_52),complement(X_52)),
    inference(resolve,[$cnf( $equal(composition(one,complement(composition(one,X_52))),complement(X_52)) )],[refute_0_143,refute_0_146]) ).

cnf(refute_0_148,plain,
    ( join(complement(X_52),composition(one,complement(composition(one,X_52)))) != complement(X_52)
    | join(complement(X_52),composition(one,complement(composition(one,X_52)))) != join(complement(X_52),complement(X_52))
    | join(complement(X_52),complement(X_52)) = complement(X_52) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(X_52),composition(one,complement(composition(one,X_52)))),complement(X_52)) ),[0],$fot(join(complement(X_52),complement(X_52)))]]) ).

cnf(refute_0_149,plain,
    ( join(complement(X_52),composition(one,complement(composition(one,X_52)))) != complement(X_52)
    | join(complement(X_52),complement(X_52)) = complement(X_52) ),
    inference(resolve,[$cnf( $equal(join(complement(X_52),composition(one,complement(composition(one,X_52)))),join(complement(X_52),complement(X_52))) )],[refute_0_147,refute_0_148]) ).

cnf(refute_0_150,plain,
    join(complement(X_52),complement(X_52)) = complement(X_52),
    inference(resolve,[$cnf( $equal(join(complement(X_52),composition(one,complement(composition(one,X_52)))),complement(X_52)) )],[refute_0_125,refute_0_149]) ).

cnf(refute_0_151,plain,
    join(complement(X_53),complement(X_53)) = complement(X_53),
    inference(subst,[],[refute_0_150:[bind(X_52,$fot(X_53))]]) ).

cnf(refute_0_152,plain,
    ( join(complement(X_53),complement(X_53)) != complement(X_53)
    | join(complement(X_53),join(complement(X_53),complement(join(complement(X_53),complement(X_53))))) != top
    | join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(X_53),join(complement(X_53),complement(join(complement(X_53),complement(X_53))))),top) ),[0,1,1,0],$fot(complement(X_53))]]) ).

cnf(refute_0_153,plain,
    ( join(complement(X_53),join(complement(X_53),complement(join(complement(X_53),complement(X_53))))) != top
    | join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) = top ),
    inference(resolve,[$cnf( $equal(join(complement(X_53),complement(X_53)),complement(X_53)) )],[refute_0_151,refute_0_152]) ).

cnf(refute_0_154,plain,
    join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) = top,
    inference(resolve,[$cnf( $equal(join(complement(X_53),join(complement(X_53),complement(join(complement(X_53),complement(X_53))))),top) )],[refute_0_99,refute_0_153]) ).

cnf(refute_0_155,plain,
    join(X_19,join(complement(X_19),X_20)) = join(top,X_20),
    inference(subst,[],[refute_0_91:[bind(X_14,$fot(X_19)),bind(X_16,$fot(X_20))]]) ).

cnf(refute_0_156,plain,
    join(X_20,complement(X_19)) = join(complement(X_19),X_20),
    inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(X_20)),bind(B,$fot(complement(X_19)))]]) ).

cnf(refute_0_157,plain,
    ( join(X_20,complement(X_19)) != join(complement(X_19),X_20)
    | join(complement(X_19),X_20) = join(X_20,complement(X_19)) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(X_20,complement(X_19)))),bind(Y,$fot(join(complement(X_19),X_20)))]]) ).

cnf(refute_0_158,plain,
    join(complement(X_19),X_20) = join(X_20,complement(X_19)),
    inference(resolve,[$cnf( $equal(join(X_20,complement(X_19)),join(complement(X_19),X_20)) )],[refute_0_156,refute_0_157]) ).

cnf(refute_0_159,plain,
    ( join(X_19,join(complement(X_19),X_20)) != join(top,X_20)
    | join(complement(X_19),X_20) != join(X_20,complement(X_19))
    | join(X_19,join(X_20,complement(X_19))) = join(top,X_20) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_19,join(complement(X_19),X_20)),join(top,X_20)) ),[0,1],$fot(join(X_20,complement(X_19)))]]) ).

cnf(refute_0_160,plain,
    ( join(X_19,join(complement(X_19),X_20)) != join(top,X_20)
    | join(X_19,join(X_20,complement(X_19))) = join(top,X_20) ),
    inference(resolve,[$cnf( $equal(join(complement(X_19),X_20),join(X_20,complement(X_19))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    join(X_19,join(X_20,complement(X_19))) = join(top,X_20),
    inference(resolve,[$cnf( $equal(join(X_19,join(complement(X_19),X_20)),join(top,X_20)) )],[refute_0_155,refute_0_160]) ).

cnf(refute_0_162,plain,
    join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) = join(top,complement(X_53)),
    inference(subst,[],[refute_0_161:[bind(X_19,$fot(complement(X_53))),bind(X_20,$fot(complement(X_53)))]]) ).

cnf(refute_0_163,plain,
    ( join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) != join(top,complement(X_53))
    | join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) != top
    | join(top,complement(X_53)) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(X_53),join(complement(X_53),complement(complement(X_53)))),top) ),[0],$fot(join(top,complement(X_53)))]]) ).

cnf(refute_0_164,plain,
    ( join(complement(X_53),join(complement(X_53),complement(complement(X_53)))) != top
    | join(top,complement(X_53)) = top ),
    inference(resolve,[$cnf( $equal(join(complement(X_53),join(complement(X_53),complement(complement(X_53)))),join(top,complement(X_53))) )],[refute_0_162,refute_0_163]) ).

cnf(refute_0_165,plain,
    join(top,complement(X_53)) = top,
    inference(resolve,[$cnf( $equal(join(complement(X_53),join(complement(X_53),complement(complement(X_53)))),top) )],[refute_0_154,refute_0_164]) ).

cnf(refute_0_166,plain,
    join(top,complement(complement(X_19))) = top,
    inference(subst,[],[refute_0_165:[bind(X_53,$fot(complement(X_19)))]]) ).

cnf(refute_0_167,plain,
    ( join(X_19,top) != join(top,complement(complement(X_19)))
    | join(top,complement(complement(X_19))) != top
    | join(X_19,top) = top ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_19,top),top) ),[0],$fot(join(top,complement(complement(X_19))))]]) ).

cnf(refute_0_168,plain,
    ( join(X_19,top) != join(top,complement(complement(X_19)))
    | join(X_19,top) = top ),
    inference(resolve,[$cnf( $equal(join(top,complement(complement(X_19))),top) )],[refute_0_166,refute_0_167]) ).

cnf(refute_0_169,plain,
    join(X_19,top) = top,
    inference(resolve,[$cnf( $equal(join(X_19,top),join(top,complement(complement(X_19)))) )],[refute_0_98,refute_0_168]) ).

cnf(refute_0_170,plain,
    join(B,top) = top,
    inference(subst,[],[refute_0_169:[bind(X_19,$fot(B))]]) ).

cnf(refute_0_171,plain,
    ( join(B,top) != top
    | join(top,join(B,complement(join(B,top)))) != top
    | join(top,join(B,complement(top))) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(top,join(B,complement(join(B,top)))),top) ),[0,1,1,0],$fot(top)]]) ).

cnf(refute_0_172,plain,
    ( join(top,join(B,complement(join(B,top)))) != top
    | join(top,join(B,complement(top))) = top ),
    inference(resolve,[$cnf( $equal(join(B,top),top) )],[refute_0_170,refute_0_171]) ).

cnf(refute_0_173,plain,
    join(top,join(B,complement(top))) = top,
    inference(resolve,[$cnf( $equal(join(top,join(B,complement(join(B,top)))),top) )],[refute_0_84,refute_0_172]) ).

cnf(refute_0_174,plain,
    join(top,join(B,complement(top))) = join(top,B),
    inference(subst,[],[refute_0_161:[bind(X_19,$fot(top)),bind(X_20,$fot(B))]]) ).

cnf(refute_0_175,plain,
    ( join(top,join(B,complement(top))) != join(top,B)
    | join(top,join(B,complement(top))) != top
    | join(top,B) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(top,join(B,complement(top))),top) ),[0],$fot(join(top,B))]]) ).

cnf(refute_0_176,plain,
    ( join(top,join(B,complement(top))) != top
    | join(top,B) = top ),
    inference(resolve,[$cnf( $equal(join(top,join(B,complement(top))),join(top,B)) )],[refute_0_174,refute_0_175]) ).

cnf(refute_0_177,plain,
    join(top,B) = top,
    inference(resolve,[$cnf( $equal(join(top,join(B,complement(top))),top) )],[refute_0_173,refute_0_176]) ).

cnf(refute_0_178,plain,
    join(top,converse(top)) = top,
    inference(subst,[],[refute_0_177:[bind(B,$fot(converse(top)))]]) ).

cnf(refute_0_179,plain,
    converse(join(converse(A),X_35)) = join(converse(converse(A)),converse(X_35)),
    inference(subst,[],[converse_additivity_9:[bind(A,$fot(converse(A))),bind(B,$fot(X_35))]]) ).

cnf(refute_0_180,plain,
    ( converse(converse(A)) != A
    | converse(join(converse(A),X_35)) != join(converse(converse(A)),converse(X_35))
    | converse(join(converse(A),X_35)) = join(A,converse(X_35)) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),X_35)),join(converse(converse(A)),converse(X_35))) ),[1,0],$fot(A)]]) ).

cnf(refute_0_181,plain,
    ( converse(join(converse(A),X_35)) != join(converse(converse(A)),converse(X_35))
    | converse(join(converse(A),X_35)) = join(A,converse(X_35)) ),
    inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_180]) ).

cnf(refute_0_182,plain,
    converse(join(converse(A),X_35)) = join(A,converse(X_35)),
    inference(resolve,[$cnf( $equal(converse(join(converse(A),X_35)),join(converse(converse(A)),converse(X_35))) )],[refute_0_179,refute_0_181]) ).

cnf(refute_0_183,plain,
    converse(join(converse(A),top)) = join(A,converse(top)),
    inference(subst,[],[refute_0_182:[bind(X_35,$fot(top))]]) ).

cnf(refute_0_184,plain,
    join(converse(A),top) = top,
    inference(subst,[],[refute_0_169:[bind(X_19,$fot(converse(A)))]]) ).

cnf(refute_0_185,plain,
    ( converse(join(converse(A),top)) != join(A,converse(top))
    | join(converse(A),top) != top
    | converse(top) = join(A,converse(top)) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),top)),join(A,converse(top))) ),[0,0],$fot(top)]]) ).

cnf(refute_0_186,plain,
    ( converse(join(converse(A),top)) != join(A,converse(top))
    | converse(top) = join(A,converse(top)) ),
    inference(resolve,[$cnf( $equal(join(converse(A),top),top) )],[refute_0_184,refute_0_185]) ).

cnf(refute_0_187,plain,
    converse(top) = join(A,converse(top)),
    inference(resolve,[$cnf( $equal(converse(join(converse(A),top)),join(A,converse(top))) )],[refute_0_183,refute_0_186]) ).

cnf(refute_0_188,plain,
    converse(top) = join(top,converse(top)),
    inference(subst,[],[refute_0_187:[bind(A,$fot(top))]]) ).

cnf(refute_0_189,plain,
    ( converse(top) != join(top,converse(top))
    | join(top,converse(top)) = converse(top) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(converse(top))),bind(Y,$fot(join(top,converse(top))))]]) ).

cnf(refute_0_190,plain,
    join(top,converse(top)) = converse(top),
    inference(resolve,[$cnf( $equal(converse(top),join(top,converse(top))) )],[refute_0_188,refute_0_189]) ).

cnf(refute_0_191,plain,
    ( join(top,converse(top)) != converse(top)
    | join(top,converse(top)) != top
    | converse(top) = top ),
    introduced(tautology,[equality,[$cnf( $equal(join(top,converse(top)),top) ),[0],$fot(converse(top))]]) ).

cnf(refute_0_192,plain,
    ( join(top,converse(top)) != top
    | converse(top) = top ),
    inference(resolve,[$cnf( $equal(join(top,converse(top)),converse(top)) )],[refute_0_190,refute_0_191]) ).

cnf(refute_0_193,plain,
    converse(top) = top,
    inference(resolve,[$cnf( $equal(join(top,converse(top)),top) )],[refute_0_178,refute_0_192]) ).

cnf(refute_0_194,plain,
    ( converse(top) != top
    | join(zero,composition(converse(top),complement(composition(top,top)))) != zero
    | join(zero,composition(top,complement(composition(top,top)))) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) ),[0,1,0],$fot(top)]]) ).

cnf(refute_0_195,plain,
    ( join(zero,composition(converse(top),complement(composition(top,top)))) != zero
    | join(zero,composition(top,complement(composition(top,top)))) = zero ),
    inference(resolve,[$cnf( $equal(converse(top),top) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    join(zero,composition(top,complement(composition(top,top)))) = zero,
    inference(resolve,[$cnf( $equal(join(zero,composition(converse(top),complement(composition(top,top)))),zero) )],[refute_0_46,refute_0_195]) ).

cnf(refute_0_197,plain,
    join(zero,join(zero,C)) = join(join(zero,zero),C),
    inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(zero))]]) ).

cnf(refute_0_198,plain,
    join(complement(top),complement(top)) = complement(top),
    inference(subst,[],[refute_0_150:[bind(X_52,$fot(top))]]) ).

cnf(refute_0_199,plain,
    ( complement(top) != zero
    | join(complement(top),complement(top)) != complement(top)
    | join(complement(top),zero) = complement(top) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) ),[0,1],$fot(zero)]]) ).

cnf(refute_0_200,plain,
    ( join(complement(top),complement(top)) != complement(top)
    | join(complement(top),zero) = complement(top) ),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_199]) ).

cnf(refute_0_201,plain,
    join(complement(top),zero) = complement(top),
    inference(resolve,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) )],[refute_0_198,refute_0_200]) ).

cnf(refute_0_202,plain,
    join(zero,complement(top)) = join(zero,complement(top)),
    introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).

cnf(refute_0_203,plain,
    ( complement(top) != zero
    | join(zero,complement(top)) != join(zero,complement(top))
    | join(zero,complement(top)) = join(zero,zero) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).

cnf(refute_0_204,plain,
    ( complement(top) != zero
    | join(zero,complement(top)) = join(zero,zero) ),
    inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    join(zero,complement(top)) = join(zero,zero),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_204]) ).

cnf(refute_0_206,plain,
    join(complement(top),zero) = join(zero,complement(top)),
    inference(subst,[],[refute_0_5:[bind(A,$fot(zero)),bind(B,$fot(complement(top)))]]) ).

cnf(refute_0_207,plain,
    ( join(complement(top),zero) != join(zero,complement(top))
    | join(zero,complement(top)) != join(zero,zero)
    | join(complement(top),zero) = join(zero,zero) ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(join(complement(top),zero))),bind(Y,$fot(join(zero,complement(top)))),bind(Z,$fot(join(zero,zero)))]]) ).

cnf(refute_0_208,plain,
    ( join(zero,complement(top)) != join(zero,zero)
    | join(complement(top),zero) = join(zero,zero) ),
    inference(resolve,[$cnf( $equal(join(complement(top),zero),join(zero,complement(top))) )],[refute_0_206,refute_0_207]) ).

cnf(refute_0_209,plain,
    join(complement(top),zero) = join(zero,zero),
    inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_205,refute_0_208]) ).

cnf(refute_0_210,plain,
    ( join(complement(top),zero) != complement(top)
    | join(complement(top),zero) != join(zero,zero)
    | join(zero,zero) = complement(top) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(top),zero),complement(top)) ),[0],$fot(join(zero,zero))]]) ).

cnf(refute_0_211,plain,
    ( join(complement(top),zero) != complement(top)
    | join(zero,zero) = complement(top) ),
    inference(resolve,[$cnf( $equal(join(complement(top),zero),join(zero,zero)) )],[refute_0_209,refute_0_210]) ).

cnf(refute_0_212,plain,
    ( complement(top) != zero
    | join(zero,zero) != complement(top)
    | join(zero,zero) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).

cnf(refute_0_213,plain,
    ( join(zero,zero) != complement(top)
    | join(zero,zero) = zero ),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_212]) ).

cnf(refute_0_214,plain,
    ( join(complement(top),zero) != complement(top)
    | join(zero,zero) = zero ),
    inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_211,refute_0_213]) ).

cnf(refute_0_215,plain,
    join(zero,zero) = zero,
    inference(resolve,[$cnf( $equal(join(complement(top),zero),complement(top)) )],[refute_0_201,refute_0_214]) ).

cnf(refute_0_216,plain,
    ( join(zero,join(zero,C)) != join(join(zero,zero),C)
    | join(zero,zero) != zero
    | join(zero,join(zero,C)) = join(zero,C) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) ),[1,0],$fot(zero)]]) ).

cnf(refute_0_217,plain,
    ( join(zero,join(zero,C)) != join(join(zero,zero),C)
    | join(zero,join(zero,C)) = join(zero,C) ),
    inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    join(zero,join(zero,C)) = join(zero,C),
    inference(resolve,[$cnf( $equal(join(zero,join(zero,C)),join(join(zero,zero),C)) )],[refute_0_197,refute_0_217]) ).

cnf(refute_0_219,plain,
    join(zero,join(zero,meet(X_78,top))) = join(zero,meet(X_78,top)),
    inference(subst,[],[refute_0_218:[bind(C,$fot(meet(X_78,top)))]]) ).

cnf(refute_0_220,plain,
    join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
    inference(subst,[],[refute_0_5:[bind(A,$fot(complement(join(complement(A),B)))),bind(B,$fot(complement(join(complement(A),complement(B)))))]]) ).

cnf(refute_0_221,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_222,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_220,refute_0_221]) ).

cnf(refute_0_223,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_222]) ).

cnf(refute_0_224,plain,
    join(complement(join(complement(A),B)),meet(A,B)) = join(meet(A,B),complement(join(complement(A),B))),
    inference(subst,[],[refute_0_5:[bind(A,$fot(meet(A,B))),bind(B,$fot(complement(join(complement(A),B))))]]) ).

cnf(refute_0_225,plain,
    ( meet(A,B) != complement(join(complement(A),complement(B)))
    | complement(join(complement(A),complement(B))) = meet(A,B) ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(meet(A,B))),bind(Y,$fot(complement(join(complement(A),complement(B)))))]]) ).

cnf(refute_0_226,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_225]) ).

cnf(refute_0_227,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_228,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_229,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_227,refute_0_228]) ).

cnf(refute_0_230,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_226,refute_0_229]) ).

cnf(refute_0_231,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_31:[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_232,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_230,refute_0_231]) ).

cnf(refute_0_233,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_224,refute_0_232]) ).

cnf(refute_0_234,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_235,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_233,refute_0_234]) ).

cnf(refute_0_236,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_223,refute_0_235]) ).

cnf(refute_0_237,plain,
    X_76 = join(meet(X_76,top),complement(join(complement(X_76),top))),
    inference(subst,[],[refute_0_236:[bind(A,$fot(X_76)),bind(B,$fot(top))]]) ).

cnf(refute_0_238,plain,
    join(complement(X_76),top) = top,
    inference(subst,[],[refute_0_169:[bind(X_19,$fot(complement(X_76)))]]) ).

cnf(refute_0_239,plain,
    ( X_76 != join(meet(X_76,top),complement(join(complement(X_76),top)))
    | join(complement(X_76),top) != top
    | X_76 = join(meet(X_76,top),complement(top)) ),
    introduced(tautology,[equality,[$cnf( $equal(X_76,join(meet(X_76,top),complement(join(complement(X_76),top)))) ),[1,1,0],$fot(top)]]) ).

cnf(refute_0_240,plain,
    ( X_76 != join(meet(X_76,top),complement(join(complement(X_76),top)))
    | X_76 = join(meet(X_76,top),complement(top)) ),
    inference(resolve,[$cnf( $equal(join(complement(X_76),top),top) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    X_76 = join(meet(X_76,top),complement(top)),
    inference(resolve,[$cnf( $equal(X_76,join(meet(X_76,top),complement(join(complement(X_76),top)))) )],[refute_0_237,refute_0_240]) ).

cnf(refute_0_242,plain,
    join(complement(top),meet(X_76,top)) = join(complement(top),meet(X_76,top)),
    introduced(tautology,[refl,[$fot(join(complement(top),meet(X_76,top)))]]) ).

cnf(refute_0_243,plain,
    ( complement(top) != zero
    | join(complement(top),meet(X_76,top)) != join(complement(top),meet(X_76,top))
    | join(complement(top),meet(X_76,top)) = join(zero,meet(X_76,top)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(complement(top),meet(X_76,top)),join(complement(top),meet(X_76,top))) ),[1,0],$fot(zero)]]) ).

cnf(refute_0_244,plain,
    ( complement(top) != zero
    | join(complement(top),meet(X_76,top)) = join(zero,meet(X_76,top)) ),
    inference(resolve,[$cnf( $equal(join(complement(top),meet(X_76,top)),join(complement(top),meet(X_76,top))) )],[refute_0_242,refute_0_243]) ).

cnf(refute_0_245,plain,
    join(complement(top),meet(X_76,top)) = join(zero,meet(X_76,top)),
    inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_39,refute_0_244]) ).

cnf(refute_0_246,plain,
    join(meet(X_76,top),complement(top)) = join(complement(top),meet(X_76,top)),
    inference(subst,[],[refute_0_5:[bind(A,$fot(complement(top))),bind(B,$fot(meet(X_76,top)))]]) ).

cnf(refute_0_247,plain,
    ( join(complement(top),meet(X_76,top)) != join(zero,meet(X_76,top))
    | join(meet(X_76,top),complement(top)) != join(complement(top),meet(X_76,top))
    | join(meet(X_76,top),complement(top)) = join(zero,meet(X_76,top)) ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(join(meet(X_76,top),complement(top)))),bind(Y,$fot(join(complement(top),meet(X_76,top)))),bind(Z,$fot(join(zero,meet(X_76,top))))]]) ).

cnf(refute_0_248,plain,
    ( join(complement(top),meet(X_76,top)) != join(zero,meet(X_76,top))
    | join(meet(X_76,top),complement(top)) = join(zero,meet(X_76,top)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_76,top),complement(top)),join(complement(top),meet(X_76,top))) )],[refute_0_246,refute_0_247]) ).

cnf(refute_0_249,plain,
    join(meet(X_76,top),complement(top)) = join(zero,meet(X_76,top)),
    inference(resolve,[$cnf( $equal(join(complement(top),meet(X_76,top)),join(zero,meet(X_76,top))) )],[refute_0_245,refute_0_248]) ).

cnf(refute_0_250,plain,
    ( X_76 != join(meet(X_76,top),complement(top))
    | join(meet(X_76,top),complement(top)) != join(zero,meet(X_76,top))
    | X_76 = join(zero,meet(X_76,top)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(X_76,join(zero,meet(X_76,top))) ),[0],$fot(join(meet(X_76,top),complement(top)))]]) ).

cnf(refute_0_251,plain,
    ( X_76 != join(meet(X_76,top),complement(top))
    | X_76 = join(zero,meet(X_76,top)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_76,top),complement(top)),join(zero,meet(X_76,top))) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    X_76 = join(zero,meet(X_76,top)),
    inference(resolve,[$cnf( $equal(X_76,join(meet(X_76,top),complement(top))) )],[refute_0_241,refute_0_251]) ).

cnf(refute_0_253,plain,
    X_78 = join(zero,meet(X_78,top)),
    inference(subst,[],[refute_0_252:[bind(X_76,$fot(X_78))]]) ).

cnf(refute_0_254,plain,
    ( X_78 != join(zero,meet(X_78,top))
    | join(zero,meet(X_78,top)) = X_78 ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(X_78)),bind(Y,$fot(join(zero,meet(X_78,top))))]]) ).

cnf(refute_0_255,plain,
    join(zero,meet(X_78,top)) = X_78,
    inference(resolve,[$cnf( $equal(X_78,join(zero,meet(X_78,top))) )],[refute_0_253,refute_0_254]) ).

cnf(refute_0_256,plain,
    ( join(zero,join(zero,meet(X_78,top))) != join(zero,meet(X_78,top))
    | join(zero,meet(X_78,top)) != X_78
    | join(zero,X_78) = join(zero,meet(X_78,top)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,meet(X_78,top))),join(zero,meet(X_78,top))) ),[0,1],$fot(X_78)]]) ).

cnf(refute_0_257,plain,
    ( join(zero,join(zero,meet(X_78,top))) != join(zero,meet(X_78,top))
    | join(zero,X_78) = join(zero,meet(X_78,top)) ),
    inference(resolve,[$cnf( $equal(join(zero,meet(X_78,top)),X_78) )],[refute_0_255,refute_0_256]) ).

cnf(refute_0_258,plain,
    join(zero,X_78) = join(zero,meet(X_78,top)),
    inference(resolve,[$cnf( $equal(join(zero,join(zero,meet(X_78,top))),join(zero,meet(X_78,top))) )],[refute_0_219,refute_0_257]) ).

cnf(refute_0_259,plain,
    ( join(zero,X_78) != join(zero,meet(X_78,top))
    | join(zero,meet(X_78,top)) != X_78
    | join(zero,X_78) = X_78 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_78),X_78) ),[0],$fot(join(zero,meet(X_78,top)))]]) ).

cnf(refute_0_260,plain,
    ( join(zero,X_78) != join(zero,meet(X_78,top))
    | join(zero,X_78) = X_78 ),
    inference(resolve,[$cnf( $equal(join(zero,meet(X_78,top)),X_78) )],[refute_0_255,refute_0_259]) ).

cnf(refute_0_261,plain,
    join(zero,X_78) = X_78,
    inference(resolve,[$cnf( $equal(join(zero,X_78),join(zero,meet(X_78,top))) )],[refute_0_258,refute_0_260]) ).

cnf(refute_0_262,plain,
    join(zero,composition(top,complement(composition(top,top)))) = composition(top,complement(composition(top,top))),
    inference(subst,[],[refute_0_261:[bind(X_78,$fot(composition(top,complement(composition(top,top)))))]]) ).

cnf(refute_0_263,plain,
    ( join(zero,composition(top,complement(composition(top,top)))) != composition(top,complement(composition(top,top)))
    | join(zero,composition(top,complement(composition(top,top)))) != zero
    | composition(top,complement(composition(top,top))) = zero ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) ),[0],$fot(composition(top,complement(composition(top,top))))]]) ).

cnf(refute_0_264,plain,
    ( join(zero,composition(top,complement(composition(top,top)))) != zero
    | composition(top,complement(composition(top,top))) = zero ),
    inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),composition(top,complement(composition(top,top)))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    composition(top,complement(composition(top,top))) = zero,
    inference(resolve,[$cnf( $equal(join(zero,composition(top,complement(composition(top,top)))),zero) )],[refute_0_196,refute_0_264]) ).

cnf(refute_0_266,plain,
    ( composition(A,composition(top,complement(composition(top,top)))) != composition(composition(A,top),complement(composition(top,top)))
    | composition(top,complement(composition(top,top))) != zero
    | composition(A,zero) = composition(composition(A,top),complement(composition(top,top))) ),
    introduced(tautology,[equality,[$cnf( $equal(composition(A,composition(top,complement(composition(top,top)))),composition(composition(A,top),complement(composition(top,top)))) ),[0,1],$fot(zero)]]) ).

cnf(refute_0_267,plain,
    ( composition(A,composition(top,complement(composition(top,top)))) != composition(composition(A,top),complement(composition(top,top)))
    | composition(A,zero) = composition(composition(A,top),complement(composition(top,top))) ),
    inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_265,refute_0_266]) ).

cnf(refute_0_268,plain,
    composition(A,zero) = composition(composition(A,top),complement(composition(top,top))),
    inference(resolve,[$cnf( $equal(composition(A,composition(top,complement(composition(top,top)))),composition(composition(A,top),complement(composition(top,top)))) )],[refute_0_0,refute_0_267]) ).

cnf(refute_0_269,plain,
    composition(join(top,B),complement(composition(top,top))) = join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top)))),
    inference(subst,[],[composition_distributivity_7:[bind(A,$fot(top)),bind(C,$fot(complement(composition(top,top))))]]) ).

cnf(refute_0_270,plain,
    ( composition(join(top,B),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))
    | composition(top,complement(composition(top,top))) != zero
    | composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))) ),
    introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))) ),[1,0],$fot(zero)]]) ).

cnf(refute_0_271,plain,
    ( composition(join(top,B),complement(composition(top,top))) != join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))
    | composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))) ),
    inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_265,refute_0_270]) ).

cnf(refute_0_272,plain,
    composition(join(top,B),complement(composition(top,top))) = join(zero,composition(B,complement(composition(top,top)))),
    inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(composition(top,complement(composition(top,top))),composition(B,complement(composition(top,top))))) )],[refute_0_269,refute_0_271]) ).

cnf(refute_0_273,plain,
    composition(join(top,B),complement(composition(top,top))) = composition(join(top,B),complement(composition(top,top))),
    introduced(tautology,[refl,[$fot(composition(join(top,B),complement(composition(top,top))))]]) ).

cnf(refute_0_274,plain,
    ( composition(join(top,B),complement(composition(top,top))) != composition(join(top,B),complement(composition(top,top)))
    | join(top,B) != top
    | composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
    introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(join(top,B),complement(composition(top,top)))) ),[1,0],$fot(top)]]) ).

cnf(refute_0_275,plain,
    ( join(top,B) != top
    | composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))) ),
    inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(join(top,B),complement(composition(top,top)))) )],[refute_0_273,refute_0_274]) ).

cnf(refute_0_276,plain,
    composition(join(top,B),complement(composition(top,top))) = composition(top,complement(composition(top,top))),
    inference(resolve,[$cnf( $equal(join(top,B),top) )],[refute_0_177,refute_0_275]) ).

cnf(refute_0_277,plain,
    ( composition(join(top,B),complement(composition(top,top))) != composition(top,complement(composition(top,top)))
    | composition(top,complement(composition(top,top))) != zero
    | composition(join(top,B),complement(composition(top,top))) = zero ),
    inference(subst,[],[refute_0_31:[bind(X,$fot(composition(join(top,B),complement(composition(top,top))))),bind(Y,$fot(composition(top,complement(composition(top,top))))),bind(Z,$fot(zero))]]) ).

cnf(refute_0_278,plain,
    ( composition(top,complement(composition(top,top))) != zero
    | composition(join(top,B),complement(composition(top,top))) = zero ),
    inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),composition(top,complement(composition(top,top)))) )],[refute_0_276,refute_0_277]) ).

cnf(refute_0_279,plain,
    composition(join(top,B),complement(composition(top,top))) = zero,
    inference(resolve,[$cnf( $equal(composition(top,complement(composition(top,top))),zero) )],[refute_0_265,refute_0_278]) ).

cnf(refute_0_280,plain,
    ( composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
    | composition(join(top,B),complement(composition(top,top))) != zero
    | zero = join(zero,composition(B,complement(composition(top,top)))) ),
    introduced(tautology,[equality,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(zero,composition(B,complement(composition(top,top))))) ),[0],$fot(zero)]]) ).

cnf(refute_0_281,plain,
    ( composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
    | zero = join(zero,composition(B,complement(composition(top,top)))) ),
    inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),zero) )],[refute_0_279,refute_0_280]) ).

cnf(refute_0_282,plain,
    join(zero,composition(B,complement(composition(top,top)))) = composition(B,complement(composition(top,top))),
    inference(subst,[],[refute_0_261:[bind(X_78,$fot(composition(B,complement(composition(top,top)))))]]) ).

cnf(refute_0_283,plain,
    ( join(zero,composition(B,complement(composition(top,top)))) != composition(B,complement(composition(top,top)))
    | zero != join(zero,composition(B,complement(composition(top,top))))
    | zero = composition(B,complement(composition(top,top))) ),
    introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,composition(B,complement(composition(top,top))))) ),[1],$fot(composition(B,complement(composition(top,top))))]]) ).

cnf(refute_0_284,plain,
    ( zero != join(zero,composition(B,complement(composition(top,top))))
    | zero = composition(B,complement(composition(top,top))) ),
    inference(resolve,[$cnf( $equal(join(zero,composition(B,complement(composition(top,top)))),composition(B,complement(composition(top,top)))) )],[refute_0_282,refute_0_283]) ).

cnf(refute_0_285,plain,
    ( composition(join(top,B),complement(composition(top,top))) != join(zero,composition(B,complement(composition(top,top))))
    | zero = composition(B,complement(composition(top,top))) ),
    inference(resolve,[$cnf( $equal(zero,join(zero,composition(B,complement(composition(top,top))))) )],[refute_0_281,refute_0_284]) ).

cnf(refute_0_286,plain,
    zero = composition(B,complement(composition(top,top))),
    inference(resolve,[$cnf( $equal(composition(join(top,B),complement(composition(top,top))),join(zero,composition(B,complement(composition(top,top))))) )],[refute_0_272,refute_0_285]) ).

cnf(refute_0_287,plain,
    ( zero != composition(B,complement(composition(top,top)))
    | composition(B,complement(composition(top,top))) = zero ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(composition(B,complement(composition(top,top)))))]]) ).

cnf(refute_0_288,plain,
    composition(B,complement(composition(top,top))) = zero,
    inference(resolve,[$cnf( $equal(zero,composition(B,complement(composition(top,top)))) )],[refute_0_286,refute_0_287]) ).

cnf(refute_0_289,plain,
    composition(composition(A,top),complement(composition(top,top))) = zero,
    inference(subst,[],[refute_0_288:[bind(B,$fot(composition(A,top)))]]) ).

cnf(refute_0_290,plain,
    ( composition(A,zero) != composition(composition(A,top),complement(composition(top,top)))
    | composition(composition(A,top),complement(composition(top,top))) != zero
    | composition(A,zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(composition(A,zero),zero) ),[0],$fot(composition(composition(A,top),complement(composition(top,top))))]]) ).

cnf(refute_0_291,plain,
    ( composition(A,zero) != composition(composition(A,top),complement(composition(top,top)))
    | composition(A,zero) = zero ),
    inference(resolve,[$cnf( $equal(composition(composition(A,top),complement(composition(top,top))),zero) )],[refute_0_289,refute_0_290]) ).

cnf(refute_0_292,plain,
    composition(A,zero) = zero,
    inference(resolve,[$cnf( $equal(composition(A,zero),composition(composition(A,top),complement(composition(top,top)))) )],[refute_0_268,refute_0_291]) ).

cnf(refute_0_293,plain,
    composition(sk1,zero) = zero,
    inference(subst,[],[refute_0_292:[bind(A,$fot(sk1))]]) ).

cnf(refute_0_294,plain,
    ( composition(sk1,zero) != zero
    | zero != zero
    | composition(sk1,zero) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(composition(sk1,zero),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_295,plain,
    ( zero != zero
    | composition(sk1,zero) = zero ),
    inference(resolve,[$cnf( $equal(composition(sk1,zero),zero) )],[refute_0_293,refute_0_294]) ).

cnf(refute_0_296,plain,
    ( composition(zero,sk1) != zero
    | zero != zero ),
    inference(resolve,[$cnf( $equal(composition(sk1,zero),zero) )],[refute_0_295,goals_14]) ).

cnf(refute_0_297,plain,
    zero = zero,
    introduced(tautology,[refl,[$fot(zero)]]) ).

cnf(refute_0_298,plain,
    composition(zero,sk1) != zero,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_297,refute_0_296]) ).

cnf(refute_0_299,plain,
    converse(composition(converse(A),zero)) = composition(converse(zero),A),
    inference(subst,[],[refute_0_105:[bind(X_7,$fot(zero))]]) ).

cnf(refute_0_300,plain,
    composition(converse(A),zero) = zero,
    inference(subst,[],[refute_0_292:[bind(A,$fot(converse(A)))]]) ).

cnf(refute_0_301,plain,
    ( composition(converse(A),zero) != zero
    | converse(composition(converse(A),zero)) != composition(converse(zero),A)
    | converse(zero) = composition(converse(zero),A) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(A),zero)),composition(converse(zero),A)) ),[0,0],$fot(zero)]]) ).

cnf(refute_0_302,plain,
    ( converse(composition(converse(A),zero)) != composition(converse(zero),A)
    | converse(zero) = composition(converse(zero),A) ),
    inference(resolve,[$cnf( $equal(composition(converse(A),zero),zero) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    converse(zero) = composition(converse(zero),A),
    inference(resolve,[$cnf( $equal(converse(composition(converse(A),zero)),composition(converse(zero),A)) )],[refute_0_299,refute_0_302]) ).

cnf(refute_0_304,plain,
    converse(join(converse(A),zero)) = join(A,converse(zero)),
    inference(subst,[],[refute_0_182:[bind(X_35,$fot(zero))]]) ).

cnf(refute_0_305,plain,
    join(join(zero,X_63),zero) = join(zero,join(zero,X_63)),
    inference(subst,[],[maddux1_join_commutativity_1:[bind(A,$fot(join(zero,X_63))),bind(B,$fot(zero))]]) ).

cnf(refute_0_306,plain,
    join(zero,join(zero,X_63)) = join(zero,X_63),
    inference(subst,[],[refute_0_218:[bind(C,$fot(X_63))]]) ).

cnf(refute_0_307,plain,
    ( join(join(zero,X_63),zero) != join(zero,join(zero,X_63))
    | join(zero,join(zero,X_63)) != join(zero,X_63)
    | join(join(zero,X_63),zero) = join(zero,X_63) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(join(zero,X_63),zero),join(zero,X_63)) ),[0],$fot(join(zero,join(zero,X_63)))]]) ).

cnf(refute_0_308,plain,
    ( join(join(zero,X_63),zero) != join(zero,join(zero,X_63))
    | join(join(zero,X_63),zero) = join(zero,X_63) ),
    inference(resolve,[$cnf( $equal(join(zero,join(zero,X_63)),join(zero,X_63)) )],[refute_0_306,refute_0_307]) ).

cnf(refute_0_309,plain,
    join(join(zero,X_63),zero) = join(zero,X_63),
    inference(resolve,[$cnf( $equal(join(join(zero,X_63),zero),join(zero,join(zero,X_63))) )],[refute_0_305,refute_0_308]) ).

cnf(refute_0_310,plain,
    join(join(zero,X_63),zero) = join(zero,join(X_63,zero)),
    inference(subst,[],[refute_0_69:[bind(A,$fot(zero)),bind(B,$fot(X_63)),bind(C,$fot(zero))]]) ).

cnf(refute_0_311,plain,
    ( join(join(zero,X_63),zero) != join(zero,X_63)
    | join(join(zero,X_63),zero) != join(zero,join(X_63,zero))
    | join(zero,join(X_63,zero)) = join(zero,X_63) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_63),zero),join(zero,X_63)) ),[0],$fot(join(zero,join(X_63,zero)))]]) ).

cnf(refute_0_312,plain,
    ( join(join(zero,X_63),zero) != join(zero,X_63)
    | join(zero,join(X_63,zero)) = join(zero,X_63) ),
    inference(resolve,[$cnf( $equal(join(join(zero,X_63),zero),join(zero,join(X_63,zero))) )],[refute_0_310,refute_0_311]) ).

cnf(refute_0_313,plain,
    join(zero,join(X_63,zero)) = join(zero,X_63),
    inference(resolve,[$cnf( $equal(join(join(zero,X_63),zero),join(zero,X_63)) )],[refute_0_309,refute_0_312]) ).

cnf(refute_0_314,plain,
    join(zero,join(meet(X_78,top),zero)) = join(zero,meet(X_78,top)),
    inference(subst,[],[refute_0_313:[bind(X_63,$fot(meet(X_78,top)))]]) ).

cnf(refute_0_315,plain,
    ( join(zero,join(meet(X_78,top),zero)) != join(zero,meet(X_78,top))
    | join(zero,meet(X_78,top)) != X_78
    | join(zero,join(meet(X_78,top),zero)) = X_78 ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,join(meet(X_78,top),zero)),X_78) ),[0],$fot(join(zero,meet(X_78,top)))]]) ).

cnf(refute_0_316,plain,
    ( join(zero,join(meet(X_78,top),zero)) != join(zero,meet(X_78,top))
    | join(zero,join(meet(X_78,top),zero)) = X_78 ),
    inference(resolve,[$cnf( $equal(join(zero,meet(X_78,top)),X_78) )],[refute_0_255,refute_0_315]) ).

cnf(refute_0_317,plain,
    join(zero,join(meet(X_78,top),zero)) = X_78,
    inference(resolve,[$cnf( $equal(join(zero,join(meet(X_78,top),zero)),join(zero,meet(X_78,top))) )],[refute_0_314,refute_0_316]) ).

cnf(refute_0_318,plain,
    join(zero,join(meet(X_78,top),C)) = join(join(zero,meet(X_78,top)),C),
    inference(subst,[],[maddux2_join_associativity_2:[bind(A,$fot(zero)),bind(B,$fot(meet(X_78,top)))]]) ).

cnf(refute_0_319,plain,
    ( join(zero,join(meet(X_78,top),C)) != join(join(zero,meet(X_78,top)),C)
    | join(zero,meet(X_78,top)) != X_78
    | join(zero,join(meet(X_78,top),C)) = join(X_78,C) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_78,top),C)),join(join(zero,meet(X_78,top)),C)) ),[1,0],$fot(X_78)]]) ).

cnf(refute_0_320,plain,
    ( join(zero,join(meet(X_78,top),C)) != join(join(zero,meet(X_78,top)),C)
    | join(zero,join(meet(X_78,top),C)) = join(X_78,C) ),
    inference(resolve,[$cnf( $equal(join(zero,meet(X_78,top)),X_78) )],[refute_0_255,refute_0_319]) ).

cnf(refute_0_321,plain,
    join(zero,join(meet(X_78,top),C)) = join(X_78,C),
    inference(resolve,[$cnf( $equal(join(zero,join(meet(X_78,top),C)),join(join(zero,meet(X_78,top)),C)) )],[refute_0_318,refute_0_320]) ).

cnf(refute_0_322,plain,
    join(zero,join(meet(X_78,top),zero)) = join(X_78,zero),
    inference(subst,[],[refute_0_321:[bind(C,$fot(zero))]]) ).

cnf(refute_0_323,plain,
    ( join(zero,join(meet(X_78,top),zero)) != X_78
    | join(zero,join(meet(X_78,top),zero)) != join(X_78,zero)
    | join(X_78,zero) = X_78 ),
    introduced(tautology,[equality,[$cnf( $equal(join(zero,join(meet(X_78,top),zero)),X_78) ),[0],$fot(join(X_78,zero))]]) ).

cnf(refute_0_324,plain,
    ( join(zero,join(meet(X_78,top),zero)) != X_78
    | join(X_78,zero) = X_78 ),
    inference(resolve,[$cnf( $equal(join(zero,join(meet(X_78,top),zero)),join(X_78,zero)) )],[refute_0_322,refute_0_323]) ).

cnf(refute_0_325,plain,
    join(X_78,zero) = X_78,
    inference(resolve,[$cnf( $equal(join(zero,join(meet(X_78,top),zero)),X_78) )],[refute_0_317,refute_0_324]) ).

cnf(refute_0_326,plain,
    join(converse(A),zero) = converse(A),
    inference(subst,[],[refute_0_325:[bind(X_78,$fot(converse(A)))]]) ).

cnf(refute_0_327,plain,
    ( converse(join(converse(A),zero)) != join(A,converse(zero))
    | join(converse(A),zero) != converse(A)
    | converse(converse(A)) = join(A,converse(zero)) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(join(converse(A),zero)),join(A,converse(zero))) ),[0,0],$fot(converse(A))]]) ).

cnf(refute_0_328,plain,
    ( converse(join(converse(A),zero)) != join(A,converse(zero))
    | converse(converse(A)) = join(A,converse(zero)) ),
    inference(resolve,[$cnf( $equal(join(converse(A),zero),converse(A)) )],[refute_0_326,refute_0_327]) ).

cnf(refute_0_329,plain,
    converse(converse(A)) = join(A,converse(zero)),
    inference(resolve,[$cnf( $equal(converse(join(converse(A),zero)),join(A,converse(zero))) )],[refute_0_304,refute_0_328]) ).

cnf(refute_0_330,plain,
    ( converse(converse(A)) != A
    | converse(converse(A)) != join(A,converse(zero))
    | A = join(A,converse(zero)) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(converse(A)),join(A,converse(zero))) ),[0],$fot(A)]]) ).

cnf(refute_0_331,plain,
    ( converse(converse(A)) != join(A,converse(zero))
    | A = join(A,converse(zero)) ),
    inference(resolve,[$cnf( $equal(converse(converse(A)),A) )],[converse_idempotence_8,refute_0_330]) ).

cnf(refute_0_332,plain,
    A = join(A,converse(zero)),
    inference(resolve,[$cnf( $equal(converse(converse(A)),join(A,converse(zero))) )],[refute_0_329,refute_0_331]) ).

cnf(refute_0_333,plain,
    zero = join(zero,converse(zero)),
    inference(subst,[],[refute_0_332:[bind(A,$fot(zero))]]) ).

cnf(refute_0_334,plain,
    join(zero,converse(zero)) = converse(zero),
    inference(subst,[],[refute_0_261:[bind(X_78,$fot(converse(zero)))]]) ).

cnf(refute_0_335,plain,
    ( join(zero,converse(zero)) != converse(zero)
    | zero != join(zero,converse(zero))
    | zero = converse(zero) ),
    introduced(tautology,[equality,[$cnf( $equal(zero,join(zero,converse(zero))) ),[1],$fot(converse(zero))]]) ).

cnf(refute_0_336,plain,
    ( zero != join(zero,converse(zero))
    | zero = converse(zero) ),
    inference(resolve,[$cnf( $equal(join(zero,converse(zero)),converse(zero)) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    zero = converse(zero),
    inference(resolve,[$cnf( $equal(zero,join(zero,converse(zero))) )],[refute_0_333,refute_0_336]) ).

cnf(refute_0_338,plain,
    ( zero != converse(zero)
    | converse(zero) = zero ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(converse(zero)))]]) ).

cnf(refute_0_339,plain,
    converse(zero) = zero,
    inference(resolve,[$cnf( $equal(zero,converse(zero)) )],[refute_0_337,refute_0_338]) ).

cnf(refute_0_340,plain,
    ( converse(zero) != composition(converse(zero),A)
    | converse(zero) != zero
    | zero = composition(converse(zero),A) ),
    introduced(tautology,[equality,[$cnf( $equal(converse(zero),composition(converse(zero),A)) ),[0],$fot(zero)]]) ).

cnf(refute_0_341,plain,
    ( converse(zero) != composition(converse(zero),A)
    | zero = composition(converse(zero),A) ),
    inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_339,refute_0_340]) ).

cnf(refute_0_342,plain,
    composition(converse(zero),A) = composition(converse(zero),A),
    introduced(tautology,[refl,[$fot(composition(converse(zero),A))]]) ).

cnf(refute_0_343,plain,
    ( composition(converse(zero),A) != composition(converse(zero),A)
    | converse(zero) != zero
    | composition(converse(zero),A) = composition(zero,A) ),
    introduced(tautology,[equality,[$cnf( $equal(composition(converse(zero),A),composition(converse(zero),A)) ),[1,0],$fot(zero)]]) ).

cnf(refute_0_344,plain,
    ( converse(zero) != zero
    | composition(converse(zero),A) = composition(zero,A) ),
    inference(resolve,[$cnf( $equal(composition(converse(zero),A),composition(converse(zero),A)) )],[refute_0_342,refute_0_343]) ).

cnf(refute_0_345,plain,
    composition(converse(zero),A) = composition(zero,A),
    inference(resolve,[$cnf( $equal(converse(zero),zero) )],[refute_0_339,refute_0_344]) ).

cnf(refute_0_346,plain,
    ( composition(converse(zero),A) != composition(zero,A)
    | zero != composition(converse(zero),A)
    | zero = composition(zero,A) ),
    introduced(tautology,[equality,[$cnf( $equal(zero,composition(converse(zero),A)) ),[1],$fot(composition(zero,A))]]) ).

cnf(refute_0_347,plain,
    ( zero != composition(converse(zero),A)
    | zero = composition(zero,A) ),
    inference(resolve,[$cnf( $equal(composition(converse(zero),A),composition(zero,A)) )],[refute_0_345,refute_0_346]) ).

cnf(refute_0_348,plain,
    ( converse(zero) != composition(converse(zero),A)
    | zero = composition(zero,A) ),
    inference(resolve,[$cnf( $equal(zero,composition(converse(zero),A)) )],[refute_0_341,refute_0_347]) ).

cnf(refute_0_349,plain,
    zero = composition(zero,A),
    inference(resolve,[$cnf( $equal(converse(zero),composition(converse(zero),A)) )],[refute_0_303,refute_0_348]) ).

cnf(refute_0_350,plain,
    ( zero != composition(zero,A)
    | composition(zero,A) = zero ),
    inference(subst,[],[refute_0_3:[bind(X,$fot(zero)),bind(Y,$fot(composition(zero,A)))]]) ).

cnf(refute_0_351,plain,
    composition(zero,A) = zero,
    inference(resolve,[$cnf( $equal(zero,composition(zero,A)) )],[refute_0_349,refute_0_350]) ).

cnf(refute_0_352,plain,
    composition(zero,sk1) = zero,
    inference(subst,[],[refute_0_351:[bind(A,$fot(sk1))]]) ).

cnf(refute_0_353,plain,
    ( composition(zero,sk1) != zero
    | zero != zero
    | composition(zero,sk1) = zero ),
    introduced(tautology,[equality,[$cnf( ~ $equal(composition(zero,sk1),zero) ),[0],$fot(zero)]]) ).

cnf(refute_0_354,plain,
    ( zero != zero
    | composition(zero,sk1) = zero ),
    inference(resolve,[$cnf( $equal(composition(zero,sk1),zero) )],[refute_0_352,refute_0_353]) ).

cnf(refute_0_355,plain,
    zero != zero,
    inference(resolve,[$cnf( $equal(composition(zero,sk1),zero) )],[refute_0_354,refute_0_298]) ).

cnf(refute_0_356,plain,
    $false,
    inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_297,refute_0_355]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : REL013-1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n004.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jul  8 15:43:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.54/0.74  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.74  
% 0.54/0.74  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.54/0.78  
%------------------------------------------------------------------------------