%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 : Sun Jul 17 05:59:05 EDT 2022

% Result   : Unsatisfiable 0.46s 0.63s
% Output   : CNFRefutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   56
%            Number of leaves      :   97
% Syntax   : Number of clauses     :  446 ( 227 unt;   0 nHn; 261 RR)
%            Number of literals    :  763 ( 762 equ; 318 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  655 (  12 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(idempotence_of_join,axiom,
    join(X,X) = X ).

cnf(absorption1,axiom,
    meet(X,join(X,Y)) = X ).

cnf(absorption2,axiom,
    join(X,meet(X,Y)) = X ).

cnf(commutativity_of_meet,axiom,
    meet(X,Y) = meet(Y,X) ).

cnf(commutativity_of_join,axiom,
    join(X,Y) = join(Y,X) ).

cnf(associativity_of_meet,axiom,
    meet(meet(X,Y),Z) = meet(X,meet(Y,Z)) ).

cnf(associativity_of_join,axiom,
    join(join(X,Y),Z) = join(X,join(Y,Z)) ).

cnf(dist_join,hypothesis,
    join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).

cnf(dist_meet,hypothesis,
    meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).

cnf(lhs1,hypothesis,
    join(xx,yy) = join(xx,zz) ).

cnf(lhs2,hypothesis,
    meet(xx,yy) = meet(xx,zz) ).

cnf(rhs,negated_conjecture,
    yy != zz ).

cnf(refute_0_0,plain,
    meet(yy,join(X_57,zz)) = join(meet(yy,X_57),meet(yy,zz)),
    inference(subst,[],[dist_meet:[bind(X,$fot(yy)),bind(Y,$fot(X_57)),bind(Z,$fot(zz))]]) ).

cnf(refute_0_1,plain,
    ( join(X,Y) != join(Y,X)
    | meet(X,join(X,Y)) != X
    | meet(X,join(Y,X)) = X ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,Y)),X) ),[0,1],$fot(join(Y,X))]]) ).

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

cnf(refute_0_3,plain,
    meet(X,join(Y,X)) = X,
    inference(resolve,[$cnf( $equal(meet(X,join(X,Y)),X) )],[absorption1,refute_0_2]) ).

cnf(refute_0_4,plain,
    meet(zz,join(yy,zz)) = zz,
    inference(subst,[],[refute_0_3:[bind(X,$fot(zz)),bind(Y,$fot(yy))]]) ).

cnf(refute_0_5,plain,
    meet(join(yy,zz),join(xx,join(yy,zz))) = join(yy,zz),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(yy,zz))),bind(Y,$fot(xx))]]) ).

cnf(refute_0_6,plain,
    ( join(X,meet(X,Y)) != X
    | meet(X,Y) != meet(Y,X)
    | join(X,meet(Y,X)) = X ),
    introduced(tautology,[equality,[$cnf( $equal(join(X,meet(X,Y)),X) ),[0,1],$fot(meet(Y,X))]]) ).

cnf(refute_0_7,plain,
    ( join(X,meet(X,Y)) != X
    | join(X,meet(Y,X)) = X ),
    inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_6]) ).

cnf(refute_0_8,plain,
    join(X,meet(Y,X)) = X,
    inference(resolve,[$cnf( $equal(join(X,meet(X,Y)),X) )],[absorption2,refute_0_7]) ).

cnf(refute_0_9,plain,
    join(join(xx,yy),meet(zz,join(xx,yy))) = join(xx,yy),
    inference(subst,[],[refute_0_8:[bind(X,$fot(join(xx,yy))),bind(Y,$fot(zz))]]) ).

cnf(refute_0_10,plain,
    meet(zz,join(xx,zz)) = zz,
    inference(subst,[],[refute_0_3:[bind(X,$fot(zz)),bind(Y,$fot(xx))]]) ).

cnf(refute_0_11,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_12,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_13,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_11,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( join(xx,yy) != join(xx,zz)
    | join(xx,zz) = join(xx,yy) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(xx,yy))),bind(Y0,$fot(join(xx,zz)))]]) ).

cnf(refute_0_15,plain,
    join(xx,zz) = join(xx,yy),
    inference(resolve,[$cnf( $equal(join(xx,yy),join(xx,zz)) )],[lhs1,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( join(xx,zz) != join(xx,yy)
    | meet(zz,join(xx,zz)) != zz
    | meet(zz,join(xx,yy)) = zz ),
    introduced(tautology,[equality,[$cnf( $equal(meet(zz,join(xx,zz)),zz) ),[0,1],$fot(join(xx,yy))]]) ).

cnf(refute_0_17,plain,
    ( meet(zz,join(xx,zz)) != zz
    | meet(zz,join(xx,yy)) = zz ),
    inference(resolve,[$cnf( $equal(join(xx,zz),join(xx,yy)) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    meet(zz,join(xx,yy)) = zz,
    inference(resolve,[$cnf( $equal(meet(zz,join(xx,zz)),zz) )],[refute_0_10,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( join(join(xx,yy),meet(zz,join(xx,yy))) != join(xx,yy)
    | meet(zz,join(xx,yy)) != zz
    | join(join(xx,yy),zz) = join(xx,yy) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(xx,yy),meet(zz,join(xx,yy))),join(xx,yy)) ),[0,1],$fot(zz)]]) ).

cnf(refute_0_20,plain,
    ( join(join(xx,yy),meet(zz,join(xx,yy))) != join(xx,yy)
    | join(join(xx,yy),zz) = join(xx,yy) ),
    inference(resolve,[$cnf( $equal(meet(zz,join(xx,yy)),zz) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    join(join(xx,yy),zz) = join(xx,yy),
    inference(resolve,[$cnf( $equal(join(join(xx,yy),meet(zz,join(xx,yy))),join(xx,yy)) )],[refute_0_9,refute_0_20]) ).

cnf(refute_0_22,plain,
    join(join(xx,yy),zz) = join(xx,join(yy,zz)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(xx)),bind(Y,$fot(yy)),bind(Z,$fot(zz))]]) ).

cnf(refute_0_23,plain,
    ( join(join(xx,yy),zz) != join(xx,join(yy,zz))
    | join(join(xx,yy),zz) != join(xx,yy)
    | join(xx,join(yy,zz)) = join(xx,yy) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(xx,yy),zz),join(xx,yy)) ),[0],$fot(join(xx,join(yy,zz)))]]) ).

cnf(refute_0_24,plain,
    ( join(join(xx,yy),zz) != join(xx,yy)
    | join(xx,join(yy,zz)) = join(xx,yy) ),
    inference(resolve,[$cnf( $equal(join(join(xx,yy),zz),join(xx,join(yy,zz))) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    join(xx,join(yy,zz)) = join(xx,yy),
    inference(resolve,[$cnf( $equal(join(join(xx,yy),zz),join(xx,yy)) )],[refute_0_21,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( join(xx,join(yy,zz)) != join(xx,yy)
    | meet(join(yy,zz),join(xx,join(yy,zz))) != join(yy,zz)
    | meet(join(yy,zz),join(xx,yy)) = join(yy,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(yy,zz),join(xx,join(yy,zz))),join(yy,zz)) ),[0,1],$fot(join(xx,yy))]]) ).

cnf(refute_0_27,plain,
    ( meet(join(yy,zz),join(xx,join(yy,zz))) != join(yy,zz)
    | meet(join(yy,zz),join(xx,yy)) = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(join(xx,join(yy,zz)),join(xx,yy)) )],[refute_0_25,refute_0_26]) ).

cnf(refute_0_28,plain,
    meet(join(yy,zz),join(xx,yy)) = join(yy,zz),
    inference(resolve,[$cnf( $equal(meet(join(yy,zz),join(xx,join(yy,zz))),join(yy,zz)) )],[refute_0_5,refute_0_27]) ).

cnf(refute_0_29,plain,
    ( meet(X,Y) != meet(Y,X)
    | meet(Y,X) = meet(X,Y) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(X,Y))),bind(Y0,$fot(meet(Y,X)))]]) ).

cnf(refute_0_30,plain,
    meet(Y,X) = meet(X,Y),
    inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_29]) ).

cnf(refute_0_31,plain,
    meet(join(yy,zz),join(xx,yy)) = meet(join(xx,yy),join(yy,zz)),
    inference(subst,[],[refute_0_30:[bind(X,$fot(join(xx,yy))),bind(Y,$fot(join(yy,zz)))]]) ).

cnf(refute_0_32,plain,
    ( meet(join(yy,zz),join(xx,yy)) != join(yy,zz)
    | meet(join(yy,zz),join(xx,yy)) != meet(join(xx,yy),join(yy,zz))
    | meet(join(xx,yy),join(yy,zz)) = join(yy,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(yy,zz),join(xx,yy)),join(yy,zz)) ),[0],$fot(meet(join(xx,yy),join(yy,zz)))]]) ).

cnf(refute_0_33,plain,
    ( meet(join(yy,zz),join(xx,yy)) != join(yy,zz)
    | meet(join(xx,yy),join(yy,zz)) = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(meet(join(yy,zz),join(xx,yy)),meet(join(xx,yy),join(yy,zz))) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    meet(join(xx,yy),join(yy,zz)) = join(yy,zz),
    inference(resolve,[$cnf( $equal(meet(join(yy,zz),join(xx,yy)),join(yy,zz)) )],[refute_0_28,refute_0_33]) ).

cnf(refute_0_35,plain,
    join(yy,meet(xx,yy)) = yy,
    inference(subst,[],[refute_0_8:[bind(X,$fot(yy)),bind(Y,$fot(xx))]]) ).

cnf(refute_0_36,plain,
    ( meet(xx,yy) != meet(xx,zz)
    | meet(xx,zz) = meet(xx,yy) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(xx,yy))),bind(Y0,$fot(meet(xx,zz)))]]) ).

cnf(refute_0_37,plain,
    meet(xx,zz) = meet(xx,yy),
    inference(resolve,[$cnf( $equal(meet(xx,yy),meet(xx,zz)) )],[lhs2,refute_0_36]) ).

cnf(refute_0_38,plain,
    join(yy,meet(xx,zz)) = join(yy,meet(xx,zz)),
    introduced(tautology,[refl,[$fot(join(yy,meet(xx,zz)))]]) ).

cnf(refute_0_39,plain,
    ( join(yy,meet(xx,zz)) != join(yy,meet(xx,zz))
    | meet(xx,zz) != meet(xx,yy)
    | join(yy,meet(xx,zz)) = join(yy,meet(xx,yy)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,meet(xx,zz)),join(yy,meet(xx,zz))) ),[1,1],$fot(meet(xx,yy))]]) ).

cnf(refute_0_40,plain,
    ( meet(xx,zz) != meet(xx,yy)
    | join(yy,meet(xx,zz)) = join(yy,meet(xx,yy)) ),
    inference(resolve,[$cnf( $equal(join(yy,meet(xx,zz)),join(yy,meet(xx,zz))) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    join(yy,meet(xx,zz)) = join(yy,meet(xx,yy)),
    inference(resolve,[$cnf( $equal(meet(xx,zz),meet(xx,yy)) )],[refute_0_37,refute_0_40]) ).

cnf(refute_0_42,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_43,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_13,refute_0_42]) ).

cnf(refute_0_44,plain,
    ( join(yy,meet(xx,yy)) != yy
    | join(yy,meet(xx,zz)) != join(yy,meet(xx,yy))
    | join(yy,meet(xx,zz)) = yy ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(yy,meet(xx,zz)))),bind(Y0,$fot(join(yy,meet(xx,yy)))),bind(Z0,$fot(yy))]]) ).

cnf(refute_0_45,plain,
    ( join(yy,meet(xx,yy)) != yy
    | join(yy,meet(xx,zz)) = yy ),
    inference(resolve,[$cnf( $equal(join(yy,meet(xx,zz)),join(yy,meet(xx,yy))) )],[refute_0_41,refute_0_44]) ).

cnf(refute_0_46,plain,
    join(yy,meet(xx,zz)) = yy,
    inference(resolve,[$cnf( $equal(join(yy,meet(xx,yy)),yy) )],[refute_0_35,refute_0_45]) ).

cnf(refute_0_47,plain,
    join(X_44,meet(X_45,X_46)) = meet(join(X_44,X_45),join(X_44,X_46)),
    inference(subst,[],[dist_join:[bind(X,$fot(X_44)),bind(Y,$fot(X_45)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_48,plain,
    join(X_45,X_44) = join(X_44,X_45),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_45)),bind(Y,$fot(X_44))]]) ).

cnf(refute_0_49,plain,
    ( join(X_45,X_44) != join(X_44,X_45)
    | join(X_44,X_45) = join(X_45,X_44) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_45,X_44))),bind(Y0,$fot(join(X_44,X_45)))]]) ).

cnf(refute_0_50,plain,
    join(X_44,X_45) = join(X_45,X_44),
    inference(resolve,[$cnf( $equal(join(X_45,X_44),join(X_44,X_45)) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    ( join(X_44,X_45) != join(X_45,X_44)
    | join(X_44,meet(X_45,X_46)) != meet(join(X_44,X_45),join(X_44,X_46))
    | join(X_44,meet(X_45,X_46)) = meet(join(X_45,X_44),join(X_44,X_46)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_44,meet(X_45,X_46)),meet(join(X_44,X_45),join(X_44,X_46))) ),[1,0],$fot(join(X_45,X_44))]]) ).

cnf(refute_0_52,plain,
    ( join(X_44,meet(X_45,X_46)) != meet(join(X_44,X_45),join(X_44,X_46))
    | join(X_44,meet(X_45,X_46)) = meet(join(X_45,X_44),join(X_44,X_46)) ),
    inference(resolve,[$cnf( $equal(join(X_44,X_45),join(X_45,X_44)) )],[refute_0_50,refute_0_51]) ).

cnf(refute_0_53,plain,
    join(X_44,meet(X_45,X_46)) = meet(join(X_45,X_44),join(X_44,X_46)),
    inference(resolve,[$cnf( $equal(join(X_44,meet(X_45,X_46)),meet(join(X_44,X_45),join(X_44,X_46))) )],[refute_0_47,refute_0_52]) ).

cnf(refute_0_54,plain,
    ( join(X_44,meet(X_45,X_46)) != meet(join(X_45,X_44),join(X_44,X_46))
    | meet(join(X_45,X_44),join(X_44,X_46)) = join(X_44,meet(X_45,X_46)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_44,meet(X_45,X_46)))),bind(Y0,$fot(meet(join(X_45,X_44),join(X_44,X_46))))]]) ).

cnf(refute_0_55,plain,
    meet(join(X_45,X_44),join(X_44,X_46)) = join(X_44,meet(X_45,X_46)),
    inference(resolve,[$cnf( $equal(join(X_44,meet(X_45,X_46)),meet(join(X_45,X_44),join(X_44,X_46))) )],[refute_0_53,refute_0_54]) ).

cnf(refute_0_56,plain,
    meet(join(xx,yy),join(yy,zz)) = join(yy,meet(xx,zz)),
    inference(subst,[],[refute_0_55:[bind(X_44,$fot(yy)),bind(X_45,$fot(xx)),bind(X_46,$fot(zz))]]) ).

cnf(refute_0_57,plain,
    ( join(yy,meet(xx,zz)) != yy
    | meet(join(xx,yy),join(yy,zz)) != join(yy,meet(xx,zz))
    | meet(join(xx,yy),join(yy,zz)) = yy ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(meet(join(xx,yy),join(yy,zz)))),bind(Y0,$fot(join(yy,meet(xx,zz)))),bind(Z0,$fot(yy))]]) ).

cnf(refute_0_58,plain,
    ( join(yy,meet(xx,zz)) != yy
    | meet(join(xx,yy),join(yy,zz)) = yy ),
    inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(yy,zz)),join(yy,meet(xx,zz))) )],[refute_0_56,refute_0_57]) ).

cnf(refute_0_59,plain,
    meet(join(xx,yy),join(yy,zz)) = yy,
    inference(resolve,[$cnf( $equal(join(yy,meet(xx,zz)),yy) )],[refute_0_46,refute_0_58]) ).

cnf(refute_0_60,plain,
    ( meet(join(xx,yy),join(yy,zz)) != join(yy,zz)
    | meet(join(xx,yy),join(yy,zz)) != yy
    | yy = join(yy,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(xx,yy),join(yy,zz)),join(yy,zz)) ),[0],$fot(yy)]]) ).

cnf(refute_0_61,plain,
    ( meet(join(xx,yy),join(yy,zz)) != join(yy,zz)
    | yy = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(yy,zz)),yy) )],[refute_0_59,refute_0_60]) ).

cnf(refute_0_62,plain,
    yy = join(yy,zz),
    inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(yy,zz)),join(yy,zz)) )],[refute_0_34,refute_0_61]) ).

cnf(refute_0_63,plain,
    ( yy != join(yy,zz)
    | join(yy,zz) = yy ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(yy)),bind(Y0,$fot(join(yy,zz)))]]) ).

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

cnf(refute_0_65,plain,
    ( join(yy,zz) != yy
    | meet(zz,join(yy,zz)) != zz
    | meet(zz,yy) = zz ),
    introduced(tautology,[equality,[$cnf( $equal(meet(zz,join(yy,zz)),zz) ),[0,1],$fot(yy)]]) ).

cnf(refute_0_66,plain,
    ( meet(zz,join(yy,zz)) != zz
    | meet(zz,yy) = zz ),
    inference(resolve,[$cnf( $equal(join(yy,zz),yy) )],[refute_0_64,refute_0_65]) ).

cnf(refute_0_67,plain,
    meet(zz,yy) = zz,
    inference(resolve,[$cnf( $equal(meet(zz,join(yy,zz)),zz) )],[refute_0_4,refute_0_66]) ).

cnf(refute_0_68,plain,
    meet(zz,yy) = meet(yy,zz),
    inference(subst,[],[refute_0_30:[bind(X,$fot(yy)),bind(Y,$fot(zz))]]) ).

cnf(refute_0_69,plain,
    ( meet(zz,yy) != meet(yy,zz)
    | meet(zz,yy) != zz
    | meet(yy,zz) = zz ),
    introduced(tautology,[equality,[$cnf( $equal(meet(zz,yy),zz) ),[0],$fot(meet(yy,zz))]]) ).

cnf(refute_0_70,plain,
    ( meet(zz,yy) != zz
    | meet(yy,zz) = zz ),
    inference(resolve,[$cnf( $equal(meet(zz,yy),meet(yy,zz)) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    meet(yy,zz) = zz,
    inference(resolve,[$cnf( $equal(meet(zz,yy),zz) )],[refute_0_67,refute_0_70]) ).

cnf(refute_0_72,plain,
    ( meet(yy,join(X_57,zz)) != join(meet(yy,X_57),meet(yy,zz))
    | meet(yy,zz) != zz
    | meet(yy,join(X_57,zz)) = join(meet(yy,X_57),zz) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(yy,join(X_57,zz)),join(meet(yy,X_57),meet(yy,zz))) ),[1,1],$fot(zz)]]) ).

cnf(refute_0_73,plain,
    ( meet(yy,join(X_57,zz)) != join(meet(yy,X_57),meet(yy,zz))
    | meet(yy,join(X_57,zz)) = join(meet(yy,X_57),zz) ),
    inference(resolve,[$cnf( $equal(meet(yy,zz),zz) )],[refute_0_71,refute_0_72]) ).

cnf(refute_0_74,plain,
    meet(yy,join(X_57,zz)) = join(meet(yy,X_57),zz),
    inference(resolve,[$cnf( $equal(meet(yy,join(X_57,zz)),join(meet(yy,X_57),meet(yy,zz))) )],[refute_0_0,refute_0_73]) ).

cnf(refute_0_75,plain,
    meet(join(zz,X_43),join(yy,join(zz,X_43))) = join(zz,X_43),
    inference(subst,[],[refute_0_3:[bind(X,$fot(join(zz,X_43))),bind(Y,$fot(yy))]]) ).

cnf(refute_0_76,plain,
    join(join(X_13,Y),meet(X_13,join(X_13,Y))) = join(X_13,Y),
    inference(subst,[],[refute_0_8:[bind(X,$fot(join(X_13,Y))),bind(Y,$fot(X_13))]]) ).

cnf(refute_0_77,plain,
    meet(X_13,join(X_13,Y)) = X_13,
    inference(subst,[],[absorption1:[bind(X,$fot(X_13))]]) ).

cnf(refute_0_78,plain,
    ( join(join(X_13,Y),meet(X_13,join(X_13,Y))) != join(X_13,Y)
    | meet(X_13,join(X_13,Y)) != X_13
    | join(join(X_13,Y),X_13) = join(X_13,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_13,Y),meet(X_13,join(X_13,Y))),join(X_13,Y)) ),[0,1],$fot(X_13)]]) ).

cnf(refute_0_79,plain,
    ( join(join(X_13,Y),meet(X_13,join(X_13,Y))) != join(X_13,Y)
    | join(join(X_13,Y),X_13) = join(X_13,Y) ),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_13,Y)),X_13) )],[refute_0_77,refute_0_78]) ).

cnf(refute_0_80,plain,
    join(join(X_13,Y),X_13) = join(X_13,Y),
    inference(resolve,[$cnf( $equal(join(join(X_13,Y),meet(X_13,join(X_13,Y))),join(X_13,Y)) )],[refute_0_76,refute_0_79]) ).

cnf(refute_0_81,plain,
    join(join(X_13,Y),X_13) = join(X_13,join(Y,X_13)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_13)),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_82,plain,
    ( join(join(X_13,Y),X_13) != join(X_13,Y)
    | join(join(X_13,Y),X_13) != join(X_13,join(Y,X_13))
    | join(X_13,join(Y,X_13)) = join(X_13,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,Y)) ),[0],$fot(join(X_13,join(Y,X_13)))]]) ).

cnf(refute_0_83,plain,
    ( join(join(X_13,Y),X_13) != join(X_13,Y)
    | join(X_13,join(Y,X_13)) = join(X_13,Y) ),
    inference(resolve,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,join(Y,X_13))) )],[refute_0_81,refute_0_82]) ).

cnf(refute_0_84,plain,
    join(X_13,join(Y,X_13)) = join(X_13,Y),
    inference(resolve,[$cnf( $equal(join(join(X_13,Y),X_13),join(X_13,Y)) )],[refute_0_80,refute_0_83]) ).

cnf(refute_0_85,plain,
    join(join(X_24,join(yy,zz)),join(yy,join(X_24,join(yy,zz)))) = join(join(X_24,join(yy,zz)),yy),
    inference(subst,[],[refute_0_84:[bind(Y,$fot(yy)),bind(X_13,$fot(join(X_24,join(yy,zz))))]]) ).

cnf(refute_0_86,plain,
    join(join(X_24,yy),join(yy,zz)) = join(X_24,join(yy,join(yy,zz))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(yy)),bind(Z,$fot(join(yy,zz)))]]) ).

cnf(refute_0_87,plain,
    join(join(yy,zz),meet(join(xx,yy),join(yy,zz))) = join(yy,zz),
    inference(subst,[],[refute_0_8:[bind(X,$fot(join(yy,zz))),bind(Y,$fot(join(xx,yy)))]]) ).

cnf(refute_0_88,plain,
    ( join(join(yy,zz),meet(join(xx,yy),join(yy,zz))) != join(yy,zz)
    | meet(join(xx,yy),join(yy,zz)) != join(yy,zz)
    | join(join(yy,zz),join(yy,zz)) = join(yy,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(yy,zz),meet(join(xx,yy),join(yy,zz))),join(yy,zz)) ),[0,1],$fot(join(yy,zz))]]) ).

cnf(refute_0_89,plain,
    ( join(join(yy,zz),meet(join(xx,yy),join(yy,zz))) != join(yy,zz)
    | join(join(yy,zz),join(yy,zz)) = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(meet(join(xx,yy),join(yy,zz)),join(yy,zz)) )],[refute_0_34,refute_0_88]) ).

cnf(refute_0_90,plain,
    join(join(yy,zz),join(yy,zz)) = join(yy,zz),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),meet(join(xx,yy),join(yy,zz))),join(yy,zz)) )],[refute_0_87,refute_0_89]) ).

cnf(refute_0_91,plain,
    ( join(X,Y) != join(Y,X)
    | join(Y,X) = join(X,Y) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).

cnf(refute_0_92,plain,
    join(Y,X) = join(X,Y),
    inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_91]) ).

cnf(refute_0_93,plain,
    join(zz,yy) = join(yy,zz),
    inference(subst,[],[refute_0_92:[bind(X,$fot(yy)),bind(Y,$fot(zz))]]) ).

cnf(refute_0_94,plain,
    join(zz,join(yy,zz)) = join(zz,yy),
    inference(subst,[],[refute_0_84:[bind(Y,$fot(yy)),bind(X_13,$fot(zz))]]) ).

cnf(refute_0_95,plain,
    ( join(zz,join(yy,zz)) != join(zz,yy)
    | join(zz,yy) != join(yy,zz)
    | join(zz,join(yy,zz)) = join(yy,zz) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(zz,join(yy,zz)))),bind(Y0,$fot(join(zz,yy))),bind(Z0,$fot(join(yy,zz)))]]) ).

cnf(refute_0_96,plain,
    ( join(zz,yy) != join(yy,zz)
    | join(zz,join(yy,zz)) = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(join(zz,join(yy,zz)),join(zz,yy)) )],[refute_0_94,refute_0_95]) ).

cnf(refute_0_97,plain,
    join(zz,join(yy,zz)) = join(yy,zz),
    inference(resolve,[$cnf( $equal(join(zz,yy),join(yy,zz)) )],[refute_0_93,refute_0_96]) ).

cnf(refute_0_98,plain,
    join(yy,join(zz,join(yy,zz))) = join(yy,join(zz,join(yy,zz))),
    introduced(tautology,[refl,[$fot(join(yy,join(zz,join(yy,zz))))]]) ).

cnf(refute_0_99,plain,
    ( join(yy,join(zz,join(yy,zz))) != join(yy,join(zz,join(yy,zz)))
    | join(zz,join(yy,zz)) != join(yy,zz)
    | join(yy,join(zz,join(yy,zz))) = join(yy,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,join(yy,zz))),join(yy,join(zz,join(yy,zz)))) ),[1,1],$fot(join(yy,zz))]]) ).

cnf(refute_0_100,plain,
    ( join(zz,join(yy,zz)) != join(yy,zz)
    | join(yy,join(zz,join(yy,zz))) = join(yy,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(yy,zz))),join(yy,join(zz,join(yy,zz)))) )],[refute_0_98,refute_0_99]) ).

cnf(refute_0_101,plain,
    join(yy,join(zz,join(yy,zz))) = join(yy,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(zz,join(yy,zz)),join(yy,zz)) )],[refute_0_97,refute_0_100]) ).

cnf(refute_0_102,plain,
    join(join(yy,zz),join(yy,zz)) = join(yy,join(zz,join(yy,zz))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(yy)),bind(Y,$fot(zz)),bind(Z,$fot(join(yy,zz)))]]) ).

cnf(refute_0_103,plain,
    ( join(join(yy,zz),join(yy,zz)) != join(yy,join(zz,join(yy,zz)))
    | join(yy,join(zz,join(yy,zz))) != join(yy,join(yy,zz))
    | join(join(yy,zz),join(yy,zz)) = join(yy,join(yy,zz)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(yy,zz),join(yy,zz)))),bind(Y0,$fot(join(yy,join(zz,join(yy,zz))))),bind(Z0,$fot(join(yy,join(yy,zz))))]]) ).

cnf(refute_0_104,plain,
    ( join(yy,join(zz,join(yy,zz))) != join(yy,join(yy,zz))
    | join(join(yy,zz),join(yy,zz)) = join(yy,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),join(yy,zz)),join(yy,join(zz,join(yy,zz)))) )],[refute_0_102,refute_0_103]) ).

cnf(refute_0_105,plain,
    join(join(yy,zz),join(yy,zz)) = join(yy,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(yy,zz))),join(yy,join(yy,zz))) )],[refute_0_101,refute_0_104]) ).

cnf(refute_0_106,plain,
    ( join(join(yy,zz),join(yy,zz)) != join(yy,join(yy,zz))
    | join(join(yy,zz),join(yy,zz)) != join(yy,zz)
    | join(yy,join(yy,zz)) = join(yy,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(yy,zz),join(yy,zz)),join(yy,zz)) ),[0],$fot(join(yy,join(yy,zz)))]]) ).

cnf(refute_0_107,plain,
    ( join(join(yy,zz),join(yy,zz)) != join(yy,zz)
    | join(yy,join(yy,zz)) = join(yy,zz) ),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),join(yy,zz)),join(yy,join(yy,zz))) )],[refute_0_105,refute_0_106]) ).

cnf(refute_0_108,plain,
    join(yy,join(yy,zz)) = join(yy,zz),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),join(yy,zz)),join(yy,zz)) )],[refute_0_90,refute_0_107]) ).

cnf(refute_0_109,plain,
    ( join(join(X_24,yy),join(yy,zz)) != join(X_24,join(yy,join(yy,zz)))
    | join(yy,join(yy,zz)) != join(yy,zz)
    | join(join(X_24,yy),join(yy,zz)) = join(X_24,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(X_24,join(yy,join(yy,zz)))) ),[1,1],$fot(join(yy,zz))]]) ).

cnf(refute_0_110,plain,
    ( join(join(X_24,yy),join(yy,zz)) != join(X_24,join(yy,join(yy,zz)))
    | join(join(X_24,yy),join(yy,zz)) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(yy,zz)),join(yy,zz)) )],[refute_0_108,refute_0_109]) ).

cnf(refute_0_111,plain,
    join(join(X_24,yy),join(yy,zz)) = join(X_24,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(X_24,join(yy,join(yy,zz)))) )],[refute_0_86,refute_0_110]) ).

cnf(refute_0_112,plain,
    join(join(X_24,yy),zz) = join(X_24,join(yy,zz)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(yy)),bind(Z,$fot(zz))]]) ).

cnf(refute_0_113,plain,
    join(yy,join(join(X_24,yy),zz)) = join(yy,join(join(X_24,yy),zz)),
    introduced(tautology,[refl,[$fot(join(yy,join(join(X_24,yy),zz)))]]) ).

cnf(refute_0_114,plain,
    ( join(join(X_24,yy),zz) != join(X_24,join(yy,zz))
    | join(yy,join(join(X_24,yy),zz)) != join(yy,join(join(X_24,yy),zz))
    | join(yy,join(join(X_24,yy),zz)) = join(yy,join(X_24,join(yy,zz))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(join(X_24,yy),zz)),join(yy,join(join(X_24,yy),zz))) ),[1,1],$fot(join(X_24,join(yy,zz)))]]) ).

cnf(refute_0_115,plain,
    ( join(join(X_24,yy),zz) != join(X_24,join(yy,zz))
    | join(yy,join(join(X_24,yy),zz)) = join(yy,join(X_24,join(yy,zz))) ),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X_24,yy),zz)),join(yy,join(join(X_24,yy),zz))) )],[refute_0_113,refute_0_114]) ).

cnf(refute_0_116,plain,
    join(yy,join(join(X_24,yy),zz)) = join(yy,join(X_24,join(yy,zz))),
    inference(resolve,[$cnf( $equal(join(join(X_24,yy),zz),join(X_24,join(yy,zz))) )],[refute_0_112,refute_0_115]) ).

cnf(refute_0_117,plain,
    join(join(X_24,X_25),X_26) = join(X_24,join(X_25,X_26)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).

cnf(refute_0_118,plain,
    join(X_25,X_24) = join(X_24,X_25),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_24))]]) ).

cnf(refute_0_119,plain,
    ( join(X_25,X_24) != join(X_24,X_25)
    | join(X_24,X_25) = join(X_25,X_24) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_25,X_24))),bind(Y0,$fot(join(X_24,X_25)))]]) ).

cnf(refute_0_120,plain,
    join(X_24,X_25) = join(X_25,X_24),
    inference(resolve,[$cnf( $equal(join(X_25,X_24),join(X_24,X_25)) )],[refute_0_118,refute_0_119]) ).

cnf(refute_0_121,plain,
    ( join(X_24,X_25) != join(X_25,X_24)
    | join(join(X_24,X_25),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_25,X_24),X_26) = join(X_24,join(X_25,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_25,X_26))) ),[0,0],$fot(join(X_25,X_24))]]) ).

cnf(refute_0_122,plain,
    ( join(join(X_24,X_25),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_25,X_24),X_26) = join(X_24,join(X_25,X_26)) ),
    inference(resolve,[$cnf( $equal(join(X_24,X_25),join(X_25,X_24)) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    join(join(X_25,X_24),X_26) = join(X_24,join(X_25,X_26)),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_25,X_26))) )],[refute_0_117,refute_0_122]) ).

cnf(refute_0_124,plain,
    join(join(X_25,X_24),X_26) = join(X_25,join(X_24,X_26)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_24)),bind(Z,$fot(X_26))]]) ).

cnf(refute_0_125,plain,
    ( join(join(X_25,X_24),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_25,X_24),X_26) != join(X_25,join(X_24,X_26))
    | join(X_25,join(X_24,X_26)) = join(X_24,join(X_25,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_25,X_24),X_26),join(X_24,join(X_25,X_26))) ),[0],$fot(join(X_25,join(X_24,X_26)))]]) ).

cnf(refute_0_126,plain,
    ( join(join(X_25,X_24),X_26) != join(X_24,join(X_25,X_26))
    | join(X_25,join(X_24,X_26)) = join(X_24,join(X_25,X_26)) ),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_24),X_26),join(X_25,join(X_24,X_26))) )],[refute_0_124,refute_0_125]) ).

cnf(refute_0_127,plain,
    join(X_25,join(X_24,X_26)) = join(X_24,join(X_25,X_26)),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_24),X_26),join(X_24,join(X_25,X_26))) )],[refute_0_123,refute_0_126]) ).

cnf(refute_0_128,plain,
    ( join(X_25,join(X_24,X_26)) != join(X_24,join(X_25,X_26))
    | join(X_24,join(X_25,X_26)) = join(X_25,join(X_24,X_26)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_25,join(X_24,X_26)))),bind(Y0,$fot(join(X_24,join(X_25,X_26))))]]) ).

cnf(refute_0_129,plain,
    join(X_24,join(X_25,X_26)) = join(X_25,join(X_24,X_26)),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_24,X_26)),join(X_24,join(X_25,X_26))) )],[refute_0_127,refute_0_128]) ).

cnf(refute_0_130,plain,
    join(join(X_24,yy),join(yy,zz)) = join(yy,join(join(X_24,yy),zz)),
    inference(subst,[],[refute_0_129:[bind(X_24,$fot(join(X_24,yy))),bind(X_25,$fot(yy)),bind(X_26,$fot(zz))]]) ).

cnf(refute_0_131,plain,
    ( join(join(X_24,yy),join(yy,zz)) != join(yy,join(join(X_24,yy),zz))
    | join(yy,join(join(X_24,yy),zz)) != join(yy,join(X_24,join(yy,zz)))
    | join(join(X_24,yy),join(yy,zz)) = join(yy,join(X_24,join(yy,zz))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_24,yy),join(yy,zz)))),bind(Y0,$fot(join(yy,join(join(X_24,yy),zz)))),bind(Z0,$fot(join(yy,join(X_24,join(yy,zz)))))]]) ).

cnf(refute_0_132,plain,
    ( join(yy,join(join(X_24,yy),zz)) != join(yy,join(X_24,join(yy,zz)))
    | join(join(X_24,yy),join(yy,zz)) = join(yy,join(X_24,join(yy,zz))) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(yy,join(join(X_24,yy),zz))) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    join(join(X_24,yy),join(yy,zz)) = join(yy,join(X_24,join(yy,zz))),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X_24,yy),zz)),join(yy,join(X_24,join(yy,zz)))) )],[refute_0_116,refute_0_132]) ).

cnf(refute_0_134,plain,
    ( join(join(X_24,yy),join(yy,zz)) != join(X_24,join(yy,zz))
    | join(join(X_24,yy),join(yy,zz)) != join(yy,join(X_24,join(yy,zz)))
    | join(yy,join(X_24,join(yy,zz))) = join(X_24,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(X_24,join(yy,zz))) ),[0],$fot(join(yy,join(X_24,join(yy,zz))))]]) ).

cnf(refute_0_135,plain,
    ( join(join(X_24,yy),join(yy,zz)) != join(X_24,join(yy,zz))
    | join(yy,join(X_24,join(yy,zz))) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(yy,join(X_24,join(yy,zz)))) )],[refute_0_133,refute_0_134]) ).

cnf(refute_0_136,plain,
    join(yy,join(X_24,join(yy,zz))) = join(X_24,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(join(X_24,yy),join(yy,zz)),join(X_24,join(yy,zz))) )],[refute_0_111,refute_0_135]) ).

cnf(refute_0_137,plain,
    ( join(join(X_24,join(yy,zz)),join(yy,join(X_24,join(yy,zz)))) != join(join(X_24,join(yy,zz)),yy)
    | join(yy,join(X_24,join(yy,zz))) != join(X_24,join(yy,zz))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(join(X_24,join(yy,zz)),yy) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(yy,join(X_24,join(yy,zz)))),join(join(X_24,join(yy,zz)),yy)) ),[0,1],$fot(join(X_24,join(yy,zz)))]]) ).

cnf(refute_0_138,plain,
    ( join(join(X_24,join(yy,zz)),join(yy,join(X_24,join(yy,zz)))) != join(join(X_24,join(yy,zz)),yy)
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(join(X_24,join(yy,zz)),yy) ),
    inference(resolve,[$cnf( $equal(join(yy,join(X_24,join(yy,zz))),join(X_24,join(yy,zz))) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(join(X_24,join(yy,zz)),yy),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(yy,join(X_24,join(yy,zz)))),join(join(X_24,join(yy,zz)),yy)) )],[refute_0_85,refute_0_138]) ).

cnf(refute_0_140,plain,
    join(join(X_25,X_25),X_26) = join(X_25,join(X_25,X_26)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_25)),bind(Z,$fot(X_26))]]) ).

cnf(refute_0_141,plain,
    join(X_25,X_25) = X_25,
    inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_25))]]) ).

cnf(refute_0_142,plain,
    ( join(X_25,X_25) != X_25
    | join(join(X_25,X_25),X_26) != join(X_25,join(X_25,X_26))
    | join(X_25,X_26) = join(X_25,join(X_25,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_25,X_25),X_26),join(X_25,join(X_25,X_26))) ),[0,0],$fot(X_25)]]) ).

cnf(refute_0_143,plain,
    ( join(join(X_25,X_25),X_26) != join(X_25,join(X_25,X_26))
    | join(X_25,X_26) = join(X_25,join(X_25,X_26)) ),
    inference(resolve,[$cnf( $equal(join(X_25,X_25),X_25) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    join(X_25,X_26) = join(X_25,join(X_25,X_26)),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_25),X_26),join(X_25,join(X_25,X_26))) )],[refute_0_140,refute_0_143]) ).

cnf(refute_0_145,plain,
    ( join(X_25,X_26) != join(X_25,join(X_25,X_26))
    | join(X_25,join(X_25,X_26)) = join(X_25,X_26) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_25,X_26))),bind(Y0,$fot(join(X_25,join(X_25,X_26))))]]) ).

cnf(refute_0_146,plain,
    join(X_25,join(X_25,X_26)) = join(X_25,X_26),
    inference(resolve,[$cnf( $equal(join(X_25,X_26),join(X_25,join(X_25,X_26))) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    join(yy,join(yy,join(zz,X_24))) = join(yy,join(zz,X_24)),
    inference(subst,[],[refute_0_146:[bind(X_25,$fot(yy)),bind(X_26,$fot(join(zz,X_24)))]]) ).

cnf(refute_0_148,plain,
    join(zz,join(zz,X_24)) = join(zz,X_24),
    inference(subst,[],[refute_0_146:[bind(X_25,$fot(zz)),bind(X_26,$fot(X_24))]]) ).

cnf(refute_0_149,plain,
    join(yy,join(zz,join(zz,X_24))) = join(yy,join(zz,join(zz,X_24))),
    introduced(tautology,[refl,[$fot(join(yy,join(zz,join(zz,X_24))))]]) ).

cnf(refute_0_150,plain,
    ( join(yy,join(zz,join(zz,X_24))) != join(yy,join(zz,join(zz,X_24)))
    | join(zz,join(zz,X_24)) != join(zz,X_24)
    | join(yy,join(zz,join(zz,X_24))) = join(yy,join(zz,X_24)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,join(zz,X_24))),join(yy,join(zz,join(zz,X_24)))) ),[1,1],$fot(join(zz,X_24))]]) ).

cnf(refute_0_151,plain,
    ( join(zz,join(zz,X_24)) != join(zz,X_24)
    | join(yy,join(zz,join(zz,X_24))) = join(yy,join(zz,X_24)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(zz,X_24))),join(yy,join(zz,join(zz,X_24)))) )],[refute_0_149,refute_0_150]) ).

cnf(refute_0_152,plain,
    join(yy,join(zz,join(zz,X_24))) = join(yy,join(zz,X_24)),
    inference(resolve,[$cnf( $equal(join(zz,join(zz,X_24)),join(zz,X_24)) )],[refute_0_148,refute_0_151]) ).

cnf(refute_0_153,plain,
    join(join(X,join(X_41,X)),Z) = join(X,join(join(X_41,X),Z)),
    inference(subst,[],[associativity_of_join:[bind(Y,$fot(join(X_41,X)))]]) ).

cnf(refute_0_154,plain,
    join(X,join(X_41,X)) = join(X,X_41),
    inference(subst,[],[refute_0_84:[bind(Y,$fot(X_41)),bind(X_13,$fot(X))]]) ).

cnf(refute_0_155,plain,
    ( join(X,join(X_41,X)) != join(X,X_41)
    | join(join(X,join(X_41,X)),Z) != join(X,join(join(X_41,X),Z))
    | join(join(X,X_41),Z) = join(X,join(join(X_41,X),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,join(X_41,X)),Z),join(X,join(join(X_41,X),Z))) ),[0,0],$fot(join(X,X_41))]]) ).

cnf(refute_0_156,plain,
    ( join(join(X,join(X_41,X)),Z) != join(X,join(join(X_41,X),Z))
    | join(join(X,X_41),Z) = join(X,join(join(X_41,X),Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(X_41,X)),join(X,X_41)) )],[refute_0_154,refute_0_155]) ).

cnf(refute_0_157,plain,
    join(join(X,X_41),Z) = join(X,join(join(X_41,X),Z)),
    inference(resolve,[$cnf( $equal(join(join(X,join(X_41,X)),Z),join(X,join(join(X_41,X),Z))) )],[refute_0_153,refute_0_156]) ).

cnf(refute_0_158,plain,
    join(join(X,X_41),Z) = join(X,join(X_41,Z)),
    inference(subst,[],[associativity_of_join:[bind(Y,$fot(X_41))]]) ).

cnf(refute_0_159,plain,
    ( join(join(X,X_41),Z) != join(X,join(X_41,Z))
    | join(join(X,X_41),Z) != join(X,join(join(X_41,X),Z))
    | join(X,join(X_41,Z)) = join(X,join(join(X_41,X),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,X_41),Z),join(X,join(join(X_41,X),Z))) ),[0],$fot(join(X,join(X_41,Z)))]]) ).

cnf(refute_0_160,plain,
    ( join(join(X,X_41),Z) != join(X,join(join(X_41,X),Z))
    | join(X,join(X_41,Z)) = join(X,join(join(X_41,X),Z)) ),
    inference(resolve,[$cnf( $equal(join(join(X,X_41),Z),join(X,join(X_41,Z))) )],[refute_0_158,refute_0_159]) ).

cnf(refute_0_161,plain,
    join(join(X,Y),join(X_41,Y)) = join(X,join(Y,join(X_41,Y))),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(join(X_41,Y)))]]) ).

cnf(refute_0_162,plain,
    join(Y,join(X_41,Y)) = join(Y,X_41),
    inference(subst,[],[refute_0_84:[bind(Y,$fot(X_41)),bind(X_13,$fot(Y))]]) ).

cnf(refute_0_163,plain,
    ( join(Y,join(X_41,Y)) != join(Y,X_41)
    | join(join(X,Y),join(X_41,Y)) != join(X,join(Y,join(X_41,Y)))
    | join(join(X,Y),join(X_41,Y)) = join(X,join(Y,X_41)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(X,join(Y,join(X_41,Y)))) ),[1,1],$fot(join(Y,X_41))]]) ).

cnf(refute_0_164,plain,
    ( join(join(X,Y),join(X_41,Y)) != join(X,join(Y,join(X_41,Y)))
    | join(join(X,Y),join(X_41,Y)) = join(X,join(Y,X_41)) ),
    inference(resolve,[$cnf( $equal(join(Y,join(X_41,Y)),join(Y,X_41)) )],[refute_0_162,refute_0_163]) ).

cnf(refute_0_165,plain,
    join(join(X,Y),join(X_41,Y)) = join(X,join(Y,X_41)),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(X,join(Y,join(X_41,Y)))) )],[refute_0_161,refute_0_164]) ).

cnf(refute_0_166,plain,
    join(join(X,Y),X_41) = join(X,join(Y,X_41)),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_41))]]) ).

cnf(refute_0_167,plain,
    join(Y,join(join(X,Y),X_41)) = join(Y,join(join(X,Y),X_41)),
    introduced(tautology,[refl,[$fot(join(Y,join(join(X,Y),X_41)))]]) ).

cnf(refute_0_168,plain,
    ( join(Y,join(join(X,Y),X_41)) != join(Y,join(join(X,Y),X_41))
    | join(join(X,Y),X_41) != join(X,join(Y,X_41))
    | join(Y,join(join(X,Y),X_41)) = join(Y,join(X,join(Y,X_41))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(Y,join(join(X,Y),X_41)),join(Y,join(join(X,Y),X_41))) ),[1,1],$fot(join(X,join(Y,X_41)))]]) ).

cnf(refute_0_169,plain,
    ( join(join(X,Y),X_41) != join(X,join(Y,X_41))
    | join(Y,join(join(X,Y),X_41)) = join(Y,join(X,join(Y,X_41))) ),
    inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_41)),join(Y,join(join(X,Y),X_41))) )],[refute_0_167,refute_0_168]) ).

cnf(refute_0_170,plain,
    join(Y,join(join(X,Y),X_41)) = join(Y,join(X,join(Y,X_41))),
    inference(resolve,[$cnf( $equal(join(join(X,Y),X_41),join(X,join(Y,X_41))) )],[refute_0_166,refute_0_169]) ).

cnf(refute_0_171,plain,
    join(X,join(X_24,X_25)) = join(join(X_24,X_25),X),
    inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_24,X_25)))]]) ).

cnf(refute_0_172,plain,
    join(join(X_24,X_25),X) = join(X_24,join(X_25,X)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(X_25)),bind(Z,$fot(X))]]) ).

cnf(refute_0_173,plain,
    ( join(X,join(X_24,X_25)) != join(join(X_24,X_25),X)
    | join(join(X_24,X_25),X) != join(X_24,join(X_25,X))
    | join(X,join(X_24,X_25)) = join(X_24,join(X_25,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_24,X_25)),join(X_24,join(X_25,X))) ),[0],$fot(join(join(X_24,X_25),X))]]) ).

cnf(refute_0_174,plain,
    ( join(X,join(X_24,X_25)) != join(join(X_24,X_25),X)
    | join(X,join(X_24,X_25)) = join(X_24,join(X_25,X)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X),join(X_24,join(X_25,X))) )],[refute_0_172,refute_0_173]) ).

cnf(refute_0_175,plain,
    join(X,join(X_24,X_25)) = join(X_24,join(X_25,X)),
    inference(resolve,[$cnf( $equal(join(X,join(X_24,X_25)),join(join(X_24,X_25),X)) )],[refute_0_171,refute_0_174]) ).

cnf(refute_0_176,plain,
    ( join(X,join(X_24,X_25)) != join(X_24,join(X_25,X))
    | join(X_24,join(X_25,X)) = join(X,join(X_24,X_25)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X,join(X_24,X_25)))),bind(Y0,$fot(join(X_24,join(X_25,X))))]]) ).

cnf(refute_0_177,plain,
    join(X_24,join(X_25,X)) = join(X,join(X_24,X_25)),
    inference(resolve,[$cnf( $equal(join(X,join(X_24,X_25)),join(X_24,join(X_25,X))) )],[refute_0_175,refute_0_176]) ).

cnf(refute_0_178,plain,
    join(join(X,Y),join(X_41,Y)) = join(Y,join(join(X,Y),X_41)),
    inference(subst,[],[refute_0_177:[bind(X,$fot(Y)),bind(X_24,$fot(join(X,Y))),bind(X_25,$fot(X_41))]]) ).

cnf(refute_0_179,plain,
    ( join(Y,join(join(X,Y),X_41)) != join(Y,join(X,join(Y,X_41)))
    | join(join(X,Y),join(X_41,Y)) != join(Y,join(join(X,Y),X_41))
    | join(join(X,Y),join(X_41,Y)) = join(Y,join(X,join(Y,X_41))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X,Y),join(X_41,Y)))),bind(Y0,$fot(join(Y,join(join(X,Y),X_41)))),bind(Z0,$fot(join(Y,join(X,join(Y,X_41)))))]]) ).

cnf(refute_0_180,plain,
    ( join(Y,join(join(X,Y),X_41)) != join(Y,join(X,join(Y,X_41)))
    | join(join(X,Y),join(X_41,Y)) = join(Y,join(X,join(Y,X_41))) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(Y,join(join(X,Y),X_41))) )],[refute_0_178,refute_0_179]) ).

cnf(refute_0_181,plain,
    join(join(X,Y),join(X_41,Y)) = join(Y,join(X,join(Y,X_41))),
    inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_41)),join(Y,join(X,join(Y,X_41)))) )],[refute_0_170,refute_0_180]) ).

cnf(refute_0_182,plain,
    ( join(join(X,Y),join(X_41,Y)) != join(X,join(Y,X_41))
    | join(join(X,Y),join(X_41,Y)) != join(Y,join(X,join(Y,X_41)))
    | join(Y,join(X,join(Y,X_41))) = join(X,join(Y,X_41)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(X,join(Y,X_41))) ),[0],$fot(join(Y,join(X,join(Y,X_41))))]]) ).

cnf(refute_0_183,plain,
    ( join(join(X,Y),join(X_41,Y)) != join(X,join(Y,X_41))
    | join(Y,join(X,join(Y,X_41))) = join(X,join(Y,X_41)) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(Y,join(X,join(Y,X_41)))) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    join(Y,join(X,join(Y,X_41))) = join(X,join(Y,X_41)),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(X_41,Y)),join(X,join(Y,X_41))) )],[refute_0_165,refute_0_183]) ).

cnf(refute_0_185,plain,
    join(X,join(X_41,join(X,Z))) = join(X_41,join(X,Z)),
    inference(subst,[],[refute_0_184:[bind(X,$fot(X_41)),bind(Y,$fot(X)),bind(X_41,$fot(Z))]]) ).

cnf(refute_0_186,plain,
    join(join(X_41,X),Z) = join(X_41,join(X,Z)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_41)),bind(Y,$fot(X))]]) ).

cnf(refute_0_187,plain,
    join(X,join(join(X_41,X),Z)) = join(X,join(join(X_41,X),Z)),
    introduced(tautology,[refl,[$fot(join(X,join(join(X_41,X),Z)))]]) ).

cnf(refute_0_188,plain,
    ( join(X,join(join(X_41,X),Z)) != join(X,join(join(X_41,X),Z))
    | join(join(X_41,X),Z) != join(X_41,join(X,Z))
    | join(X,join(join(X_41,X),Z)) = join(X,join(X_41,join(X,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X,join(join(X_41,X),Z)),join(X,join(join(X_41,X),Z))) ),[1,1],$fot(join(X_41,join(X,Z)))]]) ).

cnf(refute_0_189,plain,
    ( join(join(X_41,X),Z) != join(X_41,join(X,Z))
    | join(X,join(join(X_41,X),Z)) = join(X,join(X_41,join(X,Z))) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_41,X),Z)),join(X,join(join(X_41,X),Z))) )],[refute_0_187,refute_0_188]) ).

cnf(refute_0_190,plain,
    join(X,join(join(X_41,X),Z)) = join(X,join(X_41,join(X,Z))),
    inference(resolve,[$cnf( $equal(join(join(X_41,X),Z),join(X_41,join(X,Z))) )],[refute_0_186,refute_0_189]) ).

cnf(refute_0_191,plain,
    ( join(X,join(X_41,join(X,Z))) != join(X_41,join(X,Z))
    | join(X,join(join(X_41,X),Z)) != join(X,join(X_41,join(X,Z)))
    | join(X,join(join(X_41,X),Z)) = join(X_41,join(X,Z)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(X,join(join(X_41,X),Z)))),bind(Y0,$fot(join(X,join(X_41,join(X,Z))))),bind(Z0,$fot(join(X_41,join(X,Z))))]]) ).

cnf(refute_0_192,plain,
    ( join(X,join(X_41,join(X,Z))) != join(X_41,join(X,Z))
    | join(X,join(join(X_41,X),Z)) = join(X_41,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_41,X),Z)),join(X,join(X_41,join(X,Z)))) )],[refute_0_190,refute_0_191]) ).

cnf(refute_0_193,plain,
    join(X,join(join(X_41,X),Z)) = join(X_41,join(X,Z)),
    inference(resolve,[$cnf( $equal(join(X,join(X_41,join(X,Z))),join(X_41,join(X,Z))) )],[refute_0_185,refute_0_192]) ).

cnf(refute_0_194,plain,
    ( join(X,join(X_41,Z)) != join(X,join(join(X_41,X),Z))
    | join(X,join(join(X_41,X),Z)) != join(X_41,join(X,Z))
    | join(X,join(X_41,Z)) = join(X_41,join(X,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_41,Z)),join(X_41,join(X,Z))) ),[0],$fot(join(X,join(join(X_41,X),Z)))]]) ).

cnf(refute_0_195,plain,
    ( join(X,join(X_41,Z)) != join(X,join(join(X_41,X),Z))
    | join(X,join(X_41,Z)) = join(X_41,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_41,X),Z)),join(X_41,join(X,Z))) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    ( join(join(X,X_41),Z) != join(X,join(join(X_41,X),Z))
    | join(X,join(X_41,Z)) = join(X_41,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(X_41,Z)),join(X,join(join(X_41,X),Z))) )],[refute_0_160,refute_0_195]) ).

cnf(refute_0_197,plain,
    join(X,join(X_41,Z)) = join(X_41,join(X,Z)),
    inference(resolve,[$cnf( $equal(join(join(X,X_41),Z),join(X,join(join(X_41,X),Z))) )],[refute_0_157,refute_0_196]) ).

cnf(refute_0_198,plain,
    ( join(X,join(X_41,Z)) != join(X_41,join(X,Z))
    | join(X_41,join(X,Z)) = join(X,join(X_41,Z)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X,join(X_41,Z)))),bind(Y0,$fot(join(X_41,join(X,Z))))]]) ).

cnf(refute_0_199,plain,
    join(X_41,join(X,Z)) = join(X,join(X_41,Z)),
    inference(resolve,[$cnf( $equal(join(X,join(X_41,Z)),join(X_41,join(X,Z))) )],[refute_0_197,refute_0_198]) ).

cnf(refute_0_200,plain,
    join(zz,join(yy,join(zz,X_24))) = join(yy,join(zz,join(zz,X_24))),
    inference(subst,[],[refute_0_199:[bind(X,$fot(yy)),bind(Z,$fot(join(zz,X_24))),bind(X_41,$fot(zz))]]) ).

cnf(refute_0_201,plain,
    ( join(yy,join(zz,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(zz,join(yy,join(zz,X_24))) != join(yy,join(zz,join(zz,X_24)))
    | join(zz,join(yy,join(zz,X_24))) = join(yy,join(zz,X_24)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(zz,join(yy,join(zz,X_24))))),bind(Y0,$fot(join(yy,join(zz,join(zz,X_24))))),bind(Z0,$fot(join(yy,join(zz,X_24))))]]) ).

cnf(refute_0_202,plain,
    ( join(yy,join(zz,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(zz,join(yy,join(zz,X_24))) = join(yy,join(zz,X_24)) ),
    inference(resolve,[$cnf( $equal(join(zz,join(yy,join(zz,X_24))),join(yy,join(zz,join(zz,X_24)))) )],[refute_0_200,refute_0_201]) ).

cnf(refute_0_203,plain,
    join(zz,join(yy,join(zz,X_24))) = join(yy,join(zz,X_24)),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(zz,X_24))),join(yy,join(zz,X_24))) )],[refute_0_152,refute_0_202]) ).

cnf(refute_0_204,plain,
    join(join(yy,zz),X_24) = join(yy,join(zz,X_24)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(yy)),bind(Y,$fot(zz)),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_205,plain,
    join(zz,join(join(yy,zz),X_24)) = join(zz,join(join(yy,zz),X_24)),
    introduced(tautology,[refl,[$fot(join(zz,join(join(yy,zz),X_24)))]]) ).

cnf(refute_0_206,plain,
    ( join(join(yy,zz),X_24) != join(yy,join(zz,X_24))
    | join(zz,join(join(yy,zz),X_24)) != join(zz,join(join(yy,zz),X_24))
    | join(zz,join(join(yy,zz),X_24)) = join(zz,join(yy,join(zz,X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zz,join(join(yy,zz),X_24)),join(zz,join(join(yy,zz),X_24))) ),[1,1],$fot(join(yy,join(zz,X_24)))]]) ).

cnf(refute_0_207,plain,
    ( join(join(yy,zz),X_24) != join(yy,join(zz,X_24))
    | join(zz,join(join(yy,zz),X_24)) = join(zz,join(yy,join(zz,X_24))) ),
    inference(resolve,[$cnf( $equal(join(zz,join(join(yy,zz),X_24)),join(zz,join(join(yy,zz),X_24))) )],[refute_0_205,refute_0_206]) ).

cnf(refute_0_208,plain,
    join(zz,join(join(yy,zz),X_24)) = join(zz,join(yy,join(zz,X_24))),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),X_24),join(yy,join(zz,X_24))) )],[refute_0_204,refute_0_207]) ).

cnf(refute_0_209,plain,
    ( join(zz,join(join(yy,zz),X_24)) != join(zz,join(yy,join(zz,X_24)))
    | join(zz,join(yy,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(zz,join(join(yy,zz),X_24)) = join(yy,join(zz,X_24)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(zz,join(join(yy,zz),X_24)))),bind(Y0,$fot(join(zz,join(yy,join(zz,X_24))))),bind(Z0,$fot(join(yy,join(zz,X_24))))]]) ).

cnf(refute_0_210,plain,
    ( join(zz,join(yy,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(zz,join(join(yy,zz),X_24)) = join(yy,join(zz,X_24)) ),
    inference(resolve,[$cnf( $equal(join(zz,join(join(yy,zz),X_24)),join(zz,join(yy,join(zz,X_24)))) )],[refute_0_208,refute_0_209]) ).

cnf(refute_0_211,plain,
    join(zz,join(join(yy,zz),X_24)) = join(yy,join(zz,X_24)),
    inference(resolve,[$cnf( $equal(join(zz,join(yy,join(zz,X_24))),join(yy,join(zz,X_24))) )],[refute_0_203,refute_0_210]) ).

cnf(refute_0_212,plain,
    join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(zz,join(join(yy,zz),X_24))),
    introduced(tautology,[refl,[$fot(join(yy,join(zz,join(join(yy,zz),X_24))))]]) ).

cnf(refute_0_213,plain,
    ( join(yy,join(zz,join(join(yy,zz),X_24))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(zz,join(join(yy,zz),X_24)) != join(yy,join(zz,X_24))
    | join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(yy,join(zz,X_24))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,join(join(yy,zz),X_24))),join(yy,join(zz,join(join(yy,zz),X_24)))) ),[1,1],$fot(join(yy,join(zz,X_24)))]]) ).

cnf(refute_0_214,plain,
    ( join(zz,join(join(yy,zz),X_24)) != join(yy,join(zz,X_24))
    | join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(yy,join(zz,X_24))) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(join(yy,zz),X_24))),join(yy,join(zz,join(join(yy,zz),X_24)))) )],[refute_0_212,refute_0_213]) ).

cnf(refute_0_215,plain,
    join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(yy,join(zz,X_24))),
    inference(resolve,[$cnf( $equal(join(zz,join(join(yy,zz),X_24)),join(yy,join(zz,X_24))) )],[refute_0_211,refute_0_214]) ).

cnf(refute_0_216,plain,
    ( join(yy,join(yy,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(yy,join(zz,join(join(yy,zz),X_24))) != join(yy,join(yy,join(zz,X_24)))
    | join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(zz,X_24)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(yy,join(zz,join(join(yy,zz),X_24))))),bind(Y0,$fot(join(yy,join(yy,join(zz,X_24))))),bind(Z0,$fot(join(yy,join(zz,X_24))))]]) ).

cnf(refute_0_217,plain,
    ( join(yy,join(yy,join(zz,X_24))) != join(yy,join(zz,X_24))
    | join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(zz,X_24)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(join(yy,zz),X_24))),join(yy,join(yy,join(zz,X_24)))) )],[refute_0_215,refute_0_216]) ).

cnf(refute_0_218,plain,
    join(yy,join(zz,join(join(yy,zz),X_24))) = join(yy,join(zz,X_24)),
    inference(resolve,[$cnf( $equal(join(yy,join(yy,join(zz,X_24))),join(yy,join(zz,X_24))) )],[refute_0_147,refute_0_217]) ).

cnf(refute_0_219,plain,
    join(yy,join(join(X,Y),join(yy,zz))) = join(join(X,Y),join(yy,zz)),
    inference(subst,[],[refute_0_136:[bind(X_24,$fot(join(X,Y)))]]) ).

cnf(refute_0_220,plain,
    join(join(X,Y),join(yy,zz)) = join(X,join(Y,join(yy,zz))),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(join(yy,zz)))]]) ).

cnf(refute_0_221,plain,
    ( join(join(X,Y),join(yy,zz)) != join(X,join(Y,join(yy,zz)))
    | join(yy,join(join(X,Y),join(yy,zz))) != join(join(X,Y),join(yy,zz))
    | join(yy,join(join(X,Y),join(yy,zz))) = join(X,join(Y,join(yy,zz))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(join(X,Y),join(yy,zz))) ),[1],$fot(join(X,join(Y,join(yy,zz))))]]) ).

cnf(refute_0_222,plain,
    ( join(yy,join(join(X,Y),join(yy,zz))) != join(join(X,Y),join(yy,zz))
    | join(yy,join(join(X,Y),join(yy,zz))) = join(X,join(Y,join(yy,zz))) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(yy,zz)),join(X,join(Y,join(yy,zz)))) )],[refute_0_220,refute_0_221]) ).

cnf(refute_0_223,plain,
    join(yy,join(join(X,Y),join(yy,zz))) = join(X,join(Y,join(yy,zz))),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(join(X,Y),join(yy,zz))) )],[refute_0_219,refute_0_222]) ).

cnf(refute_0_224,plain,
    join(join(yy,Y),join(yy,zz)) = join(yy,join(Y,join(yy,zz))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(yy)),bind(Z,$fot(join(yy,zz)))]]) ).

cnf(refute_0_225,plain,
    join(yy,join(Y,join(yy,zz))) = join(Y,join(yy,zz)),
    inference(subst,[],[refute_0_136:[bind(X_24,$fot(Y))]]) ).

cnf(refute_0_226,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(yy,join(Y,join(yy,zz)))
    | join(yy,join(Y,join(yy,zz))) != join(Y,join(yy,zz))
    | join(join(yy,Y),join(yy,zz)) = join(Y,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(join(yy,Y),join(yy,zz)),join(Y,join(yy,zz))) ),[0],$fot(join(yy,join(Y,join(yy,zz))))]]) ).

cnf(refute_0_227,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(yy,join(Y,join(yy,zz)))
    | join(join(yy,Y),join(yy,zz)) = join(Y,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(Y,join(yy,zz))),join(Y,join(yy,zz))) )],[refute_0_225,refute_0_226]) ).

cnf(refute_0_228,plain,
    join(join(yy,Y),join(yy,zz)) = join(Y,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(yy,join(Y,join(yy,zz)))) )],[refute_0_224,refute_0_227]) ).

cnf(refute_0_229,plain,
    join(yy,join(yy,join(zz,Y))) = join(yy,join(zz,Y)),
    inference(subst,[],[refute_0_146:[bind(X_25,$fot(yy)),bind(X_26,$fot(join(zz,Y)))]]) ).

cnf(refute_0_230,plain,
    join(zz,join(yy,Y)) = join(yy,join(zz,Y)),
    inference(subst,[],[refute_0_129:[bind(X_24,$fot(zz)),bind(X_25,$fot(yy)),bind(X_26,$fot(Y))]]) ).

cnf(refute_0_231,plain,
    join(yy,join(zz,join(yy,Y))) = join(yy,join(zz,join(yy,Y))),
    introduced(tautology,[refl,[$fot(join(yy,join(zz,join(yy,Y))))]]) ).

cnf(refute_0_232,plain,
    ( join(yy,join(zz,join(yy,Y))) != join(yy,join(zz,join(yy,Y)))
    | join(zz,join(yy,Y)) != join(yy,join(zz,Y))
    | join(yy,join(zz,join(yy,Y))) = join(yy,join(yy,join(zz,Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,join(yy,Y))),join(yy,join(zz,join(yy,Y)))) ),[1,1],$fot(join(yy,join(zz,Y)))]]) ).

cnf(refute_0_233,plain,
    ( join(zz,join(yy,Y)) != join(yy,join(zz,Y))
    | join(yy,join(zz,join(yy,Y))) = join(yy,join(yy,join(zz,Y))) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(yy,Y))),join(yy,join(zz,join(yy,Y)))) )],[refute_0_231,refute_0_232]) ).

cnf(refute_0_234,plain,
    join(yy,join(zz,join(yy,Y))) = join(yy,join(yy,join(zz,Y))),
    inference(resolve,[$cnf( $equal(join(zz,join(yy,Y)),join(yy,join(zz,Y))) )],[refute_0_230,refute_0_233]) ).

cnf(refute_0_235,plain,
    ( join(yy,join(yy,join(zz,Y))) != join(yy,join(zz,Y))
    | join(yy,join(zz,join(yy,Y))) != join(yy,join(yy,join(zz,Y)))
    | join(yy,join(zz,join(yy,Y))) = join(yy,join(zz,Y)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(yy,join(zz,join(yy,Y))))),bind(Y0,$fot(join(yy,join(yy,join(zz,Y))))),bind(Z0,$fot(join(yy,join(zz,Y))))]]) ).

cnf(refute_0_236,plain,
    ( join(yy,join(yy,join(zz,Y))) != join(yy,join(zz,Y))
    | join(yy,join(zz,join(yy,Y))) = join(yy,join(zz,Y)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(yy,Y))),join(yy,join(yy,join(zz,Y)))) )],[refute_0_234,refute_0_235]) ).

cnf(refute_0_237,plain,
    join(yy,join(zz,join(yy,Y))) = join(yy,join(zz,Y)),
    inference(resolve,[$cnf( $equal(join(yy,join(yy,join(zz,Y))),join(yy,join(zz,Y))) )],[refute_0_229,refute_0_236]) ).

cnf(refute_0_238,plain,
    join(X_26,X_25) = join(X_25,X_26),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_26)),bind(Y,$fot(X_25))]]) ).

cnf(refute_0_239,plain,
    ( join(X_26,X_25) != join(X_25,X_26)
    | join(X_25,X_26) = join(X_26,X_25) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_26,X_25))),bind(Y0,$fot(join(X_25,X_26)))]]) ).

cnf(refute_0_240,plain,
    join(X_25,X_26) = join(X_26,X_25),
    inference(resolve,[$cnf( $equal(join(X_26,X_25),join(X_25,X_26)) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    ( join(X_25,X_26) != join(X_26,X_25)
    | join(join(X_24,X_25),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_24,X_25),X_26) = join(X_24,join(X_26,X_25)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_25,X_26))) ),[1,1],$fot(join(X_26,X_25))]]) ).

cnf(refute_0_242,plain,
    ( join(join(X_24,X_25),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_24,X_25),X_26) = join(X_24,join(X_26,X_25)) ),
    inference(resolve,[$cnf( $equal(join(X_25,X_26),join(X_26,X_25)) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    join(join(X_24,X_25),X_26) = join(X_24,join(X_26,X_25)),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_25,X_26))) )],[refute_0_117,refute_0_242]) ).

cnf(refute_0_244,plain,
    ( join(join(X_24,X_25),X_26) != join(X_24,join(X_25,X_26))
    | join(join(X_24,X_25),X_26) != join(X_24,join(X_26,X_25))
    | join(X_24,join(X_25,X_26)) = join(X_24,join(X_26,X_25)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_26,X_25))) ),[0],$fot(join(X_24,join(X_25,X_26)))]]) ).

cnf(refute_0_245,plain,
    ( join(join(X_24,X_25),X_26) != join(X_24,join(X_26,X_25))
    | join(X_24,join(X_25,X_26)) = join(X_24,join(X_26,X_25)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_25,X_26))) )],[refute_0_117,refute_0_244]) ).

cnf(refute_0_246,plain,
    join(X_24,join(X_25,X_26)) = join(X_24,join(X_26,X_25)),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X_26),join(X_24,join(X_26,X_25))) )],[refute_0_243,refute_0_245]) ).

cnf(refute_0_247,plain,
    ( join(X_24,join(X_25,X_26)) != join(X_24,join(X_26,X_25))
    | join(X_24,join(X_26,X_25)) = join(X_24,join(X_25,X_26)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_24,join(X_25,X_26)))),bind(Y0,$fot(join(X_24,join(X_26,X_25))))]]) ).

cnf(refute_0_248,plain,
    join(X_24,join(X_26,X_25)) = join(X_24,join(X_25,X_26)),
    inference(resolve,[$cnf( $equal(join(X_24,join(X_25,X_26)),join(X_24,join(X_26,X_25))) )],[refute_0_246,refute_0_247]) ).

cnf(refute_0_249,plain,
    join(yy,join(join(yy,Y),zz)) = join(yy,join(zz,join(yy,Y))),
    inference(subst,[],[refute_0_248:[bind(X_24,$fot(yy)),bind(X_25,$fot(zz)),bind(X_26,$fot(join(yy,Y)))]]) ).

cnf(refute_0_250,plain,
    join(join(yy,Y),join(yy,zz)) = join(yy,join(join(yy,Y),zz)),
    inference(subst,[],[refute_0_129:[bind(X_24,$fot(join(yy,Y))),bind(X_25,$fot(yy)),bind(X_26,$fot(zz))]]) ).

cnf(refute_0_251,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(yy,join(join(yy,Y),zz))
    | join(yy,join(join(yy,Y),zz)) != join(yy,join(zz,join(yy,Y)))
    | join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,join(yy,Y))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(yy,Y),join(yy,zz)))),bind(Y0,$fot(join(yy,join(join(yy,Y),zz)))),bind(Z0,$fot(join(yy,join(zz,join(yy,Y)))))]]) ).

cnf(refute_0_252,plain,
    ( join(yy,join(join(yy,Y),zz)) != join(yy,join(zz,join(yy,Y)))
    | join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,join(yy,Y))) ),
    inference(resolve,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(yy,join(join(yy,Y),zz))) )],[refute_0_250,refute_0_251]) ).

cnf(refute_0_253,plain,
    join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,join(yy,Y))),
    inference(resolve,[$cnf( $equal(join(yy,join(join(yy,Y),zz)),join(yy,join(zz,join(yy,Y)))) )],[refute_0_249,refute_0_252]) ).

cnf(refute_0_254,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(yy,join(zz,join(yy,Y)))
    | join(yy,join(zz,join(yy,Y))) != join(yy,join(zz,Y))
    | join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,Y)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(yy,Y),join(yy,zz)))),bind(Y0,$fot(join(yy,join(zz,join(yy,Y))))),bind(Z0,$fot(join(yy,join(zz,Y))))]]) ).

cnf(refute_0_255,plain,
    ( join(yy,join(zz,join(yy,Y))) != join(yy,join(zz,Y))
    | join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,Y)) ),
    inference(resolve,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(yy,join(zz,join(yy,Y)))) )],[refute_0_253,refute_0_254]) ).

cnf(refute_0_256,plain,
    join(join(yy,Y),join(yy,zz)) = join(yy,join(zz,Y)),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(yy,Y))),join(yy,join(zz,Y))) )],[refute_0_237,refute_0_255]) ).

cnf(refute_0_257,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(Y,join(yy,zz))
    | join(join(yy,Y),join(yy,zz)) != join(yy,join(zz,Y))
    | join(yy,join(zz,Y)) = join(Y,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(Y,join(yy,zz))) ),[0],$fot(join(yy,join(zz,Y)))]]) ).

cnf(refute_0_258,plain,
    ( join(join(yy,Y),join(yy,zz)) != join(Y,join(yy,zz))
    | join(yy,join(zz,Y)) = join(Y,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(yy,join(zz,Y))) )],[refute_0_256,refute_0_257]) ).

cnf(refute_0_259,plain,
    join(yy,join(zz,Y)) = join(Y,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(join(yy,Y),join(yy,zz)),join(Y,join(yy,zz))) )],[refute_0_228,refute_0_258]) ).

cnf(refute_0_260,plain,
    ( join(yy,join(zz,Y)) != join(Y,join(yy,zz))
    | join(Y,join(yy,zz)) = join(yy,join(zz,Y)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(yy,join(zz,Y)))),bind(Y0,$fot(join(Y,join(yy,zz))))]]) ).

cnf(refute_0_261,plain,
    join(Y,join(yy,zz)) = join(yy,join(zz,Y)),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,Y)),join(Y,join(yy,zz))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    join(join(X,Y),join(yy,zz)) = join(yy,join(zz,join(X,Y))),
    inference(subst,[],[refute_0_261:[bind(Y,$fot(join(X,Y)))]]) ).

cnf(refute_0_263,plain,
    ( join(join(X,Y),join(yy,zz)) != join(yy,join(zz,join(X,Y)))
    | join(yy,join(join(X,Y),join(yy,zz))) != join(join(X,Y),join(yy,zz))
    | join(yy,join(join(X,Y),join(yy,zz))) = join(yy,join(zz,join(X,Y))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(yy,join(join(X,Y),join(yy,zz))))),bind(Y0,$fot(join(join(X,Y),join(yy,zz)))),bind(Z0,$fot(join(yy,join(zz,join(X,Y)))))]]) ).

cnf(refute_0_264,plain,
    ( join(join(X,Y),join(yy,zz)) != join(yy,join(zz,join(X,Y)))
    | join(yy,join(join(X,Y),join(yy,zz))) = join(yy,join(zz,join(X,Y))) ),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(join(X,Y),join(yy,zz))) )],[refute_0_219,refute_0_263]) ).

cnf(refute_0_265,plain,
    join(yy,join(join(X,Y),join(yy,zz))) = join(yy,join(zz,join(X,Y))),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(yy,zz)),join(yy,join(zz,join(X,Y)))) )],[refute_0_262,refute_0_264]) ).

cnf(refute_0_266,plain,
    ( join(yy,join(join(X,Y),join(yy,zz))) != join(X,join(Y,join(yy,zz)))
    | join(yy,join(join(X,Y),join(yy,zz))) != join(yy,join(zz,join(X,Y)))
    | join(yy,join(zz,join(X,Y))) = join(X,join(Y,join(yy,zz))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(X,join(Y,join(yy,zz)))) ),[0],$fot(join(yy,join(zz,join(X,Y))))]]) ).

cnf(refute_0_267,plain,
    ( join(yy,join(join(X,Y),join(yy,zz))) != join(X,join(Y,join(yy,zz)))
    | join(yy,join(zz,join(X,Y))) = join(X,join(Y,join(yy,zz))) ),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(yy,join(zz,join(X,Y)))) )],[refute_0_265,refute_0_266]) ).

cnf(refute_0_268,plain,
    join(yy,join(zz,join(X,Y))) = join(X,join(Y,join(yy,zz))),
    inference(resolve,[$cnf( $equal(join(yy,join(join(X,Y),join(yy,zz))),join(X,join(Y,join(yy,zz)))) )],[refute_0_223,refute_0_267]) ).

cnf(refute_0_269,plain,
    ( join(yy,join(zz,join(X,Y))) != join(X,join(Y,join(yy,zz)))
    | join(X,join(Y,join(yy,zz))) = join(yy,join(zz,join(X,Y))) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(yy,join(zz,join(X,Y))))),bind(Y0,$fot(join(X,join(Y,join(yy,zz)))))]]) ).

cnf(refute_0_270,plain,
    join(X,join(Y,join(yy,zz))) = join(yy,join(zz,join(X,Y))),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(X,Y))),join(X,join(Y,join(yy,zz)))) )],[refute_0_268,refute_0_269]) ).

cnf(refute_0_271,plain,
    join(join(yy,zz),join(X_24,join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))),
    inference(subst,[],[refute_0_270:[bind(X,$fot(join(yy,zz))),bind(Y,$fot(X_24))]]) ).

cnf(refute_0_272,plain,
    join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) = join(join(yy,zz),join(X_24,join(yy,zz))),
    inference(subst,[],[refute_0_184:[bind(X,$fot(join(yy,zz))),bind(Y,$fot(X_24)),bind(X_41,$fot(join(yy,zz)))]]) ).

cnf(refute_0_273,plain,
    ( join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) != join(join(yy,zz),join(X_24,join(yy,zz)))
    | join(join(yy,zz),join(X_24,join(yy,zz))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))))),bind(Y0,$fot(join(join(yy,zz),join(X_24,join(yy,zz))))),bind(Z0,$fot(join(yy,join(zz,join(join(yy,zz),X_24)))))]]) ).

cnf(refute_0_274,plain,
    ( join(join(yy,zz),join(X_24,join(yy,zz))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(resolve,[$cnf( $equal(join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))),join(join(yy,zz),join(X_24,join(yy,zz)))) )],[refute_0_272,refute_0_273]) ).

cnf(refute_0_275,plain,
    join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) = join(yy,join(zz,join(join(yy,zz),X_24))),
    inference(resolve,[$cnf( $equal(join(join(yy,zz),join(X_24,join(yy,zz))),join(yy,join(zz,join(join(yy,zz),X_24)))) )],[refute_0_271,refute_0_274]) ).

cnf(refute_0_276,plain,
    join(join(X_39,join(X_40,Y)),meet(Y,join(X_39,join(X_40,Y)))) = join(X_39,join(X_40,Y)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(join(X_39,join(X_40,Y))))]]) ).

cnf(refute_0_277,plain,
    meet(X,join(join(X_24,X_25),X)) = X,
    inference(subst,[],[refute_0_3:[bind(Y,$fot(join(X_24,X_25)))]]) ).

cnf(refute_0_278,plain,
    ( join(join(X_24,X_25),X) != join(X_24,join(X_25,X))
    | meet(X,join(join(X_24,X_25),X)) != X
    | meet(X,join(X_24,join(X_25,X))) = X ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(join(X_24,X_25),X)),X) ),[0,1],$fot(join(X_24,join(X_25,X)))]]) ).

cnf(refute_0_279,plain,
    ( meet(X,join(join(X_24,X_25),X)) != X
    | meet(X,join(X_24,join(X_25,X))) = X ),
    inference(resolve,[$cnf( $equal(join(join(X_24,X_25),X),join(X_24,join(X_25,X))) )],[refute_0_172,refute_0_278]) ).

cnf(refute_0_280,plain,
    meet(X,join(X_24,join(X_25,X))) = X,
    inference(resolve,[$cnf( $equal(meet(X,join(join(X_24,X_25),X)),X) )],[refute_0_277,refute_0_279]) ).

cnf(refute_0_281,plain,
    meet(Y,join(X_39,join(X_40,Y))) = Y,
    inference(subst,[],[refute_0_280:[bind(X,$fot(Y)),bind(X_24,$fot(X_39)),bind(X_25,$fot(X_40))]]) ).

cnf(refute_0_282,plain,
    ( join(join(X_39,join(X_40,Y)),meet(Y,join(X_39,join(X_40,Y)))) != join(X_39,join(X_40,Y))
    | meet(Y,join(X_39,join(X_40,Y))) != Y
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(X_40,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_39,join(X_40,Y)),meet(Y,join(X_39,join(X_40,Y)))),join(X_39,join(X_40,Y))) ),[0,1],$fot(Y)]]) ).

cnf(refute_0_283,plain,
    ( join(join(X_39,join(X_40,Y)),meet(Y,join(X_39,join(X_40,Y)))) != join(X_39,join(X_40,Y))
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(X_40,Y)) ),
    inference(resolve,[$cnf( $equal(meet(Y,join(X_39,join(X_40,Y))),Y) )],[refute_0_281,refute_0_282]) ).

cnf(refute_0_284,plain,
    join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(X_40,Y)),
    inference(resolve,[$cnf( $equal(join(join(X_39,join(X_40,Y)),meet(Y,join(X_39,join(X_40,Y)))),join(X_39,join(X_40,Y))) )],[refute_0_276,refute_0_283]) ).

cnf(refute_0_285,plain,
    join(Y,join(X_40,Y)) = join(Y,X_40),
    inference(subst,[],[refute_0_84:[bind(Y,$fot(X_40)),bind(X_13,$fot(Y))]]) ).

cnf(refute_0_286,plain,
    join(X_39,join(Y,join(X_40,Y))) = join(X_39,join(Y,join(X_40,Y))),
    introduced(tautology,[refl,[$fot(join(X_39,join(Y,join(X_40,Y))))]]) ).

cnf(refute_0_287,plain,
    ( join(Y,join(X_40,Y)) != join(Y,X_40)
    | join(X_39,join(Y,join(X_40,Y))) != join(X_39,join(Y,join(X_40,Y)))
    | join(X_39,join(Y,join(X_40,Y))) = join(X_39,join(Y,X_40)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_39,join(Y,join(X_40,Y))),join(X_39,join(Y,join(X_40,Y)))) ),[1,1],$fot(join(Y,X_40))]]) ).

cnf(refute_0_288,plain,
    ( join(Y,join(X_40,Y)) != join(Y,X_40)
    | join(X_39,join(Y,join(X_40,Y))) = join(X_39,join(Y,X_40)) ),
    inference(resolve,[$cnf( $equal(join(X_39,join(Y,join(X_40,Y))),join(X_39,join(Y,join(X_40,Y)))) )],[refute_0_286,refute_0_287]) ).

cnf(refute_0_289,plain,
    join(X_39,join(Y,join(X_40,Y))) = join(X_39,join(Y,X_40)),
    inference(resolve,[$cnf( $equal(join(Y,join(X_40,Y)),join(Y,X_40)) )],[refute_0_285,refute_0_288]) ).

cnf(refute_0_290,plain,
    join(X_39,join(join(X_40,Y),Y)) = join(X_39,join(Y,join(X_40,Y))),
    inference(subst,[],[refute_0_248:[bind(X_24,$fot(X_39)),bind(X_25,$fot(Y)),bind(X_26,$fot(join(X_40,Y)))]]) ).

cnf(refute_0_291,plain,
    join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(join(X_40,Y),Y)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_39)),bind(Y,$fot(join(X_40,Y))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_292,plain,
    ( join(X_39,join(join(X_40,Y),Y)) != join(X_39,join(Y,join(X_40,Y)))
    | join(join(X_39,join(X_40,Y)),Y) != join(X_39,join(join(X_40,Y),Y))
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,join(X_40,Y))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_39,join(X_40,Y)),Y))),bind(Y0,$fot(join(X_39,join(join(X_40,Y),Y)))),bind(Z0,$fot(join(X_39,join(Y,join(X_40,Y)))))]]) ).

cnf(refute_0_293,plain,
    ( join(X_39,join(join(X_40,Y),Y)) != join(X_39,join(Y,join(X_40,Y)))
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,join(X_40,Y))) ),
    inference(resolve,[$cnf( $equal(join(join(X_39,join(X_40,Y)),Y),join(X_39,join(join(X_40,Y),Y))) )],[refute_0_291,refute_0_292]) ).

cnf(refute_0_294,plain,
    join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,join(X_40,Y))),
    inference(resolve,[$cnf( $equal(join(X_39,join(join(X_40,Y),Y)),join(X_39,join(Y,join(X_40,Y)))) )],[refute_0_290,refute_0_293]) ).

cnf(refute_0_295,plain,
    ( join(X_39,join(Y,join(X_40,Y))) != join(X_39,join(Y,X_40))
    | join(join(X_39,join(X_40,Y)),Y) != join(X_39,join(Y,join(X_40,Y)))
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,X_40)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_39,join(X_40,Y)),Y))),bind(Y0,$fot(join(X_39,join(Y,join(X_40,Y))))),bind(Z0,$fot(join(X_39,join(Y,X_40))))]]) ).

cnf(refute_0_296,plain,
    ( join(X_39,join(Y,join(X_40,Y))) != join(X_39,join(Y,X_40))
    | join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,X_40)) ),
    inference(resolve,[$cnf( $equal(join(join(X_39,join(X_40,Y)),Y),join(X_39,join(Y,join(X_40,Y)))) )],[refute_0_294,refute_0_295]) ).

cnf(refute_0_297,plain,
    join(join(X_39,join(X_40,Y)),Y) = join(X_39,join(Y,X_40)),
    inference(resolve,[$cnf( $equal(join(X_39,join(Y,join(X_40,Y))),join(X_39,join(Y,X_40))) )],[refute_0_289,refute_0_296]) ).

cnf(refute_0_298,plain,
    ( join(join(X_39,join(X_40,Y)),Y) != join(X_39,join(Y,X_40))
    | join(join(X_39,join(X_40,Y)),Y) != join(X_39,join(X_40,Y))
    | join(X_39,join(Y,X_40)) = join(X_39,join(X_40,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_39,join(X_40,Y)),Y),join(X_39,join(X_40,Y))) ),[0],$fot(join(X_39,join(Y,X_40)))]]) ).

cnf(refute_0_299,plain,
    ( join(join(X_39,join(X_40,Y)),Y) != join(X_39,join(X_40,Y))
    | join(X_39,join(Y,X_40)) = join(X_39,join(X_40,Y)) ),
    inference(resolve,[$cnf( $equal(join(join(X_39,join(X_40,Y)),Y),join(X_39,join(Y,X_40))) )],[refute_0_297,refute_0_298]) ).

cnf(refute_0_300,plain,
    join(X_39,join(Y,X_40)) = join(X_39,join(X_40,Y)),
    inference(resolve,[$cnf( $equal(join(join(X_39,join(X_40,Y)),Y),join(X_39,join(X_40,Y))) )],[refute_0_284,refute_0_299]) ).

cnf(refute_0_301,plain,
    ( join(X_39,join(Y,X_40)) != join(X_39,join(X_40,Y))
    | join(X_39,join(X_40,Y)) = join(X_39,join(Y,X_40)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(X_39,join(Y,X_40)))),bind(Y0,$fot(join(X_39,join(X_40,Y))))]]) ).

cnf(refute_0_302,plain,
    join(X_39,join(X_40,Y)) = join(X_39,join(Y,X_40)),
    inference(resolve,[$cnf( $equal(join(X_39,join(Y,X_40)),join(X_39,join(X_40,Y))) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) = join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))),
    inference(subst,[],[refute_0_302:[bind(Y,$fot(join(yy,zz))),bind(X_39,$fot(X_24)),bind(X_40,$fot(join(X_24,join(yy,zz))))]]) ).

cnf(refute_0_304,plain,
    ( join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) != join(X_24,join(join(yy,zz),join(X_24,join(yy,zz))))
    | join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))))),bind(Y0,$fot(join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))))),bind(Z0,$fot(join(yy,join(zz,join(join(yy,zz),X_24)))))]]) ).

cnf(refute_0_305,plain,
    ( join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(resolve,[$cnf( $equal(join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))),join(X_24,join(join(yy,zz),join(X_24,join(yy,zz))))) )],[refute_0_303,refute_0_304]) ).

cnf(refute_0_306,plain,
    join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))),
    inference(resolve,[$cnf( $equal(join(X_24,join(join(yy,zz),join(X_24,join(yy,zz)))),join(yy,join(zz,join(join(yy,zz),X_24)))) )],[refute_0_275,refute_0_305]) ).

cnf(refute_0_307,plain,
    join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))),
    inference(subst,[],[refute_0_199:[bind(X,$fot(X_24)),bind(Z,$fot(join(yy,zz))),bind(X_41,$fot(join(X_24,join(yy,zz))))]]) ).

cnf(refute_0_308,plain,
    ( join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz)))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))))),bind(Y0,$fot(join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))))),bind(Z0,$fot(join(yy,join(zz,join(join(yy,zz),X_24)))))]]) ).

cnf(refute_0_309,plain,
    ( join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))),join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz)))) )],[refute_0_307,refute_0_308]) ).

cnf(refute_0_310,plain,
    join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,join(join(yy,zz),X_24))),
    inference(resolve,[$cnf( $equal(join(X_24,join(join(X_24,join(yy,zz)),join(yy,zz))),join(yy,join(zz,join(join(yy,zz),X_24)))) )],[refute_0_306,refute_0_309]) ).

cnf(refute_0_311,plain,
    ( join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(yy,join(zz,join(join(yy,zz),X_24)))
    | join(yy,join(zz,join(join(yy,zz),X_24))) != join(yy,join(zz,X_24))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,X_24)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))))),bind(Y0,$fot(join(yy,join(zz,join(join(yy,zz),X_24))))),bind(Z0,$fot(join(yy,join(zz,X_24))))]]) ).

cnf(refute_0_312,plain,
    ( join(yy,join(zz,join(join(yy,zz),X_24))) != join(yy,join(zz,X_24))
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,X_24)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))),join(yy,join(zz,join(join(yy,zz),X_24)))) )],[refute_0_310,refute_0_311]) ).

cnf(refute_0_313,plain,
    join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) = join(yy,join(zz,X_24)),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,join(join(yy,zz),X_24))),join(yy,join(zz,X_24))) )],[refute_0_218,refute_0_312]) ).

cnf(refute_0_314,plain,
    ( join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(join(X_24,join(yy,zz)),yy)
    | join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(yy,join(zz,X_24))
    | join(yy,join(zz,X_24)) = join(join(X_24,join(yy,zz)),yy) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))),join(join(X_24,join(yy,zz)),yy)) ),[0],$fot(join(yy,join(zz,X_24)))]]) ).

cnf(refute_0_315,plain,
    ( join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(join(X_24,join(yy,zz)),yy)
    | join(yy,join(zz,X_24)) = join(join(X_24,join(yy,zz)),yy) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))),join(yy,join(zz,X_24))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    join(X_24,join(yy,join(yy,zz))) = join(X_24,join(yy,join(yy,zz))),
    introduced(tautology,[refl,[$fot(join(X_24,join(yy,join(yy,zz))))]]) ).

cnf(refute_0_317,plain,
    ( join(X_24,join(yy,join(yy,zz))) != join(X_24,join(yy,join(yy,zz)))
    | join(yy,join(yy,zz)) != join(yy,zz)
    | join(X_24,join(yy,join(yy,zz))) = join(X_24,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_24,join(yy,join(yy,zz))),join(X_24,join(yy,join(yy,zz)))) ),[1,1],$fot(join(yy,zz))]]) ).

cnf(refute_0_318,plain,
    ( join(yy,join(yy,zz)) != join(yy,zz)
    | join(X_24,join(yy,join(yy,zz))) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(X_24,join(yy,join(yy,zz))),join(X_24,join(yy,join(yy,zz)))) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    join(X_24,join(yy,join(yy,zz))) = join(X_24,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(yy,join(yy,zz)),join(yy,zz)) )],[refute_0_108,refute_0_318]) ).

cnf(refute_0_320,plain,
    join(X_24,join(join(yy,zz),yy)) = join(X_24,join(yy,join(yy,zz))),
    inference(subst,[],[refute_0_302:[bind(Y,$fot(yy)),bind(X_39,$fot(X_24)),bind(X_40,$fot(join(yy,zz)))]]) ).

cnf(refute_0_321,plain,
    join(join(X_24,join(yy,zz)),yy) = join(X_24,join(join(yy,zz),yy)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_24)),bind(Y,$fot(join(yy,zz))),bind(Z,$fot(yy))]]) ).

cnf(refute_0_322,plain,
    ( join(X_24,join(join(yy,zz),yy)) != join(X_24,join(yy,join(yy,zz)))
    | join(join(X_24,join(yy,zz)),yy) != join(X_24,join(join(yy,zz),yy))
    | join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,join(yy,zz))) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_24,join(yy,zz)),yy))),bind(Y0,$fot(join(X_24,join(join(yy,zz),yy)))),bind(Z0,$fot(join(X_24,join(yy,join(yy,zz)))))]]) ).

cnf(refute_0_323,plain,
    ( join(X_24,join(join(yy,zz),yy)) != join(X_24,join(yy,join(yy,zz)))
    | join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,join(yy,zz))) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),yy),join(X_24,join(join(yy,zz),yy))) )],[refute_0_321,refute_0_322]) ).

cnf(refute_0_324,plain,
    join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,join(yy,zz))),
    inference(resolve,[$cnf( $equal(join(X_24,join(join(yy,zz),yy)),join(X_24,join(yy,join(yy,zz)))) )],[refute_0_320,refute_0_323]) ).

cnf(refute_0_325,plain,
    ( join(X_24,join(yy,join(yy,zz))) != join(X_24,join(yy,zz))
    | join(join(X_24,join(yy,zz)),yy) != join(X_24,join(yy,join(yy,zz)))
    | join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,zz)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(join(X_24,join(yy,zz)),yy))),bind(Y0,$fot(join(X_24,join(yy,join(yy,zz))))),bind(Z0,$fot(join(X_24,join(yy,zz))))]]) ).

cnf(refute_0_326,plain,
    ( join(X_24,join(yy,join(yy,zz))) != join(X_24,join(yy,zz))
    | join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),yy),join(X_24,join(yy,join(yy,zz)))) )],[refute_0_324,refute_0_325]) ).

cnf(refute_0_327,plain,
    join(join(X_24,join(yy,zz)),yy) = join(X_24,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(X_24,join(yy,join(yy,zz))),join(X_24,join(yy,zz))) )],[refute_0_319,refute_0_326]) ).

cnf(refute_0_328,plain,
    ( join(join(X_24,join(yy,zz)),yy) != join(X_24,join(yy,zz))
    | join(yy,join(zz,X_24)) != join(join(X_24,join(yy,zz)),yy)
    | join(yy,join(zz,X_24)) = join(X_24,join(yy,zz)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(yy,join(zz,X_24)),join(join(X_24,join(yy,zz)),yy)) ),[1],$fot(join(X_24,join(yy,zz)))]]) ).

cnf(refute_0_329,plain,
    ( join(yy,join(zz,X_24)) != join(join(X_24,join(yy,zz)),yy)
    | join(yy,join(zz,X_24)) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),yy),join(X_24,join(yy,zz))) )],[refute_0_327,refute_0_328]) ).

cnf(refute_0_330,plain,
    ( join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))) != join(join(X_24,join(yy,zz)),yy)
    | join(yy,join(zz,X_24)) = join(X_24,join(yy,zz)) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,X_24)),join(join(X_24,join(yy,zz)),yy)) )],[refute_0_315,refute_0_329]) ).

cnf(refute_0_331,plain,
    join(yy,join(zz,X_24)) = join(X_24,join(yy,zz)),
    inference(resolve,[$cnf( $equal(join(join(X_24,join(yy,zz)),join(X_24,join(yy,zz))),join(join(X_24,join(yy,zz)),yy)) )],[refute_0_139,refute_0_330]) ).

cnf(refute_0_332,plain,
    join(yy,join(zz,X_43)) = join(X_43,join(yy,zz)),
    inference(subst,[],[refute_0_331:[bind(X_24,$fot(X_43))]]) ).

cnf(refute_0_333,plain,
    ( join(yy,join(zz,X_43)) != join(X_43,join(yy,zz))
    | meet(join(zz,X_43),join(yy,join(zz,X_43))) != join(zz,X_43)
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(zz,X_43) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(zz,X_43),join(yy,join(zz,X_43))),join(zz,X_43)) ),[0,1],$fot(join(X_43,join(yy,zz)))]]) ).

cnf(refute_0_334,plain,
    ( meet(join(zz,X_43),join(yy,join(zz,X_43))) != join(zz,X_43)
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(zz,X_43) ),
    inference(resolve,[$cnf( $equal(join(yy,join(zz,X_43)),join(X_43,join(yy,zz))) )],[refute_0_332,refute_0_333]) ).

cnf(refute_0_335,plain,
    meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(zz,X_43),
    inference(resolve,[$cnf( $equal(meet(join(zz,X_43),join(yy,join(zz,X_43))),join(zz,X_43)) )],[refute_0_75,refute_0_334]) ).

cnf(refute_0_336,plain,
    join(X_43,meet(zz,join(yy,zz))) = join(X_43,meet(zz,join(yy,zz))),
    introduced(tautology,[refl,[$fot(join(X_43,meet(zz,join(yy,zz))))]]) ).

cnf(refute_0_337,plain,
    ( join(X_43,meet(zz,join(yy,zz))) != join(X_43,meet(zz,join(yy,zz)))
    | meet(zz,join(yy,zz)) != zz
    | join(X_43,meet(zz,join(yy,zz))) = join(X_43,zz) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_43,meet(zz,join(yy,zz))),join(X_43,meet(zz,join(yy,zz)))) ),[1,1],$fot(zz)]]) ).

cnf(refute_0_338,plain,
    ( meet(zz,join(yy,zz)) != zz
    | join(X_43,meet(zz,join(yy,zz))) = join(X_43,zz) ),
    inference(resolve,[$cnf( $equal(join(X_43,meet(zz,join(yy,zz))),join(X_43,meet(zz,join(yy,zz)))) )],[refute_0_336,refute_0_337]) ).

cnf(refute_0_339,plain,
    join(X_43,meet(zz,join(yy,zz))) = join(X_43,zz),
    inference(resolve,[$cnf( $equal(meet(zz,join(yy,zz)),zz) )],[refute_0_4,refute_0_338]) ).

cnf(refute_0_340,plain,
    meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(X_43,meet(zz,join(yy,zz))),
    inference(subst,[],[refute_0_55:[bind(X_44,$fot(X_43)),bind(X_45,$fot(zz)),bind(X_46,$fot(join(yy,zz)))]]) ).

cnf(refute_0_341,plain,
    ( join(X_43,meet(zz,join(yy,zz))) != join(X_43,zz)
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) != join(X_43,meet(zz,join(yy,zz)))
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(X_43,zz) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(meet(join(zz,X_43),join(X_43,join(yy,zz))))),bind(Y0,$fot(join(X_43,meet(zz,join(yy,zz))))),bind(Z0,$fot(join(X_43,zz)))]]) ).

cnf(refute_0_342,plain,
    ( join(X_43,meet(zz,join(yy,zz))) != join(X_43,zz)
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(X_43,zz) ),
    inference(resolve,[$cnf( $equal(meet(join(zz,X_43),join(X_43,join(yy,zz))),join(X_43,meet(zz,join(yy,zz)))) )],[refute_0_340,refute_0_341]) ).

cnf(refute_0_343,plain,
    meet(join(zz,X_43),join(X_43,join(yy,zz))) = join(X_43,zz),
    inference(resolve,[$cnf( $equal(join(X_43,meet(zz,join(yy,zz))),join(X_43,zz)) )],[refute_0_339,refute_0_342]) ).

cnf(refute_0_344,plain,
    ( meet(join(zz,X_43),join(X_43,join(yy,zz))) != join(X_43,zz)
    | meet(join(zz,X_43),join(X_43,join(yy,zz))) != join(zz,X_43)
    | join(X_43,zz) = join(zz,X_43) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(zz,X_43),join(X_43,join(yy,zz))),join(zz,X_43)) ),[0],$fot(join(X_43,zz))]]) ).

cnf(refute_0_345,plain,
    ( meet(join(zz,X_43),join(X_43,join(yy,zz))) != join(zz,X_43)
    | join(X_43,zz) = join(zz,X_43) ),
    inference(resolve,[$cnf( $equal(meet(join(zz,X_43),join(X_43,join(yy,zz))),join(X_43,zz)) )],[refute_0_343,refute_0_344]) ).

cnf(refute_0_346,plain,
    join(X_43,zz) = join(zz,X_43),
    inference(resolve,[$cnf( $equal(meet(join(zz,X_43),join(X_43,join(yy,zz))),join(zz,X_43)) )],[refute_0_335,refute_0_345]) ).

cnf(refute_0_347,plain,
    join(meet(yy,X_57),zz) = join(zz,meet(yy,X_57)),
    inference(subst,[],[refute_0_346:[bind(X_43,$fot(meet(yy,X_57)))]]) ).

cnf(refute_0_348,plain,
    ( join(meet(yy,X_57),zz) != join(zz,meet(yy,X_57))
    | meet(yy,join(X_57,zz)) != join(meet(yy,X_57),zz)
    | meet(yy,join(X_57,zz)) = join(zz,meet(yy,X_57)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(yy,join(X_57,zz)),join(meet(yy,X_57),zz)) ),[1],$fot(join(zz,meet(yy,X_57)))]]) ).

cnf(refute_0_349,plain,
    ( meet(yy,join(X_57,zz)) != join(meet(yy,X_57),zz)
    | meet(yy,join(X_57,zz)) = join(zz,meet(yy,X_57)) ),
    inference(resolve,[$cnf( $equal(join(meet(yy,X_57),zz),join(zz,meet(yy,X_57))) )],[refute_0_347,refute_0_348]) ).

cnf(refute_0_350,plain,
    meet(yy,join(X_57,zz)) = join(zz,meet(yy,X_57)),
    inference(resolve,[$cnf( $equal(meet(yy,join(X_57,zz)),join(meet(yy,X_57),zz)) )],[refute_0_74,refute_0_349]) ).

cnf(refute_0_351,plain,
    meet(yy,join(xx,zz)) = join(zz,meet(yy,xx)),
    inference(subst,[],[refute_0_350:[bind(X_57,$fot(xx))]]) ).

cnf(refute_0_352,plain,
    ( join(xx,zz) != join(xx,yy)
    | meet(yy,join(xx,zz)) != join(zz,meet(yy,xx))
    | meet(yy,join(xx,yy)) = join(zz,meet(yy,xx)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(yy,join(xx,zz)),join(zz,meet(yy,xx))) ),[0,1],$fot(join(xx,yy))]]) ).

cnf(refute_0_353,plain,
    ( meet(yy,join(xx,zz)) != join(zz,meet(yy,xx))
    | meet(yy,join(xx,yy)) = join(zz,meet(yy,xx)) ),
    inference(resolve,[$cnf( $equal(join(xx,zz),join(xx,yy)) )],[refute_0_15,refute_0_352]) ).

cnf(refute_0_354,plain,
    meet(yy,join(xx,yy)) = join(zz,meet(yy,xx)),
    inference(resolve,[$cnf( $equal(meet(yy,join(xx,zz)),join(zz,meet(yy,xx))) )],[refute_0_351,refute_0_353]) ).

cnf(refute_0_355,plain,
    meet(yy,join(xx,yy)) = yy,
    inference(subst,[],[refute_0_3:[bind(X,$fot(yy)),bind(Y,$fot(xx))]]) ).

cnf(refute_0_356,plain,
    ( meet(yy,join(xx,yy)) != join(zz,meet(yy,xx))
    | meet(yy,join(xx,yy)) != yy
    | yy = join(zz,meet(yy,xx)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(yy,join(xx,yy)),join(zz,meet(yy,xx))) ),[0],$fot(yy)]]) ).

cnf(refute_0_357,plain,
    ( meet(yy,join(xx,yy)) != join(zz,meet(yy,xx))
    | yy = join(zz,meet(yy,xx)) ),
    inference(resolve,[$cnf( $equal(meet(yy,join(xx,yy)),yy) )],[refute_0_355,refute_0_356]) ).

cnf(refute_0_358,plain,
    join(zz,meet(xx,zz)) = zz,
    inference(subst,[],[refute_0_8:[bind(X,$fot(zz)),bind(Y,$fot(xx))]]) ).

cnf(refute_0_359,plain,
    ( join(zz,meet(xx,zz)) != zz
    | meet(xx,zz) != meet(xx,yy)
    | join(zz,meet(xx,yy)) = zz ),
    introduced(tautology,[equality,[$cnf( $equal(join(zz,meet(xx,zz)),zz) ),[0,1],$fot(meet(xx,yy))]]) ).

cnf(refute_0_360,plain,
    ( join(zz,meet(xx,zz)) != zz
    | join(zz,meet(xx,yy)) = zz ),
    inference(resolve,[$cnf( $equal(meet(xx,zz),meet(xx,yy)) )],[refute_0_37,refute_0_359]) ).

cnf(refute_0_361,plain,
    join(zz,meet(xx,yy)) = zz,
    inference(resolve,[$cnf( $equal(join(zz,meet(xx,zz)),zz) )],[refute_0_358,refute_0_360]) ).

cnf(refute_0_362,plain,
    meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) = meet(X_9,Y),
    inference(subst,[],[refute_0_3:[bind(X,$fot(meet(X_9,Y))),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_363,plain,
    join(X_9,meet(X_9,Y)) = X_9,
    inference(subst,[],[absorption2:[bind(X,$fot(X_9))]]) ).

cnf(refute_0_364,plain,
    ( join(X_9,meet(X_9,Y)) != X_9
    | meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
    | meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) ),[0,1],$fot(X_9)]]) ).

cnf(refute_0_365,plain,
    ( meet(meet(X_9,Y),join(X_9,meet(X_9,Y))) != meet(X_9,Y)
    | meet(meet(X_9,Y),X_9) = meet(X_9,Y) ),
    inference(resolve,[$cnf( $equal(join(X_9,meet(X_9,Y)),X_9) )],[refute_0_363,refute_0_364]) ).

cnf(refute_0_366,plain,
    meet(meet(X_9,Y),X_9) = meet(X_9,Y),
    inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),join(X_9,meet(X_9,Y))),meet(X_9,Y)) )],[refute_0_362,refute_0_365]) ).

cnf(refute_0_367,plain,
    meet(meet(X_9,Y),X_9) = meet(X_9,meet(Y,X_9)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_9)),bind(Z,$fot(X_9))]]) ).

cnf(refute_0_368,plain,
    ( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
    | meet(meet(X_9,Y),X_9) != meet(X_9,meet(Y,X_9))
    | meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) ),[0],$fot(meet(X_9,meet(Y,X_9)))]]) ).

cnf(refute_0_369,plain,
    ( meet(meet(X_9,Y),X_9) != meet(X_9,Y)
    | meet(X_9,meet(Y,X_9)) = meet(X_9,Y) ),
    inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,meet(Y,X_9))) )],[refute_0_367,refute_0_368]) ).

cnf(refute_0_370,plain,
    meet(X_9,meet(Y,X_9)) = meet(X_9,Y),
    inference(resolve,[$cnf( $equal(meet(meet(X_9,Y),X_9),meet(X_9,Y)) )],[refute_0_366,refute_0_369]) ).

cnf(refute_0_371,plain,
    meet(join(X_61,zz),meet(yy,join(X_61,zz))) = meet(join(X_61,zz),yy),
    inference(subst,[],[refute_0_370:[bind(Y,$fot(yy)),bind(X_9,$fot(join(X_61,zz)))]]) ).

cnf(refute_0_372,plain,
    meet(yy,join(X_61,zz)) = join(zz,meet(yy,X_61)),
    inference(subst,[],[refute_0_350:[bind(X_57,$fot(X_61))]]) ).

cnf(refute_0_373,plain,
    ( meet(join(X_61,zz),meet(yy,join(X_61,zz))) != meet(join(X_61,zz),yy)
    | meet(yy,join(X_61,zz)) != join(zz,meet(yy,X_61))
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) = meet(join(X_61,zz),yy) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_61,zz),meet(yy,join(X_61,zz))),meet(join(X_61,zz),yy)) ),[0,1],$fot(join(zz,meet(yy,X_61)))]]) ).

cnf(refute_0_374,plain,
    ( meet(join(X_61,zz),meet(yy,join(X_61,zz))) != meet(join(X_61,zz),yy)
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) = meet(join(X_61,zz),yy) ),
    inference(resolve,[$cnf( $equal(meet(yy,join(X_61,zz)),join(zz,meet(yy,X_61))) )],[refute_0_372,refute_0_373]) ).

cnf(refute_0_375,plain,
    meet(join(X_61,zz),join(zz,meet(yy,X_61))) = meet(join(X_61,zz),yy),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),meet(yy,join(X_61,zz))),meet(join(X_61,zz),yy)) )],[refute_0_371,refute_0_374]) ).

cnf(refute_0_376,plain,
    meet(X_61,meet(yy,X_61)) = meet(X_61,yy),
    inference(subst,[],[refute_0_370:[bind(Y,$fot(yy)),bind(X_9,$fot(X_61))]]) ).

cnf(refute_0_377,plain,
    join(zz,meet(X_61,meet(yy,X_61))) = join(zz,meet(X_61,meet(yy,X_61))),
    introduced(tautology,[refl,[$fot(join(zz,meet(X_61,meet(yy,X_61))))]]) ).

cnf(refute_0_378,plain,
    ( join(zz,meet(X_61,meet(yy,X_61))) != join(zz,meet(X_61,meet(yy,X_61)))
    | meet(X_61,meet(yy,X_61)) != meet(X_61,yy)
    | join(zz,meet(X_61,meet(yy,X_61))) = join(zz,meet(X_61,yy)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(zz,meet(X_61,meet(yy,X_61))),join(zz,meet(X_61,meet(yy,X_61)))) ),[1,1],$fot(meet(X_61,yy))]]) ).

cnf(refute_0_379,plain,
    ( meet(X_61,meet(yy,X_61)) != meet(X_61,yy)
    | join(zz,meet(X_61,meet(yy,X_61))) = join(zz,meet(X_61,yy)) ),
    inference(resolve,[$cnf( $equal(join(zz,meet(X_61,meet(yy,X_61))),join(zz,meet(X_61,meet(yy,X_61)))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    join(zz,meet(X_61,meet(yy,X_61))) = join(zz,meet(X_61,yy)),
    inference(resolve,[$cnf( $equal(meet(X_61,meet(yy,X_61)),meet(X_61,yy)) )],[refute_0_376,refute_0_379]) ).

cnf(refute_0_381,plain,
    meet(join(X_61,zz),join(zz,meet(yy,X_61))) = join(zz,meet(X_61,meet(yy,X_61))),
    inference(subst,[],[refute_0_55:[bind(X_44,$fot(zz)),bind(X_45,$fot(X_61)),bind(X_46,$fot(meet(yy,X_61)))]]) ).

cnf(refute_0_382,plain,
    ( join(zz,meet(X_61,meet(yy,X_61))) != join(zz,meet(X_61,yy))
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) != join(zz,meet(X_61,meet(yy,X_61)))
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) = join(zz,meet(X_61,yy)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(meet(join(X_61,zz),join(zz,meet(yy,X_61))))),bind(Y0,$fot(join(zz,meet(X_61,meet(yy,X_61))))),bind(Z0,$fot(join(zz,meet(X_61,yy))))]]) ).

cnf(refute_0_383,plain,
    ( join(zz,meet(X_61,meet(yy,X_61))) != join(zz,meet(X_61,yy))
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) = join(zz,meet(X_61,yy)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),join(zz,meet(yy,X_61))),join(zz,meet(X_61,meet(yy,X_61)))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    meet(join(X_61,zz),join(zz,meet(yy,X_61))) = join(zz,meet(X_61,yy)),
    inference(resolve,[$cnf( $equal(join(zz,meet(X_61,meet(yy,X_61))),join(zz,meet(X_61,yy))) )],[refute_0_380,refute_0_383]) ).

cnf(refute_0_385,plain,
    ( meet(join(X_61,zz),join(zz,meet(yy,X_61))) != join(zz,meet(X_61,yy))
    | meet(join(X_61,zz),join(zz,meet(yy,X_61))) != meet(join(X_61,zz),yy)
    | join(zz,meet(X_61,yy)) = meet(join(X_61,zz),yy) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_61,zz),join(zz,meet(yy,X_61))),meet(join(X_61,zz),yy)) ),[0],$fot(join(zz,meet(X_61,yy)))]]) ).

cnf(refute_0_386,plain,
    ( meet(join(X_61,zz),join(zz,meet(yy,X_61))) != meet(join(X_61,zz),yy)
    | join(zz,meet(X_61,yy)) = meet(join(X_61,zz),yy) ),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),join(zz,meet(yy,X_61))),join(zz,meet(X_61,yy))) )],[refute_0_384,refute_0_385]) ).

cnf(refute_0_387,plain,
    join(meet(X_14,Y),meet(Y,meet(X_14,Y))) = meet(X_14,Y),
    inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_14,Y)))]]) ).

cnf(refute_0_388,plain,
    meet(Y,meet(X_14,Y)) = meet(Y,X_14),
    inference(subst,[],[refute_0_370:[bind(Y,$fot(X_14)),bind(X_9,$fot(Y))]]) ).

cnf(refute_0_389,plain,
    ( join(meet(X_14,Y),meet(Y,meet(X_14,Y))) != meet(X_14,Y)
    | meet(Y,meet(X_14,Y)) != meet(Y,X_14)
    | join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X_14,Y),meet(Y,meet(X_14,Y))),meet(X_14,Y)) ),[0,1],$fot(meet(Y,X_14))]]) ).

cnf(refute_0_390,plain,
    ( join(meet(X_14,Y),meet(Y,meet(X_14,Y))) != meet(X_14,Y)
    | join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y) ),
    inference(resolve,[$cnf( $equal(meet(Y,meet(X_14,Y)),meet(Y,X_14)) )],[refute_0_388,refute_0_389]) ).

cnf(refute_0_391,plain,
    join(meet(X_14,Y),meet(Y,X_14)) = meet(X_14,Y),
    inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,meet(X_14,Y))),meet(X_14,Y)) )],[refute_0_387,refute_0_390]) ).

cnf(refute_0_392,plain,
    join(X_14,X_14) = X_14,
    inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_393,plain,
    meet(Y,join(X_14,X_14)) = meet(Y,join(X_14,X_14)),
    introduced(tautology,[refl,[$fot(meet(Y,join(X_14,X_14)))]]) ).

cnf(refute_0_394,plain,
    ( join(X_14,X_14) != X_14
    | meet(Y,join(X_14,X_14)) != meet(Y,join(X_14,X_14))
    | meet(Y,join(X_14,X_14)) = meet(Y,X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,join(X_14,X_14))) ),[1,1],$fot(X_14)]]) ).

cnf(refute_0_395,plain,
    ( join(X_14,X_14) != X_14
    | meet(Y,join(X_14,X_14)) = meet(Y,X_14) ),
    inference(resolve,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,join(X_14,X_14))) )],[refute_0_393,refute_0_394]) ).

cnf(refute_0_396,plain,
    meet(Y,join(X_14,X_14)) = meet(Y,X_14),
    inference(resolve,[$cnf( $equal(join(X_14,X_14),X_14) )],[refute_0_392,refute_0_395]) ).

cnf(refute_0_397,plain,
    meet(X_56,join(X_57,X_58)) = join(meet(X_56,X_57),meet(X_56,X_58)),
    inference(subst,[],[dist_meet:[bind(X,$fot(X_56)),bind(Y,$fot(X_57)),bind(Z,$fot(X_58))]]) ).

cnf(refute_0_398,plain,
    meet(X_57,X_56) = meet(X_56,X_57),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_57)),bind(Y,$fot(X_56))]]) ).

cnf(refute_0_399,plain,
    ( meet(X_57,X_56) != meet(X_56,X_57)
    | meet(X_56,X_57) = meet(X_57,X_56) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(X_57,X_56))),bind(Y0,$fot(meet(X_56,X_57)))]]) ).

cnf(refute_0_400,plain,
    meet(X_56,X_57) = meet(X_57,X_56),
    inference(resolve,[$cnf( $equal(meet(X_57,X_56),meet(X_56,X_57)) )],[refute_0_398,refute_0_399]) ).

cnf(refute_0_401,plain,
    ( meet(X_56,X_57) != meet(X_57,X_56)
    | meet(X_56,join(X_57,X_58)) != join(meet(X_56,X_57),meet(X_56,X_58))
    | meet(X_56,join(X_57,X_58)) = join(meet(X_57,X_56),meet(X_56,X_58)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_56,join(X_57,X_58)),join(meet(X_56,X_57),meet(X_56,X_58))) ),[1,0],$fot(meet(X_57,X_56))]]) ).

cnf(refute_0_402,plain,
    ( meet(X_56,join(X_57,X_58)) != join(meet(X_56,X_57),meet(X_56,X_58))
    | meet(X_56,join(X_57,X_58)) = join(meet(X_57,X_56),meet(X_56,X_58)) ),
    inference(resolve,[$cnf( $equal(meet(X_56,X_57),meet(X_57,X_56)) )],[refute_0_400,refute_0_401]) ).

cnf(refute_0_403,plain,
    meet(X_56,join(X_57,X_58)) = join(meet(X_57,X_56),meet(X_56,X_58)),
    inference(resolve,[$cnf( $equal(meet(X_56,join(X_57,X_58)),join(meet(X_56,X_57),meet(X_56,X_58))) )],[refute_0_397,refute_0_402]) ).

cnf(refute_0_404,plain,
    ( meet(X_56,join(X_57,X_58)) != join(meet(X_57,X_56),meet(X_56,X_58))
    | join(meet(X_57,X_56),meet(X_56,X_58)) = meet(X_56,join(X_57,X_58)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(X_56,join(X_57,X_58)))),bind(Y0,$fot(join(meet(X_57,X_56),meet(X_56,X_58))))]]) ).

cnf(refute_0_405,plain,
    join(meet(X_57,X_56),meet(X_56,X_58)) = meet(X_56,join(X_57,X_58)),
    inference(resolve,[$cnf( $equal(meet(X_56,join(X_57,X_58)),join(meet(X_57,X_56),meet(X_56,X_58))) )],[refute_0_403,refute_0_404]) ).

cnf(refute_0_406,plain,
    join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,join(X_14,X_14)),
    inference(subst,[],[refute_0_405:[bind(X_56,$fot(Y)),bind(X_57,$fot(X_14)),bind(X_58,$fot(X_14))]]) ).

cnf(refute_0_407,plain,
    ( join(meet(X_14,Y),meet(Y,X_14)) != meet(Y,join(X_14,X_14))
    | meet(Y,join(X_14,X_14)) != meet(Y,X_14)
    | join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(meet(X_14,Y),meet(Y,X_14)))),bind(Y0,$fot(meet(Y,join(X_14,X_14)))),bind(Z0,$fot(meet(Y,X_14)))]]) ).

cnf(refute_0_408,plain,
    ( meet(Y,join(X_14,X_14)) != meet(Y,X_14)
    | join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14) ),
    inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(Y,join(X_14,X_14))) )],[refute_0_406,refute_0_407]) ).

cnf(refute_0_409,plain,
    join(meet(X_14,Y),meet(Y,X_14)) = meet(Y,X_14),
    inference(resolve,[$cnf( $equal(meet(Y,join(X_14,X_14)),meet(Y,X_14)) )],[refute_0_396,refute_0_408]) ).

cnf(refute_0_410,plain,
    ( join(meet(X_14,Y),meet(Y,X_14)) != meet(Y,X_14)
    | join(meet(X_14,Y),meet(Y,X_14)) != meet(X_14,Y)
    | meet(Y,X_14) = meet(X_14,Y) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(X_14,Y)) ),[0],$fot(meet(Y,X_14))]]) ).

cnf(refute_0_411,plain,
    ( join(meet(X_14,Y),meet(Y,X_14)) != meet(X_14,Y)
    | meet(Y,X_14) = meet(X_14,Y) ),
    inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(Y,X_14)) )],[refute_0_409,refute_0_410]) ).

cnf(refute_0_412,plain,
    meet(Y,X_14) = meet(X_14,Y),
    inference(resolve,[$cnf( $equal(join(meet(X_14,Y),meet(Y,X_14)),meet(X_14,Y)) )],[refute_0_391,refute_0_411]) ).

cnf(refute_0_413,plain,
    ( meet(Y,X_14) != meet(X_14,Y)
    | meet(X_14,Y) = meet(Y,X_14) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(meet(Y,X_14))),bind(Y0,$fot(meet(X_14,Y)))]]) ).

cnf(refute_0_414,plain,
    meet(X_14,Y) = meet(Y,X_14),
    inference(resolve,[$cnf( $equal(meet(Y,X_14),meet(X_14,Y)) )],[refute_0_412,refute_0_413]) ).

cnf(refute_0_415,plain,
    meet(join(X_61,zz),yy) = meet(yy,join(X_61,zz)),
    inference(subst,[],[refute_0_414:[bind(Y,$fot(yy)),bind(X_14,$fot(join(X_61,zz)))]]) ).

cnf(refute_0_416,plain,
    ( meet(join(X_61,zz),yy) != meet(yy,join(X_61,zz))
    | meet(yy,join(X_61,zz)) != join(zz,meet(yy,X_61))
    | meet(join(X_61,zz),yy) = join(zz,meet(yy,X_61)) ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(meet(join(X_61,zz),yy))),bind(Y0,$fot(meet(yy,join(X_61,zz)))),bind(Z0,$fot(join(zz,meet(yy,X_61))))]]) ).

cnf(refute_0_417,plain,
    ( meet(yy,join(X_61,zz)) != join(zz,meet(yy,X_61))
    | meet(join(X_61,zz),yy) = join(zz,meet(yy,X_61)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),yy),meet(yy,join(X_61,zz))) )],[refute_0_415,refute_0_416]) ).

cnf(refute_0_418,plain,
    meet(join(X_61,zz),yy) = join(zz,meet(yy,X_61)),
    inference(resolve,[$cnf( $equal(meet(yy,join(X_61,zz)),join(zz,meet(yy,X_61))) )],[refute_0_372,refute_0_417]) ).

cnf(refute_0_419,plain,
    ( join(zz,meet(X_61,yy)) != meet(join(X_61,zz),yy)
    | meet(join(X_61,zz),yy) != join(zz,meet(yy,X_61))
    | join(zz,meet(X_61,yy)) = join(zz,meet(yy,X_61)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(zz,meet(X_61,yy)),join(zz,meet(yy,X_61))) ),[0],$fot(meet(join(X_61,zz),yy))]]) ).

cnf(refute_0_420,plain,
    ( join(zz,meet(X_61,yy)) != meet(join(X_61,zz),yy)
    | join(zz,meet(X_61,yy)) = join(zz,meet(yy,X_61)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),yy),join(zz,meet(yy,X_61))) )],[refute_0_418,refute_0_419]) ).

cnf(refute_0_421,plain,
    ( meet(join(X_61,zz),join(zz,meet(yy,X_61))) != meet(join(X_61,zz),yy)
    | join(zz,meet(X_61,yy)) = join(zz,meet(yy,X_61)) ),
    inference(resolve,[$cnf( $equal(join(zz,meet(X_61,yy)),meet(join(X_61,zz),yy)) )],[refute_0_386,refute_0_420]) ).

cnf(refute_0_422,plain,
    join(zz,meet(X_61,yy)) = join(zz,meet(yy,X_61)),
    inference(resolve,[$cnf( $equal(meet(join(X_61,zz),join(zz,meet(yy,X_61))),meet(join(X_61,zz),yy)) )],[refute_0_375,refute_0_421]) ).

cnf(refute_0_423,plain,
    ( join(zz,meet(X_61,yy)) != join(zz,meet(yy,X_61))
    | join(zz,meet(yy,X_61)) = join(zz,meet(X_61,yy)) ),
    inference(subst,[],[refute_0_13:[bind(X0,$fot(join(zz,meet(X_61,yy)))),bind(Y0,$fot(join(zz,meet(yy,X_61))))]]) ).

cnf(refute_0_424,plain,
    join(zz,meet(yy,X_61)) = join(zz,meet(X_61,yy)),
    inference(resolve,[$cnf( $equal(join(zz,meet(X_61,yy)),join(zz,meet(yy,X_61))) )],[refute_0_422,refute_0_423]) ).

cnf(refute_0_425,plain,
    join(zz,meet(yy,xx)) = join(zz,meet(xx,yy)),
    inference(subst,[],[refute_0_424:[bind(X_61,$fot(xx))]]) ).

cnf(refute_0_426,plain,
    ( join(zz,meet(xx,yy)) != zz
    | join(zz,meet(yy,xx)) != join(zz,meet(xx,yy))
    | join(zz,meet(yy,xx)) = zz ),
    inference(subst,[],[refute_0_43:[bind(X0,$fot(join(zz,meet(yy,xx)))),bind(Y0,$fot(join(zz,meet(xx,yy)))),bind(Z0,$fot(zz))]]) ).

cnf(refute_0_427,plain,
    ( join(zz,meet(xx,yy)) != zz
    | join(zz,meet(yy,xx)) = zz ),
    inference(resolve,[$cnf( $equal(join(zz,meet(yy,xx)),join(zz,meet(xx,yy))) )],[refute_0_425,refute_0_426]) ).

cnf(refute_0_428,plain,
    join(zz,meet(yy,xx)) = zz,
    inference(resolve,[$cnf( $equal(join(zz,meet(xx,yy)),zz) )],[refute_0_361,refute_0_427]) ).

cnf(refute_0_429,plain,
    ( join(zz,meet(yy,xx)) != zz
    | yy != join(zz,meet(yy,xx))
    | yy = zz ),
    introduced(tautology,[equality,[$cnf( $equal(yy,join(zz,meet(yy,xx))) ),[1],$fot(zz)]]) ).

cnf(refute_0_430,plain,
    ( yy != join(zz,meet(yy,xx))
    | yy = zz ),
    inference(resolve,[$cnf( $equal(join(zz,meet(yy,xx)),zz) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    ( meet(yy,join(xx,yy)) != join(zz,meet(yy,xx))
    | yy = zz ),
    inference(resolve,[$cnf( $equal(yy,join(zz,meet(yy,xx))) )],[refute_0_357,refute_0_430]) ).

cnf(refute_0_432,plain,
    yy = zz,
    inference(resolve,[$cnf( $equal(meet(yy,join(xx,yy)),join(zz,meet(yy,xx))) )],[refute_0_354,refute_0_431]) ).

cnf(refute_0_433,plain,
    $false,
    inference(resolve,[$cnf( $equal(yy,zz) )],[refute_0_432,rhs]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LAT040-1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Wed Jun 29 17:32:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.46/0.63  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.46/0.63  
% 0.46/0.63  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.48/0.68  
%------------------------------------------------------------------------------