%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 05:58:56 EDT 2022

% Result   : Unsatisfiable 4.22s 4.39s
% Output   : CNFRefutation 4.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   54
%            Number of leaves      :  136
% Syntax   : Number of clauses     :  663 ( 340 unt;   0 nHn; 331 RR)
%            Number of literals    : 1127 (1126 equ; 467 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   : 1718 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(idempotence_of_meet,axiom,
    meet(X,X) = X ).

cnf(idempotence_of_join,axiom,
    join(X,X) = 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(quasi_lattice2,axiom,
    meet(join(X,meet(Y,Z)),join(X,Y)) = join(X,meet(Y,Z)) ).

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

cnf(prove_distributivity_law_dual,negated_conjecture,
    join(a,meet(b,c)) != meet(join(a,b),join(a,c)) ).

cnf(refute_0_0,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_1,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_2,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_0,refute_0_1]) ).

cnf(refute_0_3,plain,
    ( meet(X,Y) != meet(Y,X)
    | meet(Y,X) = meet(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,Y))),bind(Y0,$fot(meet(Y,X)))]]) ).

cnf(refute_0_4,plain,
    meet(Y,X) = meet(X,Y),
    inference(resolve,[$cnf( $equal(meet(X,Y),meet(Y,X)) )],[commutativity_of_meet,refute_0_3]) ).

cnf(refute_0_5,plain,
    meet(join(X,meet(Y,Z)),join(X,Y)) = meet(join(X,Y),join(X,meet(Y,Z))),
    inference(subst,[],[refute_0_4:[bind(X,$fot(join(X,Y))),bind(Y,$fot(join(X,meet(Y,Z))))]]) ).

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

cnf(refute_0_7,plain,
    ( meet(join(X,meet(Y,Z)),join(X,Y)) != join(X,meet(Y,Z))
    | meet(join(X,Y),join(X,meet(Y,Z))) = join(X,meet(Y,Z)) ),
    inference(resolve,[$cnf( $equal(meet(join(X,meet(Y,Z)),join(X,Y)),meet(join(X,Y),join(X,meet(Y,Z)))) )],[refute_0_5,refute_0_6]) ).

cnf(refute_0_8,plain,
    meet(join(X,Y),join(X,meet(Y,Z))) = join(X,meet(Y,Z)),
    inference(resolve,[$cnf( $equal(meet(join(X,meet(Y,Z)),join(X,Y)),join(X,meet(Y,Z))) )],[quasi_lattice2,refute_0_7]) ).

cnf(refute_0_9,plain,
    meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,X_27)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(X_27))]]) ).

cnf(refute_0_10,plain,
    meet(X_27,X_26) = meet(X_26,X_27),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_27)),bind(Y,$fot(X_26))]]) ).

cnf(refute_0_11,plain,
    ( meet(X_27,X_26) != meet(X_26,X_27)
    | meet(X_26,X_27) = meet(X_27,X_26) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_27,X_26))),bind(Y0,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_12,plain,
    meet(X_26,X_27) = meet(X_27,X_26),
    inference(resolve,[$cnf( $equal(meet(X_27,X_26),meet(X_26,X_27)) )],[refute_0_10,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( meet(X_26,X_27) != meet(X_27,X_26)
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_27,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) ),[1,1],$fot(meet(X_27,X_26))]]) ).

cnf(refute_0_14,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_27,X_26)) ),
    inference(resolve,[$cnf( $equal(meet(X_26,X_27),meet(X_27,X_26)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_27,X_26)),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_9,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_27,X_26))
    | join(X_25,meet(X_26,X_27)) = join(X_25,meet(X_27,X_26)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_27,X_26))) ),[0],$fot(join(X_25,meet(X_26,X_27)))]]) ).

cnf(refute_0_17,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_27,X_26))
    | join(X_25,meet(X_26,X_27)) = join(X_25,meet(X_27,X_26)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_9,refute_0_16]) ).

cnf(refute_0_18,plain,
    join(X_25,meet(X_26,X_27)) = join(X_25,meet(X_27,X_26)),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_27,X_26))) )],[refute_0_15,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( join(X_25,meet(X_26,X_27)) != join(X_25,meet(X_27,X_26))
    | join(X_25,meet(X_27,X_26)) = join(X_25,meet(X_26,X_27)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_25,meet(X_26,X_27)))),bind(Y0,$fot(join(X_25,meet(X_27,X_26))))]]) ).

cnf(refute_0_20,plain,
    join(X_25,meet(X_27,X_26)) = join(X_25,meet(X_26,X_27)),
    inference(resolve,[$cnf( $equal(join(X_25,meet(X_26,X_27)),join(X_25,meet(X_27,X_26))) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    join(a,meet(join(a,b),c)) = join(a,meet(c,join(a,b))),
    inference(subst,[],[refute_0_20:[bind(X_25,$fot(a)),bind(X_26,$fot(c)),bind(X_27,$fot(join(a,b)))]]) ).

cnf(refute_0_22,plain,
    meet(join(X_25,join(X_25,X_11)),join(X_25,meet(join(X_25,X_11),X_27))) = join(X_25,meet(join(X_25,X_11),X_27)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_25)),bind(Y,$fot(join(X_25,X_11))),bind(Z,$fot(X_27))]]) ).

cnf(refute_0_23,plain,
    join(join(X_10,X_10),X_11) = join(X_10,join(X_10,X_11)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_10)),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_24,plain,
    join(X_10,X_10) = X_10,
    inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_10))]]) ).

cnf(refute_0_25,plain,
    ( join(X_10,X_10) != X_10
    | join(join(X_10,X_10),X_11) != join(X_10,join(X_10,X_11))
    | join(X_10,X_11) = join(X_10,join(X_10,X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_10,X_10),X_11),join(X_10,join(X_10,X_11))) ),[0,0],$fot(X_10)]]) ).

cnf(refute_0_26,plain,
    ( join(join(X_10,X_10),X_11) != join(X_10,join(X_10,X_11))
    | join(X_10,X_11) = join(X_10,join(X_10,X_11)) ),
    inference(resolve,[$cnf( $equal(join(X_10,X_10),X_10) )],[refute_0_24,refute_0_25]) ).

cnf(refute_0_27,plain,
    join(X_10,X_11) = join(X_10,join(X_10,X_11)),
    inference(resolve,[$cnf( $equal(join(join(X_10,X_10),X_11),join(X_10,join(X_10,X_11))) )],[refute_0_23,refute_0_26]) ).

cnf(refute_0_28,plain,
    join(X_25,X_11) = join(X_25,join(X_25,X_11)),
    inference(subst,[],[refute_0_27:[bind(X_10,$fot(X_25))]]) ).

cnf(refute_0_29,plain,
    ( join(X_25,X_11) != join(X_25,join(X_25,X_11))
    | join(X_25,join(X_25,X_11)) = join(X_25,X_11) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_25,X_11))),bind(Y0,$fot(join(X_25,join(X_25,X_11))))]]) ).

cnf(refute_0_30,plain,
    join(X_25,join(X_25,X_11)) = join(X_25,X_11),
    inference(resolve,[$cnf( $equal(join(X_25,X_11),join(X_25,join(X_25,X_11))) )],[refute_0_28,refute_0_29]) ).

cnf(refute_0_31,plain,
    ( join(X_25,join(X_25,X_11)) != join(X_25,X_11)
    | meet(join(X_25,join(X_25,X_11)),join(X_25,meet(join(X_25,X_11),X_27))) != join(X_25,meet(join(X_25,X_11),X_27))
    | meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) = join(X_25,meet(join(X_25,X_11),X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,join(X_25,X_11)),join(X_25,meet(join(X_25,X_11),X_27))),join(X_25,meet(join(X_25,X_11),X_27))) ),[0,0],$fot(join(X_25,X_11))]]) ).

cnf(refute_0_32,plain,
    ( meet(join(X_25,join(X_25,X_11)),join(X_25,meet(join(X_25,X_11),X_27))) != join(X_25,meet(join(X_25,X_11),X_27))
    | meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) = join(X_25,meet(join(X_25,X_11),X_27)) ),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_25,X_11)),join(X_25,X_11)) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) = join(X_25,meet(join(X_25,X_11),X_27)),
    inference(resolve,[$cnf( $equal(meet(join(X_25,join(X_25,X_11)),join(X_25,meet(join(X_25,X_11),X_27))),join(X_25,meet(join(X_25,X_11),X_27))) )],[refute_0_22,refute_0_32]) ).

cnf(refute_0_34,plain,
    meet(X,join(Y,meet(X,X_18))) = join(meet(X,Y),meet(X,meet(X,X_18))),
    inference(subst,[],[distributivity_law:[bind(Z,$fot(meet(X,X_18)))]]) ).

cnf(refute_0_35,plain,
    meet(meet(X_7,X_7),X_8) = meet(X_7,meet(X_7,X_8)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_7)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).

cnf(refute_0_36,plain,
    meet(X_7,X_7) = X_7,
    inference(subst,[],[idempotence_of_meet:[bind(X,$fot(X_7))]]) ).

cnf(refute_0_37,plain,
    ( meet(X_7,X_7) != X_7
    | meet(meet(X_7,X_7),X_8) != meet(X_7,meet(X_7,X_8))
    | meet(X_7,X_8) = meet(X_7,meet(X_7,X_8)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_7,X_7),X_8),meet(X_7,meet(X_7,X_8))) ),[0,0],$fot(X_7)]]) ).

cnf(refute_0_38,plain,
    ( meet(meet(X_7,X_7),X_8) != meet(X_7,meet(X_7,X_8))
    | meet(X_7,X_8) = meet(X_7,meet(X_7,X_8)) ),
    inference(resolve,[$cnf( $equal(meet(X_7,X_7),X_7) )],[refute_0_36,refute_0_37]) ).

cnf(refute_0_39,plain,
    meet(X_7,X_8) = meet(X_7,meet(X_7,X_8)),
    inference(resolve,[$cnf( $equal(meet(meet(X_7,X_7),X_8),meet(X_7,meet(X_7,X_8))) )],[refute_0_35,refute_0_38]) ).

cnf(refute_0_40,plain,
    meet(X,X_18) = meet(X,meet(X,X_18)),
    inference(subst,[],[refute_0_39:[bind(X_7,$fot(X)),bind(X_8,$fot(X_18))]]) ).

cnf(refute_0_41,plain,
    ( meet(X,X_18) != meet(X,meet(X,X_18))
    | meet(X,meet(X,X_18)) = meet(X,X_18) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,X_18))),bind(Y0,$fot(meet(X,meet(X,X_18))))]]) ).

cnf(refute_0_42,plain,
    meet(X,meet(X,X_18)) = meet(X,X_18),
    inference(resolve,[$cnf( $equal(meet(X,X_18),meet(X,meet(X,X_18))) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    ( meet(X,join(Y,meet(X,X_18))) != join(meet(X,Y),meet(X,meet(X,X_18)))
    | meet(X,meet(X,X_18)) != meet(X,X_18)
    | meet(X,join(Y,meet(X,X_18))) = join(meet(X,Y),meet(X,X_18)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,meet(X,X_18))),join(meet(X,Y),meet(X,meet(X,X_18)))) ),[1,1],$fot(meet(X,X_18))]]) ).

cnf(refute_0_44,plain,
    ( meet(X,join(Y,meet(X,X_18))) != join(meet(X,Y),meet(X,meet(X,X_18)))
    | meet(X,join(Y,meet(X,X_18))) = join(meet(X,Y),meet(X,X_18)) ),
    inference(resolve,[$cnf( $equal(meet(X,meet(X,X_18)),meet(X,X_18)) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    meet(X,join(Y,meet(X,X_18))) = join(meet(X,Y),meet(X,X_18)),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,meet(X,X_18))),join(meet(X,Y),meet(X,meet(X,X_18)))) )],[refute_0_34,refute_0_44]) ).

cnf(refute_0_46,plain,
    ( meet(X,join(Y,Z)) != join(meet(X,Y),meet(X,Z))
    | join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,join(Y,Z)))),bind(Y0,$fot(join(meet(X,Y),meet(X,Z))))]]) ).

cnf(refute_0_47,plain,
    join(meet(X,Y),meet(X,Z)) = meet(X,join(Y,Z)),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,Z)),join(meet(X,Y),meet(X,Z))) )],[distributivity_law,refute_0_46]) ).

cnf(refute_0_48,plain,
    join(meet(X,Y),meet(X,X_18)) = meet(X,join(Y,X_18)),
    inference(subst,[],[refute_0_47:[bind(Z,$fot(X_18))]]) ).

cnf(refute_0_49,plain,
    ( join(meet(X,Y),meet(X,X_18)) != meet(X,join(Y,X_18))
    | meet(X,join(Y,meet(X,X_18))) != join(meet(X,Y),meet(X,X_18))
    | meet(X,join(Y,meet(X,X_18))) = meet(X,join(Y,X_18)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,meet(X,X_18))),join(meet(X,Y),meet(X,X_18))) ),[1],$fot(meet(X,join(Y,X_18)))]]) ).

cnf(refute_0_50,plain,
    ( meet(X,join(Y,meet(X,X_18))) != join(meet(X,Y),meet(X,X_18))
    | meet(X,join(Y,meet(X,X_18))) = meet(X,join(Y,X_18)) ),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(X,X_18)),meet(X,join(Y,X_18))) )],[refute_0_48,refute_0_49]) ).

cnf(refute_0_51,plain,
    meet(X,join(Y,meet(X,X_18))) = meet(X,join(Y,X_18)),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,meet(X,X_18))),join(meet(X,Y),meet(X,X_18))) )],[refute_0_45,refute_0_50]) ).

cnf(refute_0_52,plain,
    meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) = meet(join(X_25,X_11),join(X_25,X_27)),
    inference(subst,[],[refute_0_51:[bind(X,$fot(join(X_25,X_11))),bind(Y,$fot(X_25)),bind(X_18,$fot(X_27))]]) ).

cnf(refute_0_53,plain,
    ( meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) != join(X_25,meet(join(X_25,X_11),X_27))
    | meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) != meet(join(X_25,X_11),join(X_25,X_27))
    | meet(join(X_25,X_11),join(X_25,X_27)) = join(X_25,meet(join(X_25,X_11),X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))),join(X_25,meet(join(X_25,X_11),X_27))) ),[0],$fot(meet(join(X_25,X_11),join(X_25,X_27)))]]) ).

cnf(refute_0_54,plain,
    ( meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))) != join(X_25,meet(join(X_25,X_11),X_27))
    | meet(join(X_25,X_11),join(X_25,X_27)) = join(X_25,meet(join(X_25,X_11),X_27)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))),meet(join(X_25,X_11),join(X_25,X_27))) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    meet(join(X_25,X_11),join(X_25,X_27)) = join(X_25,meet(join(X_25,X_11),X_27)),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_11),join(X_25,meet(join(X_25,X_11),X_27))),join(X_25,meet(join(X_25,X_11),X_27))) )],[refute_0_33,refute_0_54]) ).

cnf(refute_0_56,plain,
    meet(join(a,b),join(a,c)) = join(a,meet(join(a,b),c)),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(b)),bind(X_25,$fot(a)),bind(X_27,$fot(c))]]) ).

cnf(refute_0_57,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_58,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_2,refute_0_57]) ).

cnf(refute_0_59,plain,
    ( join(a,meet(join(a,b),c)) != join(a,meet(c,join(a,b)))
    | meet(join(a,b),join(a,c)) != join(a,meet(join(a,b),c))
    | meet(join(a,b),join(a,c)) = join(a,meet(c,join(a,b))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(a,b),join(a,c)))),bind(Y0,$fot(join(a,meet(join(a,b),c)))),bind(Z0,$fot(join(a,meet(c,join(a,b)))))]]) ).

cnf(refute_0_60,plain,
    ( join(a,meet(join(a,b),c)) != join(a,meet(c,join(a,b)))
    | meet(join(a,b),join(a,c)) = join(a,meet(c,join(a,b))) ),
    inference(resolve,[$cnf( $equal(meet(join(a,b),join(a,c)),join(a,meet(join(a,b),c))) )],[refute_0_56,refute_0_59]) ).

cnf(refute_0_61,plain,
    meet(join(a,b),join(a,c)) = join(a,meet(c,join(a,b))),
    inference(resolve,[$cnf( $equal(join(a,meet(join(a,b),c)),join(a,meet(c,join(a,b)))) )],[refute_0_21,refute_0_60]) ).

cnf(refute_0_62,plain,
    ( join(a,meet(b,c)) != join(a,meet(c,join(a,b)))
    | meet(join(a,b),join(a,c)) != join(a,meet(c,join(a,b)))
    | join(a,meet(b,c)) = meet(join(a,b),join(a,c)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(a,meet(b,c)),meet(join(a,b),join(a,c))) ),[1],$fot(join(a,meet(c,join(a,b))))]]) ).

cnf(refute_0_63,plain,
    ( join(a,meet(b,c)) != join(a,meet(c,join(a,b)))
    | join(a,meet(b,c)) = meet(join(a,b),join(a,c)) ),
    inference(resolve,[$cnf( $equal(meet(join(a,b),join(a,c)),join(a,meet(c,join(a,b)))) )],[refute_0_61,refute_0_62]) ).

cnf(refute_0_64,plain,
    join(a,meet(b,c)) != join(a,meet(c,join(a,b))),
    inference(resolve,[$cnf( $equal(join(a,meet(b,c)),meet(join(a,b),join(a,c))) )],[refute_0_63,prove_distributivity_law_dual]) ).

cnf(refute_0_65,plain,
    meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(join(X_97,X_96),X_98)),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_96)),bind(X_25,$fot(X_97)),bind(X_27,$fot(X_98))]]) ).

cnf(refute_0_66,plain,
    meet(join(X_52,X_51),Y) = meet(Y,join(X_52,X_51)),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(join(X_52,X_51)))]]) ).

cnf(refute_0_67,plain,
    join(meet(X_12,X_14),meet(X_12,X_13)) = join(meet(X_12,X_13),meet(X_12,X_14)),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(meet(X_12,X_14))),bind(Y,$fot(meet(X_12,X_13)))]]) ).

cnf(refute_0_68,plain,
    meet(X_12,join(X_13,X_14)) = join(meet(X_12,X_13),meet(X_12,X_14)),
    inference(subst,[],[distributivity_law:[bind(X,$fot(X_12)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_69,plain,
    ( meet(X_12,join(X_13,X_14)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | join(meet(X_12,X_13),meet(X_12,X_14)) = meet(X_12,join(X_13,X_14)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_12,join(X_13,X_14)))),bind(Y0,$fot(join(meet(X_12,X_13),meet(X_12,X_14))))]]) ).

cnf(refute_0_70,plain,
    join(meet(X_12,X_13),meet(X_12,X_14)) = meet(X_12,join(X_13,X_14)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_12,X_13),meet(X_12,X_14))) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    ( join(meet(X_12,X_13),meet(X_12,X_14)) != meet(X_12,join(X_13,X_14))
    | join(meet(X_12,X_14),meet(X_12,X_13)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | join(meet(X_12,X_14),meet(X_12,X_13)) = meet(X_12,join(X_13,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X_12,X_14),meet(X_12,X_13)),join(meet(X_12,X_13),meet(X_12,X_14))) ),[1],$fot(meet(X_12,join(X_13,X_14)))]]) ).

cnf(refute_0_72,plain,
    ( join(meet(X_12,X_14),meet(X_12,X_13)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | join(meet(X_12,X_14),meet(X_12,X_13)) = meet(X_12,join(X_13,X_14)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_12,X_13),meet(X_12,X_14)),meet(X_12,join(X_13,X_14))) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    join(meet(X_12,X_14),meet(X_12,X_13)) = meet(X_12,join(X_13,X_14)),
    inference(resolve,[$cnf( $equal(join(meet(X_12,X_14),meet(X_12,X_13)),join(meet(X_12,X_13),meet(X_12,X_14))) )],[refute_0_67,refute_0_72]) ).

cnf(refute_0_74,plain,
    join(meet(X_12,X_14),meet(X_12,X_13)) = meet(X_12,join(X_14,X_13)),
    inference(subst,[],[refute_0_47:[bind(X,$fot(X_12)),bind(Y,$fot(X_14)),bind(Z,$fot(X_13))]]) ).

cnf(refute_0_75,plain,
    ( join(meet(X_12,X_14),meet(X_12,X_13)) != meet(X_12,join(X_13,X_14))
    | join(meet(X_12,X_14),meet(X_12,X_13)) != meet(X_12,join(X_14,X_13))
    | meet(X_12,join(X_14,X_13)) = meet(X_12,join(X_13,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X_12,X_14),meet(X_12,X_13)),meet(X_12,join(X_13,X_14))) ),[0],$fot(meet(X_12,join(X_14,X_13)))]]) ).

cnf(refute_0_76,plain,
    ( join(meet(X_12,X_14),meet(X_12,X_13)) != meet(X_12,join(X_13,X_14))
    | meet(X_12,join(X_14,X_13)) = meet(X_12,join(X_13,X_14)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_12,X_14),meet(X_12,X_13)),meet(X_12,join(X_14,X_13))) )],[refute_0_74,refute_0_75]) ).

cnf(refute_0_77,plain,
    meet(X_12,join(X_14,X_13)) = meet(X_12,join(X_13,X_14)),
    inference(resolve,[$cnf( $equal(join(meet(X_12,X_14),meet(X_12,X_13)),meet(X_12,join(X_13,X_14))) )],[refute_0_73,refute_0_76]) ).

cnf(refute_0_78,plain,
    meet(Y,join(X_52,X_51)) = meet(Y,join(X_51,X_52)),
    inference(subst,[],[refute_0_77:[bind(X_12,$fot(Y)),bind(X_13,$fot(X_51)),bind(X_14,$fot(X_52))]]) ).

cnf(refute_0_79,plain,
    ( meet(Y,join(X_52,X_51)) != meet(Y,join(X_51,X_52))
    | meet(join(X_52,X_51),Y) != meet(Y,join(X_52,X_51))
    | meet(join(X_52,X_51),Y) = meet(Y,join(X_51,X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_52,X_51),Y),meet(Y,join(X_52,X_51))) ),[1],$fot(meet(Y,join(X_51,X_52)))]]) ).

cnf(refute_0_80,plain,
    ( meet(join(X_52,X_51),Y) != meet(Y,join(X_52,X_51))
    | meet(join(X_52,X_51),Y) = meet(Y,join(X_51,X_52)) ),
    inference(resolve,[$cnf( $equal(meet(Y,join(X_52,X_51)),meet(Y,join(X_51,X_52))) )],[refute_0_78,refute_0_79]) ).

cnf(refute_0_81,plain,
    meet(join(X_52,X_51),Y) = meet(Y,join(X_51,X_52)),
    inference(resolve,[$cnf( $equal(meet(join(X_52,X_51),Y),meet(Y,join(X_52,X_51))) )],[refute_0_66,refute_0_80]) ).

cnf(refute_0_82,plain,
    meet(join(X_97,X_96),X_98) = meet(X_98,join(X_96,X_97)),
    inference(subst,[],[refute_0_81:[bind(Y,$fot(X_98)),bind(X_51,$fot(X_96)),bind(X_52,$fot(X_97))]]) ).

cnf(refute_0_83,plain,
    ( meet(join(X_97,X_96),X_98) != meet(X_98,join(X_96,X_97))
    | meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(join(X_97,X_96),X_98))
    | meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(join(X_97,X_96),X_98))) ),[1,1],$fot(meet(X_98,join(X_96,X_97)))]]) ).

cnf(refute_0_84,plain,
    ( meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(join(X_97,X_96),X_98))
    | meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),X_98),meet(X_98,join(X_96,X_97))) )],[refute_0_82,refute_0_83]) ).

cnf(refute_0_85,plain,
    meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_98,join(X_96,X_97))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_65,refute_0_84]) ).

cnf(refute_0_86,plain,
    meet(meet(Y,X_18),Y) = meet(Y,meet(Y,X_18)),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(meet(Y,X_18)))]]) ).

cnf(refute_0_87,plain,
    meet(Y,X_18) = meet(Y,meet(Y,X_18)),
    inference(subst,[],[refute_0_39:[bind(X_7,$fot(Y)),bind(X_8,$fot(X_18))]]) ).

cnf(refute_0_88,plain,
    ( meet(Y,X_18) != meet(Y,meet(Y,X_18))
    | meet(Y,meet(Y,X_18)) = meet(Y,X_18) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(Y,X_18))),bind(Y0,$fot(meet(Y,meet(Y,X_18))))]]) ).

cnf(refute_0_89,plain,
    meet(Y,meet(Y,X_18)) = meet(Y,X_18),
    inference(resolve,[$cnf( $equal(meet(Y,X_18),meet(Y,meet(Y,X_18))) )],[refute_0_87,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( meet(Y,meet(Y,X_18)) != meet(Y,X_18)
    | meet(meet(Y,X_18),Y) != meet(Y,meet(Y,X_18))
    | meet(meet(Y,X_18),Y) = meet(Y,X_18) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(Y,X_18),Y),meet(Y,meet(Y,X_18))) ),[1],$fot(meet(Y,X_18))]]) ).

cnf(refute_0_91,plain,
    ( meet(meet(Y,X_18),Y) != meet(Y,meet(Y,X_18))
    | meet(meet(Y,X_18),Y) = meet(Y,X_18) ),
    inference(resolve,[$cnf( $equal(meet(Y,meet(Y,X_18)),meet(Y,X_18)) )],[refute_0_89,refute_0_90]) ).

cnf(refute_0_92,plain,
    meet(meet(Y,X_18),Y) = meet(Y,X_18),
    inference(resolve,[$cnf( $equal(meet(meet(Y,X_18),Y),meet(Y,meet(Y,X_18))) )],[refute_0_86,refute_0_91]) ).

cnf(refute_0_93,plain,
    meet(meet(Y,X_18),Y) = meet(Y,meet(X_18,Y)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(Y)),bind(Y,$fot(X_18)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_94,plain,
    ( meet(meet(Y,X_18),Y) != meet(Y,X_18)
    | meet(meet(Y,X_18),Y) != meet(Y,meet(X_18,Y))
    | meet(Y,meet(X_18,Y)) = meet(Y,X_18) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(Y,X_18),Y),meet(Y,X_18)) ),[0],$fot(meet(Y,meet(X_18,Y)))]]) ).

cnf(refute_0_95,plain,
    ( meet(meet(Y,X_18),Y) != meet(Y,X_18)
    | meet(Y,meet(X_18,Y)) = meet(Y,X_18) ),
    inference(resolve,[$cnf( $equal(meet(meet(Y,X_18),Y),meet(Y,meet(X_18,Y))) )],[refute_0_93,refute_0_94]) ).

cnf(refute_0_96,plain,
    meet(Y,meet(X_18,Y)) = meet(Y,X_18),
    inference(resolve,[$cnf( $equal(meet(meet(Y,X_18),Y),meet(Y,X_18)) )],[refute_0_92,refute_0_95]) ).

cnf(refute_0_97,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = meet(join(X_97,X_96),join(X_97,X_98)),
    inference(subst,[],[refute_0_96:[bind(Y,$fot(join(X_97,X_96))),bind(X_18,$fot(join(X_97,X_98)))]]) ).

cnf(refute_0_98,plain,
    ( meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(join(X_97,X_96),X_98))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != meet(join(X_97,X_96),join(X_97,X_98))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),X_98)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),meet(join(X_97,X_96),join(X_97,X_98))) ),[1],$fot(join(X_97,meet(join(X_97,X_96),X_98)))]]) ).

cnf(refute_0_99,plain,
    ( meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != meet(join(X_97,X_96),join(X_97,X_98))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),X_98)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_65,refute_0_98]) ).

cnf(refute_0_100,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),X_98)),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),meet(join(X_97,X_96),join(X_97,X_98))) )],[refute_0_97,refute_0_99]) ).

cnf(refute_0_101,plain,
    ( join(X_10,X_11) != join(X_10,join(X_10,X_11))
    | join(X_10,join(X_10,X_11)) = join(X_10,X_11) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_10,X_11))),bind(Y0,$fot(join(X_10,join(X_10,X_11))))]]) ).

cnf(refute_0_102,plain,
    join(X_10,join(X_10,X_11)) = join(X_10,X_11),
    inference(resolve,[$cnf( $equal(join(X_10,X_11),join(X_10,join(X_10,X_11))) )],[refute_0_27,refute_0_101]) ).

cnf(refute_0_103,plain,
    join(X_97,join(X_97,X_98)) = join(X_97,X_98),
    inference(subst,[],[refute_0_102:[bind(X_10,$fot(X_97)),bind(X_11,$fot(X_98))]]) ).

cnf(refute_0_104,plain,
    meet(X_96,join(X_97,join(X_97,X_98))) = meet(X_96,join(X_97,join(X_97,X_98))),
    introduced(tautology,[refl,[$fot(meet(X_96,join(X_97,join(X_97,X_98))))]]) ).

cnf(refute_0_105,plain,
    ( join(X_97,join(X_97,X_98)) != join(X_97,X_98)
    | meet(X_96,join(X_97,join(X_97,X_98))) != meet(X_96,join(X_97,join(X_97,X_98)))
    | meet(X_96,join(X_97,join(X_97,X_98))) = meet(X_96,join(X_97,X_98)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_96,join(X_97,join(X_97,X_98))),meet(X_96,join(X_97,join(X_97,X_98)))) ),[1,1],$fot(join(X_97,X_98))]]) ).

cnf(refute_0_106,plain,
    ( join(X_97,join(X_97,X_98)) != join(X_97,X_98)
    | meet(X_96,join(X_97,join(X_97,X_98))) = meet(X_96,join(X_97,X_98)) ),
    inference(resolve,[$cnf( $equal(meet(X_96,join(X_97,join(X_97,X_98))),meet(X_96,join(X_97,join(X_97,X_98)))) )],[refute_0_104,refute_0_105]) ).

cnf(refute_0_107,plain,
    meet(X_96,join(X_97,join(X_97,X_98))) = meet(X_96,join(X_97,X_98)),
    inference(resolve,[$cnf( $equal(join(X_97,join(X_97,X_98)),join(X_97,X_98)) )],[refute_0_103,refute_0_106]) ).

cnf(refute_0_108,plain,
    meet(X_13,X_12) = meet(X_12,X_13),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_13)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_109,plain,
    ( meet(X_13,X_12) != meet(X_12,X_13)
    | meet(X_12,X_13) = meet(X_13,X_12) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_13,X_12))),bind(Y0,$fot(meet(X_12,X_13)))]]) ).

cnf(refute_0_110,plain,
    meet(X_12,X_13) = meet(X_13,X_12),
    inference(resolve,[$cnf( $equal(meet(X_13,X_12),meet(X_12,X_13)) )],[refute_0_108,refute_0_109]) ).

cnf(refute_0_111,plain,
    ( meet(X_12,X_13) != meet(X_13,X_12)
    | meet(X_12,join(X_13,X_14)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | meet(X_12,join(X_13,X_14)) = join(meet(X_13,X_12),meet(X_12,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_12,X_13),meet(X_12,X_14))) ),[1,0],$fot(meet(X_13,X_12))]]) ).

cnf(refute_0_112,plain,
    ( meet(X_12,join(X_13,X_14)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | meet(X_12,join(X_13,X_14)) = join(meet(X_13,X_12),meet(X_12,X_14)) ),
    inference(resolve,[$cnf( $equal(meet(X_12,X_13),meet(X_13,X_12)) )],[refute_0_110,refute_0_111]) ).

cnf(refute_0_113,plain,
    meet(X_12,join(X_13,X_14)) = join(meet(X_13,X_12),meet(X_12,X_14)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_12,X_13),meet(X_12,X_14))) )],[refute_0_68,refute_0_112]) ).

cnf(refute_0_114,plain,
    meet(X_12,join(X_13,meet(X_49,X_12))) = join(meet(X_13,X_12),meet(X_12,meet(X_49,X_12))),
    inference(subst,[],[refute_0_113:[bind(X_14,$fot(meet(X_49,X_12)))]]) ).

cnf(refute_0_115,plain,
    meet(X_12,meet(X_49,X_12)) = meet(X_12,X_49),
    inference(subst,[],[refute_0_96:[bind(Y,$fot(X_12)),bind(X_18,$fot(X_49))]]) ).

cnf(refute_0_116,plain,
    ( meet(X_12,join(X_13,meet(X_49,X_12))) != join(meet(X_13,X_12),meet(X_12,meet(X_49,X_12)))
    | meet(X_12,meet(X_49,X_12)) != meet(X_12,X_49)
    | meet(X_12,join(X_13,meet(X_49,X_12))) = join(meet(X_13,X_12),meet(X_12,X_49)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_12,join(X_13,meet(X_49,X_12))),join(meet(X_13,X_12),meet(X_12,meet(X_49,X_12)))) ),[1,1],$fot(meet(X_12,X_49))]]) ).

cnf(refute_0_117,plain,
    ( meet(X_12,join(X_13,meet(X_49,X_12))) != join(meet(X_13,X_12),meet(X_12,meet(X_49,X_12)))
    | meet(X_12,join(X_13,meet(X_49,X_12))) = join(meet(X_13,X_12),meet(X_12,X_49)) ),
    inference(resolve,[$cnf( $equal(meet(X_12,meet(X_49,X_12)),meet(X_12,X_49)) )],[refute_0_115,refute_0_116]) ).

cnf(refute_0_118,plain,
    meet(X_12,join(X_13,meet(X_49,X_12))) = join(meet(X_13,X_12),meet(X_12,X_49)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,meet(X_49,X_12))),join(meet(X_13,X_12),meet(X_12,meet(X_49,X_12)))) )],[refute_0_114,refute_0_117]) ).

cnf(refute_0_119,plain,
    ( meet(X_12,join(X_13,X_14)) != join(meet(X_13,X_12),meet(X_12,X_14))
    | join(meet(X_13,X_12),meet(X_12,X_14)) = meet(X_12,join(X_13,X_14)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_12,join(X_13,X_14)))),bind(Y0,$fot(join(meet(X_13,X_12),meet(X_12,X_14))))]]) ).

cnf(refute_0_120,plain,
    join(meet(X_13,X_12),meet(X_12,X_14)) = meet(X_12,join(X_13,X_14)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_13,X_12),meet(X_12,X_14))) )],[refute_0_113,refute_0_119]) ).

cnf(refute_0_121,plain,
    join(meet(X_13,X_12),meet(X_12,X_49)) = meet(X_12,join(X_13,X_49)),
    inference(subst,[],[refute_0_120:[bind(X_14,$fot(X_49))]]) ).

cnf(refute_0_122,plain,
    ( join(meet(X_13,X_12),meet(X_12,X_49)) != meet(X_12,join(X_13,X_49))
    | meet(X_12,join(X_13,meet(X_49,X_12))) != join(meet(X_13,X_12),meet(X_12,X_49))
    | meet(X_12,join(X_13,meet(X_49,X_12))) = meet(X_12,join(X_13,X_49)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_12,join(X_13,meet(X_49,X_12))),join(meet(X_13,X_12),meet(X_12,X_49))) ),[1],$fot(meet(X_12,join(X_13,X_49)))]]) ).

cnf(refute_0_123,plain,
    ( meet(X_12,join(X_13,meet(X_49,X_12))) != join(meet(X_13,X_12),meet(X_12,X_49))
    | meet(X_12,join(X_13,meet(X_49,X_12))) = meet(X_12,join(X_13,X_49)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_13,X_12),meet(X_12,X_49)),meet(X_12,join(X_13,X_49))) )],[refute_0_121,refute_0_122]) ).

cnf(refute_0_124,plain,
    meet(X_12,join(X_13,meet(X_49,X_12))) = meet(X_12,join(X_13,X_49)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,meet(X_49,X_12))),join(meet(X_13,X_12),meet(X_12,X_49))) )],[refute_0_118,refute_0_123]) ).

cnf(refute_0_125,plain,
    meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))) = meet(X_96,join(X_97,join(X_97,X_98))),
    inference(subst,[],[refute_0_124:[bind(X_12,$fot(X_96)),bind(X_13,$fot(X_97)),bind(X_49,$fot(join(X_97,X_98)))]]) ).

cnf(refute_0_126,plain,
    meet(meet(X_54,X_55),Y) = meet(Y,meet(X_54,X_55)),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(meet(X_54,X_55)))]]) ).

cnf(refute_0_127,plain,
    meet(meet(X_6,X_7),X_8) = meet(X_6,meet(X_7,X_8)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_6)),bind(Y,$fot(X_7)),bind(Z,$fot(X_8))]]) ).

cnf(refute_0_128,plain,
    meet(X_8,X_7) = meet(X_7,X_8),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_8)),bind(Y,$fot(X_7))]]) ).

cnf(refute_0_129,plain,
    ( meet(X_8,X_7) != meet(X_7,X_8)
    | meet(X_7,X_8) = meet(X_8,X_7) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_8,X_7))),bind(Y0,$fot(meet(X_7,X_8)))]]) ).

cnf(refute_0_130,plain,
    meet(X_7,X_8) = meet(X_8,X_7),
    inference(resolve,[$cnf( $equal(meet(X_8,X_7),meet(X_7,X_8)) )],[refute_0_128,refute_0_129]) ).

cnf(refute_0_131,plain,
    ( meet(X_7,X_8) != meet(X_8,X_7)
    | meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_6,X_7),X_8) = meet(X_6,meet(X_8,X_7)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_7,X_8))) ),[1,1],$fot(meet(X_8,X_7))]]) ).

cnf(refute_0_132,plain,
    ( meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_6,X_7),X_8) = meet(X_6,meet(X_8,X_7)) ),
    inference(resolve,[$cnf( $equal(meet(X_7,X_8),meet(X_8,X_7)) )],[refute_0_130,refute_0_131]) ).

cnf(refute_0_133,plain,
    meet(meet(X_6,X_7),X_8) = meet(X_6,meet(X_8,X_7)),
    inference(resolve,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_7,X_8))) )],[refute_0_127,refute_0_132]) ).

cnf(refute_0_134,plain,
    ( meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_8,X_7))
    | meet(X_6,meet(X_7,X_8)) = meet(X_6,meet(X_8,X_7)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_8,X_7))) ),[0],$fot(meet(X_6,meet(X_7,X_8)))]]) ).

cnf(refute_0_135,plain,
    ( meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_8,X_7))
    | meet(X_6,meet(X_7,X_8)) = meet(X_6,meet(X_8,X_7)) ),
    inference(resolve,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_7,X_8))) )],[refute_0_127,refute_0_134]) ).

cnf(refute_0_136,plain,
    meet(X_6,meet(X_7,X_8)) = meet(X_6,meet(X_8,X_7)),
    inference(resolve,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_8,X_7))) )],[refute_0_133,refute_0_135]) ).

cnf(refute_0_137,plain,
    meet(Y,meet(X_54,X_55)) = meet(Y,meet(X_55,X_54)),
    inference(subst,[],[refute_0_136:[bind(X_6,$fot(Y)),bind(X_7,$fot(X_54)),bind(X_8,$fot(X_55))]]) ).

cnf(refute_0_138,plain,
    ( meet(Y,meet(X_54,X_55)) != meet(Y,meet(X_55,X_54))
    | meet(meet(X_54,X_55),Y) != meet(Y,meet(X_54,X_55))
    | meet(meet(X_54,X_55),Y) = meet(Y,meet(X_55,X_54)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_54,X_55),Y),meet(Y,meet(X_54,X_55))) ),[1],$fot(meet(Y,meet(X_55,X_54)))]]) ).

cnf(refute_0_139,plain,
    ( meet(meet(X_54,X_55),Y) != meet(Y,meet(X_54,X_55))
    | meet(meet(X_54,X_55),Y) = meet(Y,meet(X_55,X_54)) ),
    inference(resolve,[$cnf( $equal(meet(Y,meet(X_54,X_55)),meet(Y,meet(X_55,X_54))) )],[refute_0_137,refute_0_138]) ).

cnf(refute_0_140,plain,
    meet(meet(X_54,X_55),Y) = meet(Y,meet(X_55,X_54)),
    inference(resolve,[$cnf( $equal(meet(meet(X_54,X_55),Y),meet(Y,meet(X_54,X_55))) )],[refute_0_126,refute_0_139]) ).

cnf(refute_0_141,plain,
    meet(meet(X_54,X_55),Y) = meet(X_54,meet(X_55,Y)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_54)),bind(Y,$fot(X_55)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_142,plain,
    ( meet(meet(X_54,X_55),Y) != meet(Y,meet(X_55,X_54))
    | meet(meet(X_54,X_55),Y) != meet(X_54,meet(X_55,Y))
    | meet(X_54,meet(X_55,Y)) = meet(Y,meet(X_55,X_54)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_54,X_55),Y),meet(Y,meet(X_55,X_54))) ),[0],$fot(meet(X_54,meet(X_55,Y)))]]) ).

cnf(refute_0_143,plain,
    ( meet(meet(X_54,X_55),Y) != meet(Y,meet(X_55,X_54))
    | meet(X_54,meet(X_55,Y)) = meet(Y,meet(X_55,X_54)) ),
    inference(resolve,[$cnf( $equal(meet(meet(X_54,X_55),Y),meet(X_54,meet(X_55,Y))) )],[refute_0_141,refute_0_142]) ).

cnf(refute_0_144,plain,
    meet(X_54,meet(X_55,Y)) = meet(Y,meet(X_55,X_54)),
    inference(resolve,[$cnf( $equal(meet(meet(X_54,X_55),Y),meet(Y,meet(X_55,X_54))) )],[refute_0_140,refute_0_143]) ).

cnf(refute_0_145,plain,
    meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) = meet(Y,meet(join(X_97,X_96),join(X_97,X_98))),
    inference(subst,[],[refute_0_144:[bind(X_54,$fot(join(X_97,X_98))),bind(X_55,$fot(join(X_97,X_96)))]]) ).

cnf(refute_0_146,plain,
    ( meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(join(X_97,X_96),X_98))
    | meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) != meet(Y,meet(join(X_97,X_96),join(X_97,X_98)))
    | meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) = meet(Y,join(X_97,meet(join(X_97,X_96),X_98))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_98),meet(join(X_97,X_96),Y)),meet(Y,meet(join(X_97,X_96),join(X_97,X_98)))) ),[1,1],$fot(join(X_97,meet(join(X_97,X_96),X_98)))]]) ).

cnf(refute_0_147,plain,
    ( meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) != meet(Y,meet(join(X_97,X_96),join(X_97,X_98)))
    | meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) = meet(Y,join(X_97,meet(join(X_97,X_96),X_98))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_65,refute_0_146]) ).

cnf(refute_0_148,plain,
    meet(join(X_97,X_98),meet(join(X_97,X_96),Y)) = meet(Y,join(X_97,meet(join(X_97,X_96),X_98))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_98),meet(join(X_97,X_96),Y)),meet(Y,meet(join(X_97,X_96),join(X_97,X_98)))) )],[refute_0_145,refute_0_147]) ).

cnf(refute_0_149,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))),
    inference(subst,[],[refute_0_148:[bind(Y,$fot(X_96)),bind(X_96,$fot(X_98)),bind(X_98,$fot(X_96))]]) ).

cnf(refute_0_150,plain,
    ( meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))) != meet(X_96,join(X_97,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) != meet(X_96,join(X_97,meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,join(X_97,X_98))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))),bind(Y0,$fot(meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))))),bind(Z0,$fot(meet(X_96,join(X_97,join(X_97,X_98)))))]]) ).

cnf(refute_0_151,plain,
    ( meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))) != meet(X_96,join(X_97,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,join(X_97,X_98))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)),meet(X_96,join(X_97,meet(join(X_97,X_98),X_96)))) )],[refute_0_149,refute_0_150]) ).

cnf(refute_0_152,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,join(X_97,X_98))),
    inference(resolve,[$cnf( $equal(meet(X_96,join(X_97,meet(join(X_97,X_98),X_96))),meet(X_96,join(X_97,join(X_97,X_98)))) )],[refute_0_125,refute_0_151]) ).

cnf(refute_0_153,plain,
    ( meet(X_96,join(X_97,join(X_97,X_98))) != meet(X_96,join(X_97,X_98))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) != meet(X_96,join(X_97,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,X_98)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))),bind(Y0,$fot(meet(X_96,join(X_97,join(X_97,X_98))))),bind(Z0,$fot(meet(X_96,join(X_97,X_98))))]]) ).

cnf(refute_0_154,plain,
    ( meet(X_96,join(X_97,join(X_97,X_98))) != meet(X_96,join(X_97,X_98))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,X_98)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)),meet(X_96,join(X_97,join(X_97,X_98)))) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) = meet(X_96,join(X_97,X_98)),
    inference(resolve,[$cnf( $equal(meet(X_96,join(X_97,join(X_97,X_98))),meet(X_96,join(X_97,X_98))) )],[refute_0_107,refute_0_154]) ).

cnf(refute_0_156,plain,
    join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) = join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),
    introduced(tautology,[refl,[$fot(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))))]]) ).

cnf(refute_0_157,plain,
    ( join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) != join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) != meet(X_96,join(X_97,X_98))
    | join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))) ),[1,1],$fot(meet(X_96,join(X_97,X_98)))]]) ).

cnf(refute_0_158,plain,
    ( meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)) != meet(X_96,join(X_97,X_98))
    | join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))) )],[refute_0_156,refute_0_157]) ).

cnf(refute_0_159,plain,
    join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) = join(X_97,meet(X_96,join(X_97,X_98))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)),meet(X_96,join(X_97,X_98))) )],[refute_0_155,refute_0_158]) ).

cnf(refute_0_160,plain,
    meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))) = join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_96)),bind(X_25,$fot(X_97)),bind(X_27,$fot(meet(join(X_97,X_98),X_96)))]]) ).

cnf(refute_0_161,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))),
    inference(subst,[],[refute_0_148:[bind(Y,$fot(join(X_97,X_96))),bind(X_96,$fot(X_98)),bind(X_98,$fot(X_96))]]) ).

cnf(refute_0_162,plain,
    ( meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))) != join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))))),bind(Y0,$fot(meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))))),bind(Z0,$fot(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))))]]) ).

cnf(refute_0_163,plain,
    ( meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))) != join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96)))) )],[refute_0_161,refute_0_162]) ).

cnf(refute_0_164,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,meet(join(X_97,X_98),X_96))),join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))) )],[refute_0_160,refute_0_163]) ).

cnf(refute_0_165,plain,
    ( join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))))),bind(Y0,$fot(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))))),bind(Z0,$fot(join(X_97,meet(X_96,join(X_97,X_98)))))]]) ).

cnf(refute_0_166,plain,
    ( join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96)))) )],[refute_0_164,refute_0_165]) ).

cnf(refute_0_167,plain,
    meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) = join(X_97,meet(X_96,join(X_97,X_98))),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),meet(join(X_97,X_98),X_96))),join(X_97,meet(X_96,join(X_97,X_98)))) )],[refute_0_159,refute_0_166]) ).

cnf(refute_0_168,plain,
    ( meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != join(X_97,meet(join(X_97,X_96),X_98))
    | join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(join(X_97,X_96),X_98)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),join(X_97,meet(join(X_97,X_96),X_98))) ),[0],$fot(join(X_97,meet(X_96,join(X_97,X_98))))]]) ).

cnf(refute_0_169,plain,
    ( meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))) != join(X_97,meet(join(X_97,X_96),X_98))
    | join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(join(X_97,X_96),X_98)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),join(X_97,meet(X_96,join(X_97,X_98)))) )],[refute_0_167,refute_0_168]) ).

cnf(refute_0_170,plain,
    join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(join(X_97,X_96),X_98)),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),meet(join(X_97,X_98),join(X_97,X_96))),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_100,refute_0_169]) ).

cnf(refute_0_171,plain,
    ( join(X_97,meet(X_96,join(X_97,X_98))) != join(X_97,meet(join(X_97,X_96),X_98))
    | join(X_97,meet(join(X_97,X_96),X_98)) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_97,meet(X_96,join(X_97,X_98))))),bind(Y0,$fot(join(X_97,meet(join(X_97,X_96),X_98))))]]) ).

cnf(refute_0_172,plain,
    join(X_97,meet(join(X_97,X_96),X_98)) = join(X_97,meet(X_96,join(X_97,X_98))),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_98))),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_170,refute_0_171]) ).

cnf(refute_0_173,plain,
    ( join(X_97,meet(join(X_97,X_96),X_98)) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(join(X_97,X_96),X_98))
    | meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),join(X_97,X_98)))),bind(Y0,$fot(join(X_97,meet(join(X_97,X_96),X_98)))),bind(Z0,$fot(join(X_97,meet(X_96,join(X_97,X_98)))))]]) ).

cnf(refute_0_174,plain,
    ( join(X_97,meet(join(X_97,X_96),X_98)) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_96,join(X_97,X_98))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(join(X_97,X_96),X_98))) )],[refute_0_65,refute_0_173]) ).

cnf(refute_0_175,plain,
    meet(join(X_97,X_96),join(X_97,X_98)) = join(X_97,meet(X_96,join(X_97,X_98))),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),X_98)),join(X_97,meet(X_96,join(X_97,X_98)))) )],[refute_0_172,refute_0_174]) ).

cnf(refute_0_176,plain,
    ( meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(X_96,join(X_97,X_98)))
    | meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(X_98,join(X_96,X_97)))) ),[0],$fot(join(X_97,meet(X_96,join(X_97,X_98))))]]) ).

cnf(refute_0_177,plain,
    ( meet(join(X_97,X_96),join(X_97,X_98)) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(X_96,join(X_97,X_98)))) )],[refute_0_175,refute_0_176]) ).

cnf(refute_0_178,plain,
    join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(X_98,join(X_96,X_97))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,X_98)),join(X_97,meet(X_98,join(X_96,X_97)))) )],[refute_0_85,refute_0_177]) ).

cnf(refute_0_179,plain,
    meet(join(X_97,X_96),join(X_97,join(X_59,meet(X_97,X_59)))) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_96)),bind(X_25,$fot(X_97)),bind(X_27,$fot(join(X_59,meet(X_97,X_59))))]]) ).

cnf(refute_0_180,plain,
    meet(X_14,join(X_13,X_14)) = join(meet(X_14,X_13),meet(X_14,X_14)),
    inference(subst,[],[distributivity_law:[bind(X,$fot(X_14)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_181,plain,
    meet(X_14,X_14) = X_14,
    inference(subst,[],[idempotence_of_meet:[bind(X,$fot(X_14))]]) ).

cnf(refute_0_182,plain,
    ( meet(X_14,X_14) != X_14
    | meet(X_14,join(X_13,X_14)) != join(meet(X_14,X_13),meet(X_14,X_14))
    | meet(X_14,join(X_13,X_14)) = join(meet(X_14,X_13),X_14) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_14,join(X_13,X_14)),join(meet(X_14,X_13),meet(X_14,X_14))) ),[1,1],$fot(X_14)]]) ).

cnf(refute_0_183,plain,
    ( meet(X_14,join(X_13,X_14)) != join(meet(X_14,X_13),meet(X_14,X_14))
    | meet(X_14,join(X_13,X_14)) = join(meet(X_14,X_13),X_14) ),
    inference(resolve,[$cnf( $equal(meet(X_14,X_14),X_14) )],[refute_0_181,refute_0_182]) ).

cnf(refute_0_184,plain,
    meet(X_14,join(X_13,X_14)) = join(meet(X_14,X_13),X_14),
    inference(resolve,[$cnf( $equal(meet(X_14,join(X_13,X_14)),join(meet(X_14,X_13),meet(X_14,X_14))) )],[refute_0_180,refute_0_183]) ).

cnf(refute_0_185,plain,
    ( join(X,Y) != join(Y,X)
    | join(Y,X) = join(X,Y) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).

cnf(refute_0_186,plain,
    join(Y,X) = join(X,Y),
    inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_185]) ).

cnf(refute_0_187,plain,
    join(meet(X_14,X_13),X_14) = join(X_14,meet(X_14,X_13)),
    inference(subst,[],[refute_0_186:[bind(X,$fot(X_14)),bind(Y,$fot(meet(X_14,X_13)))]]) ).

cnf(refute_0_188,plain,
    ( join(meet(X_14,X_13),X_14) != join(X_14,meet(X_14,X_13))
    | meet(X_14,join(X_13,X_14)) != join(meet(X_14,X_13),X_14)
    | meet(X_14,join(X_13,X_14)) = join(X_14,meet(X_14,X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_14,join(X_13,X_14)),join(meet(X_14,X_13),X_14)) ),[1],$fot(join(X_14,meet(X_14,X_13)))]]) ).

cnf(refute_0_189,plain,
    ( meet(X_14,join(X_13,X_14)) != join(meet(X_14,X_13),X_14)
    | meet(X_14,join(X_13,X_14)) = join(X_14,meet(X_14,X_13)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_14,X_13),X_14),join(X_14,meet(X_14,X_13))) )],[refute_0_187,refute_0_188]) ).

cnf(refute_0_190,plain,
    meet(X_14,join(X_13,X_14)) = join(X_14,meet(X_14,X_13)),
    inference(resolve,[$cnf( $equal(meet(X_14,join(X_13,X_14)),join(meet(X_14,X_13),X_14)) )],[refute_0_184,refute_0_189]) ).

cnf(refute_0_191,plain,
    meet(join(X_13,X_20),join(X_13,join(X_13,X_20))) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)),
    inference(subst,[],[refute_0_190:[bind(X_14,$fot(join(X_13,X_20)))]]) ).

cnf(refute_0_192,plain,
    join(X_13,X_20) = join(X_13,join(X_13,X_20)),
    inference(subst,[],[refute_0_27:[bind(X_10,$fot(X_13)),bind(X_11,$fot(X_20))]]) ).

cnf(refute_0_193,plain,
    ( join(X_13,X_20) != join(X_13,join(X_13,X_20))
    | join(X_13,join(X_13,X_20)) = join(X_13,X_20) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_13,X_20))),bind(Y0,$fot(join(X_13,join(X_13,X_20))))]]) ).

cnf(refute_0_194,plain,
    join(X_13,join(X_13,X_20)) = join(X_13,X_20),
    inference(resolve,[$cnf( $equal(join(X_13,X_20),join(X_13,join(X_13,X_20))) )],[refute_0_192,refute_0_193]) ).

cnf(refute_0_195,plain,
    ( join(X_13,join(X_13,X_20)) != join(X_13,X_20)
    | meet(join(X_13,X_20),join(X_13,join(X_13,X_20))) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | meet(join(X_13,X_20),join(X_13,X_20)) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_13,X_20),join(X_13,join(X_13,X_20))),join(join(X_13,X_20),meet(join(X_13,X_20),X_13))) ),[0,1],$fot(join(X_13,X_20))]]) ).

cnf(refute_0_196,plain,
    ( meet(join(X_13,X_20),join(X_13,join(X_13,X_20))) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | meet(join(X_13,X_20),join(X_13,X_20)) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) ),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_13,X_20)),join(X_13,X_20)) )],[refute_0_194,refute_0_195]) ).

cnf(refute_0_197,plain,
    meet(join(X_13,X_20),join(X_13,X_20)) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)),
    inference(resolve,[$cnf( $equal(meet(join(X_13,X_20),join(X_13,join(X_13,X_20))),join(join(X_13,X_20),meet(join(X_13,X_20),X_13))) )],[refute_0_191,refute_0_196]) ).

cnf(refute_0_198,plain,
    meet(join(X_13,X_20),join(X_13,X_20)) = join(X_13,X_20),
    inference(subst,[],[idempotence_of_meet:[bind(X,$fot(join(X_13,X_20)))]]) ).

cnf(refute_0_199,plain,
    ( meet(join(X_13,X_20),join(X_13,X_20)) != join(X_13,X_20)
    | meet(join(X_13,X_20),join(X_13,X_20)) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | join(X_13,X_20) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_13,X_20),join(X_13,X_20)),join(join(X_13,X_20),meet(join(X_13,X_20),X_13))) ),[0],$fot(join(X_13,X_20))]]) ).

cnf(refute_0_200,plain,
    ( meet(join(X_13,X_20),join(X_13,X_20)) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | join(X_13,X_20) = join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_13,X_20),join(X_13,X_20)),join(X_13,X_20)) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    meet(X_13,join(X_13,X_14)) = join(meet(X_13,X_13),meet(X_13,X_14)),
    inference(subst,[],[distributivity_law:[bind(X,$fot(X_13)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).

cnf(refute_0_202,plain,
    meet(X_13,X_13) = X_13,
    inference(subst,[],[idempotence_of_meet:[bind(X,$fot(X_13))]]) ).

cnf(refute_0_203,plain,
    ( meet(X_13,X_13) != X_13
    | meet(X_13,join(X_13,X_14)) != join(meet(X_13,X_13),meet(X_13,X_14))
    | meet(X_13,join(X_13,X_14)) = join(X_13,meet(X_13,X_14)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_13,join(X_13,X_14)),join(meet(X_13,X_13),meet(X_13,X_14))) ),[1,0],$fot(X_13)]]) ).

cnf(refute_0_204,plain,
    ( meet(X_13,join(X_13,X_14)) != join(meet(X_13,X_13),meet(X_13,X_14))
    | meet(X_13,join(X_13,X_14)) = join(X_13,meet(X_13,X_14)) ),
    inference(resolve,[$cnf( $equal(meet(X_13,X_13),X_13) )],[refute_0_202,refute_0_203]) ).

cnf(refute_0_205,plain,
    meet(X_13,join(X_13,X_14)) = join(X_13,meet(X_13,X_14)),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_13,X_14)),join(meet(X_13,X_13),meet(X_13,X_14))) )],[refute_0_201,refute_0_204]) ).

cnf(refute_0_206,plain,
    meet(X_13,join(X_13,X_20)) = join(X_13,meet(X_13,X_20)),
    inference(subst,[],[refute_0_205:[bind(X_14,$fot(X_20))]]) ).

cnf(refute_0_207,plain,
    join(X_20,meet(X_13,join(X_13,X_20))) = join(X_20,meet(X_13,join(X_13,X_20))),
    introduced(tautology,[refl,[$fot(join(X_20,meet(X_13,join(X_13,X_20))))]]) ).

cnf(refute_0_208,plain,
    ( join(X_20,meet(X_13,join(X_13,X_20))) != join(X_20,meet(X_13,join(X_13,X_20)))
    | meet(X_13,join(X_13,X_20)) != join(X_13,meet(X_13,X_20))
    | join(X_20,meet(X_13,join(X_13,X_20))) = join(X_20,join(X_13,meet(X_13,X_20))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_20,meet(X_13,join(X_13,X_20))),join(X_20,meet(X_13,join(X_13,X_20)))) ),[1,1],$fot(join(X_13,meet(X_13,X_20)))]]) ).

cnf(refute_0_209,plain,
    ( meet(X_13,join(X_13,X_20)) != join(X_13,meet(X_13,X_20))
    | join(X_20,meet(X_13,join(X_13,X_20))) = join(X_20,join(X_13,meet(X_13,X_20))) ),
    inference(resolve,[$cnf( $equal(join(X_20,meet(X_13,join(X_13,X_20))),join(X_20,meet(X_13,join(X_13,X_20)))) )],[refute_0_207,refute_0_208]) ).

cnf(refute_0_210,plain,
    join(X_20,meet(X_13,join(X_13,X_20))) = join(X_20,join(X_13,meet(X_13,X_20))),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_13,X_20)),join(X_13,meet(X_13,X_20))) )],[refute_0_206,refute_0_209]) ).

cnf(refute_0_211,plain,
    join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) = join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),
    introduced(tautology,[refl,[$fot(join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))))]]) ).

cnf(refute_0_212,plain,
    ( join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) != join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))
    | join(X_20,meet(X_13,join(X_13,X_20))) != join(X_20,join(X_13,meet(X_13,X_20)))
    | join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))) ),[1,1],$fot(join(X_20,join(X_13,meet(X_13,X_20))))]]) ).

cnf(refute_0_213,plain,
    ( join(X_20,meet(X_13,join(X_13,X_20))) != join(X_20,join(X_13,meet(X_13,X_20)))
    | join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))) )],[refute_0_211,refute_0_212]) ).

cnf(refute_0_214,plain,
    join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))),
    inference(resolve,[$cnf( $equal(join(X_20,meet(X_13,join(X_13,X_20))),join(X_20,join(X_13,meet(X_13,X_20)))) )],[refute_0_210,refute_0_213]) ).

cnf(refute_0_215,plain,
    join(join(X_13,X_20),meet(X_13,join(X_13,X_20))) = join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_13)),bind(Y,$fot(X_20)),bind(Z,$fot(meet(X_13,join(X_13,X_20))))]]) ).

cnf(refute_0_216,plain,
    meet(X_16,join(X_15,X_16)) = join(X_16,meet(X_16,X_15)),
    inference(subst,[],[refute_0_190:[bind(X_13,$fot(X_15)),bind(X_14,$fot(X_16))]]) ).

cnf(refute_0_217,plain,
    meet(X_15,X_16) = meet(X_16,X_15),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_15)),bind(Y,$fot(X_16))]]) ).

cnf(refute_0_218,plain,
    ( meet(X_15,X_16) != meet(X_16,X_15)
    | meet(X_16,X_15) = meet(X_15,X_16) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_15,X_16))),bind(Y0,$fot(meet(X_16,X_15)))]]) ).

cnf(refute_0_219,plain,
    meet(X_16,X_15) = meet(X_15,X_16),
    inference(resolve,[$cnf( $equal(meet(X_15,X_16),meet(X_16,X_15)) )],[refute_0_217,refute_0_218]) ).

cnf(refute_0_220,plain,
    ( meet(X_16,X_15) != meet(X_15,X_16)
    | meet(X_16,join(X_15,X_16)) != join(X_16,meet(X_16,X_15))
    | meet(X_16,join(X_15,X_16)) = join(X_16,meet(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_16,join(X_15,X_16)),join(X_16,meet(X_16,X_15))) ),[1,1],$fot(meet(X_15,X_16))]]) ).

cnf(refute_0_221,plain,
    ( meet(X_16,join(X_15,X_16)) != join(X_16,meet(X_16,X_15))
    | meet(X_16,join(X_15,X_16)) = join(X_16,meet(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(meet(X_16,X_15),meet(X_15,X_16)) )],[refute_0_219,refute_0_220]) ).

cnf(refute_0_222,plain,
    meet(X_16,join(X_15,X_16)) = join(X_16,meet(X_15,X_16)),
    inference(resolve,[$cnf( $equal(meet(X_16,join(X_15,X_16)),join(X_16,meet(X_16,X_15))) )],[refute_0_216,refute_0_221]) ).

cnf(refute_0_223,plain,
    ( meet(X_16,join(X_15,X_16)) != join(X_16,meet(X_15,X_16))
    | meet(X_16,join(X_15,X_16)) != join(X_16,meet(X_16,X_15))
    | join(X_16,meet(X_16,X_15)) = join(X_16,meet(X_15,X_16)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_16,join(X_15,X_16)),join(X_16,meet(X_15,X_16))) ),[0],$fot(join(X_16,meet(X_16,X_15)))]]) ).

cnf(refute_0_224,plain,
    ( meet(X_16,join(X_15,X_16)) != join(X_16,meet(X_15,X_16))
    | join(X_16,meet(X_16,X_15)) = join(X_16,meet(X_15,X_16)) ),
    inference(resolve,[$cnf( $equal(meet(X_16,join(X_15,X_16)),join(X_16,meet(X_16,X_15))) )],[refute_0_216,refute_0_223]) ).

cnf(refute_0_225,plain,
    join(X_16,meet(X_16,X_15)) = join(X_16,meet(X_15,X_16)),
    inference(resolve,[$cnf( $equal(meet(X_16,join(X_15,X_16)),join(X_16,meet(X_15,X_16))) )],[refute_0_222,refute_0_224]) ).

cnf(refute_0_226,plain,
    join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(join(X_13,X_20),meet(X_13,join(X_13,X_20))),
    inference(subst,[],[refute_0_225:[bind(X_15,$fot(X_13)),bind(X_16,$fot(join(X_13,X_20)))]]) ).

cnf(refute_0_227,plain,
    ( join(join(X_13,X_20),meet(X_13,join(X_13,X_20))) != join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) != join(join(X_13,X_20),meet(X_13,join(X_13,X_20)))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)))),bind(Y0,$fot(join(join(X_13,X_20),meet(X_13,join(X_13,X_20))))),bind(Z0,$fot(join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))))]]) ).

cnf(refute_0_228,plain,
    ( join(join(X_13,X_20),meet(X_13,join(X_13,X_20))) != join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) ),
    inference(resolve,[$cnf( $equal(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)),join(join(X_13,X_20),meet(X_13,join(X_13,X_20)))) )],[refute_0_226,refute_0_227]) ).

cnf(refute_0_229,plain,
    join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),
    inference(resolve,[$cnf( $equal(join(join(X_13,X_20),meet(X_13,join(X_13,X_20))),join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))) )],[refute_0_215,refute_0_228]) ).

cnf(refute_0_230,plain,
    ( join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) != join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) != join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)))),bind(Y0,$fot(join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))))),bind(Z0,$fot(join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))))]]) ).

cnf(refute_0_231,plain,
    ( join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))) != join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    inference(resolve,[$cnf( $equal(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)),join(X_13,join(X_20,meet(X_13,join(X_13,X_20))))) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_20,meet(X_13,join(X_13,X_20)))),join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))) )],[refute_0_214,refute_0_231]) ).

cnf(refute_0_233,plain,
    ( join(X_13,X_20) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | join(join(X_13,X_20),meet(join(X_13,X_20),X_13)) != join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))
    | join(X_13,X_20) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_13,X_20),join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))) ),[0],$fot(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)))]]) ).

cnf(refute_0_234,plain,
    ( join(X_13,X_20) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | join(X_13,X_20) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    inference(resolve,[$cnf( $equal(join(join(X_13,X_20),meet(join(X_13,X_20),X_13)),join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))) )],[refute_0_232,refute_0_233]) ).

cnf(refute_0_235,plain,
    ( meet(join(X_13,X_20),join(X_13,X_20)) != join(join(X_13,X_20),meet(join(X_13,X_20),X_13))
    | join(X_13,X_20) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) ),
    inference(resolve,[$cnf( $equal(join(X_13,X_20),join(join(X_13,X_20),meet(join(X_13,X_20),X_13))) )],[refute_0_200,refute_0_234]) ).

cnf(refute_0_236,plain,
    join(X_13,X_20) = join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))),
    inference(resolve,[$cnf( $equal(meet(join(X_13,X_20),join(X_13,X_20)),join(join(X_13,X_20),meet(join(X_13,X_20),X_13))) )],[refute_0_197,refute_0_235]) ).

cnf(refute_0_237,plain,
    join(join(X,Y),join(Y,X_20)) = join(X,join(Y,join(Y,X_20))),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(join(Y,X_20)))]]) ).

cnf(refute_0_238,plain,
    join(Y,X_20) = join(Y,join(Y,X_20)),
    inference(subst,[],[refute_0_27:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_20))]]) ).

cnf(refute_0_239,plain,
    ( join(Y,X_20) != join(Y,join(Y,X_20))
    | join(Y,join(Y,X_20)) = join(Y,X_20) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(Y,X_20))),bind(Y0,$fot(join(Y,join(Y,X_20))))]]) ).

cnf(refute_0_240,plain,
    join(Y,join(Y,X_20)) = join(Y,X_20),
    inference(resolve,[$cnf( $equal(join(Y,X_20),join(Y,join(Y,X_20))) )],[refute_0_238,refute_0_239]) ).

cnf(refute_0_241,plain,
    ( join(Y,join(Y,X_20)) != join(Y,X_20)
    | join(join(X,Y),join(Y,X_20)) != join(X,join(Y,join(Y,X_20)))
    | join(join(X,Y),join(Y,X_20)) = join(X,join(Y,X_20)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(X,join(Y,join(Y,X_20)))) ),[1,1],$fot(join(Y,X_20))]]) ).

cnf(refute_0_242,plain,
    ( join(join(X,Y),join(Y,X_20)) != join(X,join(Y,join(Y,X_20)))
    | join(join(X,Y),join(Y,X_20)) = join(X,join(Y,X_20)) ),
    inference(resolve,[$cnf( $equal(join(Y,join(Y,X_20)),join(Y,X_20)) )],[refute_0_240,refute_0_241]) ).

cnf(refute_0_243,plain,
    join(join(X,Y),join(Y,X_20)) = join(X,join(Y,X_20)),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(X,join(Y,join(Y,X_20)))) )],[refute_0_237,refute_0_242]) ).

cnf(refute_0_244,plain,
    join(join(X,Y),X_20) = join(X,join(Y,X_20)),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_20))]]) ).

cnf(refute_0_245,plain,
    join(Y,join(join(X,Y),X_20)) = join(Y,join(join(X,Y),X_20)),
    introduced(tautology,[refl,[$fot(join(Y,join(join(X,Y),X_20)))]]) ).

cnf(refute_0_246,plain,
    ( join(Y,join(join(X,Y),X_20)) != join(Y,join(join(X,Y),X_20))
    | join(join(X,Y),X_20) != join(X,join(Y,X_20))
    | join(Y,join(join(X,Y),X_20)) = join(Y,join(X,join(Y,X_20))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(Y,join(join(X,Y),X_20)),join(Y,join(join(X,Y),X_20))) ),[1,1],$fot(join(X,join(Y,X_20)))]]) ).

cnf(refute_0_247,plain,
    ( join(join(X,Y),X_20) != join(X,join(Y,X_20))
    | join(Y,join(join(X,Y),X_20)) = join(Y,join(X,join(Y,X_20))) ),
    inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_20)),join(Y,join(join(X,Y),X_20))) )],[refute_0_245,refute_0_246]) ).

cnf(refute_0_248,plain,
    join(Y,join(join(X,Y),X_20)) = join(Y,join(X,join(Y,X_20))),
    inference(resolve,[$cnf( $equal(join(join(X,Y),X_20),join(X,join(Y,X_20))) )],[refute_0_244,refute_0_247]) ).

cnf(refute_0_249,plain,
    join(join(X_9,X_10),X_11) = join(X_9,join(X_10,X_11)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_250,plain,
    join(X_10,X_9) = join(X_9,X_10),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_10)),bind(Y,$fot(X_9))]]) ).

cnf(refute_0_251,plain,
    ( join(X_10,X_9) != join(X_9,X_10)
    | join(X_9,X_10) = join(X_10,X_9) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_10,X_9))),bind(Y0,$fot(join(X_9,X_10)))]]) ).

cnf(refute_0_252,plain,
    join(X_9,X_10) = join(X_10,X_9),
    inference(resolve,[$cnf( $equal(join(X_10,X_9),join(X_9,X_10)) )],[refute_0_250,refute_0_251]) ).

cnf(refute_0_253,plain,
    ( join(X_9,X_10) != join(X_10,X_9)
    | join(join(X_9,X_10),X_11) != join(X_9,join(X_10,X_11))
    | join(join(X_10,X_9),X_11) = join(X_9,join(X_10,X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_10,X_11))) ),[0,0],$fot(join(X_10,X_9))]]) ).

cnf(refute_0_254,plain,
    ( join(join(X_9,X_10),X_11) != join(X_9,join(X_10,X_11))
    | join(join(X_10,X_9),X_11) = join(X_9,join(X_10,X_11)) ),
    inference(resolve,[$cnf( $equal(join(X_9,X_10),join(X_10,X_9)) )],[refute_0_252,refute_0_253]) ).

cnf(refute_0_255,plain,
    join(join(X_10,X_9),X_11) = join(X_9,join(X_10,X_11)),
    inference(resolve,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_10,X_11))) )],[refute_0_249,refute_0_254]) ).

cnf(refute_0_256,plain,
    join(join(X_10,X_9),X_11) = join(X_10,join(X_9,X_11)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_10)),bind(Y,$fot(X_9)),bind(Z,$fot(X_11))]]) ).

cnf(refute_0_257,plain,
    ( join(join(X_10,X_9),X_11) != join(X_10,join(X_9,X_11))
    | join(join(X_10,X_9),X_11) != join(X_9,join(X_10,X_11))
    | join(X_10,join(X_9,X_11)) = join(X_9,join(X_10,X_11)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_10,X_9),X_11),join(X_9,join(X_10,X_11))) ),[0],$fot(join(X_10,join(X_9,X_11)))]]) ).

cnf(refute_0_258,plain,
    ( join(join(X_10,X_9),X_11) != join(X_9,join(X_10,X_11))
    | join(X_10,join(X_9,X_11)) = join(X_9,join(X_10,X_11)) ),
    inference(resolve,[$cnf( $equal(join(join(X_10,X_9),X_11),join(X_10,join(X_9,X_11))) )],[refute_0_256,refute_0_257]) ).

cnf(refute_0_259,plain,
    join(X_10,join(X_9,X_11)) = join(X_9,join(X_10,X_11)),
    inference(resolve,[$cnf( $equal(join(join(X_10,X_9),X_11),join(X_9,join(X_10,X_11))) )],[refute_0_255,refute_0_258]) ).

cnf(refute_0_260,plain,
    ( join(X_10,join(X_9,X_11)) != join(X_9,join(X_10,X_11))
    | join(X_9,join(X_10,X_11)) = join(X_10,join(X_9,X_11)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_10,join(X_9,X_11)))),bind(Y0,$fot(join(X_9,join(X_10,X_11))))]]) ).

cnf(refute_0_261,plain,
    join(X_9,join(X_10,X_11)) = join(X_10,join(X_9,X_11)),
    inference(resolve,[$cnf( $equal(join(X_10,join(X_9,X_11)),join(X_9,join(X_10,X_11))) )],[refute_0_259,refute_0_260]) ).

cnf(refute_0_262,plain,
    join(join(X,Y),join(Y,X_20)) = join(Y,join(join(X,Y),X_20)),
    inference(subst,[],[refute_0_261:[bind(X_10,$fot(Y)),bind(X_11,$fot(X_20)),bind(X_9,$fot(join(X,Y)))]]) ).

cnf(refute_0_263,plain,
    ( join(Y,join(join(X,Y),X_20)) != join(Y,join(X,join(Y,X_20)))
    | join(join(X,Y),join(Y,X_20)) != join(Y,join(join(X,Y),X_20))
    | join(join(X,Y),join(Y,X_20)) = join(Y,join(X,join(Y,X_20))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X,Y),join(Y,X_20)))),bind(Y0,$fot(join(Y,join(join(X,Y),X_20)))),bind(Z0,$fot(join(Y,join(X,join(Y,X_20)))))]]) ).

cnf(refute_0_264,plain,
    ( join(Y,join(join(X,Y),X_20)) != join(Y,join(X,join(Y,X_20)))
    | join(join(X,Y),join(Y,X_20)) = join(Y,join(X,join(Y,X_20))) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(Y,join(join(X,Y),X_20))) )],[refute_0_262,refute_0_263]) ).

cnf(refute_0_265,plain,
    join(join(X,Y),join(Y,X_20)) = join(Y,join(X,join(Y,X_20))),
    inference(resolve,[$cnf( $equal(join(Y,join(join(X,Y),X_20)),join(Y,join(X,join(Y,X_20)))) )],[refute_0_248,refute_0_264]) ).

cnf(refute_0_266,plain,
    ( join(join(X,Y),join(Y,X_20)) != join(X,join(Y,X_20))
    | join(join(X,Y),join(Y,X_20)) != join(Y,join(X,join(Y,X_20)))
    | join(Y,join(X,join(Y,X_20))) = join(X,join(Y,X_20)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(X,join(Y,X_20))) ),[0],$fot(join(Y,join(X,join(Y,X_20))))]]) ).

cnf(refute_0_267,plain,
    ( join(join(X,Y),join(Y,X_20)) != join(X,join(Y,X_20))
    | join(Y,join(X,join(Y,X_20))) = join(X,join(Y,X_20)) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(Y,join(X,join(Y,X_20)))) )],[refute_0_265,refute_0_266]) ).

cnf(refute_0_268,plain,
    join(Y,join(X,join(Y,X_20))) = join(X,join(Y,X_20)),
    inference(resolve,[$cnf( $equal(join(join(X,Y),join(Y,X_20)),join(X,join(Y,X_20))) )],[refute_0_243,refute_0_267]) ).

cnf(refute_0_269,plain,
    join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) = join(X_20,join(X_13,meet(X_13,X_20))),
    inference(subst,[],[refute_0_268:[bind(X,$fot(X_20)),bind(Y,$fot(X_13)),bind(X_20,$fot(meet(X_13,X_20)))]]) ).

cnf(refute_0_270,plain,
    ( join(X_13,X_20) != join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))
    | join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))) != join(X_20,join(X_13,meet(X_13,X_20)))
    | join(X_13,X_20) = join(X_20,join(X_13,meet(X_13,X_20))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_13,X_20),join(X_20,join(X_13,meet(X_13,X_20)))) ),[0],$fot(join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))))]]) ).

cnf(refute_0_271,plain,
    ( join(X_13,X_20) != join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))
    | join(X_13,X_20) = join(X_20,join(X_13,meet(X_13,X_20))) ),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_20,join(X_13,meet(X_13,X_20)))),join(X_20,join(X_13,meet(X_13,X_20)))) )],[refute_0_269,refute_0_270]) ).

cnf(refute_0_272,plain,
    join(X_13,X_20) = join(X_20,join(X_13,meet(X_13,X_20))),
    inference(resolve,[$cnf( $equal(join(X_13,X_20),join(X_13,join(X_20,join(X_13,meet(X_13,X_20))))) )],[refute_0_236,refute_0_271]) ).

cnf(refute_0_273,plain,
    join(X_13,join(X_59,meet(X_59,X_13))) = join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))),
    inference(subst,[],[refute_0_272:[bind(X_20,$fot(join(X_59,meet(X_59,X_13))))]]) ).

cnf(refute_0_274,plain,
    join(X_59,X_13) = join(X_13,join(X_59,meet(X_59,X_13))),
    inference(subst,[],[refute_0_272:[bind(X_13,$fot(X_59)),bind(X_20,$fot(X_13))]]) ).

cnf(refute_0_275,plain,
    ( join(X_59,X_13) != join(X_13,join(X_59,meet(X_59,X_13)))
    | join(X_13,join(X_59,meet(X_59,X_13))) = join(X_59,X_13) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_59,X_13))),bind(Y0,$fot(join(X_13,join(X_59,meet(X_59,X_13)))))]]) ).

cnf(refute_0_276,plain,
    join(X_13,join(X_59,meet(X_59,X_13))) = join(X_59,X_13),
    inference(resolve,[$cnf( $equal(join(X_59,X_13),join(X_13,join(X_59,meet(X_59,X_13)))) )],[refute_0_274,refute_0_275]) ).

cnf(refute_0_277,plain,
    ( join(X_13,join(X_59,meet(X_59,X_13))) != join(X_59,X_13)
    | join(X_13,join(X_59,meet(X_59,X_13))) != join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(X_59,X_13) = join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_13,join(X_59,meet(X_59,X_13))),join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))) ),[0],$fot(join(X_59,X_13))]]) ).

cnf(refute_0_278,plain,
    ( join(X_13,join(X_59,meet(X_59,X_13))) != join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(X_59,X_13) = join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) ),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_59,meet(X_59,X_13))),join(X_59,X_13)) )],[refute_0_276,refute_0_277]) ).

cnf(refute_0_279,plain,
    join(X_59,X_13) = join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))),
    inference(resolve,[$cnf( $equal(join(X_13,join(X_59,meet(X_59,X_13))),join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_273,refute_0_278]) ).

cnf(refute_0_280,plain,
    join(X_59,X_59) = X_59,
    inference(subst,[],[idempotence_of_join:[bind(X,$fot(X_59))]]) ).

cnf(refute_0_281,plain,
    meet(X_13,join(X_59,X_59)) = meet(X_13,join(X_59,X_59)),
    introduced(tautology,[refl,[$fot(meet(X_13,join(X_59,X_59)))]]) ).

cnf(refute_0_282,plain,
    ( join(X_59,X_59) != X_59
    | meet(X_13,join(X_59,X_59)) != meet(X_13,join(X_59,X_59))
    | meet(X_13,join(X_59,X_59)) = meet(X_13,X_59) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_13,join(X_59,X_59)),meet(X_13,join(X_59,X_59))) ),[1,1],$fot(X_59)]]) ).

cnf(refute_0_283,plain,
    ( join(X_59,X_59) != X_59
    | meet(X_13,join(X_59,X_59)) = meet(X_13,X_59) ),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_59,X_59)),meet(X_13,join(X_59,X_59))) )],[refute_0_281,refute_0_282]) ).

cnf(refute_0_284,plain,
    meet(X_13,join(X_59,X_59)) = meet(X_13,X_59),
    inference(resolve,[$cnf( $equal(join(X_59,X_59),X_59) )],[refute_0_280,refute_0_283]) ).

cnf(refute_0_285,plain,
    meet(X,join(Y,join(X_29,meet(X_29,X)))) = join(meet(X,Y),meet(X,join(X_29,meet(X_29,X)))),
    inference(subst,[],[distributivity_law:[bind(Z,$fot(join(X_29,meet(X_29,X))))]]) ).

cnf(refute_0_286,plain,
    meet(join(meet(X_26,X_27),X_26),join(meet(X_26,X_27),meet(X_26,X_27))) = join(meet(X_26,X_27),meet(X_26,X_27)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(meet(X_26,X_27))),bind(Y,$fot(X_26)),bind(Z,$fot(X_27))]]) ).

cnf(refute_0_287,plain,
    join(meet(X_26,X_27),meet(X_26,X_27)) = meet(X_26,X_27),
    inference(subst,[],[idempotence_of_join:[bind(X,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_288,plain,
    ( join(meet(X_26,X_27),meet(X_26,X_27)) != meet(X_26,X_27)
    | meet(join(meet(X_26,X_27),X_26),join(meet(X_26,X_27),meet(X_26,X_27))) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = join(meet(X_26,X_27),meet(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),join(meet(X_26,X_27),meet(X_26,X_27))),join(meet(X_26,X_27),meet(X_26,X_27))) ),[0,1],$fot(meet(X_26,X_27))]]) ).

cnf(refute_0_289,plain,
    ( meet(join(meet(X_26,X_27),X_26),join(meet(X_26,X_27),meet(X_26,X_27))) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = join(meet(X_26,X_27),meet(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_26,X_27),meet(X_26,X_27)),meet(X_26,X_27)) )],[refute_0_287,refute_0_288]) ).

cnf(refute_0_290,plain,
    meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = join(meet(X_26,X_27),meet(X_26,X_27)),
    inference(resolve,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),join(meet(X_26,X_27),meet(X_26,X_27))),join(meet(X_26,X_27),meet(X_26,X_27))) )],[refute_0_286,refute_0_289]) ).

cnf(refute_0_291,plain,
    meet(meet(X,Y),join(X_15,meet(X,Y))) = meet(X,meet(Y,join(X_15,meet(X,Y)))),
    inference(subst,[],[associativity_of_meet:[bind(Z,$fot(join(X_15,meet(X,Y))))]]) ).

cnf(refute_0_292,plain,
    meet(meet(X,Y),join(X_15,meet(X,Y))) = join(meet(X,Y),meet(meet(X,Y),X_15)),
    inference(subst,[],[refute_0_190:[bind(X_13,$fot(X_15)),bind(X_14,$fot(meet(X,Y)))]]) ).

cnf(refute_0_293,plain,
    ( meet(meet(X,Y),join(X_15,meet(X,Y))) != join(meet(X,Y),meet(meet(X,Y),X_15))
    | meet(meet(X,Y),join(X_15,meet(X,Y))) != meet(X,meet(Y,join(X_15,meet(X,Y))))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,meet(Y,join(X_15,meet(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X,Y),join(X_15,meet(X,Y))),meet(X,meet(Y,join(X_15,meet(X,Y))))) ),[0],$fot(join(meet(X,Y),meet(meet(X,Y),X_15)))]]) ).

cnf(refute_0_294,plain,
    ( meet(meet(X,Y),join(X_15,meet(X,Y))) != meet(X,meet(Y,join(X_15,meet(X,Y))))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,meet(Y,join(X_15,meet(X,Y)))) ),
    inference(resolve,[$cnf( $equal(meet(meet(X,Y),join(X_15,meet(X,Y))),join(meet(X,Y),meet(meet(X,Y),X_15))) )],[refute_0_292,refute_0_293]) ).

cnf(refute_0_295,plain,
    join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,meet(Y,join(X_15,meet(X,Y)))),
    inference(resolve,[$cnf( $equal(meet(meet(X,Y),join(X_15,meet(X,Y))),meet(X,meet(Y,join(X_15,meet(X,Y))))) )],[refute_0_291,refute_0_294]) ).

cnf(refute_0_296,plain,
    join(meet(X,Y),meet(X,meet(Y,X_15))) = meet(X,join(Y,meet(Y,X_15))),
    inference(subst,[],[refute_0_47:[bind(Z,$fot(meet(Y,X_15)))]]) ).

cnf(refute_0_297,plain,
    meet(meet(X,Y),X_15) = meet(X,meet(Y,X_15)),
    inference(subst,[],[associativity_of_meet:[bind(Z,$fot(X_15))]]) ).

cnf(refute_0_298,plain,
    join(meet(X,Y),meet(meet(X,Y),X_15)) = join(meet(X,Y),meet(meet(X,Y),X_15)),
    introduced(tautology,[refl,[$fot(join(meet(X,Y),meet(meet(X,Y),X_15)))]]) ).

cnf(refute_0_299,plain,
    ( join(meet(X,Y),meet(meet(X,Y),X_15)) != join(meet(X,Y),meet(meet(X,Y),X_15))
    | meet(meet(X,Y),X_15) != meet(X,meet(Y,X_15))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = join(meet(X,Y),meet(X,meet(Y,X_15))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),join(meet(X,Y),meet(meet(X,Y),X_15))) ),[1,1],$fot(meet(X,meet(Y,X_15)))]]) ).

cnf(refute_0_300,plain,
    ( meet(meet(X,Y),X_15) != meet(X,meet(Y,X_15))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = join(meet(X,Y),meet(X,meet(Y,X_15))) ),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),join(meet(X,Y),meet(meet(X,Y),X_15))) )],[refute_0_298,refute_0_299]) ).

cnf(refute_0_301,plain,
    join(meet(X,Y),meet(meet(X,Y),X_15)) = join(meet(X,Y),meet(X,meet(Y,X_15))),
    inference(resolve,[$cnf( $equal(meet(meet(X,Y),X_15),meet(X,meet(Y,X_15))) )],[refute_0_297,refute_0_300]) ).

cnf(refute_0_302,plain,
    ( join(meet(X,Y),meet(X,meet(Y,X_15))) != meet(X,join(Y,meet(Y,X_15)))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) != join(meet(X,Y),meet(X,meet(Y,X_15)))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,join(Y,meet(Y,X_15))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(meet(X,Y),meet(meet(X,Y),X_15)))),bind(Y0,$fot(join(meet(X,Y),meet(X,meet(Y,X_15))))),bind(Z0,$fot(meet(X,join(Y,meet(Y,X_15)))))]]) ).

cnf(refute_0_303,plain,
    ( join(meet(X,Y),meet(X,meet(Y,X_15))) != meet(X,join(Y,meet(Y,X_15)))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,join(Y,meet(Y,X_15))) ),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),join(meet(X,Y),meet(X,meet(Y,X_15)))) )],[refute_0_301,refute_0_302]) ).

cnf(refute_0_304,plain,
    join(meet(X,Y),meet(meet(X,Y),X_15)) = meet(X,join(Y,meet(Y,X_15))),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(X,meet(Y,X_15))),meet(X,join(Y,meet(Y,X_15)))) )],[refute_0_296,refute_0_303]) ).

cnf(refute_0_305,plain,
    ( join(meet(X,Y),meet(meet(X,Y),X_15)) != meet(X,join(Y,meet(Y,X_15)))
    | join(meet(X,Y),meet(meet(X,Y),X_15)) != meet(X,meet(Y,join(X_15,meet(X,Y))))
    | meet(X,join(Y,meet(Y,X_15))) = meet(X,meet(Y,join(X_15,meet(X,Y)))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),meet(X,meet(Y,join(X_15,meet(X,Y))))) ),[0],$fot(meet(X,join(Y,meet(Y,X_15))))]]) ).

cnf(refute_0_306,plain,
    ( join(meet(X,Y),meet(meet(X,Y),X_15)) != meet(X,meet(Y,join(X_15,meet(X,Y))))
    | meet(X,join(Y,meet(Y,X_15))) = meet(X,meet(Y,join(X_15,meet(X,Y)))) ),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),meet(X,join(Y,meet(Y,X_15)))) )],[refute_0_304,refute_0_305]) ).

cnf(refute_0_307,plain,
    meet(X,join(Y,meet(Y,X_15))) = meet(X,meet(Y,join(X_15,meet(X,Y)))),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(meet(X,Y),X_15)),meet(X,meet(Y,join(X_15,meet(X,Y))))) )],[refute_0_295,refute_0_306]) ).

cnf(refute_0_308,plain,
    ( meet(X,join(Y,meet(Y,X_15))) != meet(X,meet(Y,join(X_15,meet(X,Y))))
    | meet(X,meet(Y,join(X_15,meet(X,Y)))) = meet(X,join(Y,meet(Y,X_15))) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X,join(Y,meet(Y,X_15))))),bind(Y0,$fot(meet(X,meet(Y,join(X_15,meet(X,Y))))))]]) ).

cnf(refute_0_309,plain,
    meet(X,meet(Y,join(X_15,meet(X,Y)))) = meet(X,join(Y,meet(Y,X_15))),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,meet(Y,X_15))),meet(X,meet(Y,join(X_15,meet(X,Y))))) )],[refute_0_307,refute_0_308]) ).

cnf(refute_0_310,plain,
    meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))) = meet(X_26,join(X_27,meet(X_27,X_26))),
    inference(subst,[],[refute_0_309:[bind(X,$fot(X_26)),bind(Y,$fot(X_27)),bind(X_15,$fot(X_26))]]) ).

cnf(refute_0_311,plain,
    ( meet(X_6,meet(X_7,X_8)) != meet(X_6,meet(X_8,X_7))
    | meet(X_6,meet(X_8,X_7)) = meet(X_6,meet(X_7,X_8)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_6,meet(X_7,X_8)))),bind(Y0,$fot(meet(X_6,meet(X_8,X_7))))]]) ).

cnf(refute_0_312,plain,
    meet(X_6,meet(X_8,X_7)) = meet(X_6,meet(X_7,X_8)),
    inference(resolve,[$cnf( $equal(meet(X_6,meet(X_7,X_8)),meet(X_6,meet(X_8,X_7))) )],[refute_0_136,refute_0_311]) ).

cnf(refute_0_313,plain,
    meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) = meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))),
    inference(subst,[],[refute_0_312:[bind(X_6,$fot(X_26)),bind(X_7,$fot(X_27)),bind(X_8,$fot(join(X_26,meet(X_26,X_27))))]]) ).

cnf(refute_0_314,plain,
    ( meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) != meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27))))
    | meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)))),bind(Y0,$fot(meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))))),bind(Z0,$fot(meet(X_26,join(X_27,meet(X_27,X_26)))))]]) ).

cnf(refute_0_315,plain,
    ( meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(resolve,[$cnf( $equal(meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)),meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27))))) )],[refute_0_313,refute_0_314]) ).

cnf(refute_0_316,plain,
    meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))),
    inference(resolve,[$cnf( $equal(meet(X_26,meet(X_27,join(X_26,meet(X_26,X_27)))),meet(X_26,join(X_27,meet(X_27,X_26)))) )],[refute_0_310,refute_0_315]) ).

cnf(refute_0_317,plain,
    meet(meet(X,join(X,X_24)),Z) = meet(X,meet(join(X,X_24),Z)),
    inference(subst,[],[associativity_of_meet:[bind(Y,$fot(join(X,X_24)))]]) ).

cnf(refute_0_318,plain,
    meet(X,join(X,X_24)) = join(X,meet(X,X_24)),
    inference(subst,[],[refute_0_205:[bind(X_13,$fot(X)),bind(X_14,$fot(X_24))]]) ).

cnf(refute_0_319,plain,
    ( meet(X,join(X,X_24)) != join(X,meet(X,X_24))
    | meet(meet(X,join(X,X_24)),Z) != meet(X,meet(join(X,X_24),Z))
    | meet(join(X,meet(X,X_24)),Z) = meet(X,meet(join(X,X_24),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X,join(X,X_24)),Z),meet(X,meet(join(X,X_24),Z))) ),[0,0],$fot(join(X,meet(X,X_24)))]]) ).

cnf(refute_0_320,plain,
    ( meet(meet(X,join(X,X_24)),Z) != meet(X,meet(join(X,X_24),Z))
    | meet(join(X,meet(X,X_24)),Z) = meet(X,meet(join(X,X_24),Z)) ),
    inference(resolve,[$cnf( $equal(meet(X,join(X,X_24)),join(X,meet(X,X_24))) )],[refute_0_318,refute_0_319]) ).

cnf(refute_0_321,plain,
    meet(join(X,meet(X,X_24)),Z) = meet(X,meet(join(X,X_24),Z)),
    inference(resolve,[$cnf( $equal(meet(meet(X,join(X,X_24)),Z),meet(X,meet(join(X,X_24),Z))) )],[refute_0_317,refute_0_320]) ).

cnf(refute_0_322,plain,
    meet(meet(X,join(X_15,X)),Z) = meet(X,meet(join(X_15,X),Z)),
    inference(subst,[],[associativity_of_meet:[bind(Y,$fot(join(X_15,X)))]]) ).

cnf(refute_0_323,plain,
    meet(X,join(X_15,X)) = join(X,meet(X,X_15)),
    inference(subst,[],[refute_0_190:[bind(X_13,$fot(X_15)),bind(X_14,$fot(X))]]) ).

cnf(refute_0_324,plain,
    ( meet(X,join(X_15,X)) != join(X,meet(X,X_15))
    | meet(meet(X,join(X_15,X)),Z) != meet(X,meet(join(X_15,X),Z))
    | meet(join(X,meet(X,X_15)),Z) = meet(X,meet(join(X_15,X),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X,join(X_15,X)),Z),meet(X,meet(join(X_15,X),Z))) ),[0,0],$fot(join(X,meet(X,X_15)))]]) ).

cnf(refute_0_325,plain,
    ( meet(meet(X,join(X_15,X)),Z) != meet(X,meet(join(X_15,X),Z))
    | meet(join(X,meet(X,X_15)),Z) = meet(X,meet(join(X_15,X),Z)) ),
    inference(resolve,[$cnf( $equal(meet(X,join(X_15,X)),join(X,meet(X,X_15))) )],[refute_0_323,refute_0_324]) ).

cnf(refute_0_326,plain,
    meet(join(X,meet(X,X_15)),Z) = meet(X,meet(join(X_15,X),Z)),
    inference(resolve,[$cnf( $equal(meet(meet(X,join(X_15,X)),Z),meet(X,meet(join(X_15,X),Z))) )],[refute_0_322,refute_0_325]) ).

cnf(refute_0_327,plain,
    meet(join(X,meet(X,X_24)),Z) = meet(X,meet(join(X_24,X),Z)),
    inference(subst,[],[refute_0_326:[bind(X_15,$fot(X_24))]]) ).

cnf(refute_0_328,plain,
    ( meet(join(X,meet(X,X_24)),Z) != meet(X,meet(join(X,X_24),Z))
    | meet(join(X,meet(X,X_24)),Z) != meet(X,meet(join(X_24,X),Z))
    | meet(X,meet(join(X_24,X),Z)) = meet(X,meet(join(X,X_24),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X,meet(X,X_24)),Z),meet(X,meet(join(X,X_24),Z))) ),[0],$fot(meet(X,meet(join(X_24,X),Z)))]]) ).

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

cnf(refute_0_330,plain,
    meet(X,meet(join(X_24,X),Z)) = meet(X,meet(join(X,X_24),Z)),
    inference(resolve,[$cnf( $equal(meet(join(X,meet(X,X_24)),Z),meet(X,meet(join(X,X_24),Z))) )],[refute_0_321,refute_0_329]) ).

cnf(refute_0_331,plain,
    meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) = meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)),
    inference(subst,[],[refute_0_330:[bind(X,$fot(X_26)),bind(Z,$fot(X_27)),bind(X_24,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_332,plain,
    ( meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) != meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27))
    | meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)))),bind(Y0,$fot(meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)))),bind(Z0,$fot(meet(X_26,join(X_27,meet(X_27,X_26)))))]]) ).

cnf(refute_0_333,plain,
    ( meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(resolve,[$cnf( $equal(meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)),meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27))) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))),
    inference(resolve,[$cnf( $equal(meet(X_26,meet(join(X_26,meet(X_26,X_27)),X_27)),meet(X_26,join(X_27,meet(X_27,X_26)))) )],[refute_0_316,refute_0_333]) ).

cnf(refute_0_335,plain,
    meet(X_7,X_6) = meet(X_6,X_7),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_7)),bind(Y,$fot(X_6))]]) ).

cnf(refute_0_336,plain,
    ( meet(X_7,X_6) != meet(X_6,X_7)
    | meet(X_6,X_7) = meet(X_7,X_6) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_7,X_6))),bind(Y0,$fot(meet(X_6,X_7)))]]) ).

cnf(refute_0_337,plain,
    meet(X_6,X_7) = meet(X_7,X_6),
    inference(resolve,[$cnf( $equal(meet(X_7,X_6),meet(X_6,X_7)) )],[refute_0_335,refute_0_336]) ).

cnf(refute_0_338,plain,
    ( meet(X_6,X_7) != meet(X_7,X_6)
    | meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_7,X_6),X_8) = meet(X_6,meet(X_7,X_8)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_7,X_8))) ),[0,0],$fot(meet(X_7,X_6))]]) ).

cnf(refute_0_339,plain,
    ( meet(meet(X_6,X_7),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_7,X_6),X_8) = meet(X_6,meet(X_7,X_8)) ),
    inference(resolve,[$cnf( $equal(meet(X_6,X_7),meet(X_7,X_6)) )],[refute_0_337,refute_0_338]) ).

cnf(refute_0_340,plain,
    meet(meet(X_7,X_6),X_8) = meet(X_6,meet(X_7,X_8)),
    inference(resolve,[$cnf( $equal(meet(meet(X_6,X_7),X_8),meet(X_6,meet(X_7,X_8))) )],[refute_0_127,refute_0_339]) ).

cnf(refute_0_341,plain,
    meet(meet(X_7,X_6),X_8) = meet(X_7,meet(X_6,X_8)),
    inference(subst,[],[associativity_of_meet:[bind(X,$fot(X_7)),bind(Y,$fot(X_6)),bind(Z,$fot(X_8))]]) ).

cnf(refute_0_342,plain,
    ( meet(meet(X_7,X_6),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(meet(X_7,X_6),X_8) != meet(X_7,meet(X_6,X_8))
    | meet(X_7,meet(X_6,X_8)) = meet(X_6,meet(X_7,X_8)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_7,X_6),X_8),meet(X_6,meet(X_7,X_8))) ),[0],$fot(meet(X_7,meet(X_6,X_8)))]]) ).

cnf(refute_0_343,plain,
    ( meet(meet(X_7,X_6),X_8) != meet(X_6,meet(X_7,X_8))
    | meet(X_7,meet(X_6,X_8)) = meet(X_6,meet(X_7,X_8)) ),
    inference(resolve,[$cnf( $equal(meet(meet(X_7,X_6),X_8),meet(X_7,meet(X_6,X_8))) )],[refute_0_341,refute_0_342]) ).

cnf(refute_0_344,plain,
    meet(X_7,meet(X_6,X_8)) = meet(X_6,meet(X_7,X_8)),
    inference(resolve,[$cnf( $equal(meet(meet(X_7,X_6),X_8),meet(X_6,meet(X_7,X_8))) )],[refute_0_340,refute_0_343]) ).

cnf(refute_0_345,plain,
    ( meet(X_7,meet(X_6,X_8)) != meet(X_6,meet(X_7,X_8))
    | meet(X_6,meet(X_7,X_8)) = meet(X_7,meet(X_6,X_8)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_7,meet(X_6,X_8)))),bind(Y0,$fot(meet(X_6,meet(X_7,X_8))))]]) ).

cnf(refute_0_346,plain,
    meet(X_6,meet(X_7,X_8)) = meet(X_7,meet(X_6,X_8)),
    inference(resolve,[$cnf( $equal(meet(X_7,meet(X_6,X_8)),meet(X_6,meet(X_7,X_8))) )],[refute_0_344,refute_0_345]) ).

cnf(refute_0_347,plain,
    meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)),
    inference(subst,[],[refute_0_346:[bind(X_6,$fot(join(meet(X_26,X_27),X_26))),bind(X_7,$fot(X_26)),bind(X_8,$fot(X_27))]]) ).

cnf(refute_0_348,plain,
    ( meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) != meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)))),bind(Y0,$fot(meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)))),bind(Z0,$fot(meet(X_26,join(X_27,meet(X_27,X_26)))))]]) ).

cnf(refute_0_349,plain,
    ( meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))) ),
    inference(resolve,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)),meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27))) )],[refute_0_347,refute_0_348]) ).

cnf(refute_0_350,plain,
    meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) = meet(X_26,join(X_27,meet(X_27,X_26))),
    inference(resolve,[$cnf( $equal(meet(X_26,meet(join(meet(X_26,X_27),X_26),X_27)),meet(X_26,join(X_27,meet(X_27,X_26)))) )],[refute_0_334,refute_0_349]) ).

cnf(refute_0_351,plain,
    ( meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) != meet(X_26,join(X_27,meet(X_27,X_26)))
    | meet(X_26,join(X_27,meet(X_27,X_26))) = join(meet(X_26,X_27),meet(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)),join(meet(X_26,X_27),meet(X_26,X_27))) ),[0],$fot(meet(X_26,join(X_27,meet(X_27,X_26))))]]) ).

cnf(refute_0_352,plain,
    ( meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(X_26,join(X_27,meet(X_27,X_26))) = join(meet(X_26,X_27),meet(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)),meet(X_26,join(X_27,meet(X_27,X_26)))) )],[refute_0_350,refute_0_351]) ).

cnf(refute_0_353,plain,
    ( join(meet(X_26,X_27),meet(X_26,X_27)) != meet(X_26,X_27)
    | meet(X_26,join(X_27,meet(X_27,X_26))) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(X_26,join(X_27,meet(X_27,X_26))) = meet(X_26,X_27) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_26,join(X_27,meet(X_27,X_26))),join(meet(X_26,X_27),meet(X_26,X_27))) ),[1],$fot(meet(X_26,X_27))]]) ).

cnf(refute_0_354,plain,
    ( meet(X_26,join(X_27,meet(X_27,X_26))) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(X_26,join(X_27,meet(X_27,X_26))) = meet(X_26,X_27) ),
    inference(resolve,[$cnf( $equal(join(meet(X_26,X_27),meet(X_26,X_27)),meet(X_26,X_27)) )],[refute_0_287,refute_0_353]) ).

cnf(refute_0_355,plain,
    ( meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)) != join(meet(X_26,X_27),meet(X_26,X_27))
    | meet(X_26,join(X_27,meet(X_27,X_26))) = meet(X_26,X_27) ),
    inference(resolve,[$cnf( $equal(meet(X_26,join(X_27,meet(X_27,X_26))),join(meet(X_26,X_27),meet(X_26,X_27))) )],[refute_0_352,refute_0_354]) ).

cnf(refute_0_356,plain,
    meet(X_26,join(X_27,meet(X_27,X_26))) = meet(X_26,X_27),
    inference(resolve,[$cnf( $equal(meet(join(meet(X_26,X_27),X_26),meet(X_26,X_27)),join(meet(X_26,X_27),meet(X_26,X_27))) )],[refute_0_290,refute_0_355]) ).

cnf(refute_0_357,plain,
    meet(X,join(X_29,meet(X_29,X))) = meet(X,X_29),
    inference(subst,[],[refute_0_356:[bind(X_26,$fot(X)),bind(X_27,$fot(X_29))]]) ).

cnf(refute_0_358,plain,
    ( meet(X,join(Y,join(X_29,meet(X_29,X)))) != join(meet(X,Y),meet(X,join(X_29,meet(X_29,X))))
    | meet(X,join(X_29,meet(X_29,X))) != meet(X,X_29)
    | meet(X,join(Y,join(X_29,meet(X_29,X)))) = join(meet(X,Y),meet(X,X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,join(X_29,meet(X_29,X)))),join(meet(X,Y),meet(X,join(X_29,meet(X_29,X))))) ),[1,1],$fot(meet(X,X_29))]]) ).

cnf(refute_0_359,plain,
    ( meet(X,join(Y,join(X_29,meet(X_29,X)))) != join(meet(X,Y),meet(X,join(X_29,meet(X_29,X))))
    | meet(X,join(Y,join(X_29,meet(X_29,X)))) = join(meet(X,Y),meet(X,X_29)) ),
    inference(resolve,[$cnf( $equal(meet(X,join(X_29,meet(X_29,X))),meet(X,X_29)) )],[refute_0_357,refute_0_358]) ).

cnf(refute_0_360,plain,
    meet(X,join(Y,join(X_29,meet(X_29,X)))) = join(meet(X,Y),meet(X,X_29)),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,join(X_29,meet(X_29,X)))),join(meet(X,Y),meet(X,join(X_29,meet(X_29,X))))) )],[refute_0_285,refute_0_359]) ).

cnf(refute_0_361,plain,
    join(meet(X,Y),meet(X,X_29)) = meet(X,join(Y,X_29)),
    inference(subst,[],[refute_0_47:[bind(Z,$fot(X_29))]]) ).

cnf(refute_0_362,plain,
    ( join(meet(X,Y),meet(X,X_29)) != meet(X,join(Y,X_29))
    | meet(X,join(Y,join(X_29,meet(X_29,X)))) != join(meet(X,Y),meet(X,X_29))
    | meet(X,join(Y,join(X_29,meet(X_29,X)))) = meet(X,join(Y,X_29)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,join(X_29,meet(X_29,X)))),join(meet(X,Y),meet(X,X_29))) ),[1],$fot(meet(X,join(Y,X_29)))]]) ).

cnf(refute_0_363,plain,
    ( meet(X,join(Y,join(X_29,meet(X_29,X)))) != join(meet(X,Y),meet(X,X_29))
    | meet(X,join(Y,join(X_29,meet(X_29,X)))) = meet(X,join(Y,X_29)) ),
    inference(resolve,[$cnf( $equal(join(meet(X,Y),meet(X,X_29)),meet(X,join(Y,X_29))) )],[refute_0_361,refute_0_362]) ).

cnf(refute_0_364,plain,
    meet(X,join(Y,join(X_29,meet(X_29,X)))) = meet(X,join(Y,X_29)),
    inference(resolve,[$cnf( $equal(meet(X,join(Y,join(X_29,meet(X_29,X)))),join(meet(X,Y),meet(X,X_29))) )],[refute_0_360,refute_0_363]) ).

cnf(refute_0_365,plain,
    meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))) = meet(X_13,join(X_59,X_59)),
    inference(subst,[],[refute_0_364:[bind(X,$fot(X_13)),bind(Y,$fot(X_59)),bind(X_29,$fot(X_59))]]) ).

cnf(refute_0_366,plain,
    join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))),
    inference(subst,[],[refute_0_120:[bind(X_12,$fot(X_13)),bind(X_13,$fot(X_59)),bind(X_14,$fot(join(X_59,meet(X_59,X_13))))]]) ).

cnf(refute_0_367,plain,
    ( join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) != meet(X_13,join(X_59,join(X_59,meet(X_59,X_13))))
    | meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))) != meet(X_13,join(X_59,X_59))
    | join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,join(X_59,X_59)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))),bind(Y0,$fot(meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))))),bind(Z0,$fot(meet(X_13,join(X_59,X_59))))]]) ).

cnf(refute_0_368,plain,
    ( meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))) != meet(X_13,join(X_59,X_59))
    | join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,join(X_59,X_59)) ),
    inference(resolve,[$cnf( $equal(join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))),meet(X_13,join(X_59,join(X_59,meet(X_59,X_13))))) )],[refute_0_366,refute_0_367]) ).

cnf(refute_0_369,plain,
    join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,join(X_59,X_59)),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_59,join(X_59,meet(X_59,X_13)))),meet(X_13,join(X_59,X_59))) )],[refute_0_365,refute_0_368]) ).

cnf(refute_0_370,plain,
    ( join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) != meet(X_13,join(X_59,X_59))
    | meet(X_13,join(X_59,X_59)) != meet(X_13,X_59)
    | join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,X_59) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))),bind(Y0,$fot(meet(X_13,join(X_59,X_59)))),bind(Z0,$fot(meet(X_13,X_59)))]]) ).

cnf(refute_0_371,plain,
    ( meet(X_13,join(X_59,X_59)) != meet(X_13,X_59)
    | join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,X_59) ),
    inference(resolve,[$cnf( $equal(join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))),meet(X_13,join(X_59,X_59))) )],[refute_0_369,refute_0_370]) ).

cnf(refute_0_372,plain,
    join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) = meet(X_13,X_59),
    inference(resolve,[$cnf( $equal(meet(X_13,join(X_59,X_59)),meet(X_13,X_59)) )],[refute_0_284,refute_0_371]) ).

cnf(refute_0_373,plain,
    join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))),
    introduced(tautology,[refl,[$fot(join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))))]]) ).

cnf(refute_0_374,plain,
    ( join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) != meet(X_13,X_59)
    | join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_59,meet(X_13,X_59)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))) ),[1,1],$fot(meet(X_13,X_59))]]) ).

cnf(refute_0_375,plain,
    ( join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))) != meet(X_13,X_59)
    | join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_59,meet(X_13,X_59)) ),
    inference(resolve,[$cnf( $equal(join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_373,refute_0_374]) ).

cnf(refute_0_376,plain,
    join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_59,meet(X_13,X_59)),
    inference(resolve,[$cnf( $equal(join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))),meet(X_13,X_59)) )],[refute_0_372,refute_0_375]) ).

cnf(refute_0_377,plain,
    join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) = join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_59)),bind(Y,$fot(meet(X_59,X_13))),bind(Z,$fot(meet(X_13,join(X_59,meet(X_59,X_13)))))]]) ).

cnf(refute_0_378,plain,
    ( join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_59,meet(X_13,X_59))
    | join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) != join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) = join(X_59,meet(X_13,X_59)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))),bind(Y0,$fot(join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))))),bind(Z0,$fot(join(X_59,meet(X_13,X_59))))]]) ).

cnf(refute_0_379,plain,
    ( join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_59,meet(X_13,X_59))
    | join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) = join(X_59,meet(X_13,X_59)) ),
    inference(resolve,[$cnf( $equal(join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))),join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_377,refute_0_378]) ).

cnf(refute_0_380,plain,
    join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) = join(X_59,meet(X_13,X_59)),
    inference(resolve,[$cnf( $equal(join(X_59,join(meet(X_59,X_13),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_59,meet(X_13,X_59))) )],[refute_0_376,refute_0_379]) ).

cnf(refute_0_381,plain,
    join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))),
    introduced(tautology,[refl,[$fot(join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))))]]) ).

cnf(refute_0_382,plain,
    ( join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) != join(X_59,meet(X_13,X_59))
    | join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))) ),[1,1],$fot(join(X_59,meet(X_13,X_59)))]]) ).

cnf(refute_0_383,plain,
    ( join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))) != join(X_59,meet(X_13,X_59))
    | join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    inference(resolve,[$cnf( $equal(join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_381,refute_0_382]) ).

cnf(refute_0_384,plain,
    join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))),
    inference(resolve,[$cnf( $equal(join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))),join(X_59,meet(X_13,X_59))) )],[refute_0_380,refute_0_383]) ).

cnf(refute_0_385,plain,
    join(X,join(X_9,X_10)) = join(join(X_9,X_10),X),
    inference(subst,[],[commutativity_of_join:[bind(Y,$fot(join(X_9,X_10)))]]) ).

cnf(refute_0_386,plain,
    join(join(X_9,X_10),X) = join(X_9,join(X_10,X)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_9)),bind(Y,$fot(X_10)),bind(Z,$fot(X))]]) ).

cnf(refute_0_387,plain,
    ( join(X,join(X_9,X_10)) != join(join(X_9,X_10),X)
    | join(join(X_9,X_10),X) != join(X_9,join(X_10,X))
    | join(X,join(X_9,X_10)) = join(X_9,join(X_10,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_9,X_10)),join(X_9,join(X_10,X))) ),[0],$fot(join(join(X_9,X_10),X))]]) ).

cnf(refute_0_388,plain,
    ( join(X,join(X_9,X_10)) != join(join(X_9,X_10),X)
    | join(X,join(X_9,X_10)) = join(X_9,join(X_10,X)) ),
    inference(resolve,[$cnf( $equal(join(join(X_9,X_10),X),join(X_9,join(X_10,X))) )],[refute_0_386,refute_0_387]) ).

cnf(refute_0_389,plain,
    join(X,join(X_9,X_10)) = join(X_9,join(X_10,X)),
    inference(resolve,[$cnf( $equal(join(X,join(X_9,X_10)),join(join(X_9,X_10),X)) )],[refute_0_385,refute_0_388]) ).

cnf(refute_0_390,plain,
    join(join(X_20,X_43),join(X_44,X_43)) = join(X_44,join(X_43,join(X_20,X_43))),
    inference(subst,[],[refute_0_389:[bind(X,$fot(join(X_20,X_43))),bind(X_10,$fot(X_43)),bind(X_9,$fot(X_44))]]) ).

cnf(refute_0_391,plain,
    join(join(Y,X_20),Y) = join(Y,join(Y,X_20)),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(join(Y,X_20)))]]) ).

cnf(refute_0_392,plain,
    ( join(Y,join(Y,X_20)) != join(Y,X_20)
    | join(join(Y,X_20),Y) != join(Y,join(Y,X_20))
    | join(join(Y,X_20),Y) = join(Y,X_20) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(Y,X_20),Y),join(Y,join(Y,X_20))) ),[1],$fot(join(Y,X_20))]]) ).

cnf(refute_0_393,plain,
    ( join(join(Y,X_20),Y) != join(Y,join(Y,X_20))
    | join(join(Y,X_20),Y) = join(Y,X_20) ),
    inference(resolve,[$cnf( $equal(join(Y,join(Y,X_20)),join(Y,X_20)) )],[refute_0_240,refute_0_392]) ).

cnf(refute_0_394,plain,
    join(join(Y,X_20),Y) = join(Y,X_20),
    inference(resolve,[$cnf( $equal(join(join(Y,X_20),Y),join(Y,join(Y,X_20))) )],[refute_0_391,refute_0_393]) ).

cnf(refute_0_395,plain,
    join(join(Y,X_20),Y) = join(Y,join(X_20,Y)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(Y)),bind(Y,$fot(X_20)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_396,plain,
    ( join(join(Y,X_20),Y) != join(Y,X_20)
    | join(join(Y,X_20),Y) != join(Y,join(X_20,Y))
    | join(Y,join(X_20,Y)) = join(Y,X_20) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(Y,X_20),Y),join(Y,X_20)) ),[0],$fot(join(Y,join(X_20,Y)))]]) ).

cnf(refute_0_397,plain,
    ( join(join(Y,X_20),Y) != join(Y,X_20)
    | join(Y,join(X_20,Y)) = join(Y,X_20) ),
    inference(resolve,[$cnf( $equal(join(join(Y,X_20),Y),join(Y,join(X_20,Y))) )],[refute_0_395,refute_0_396]) ).

cnf(refute_0_398,plain,
    join(Y,join(X_20,Y)) = join(Y,X_20),
    inference(resolve,[$cnf( $equal(join(join(Y,X_20),Y),join(Y,X_20)) )],[refute_0_394,refute_0_397]) ).

cnf(refute_0_399,plain,
    join(X_43,join(X_20,X_43)) = join(X_43,X_20),
    inference(subst,[],[refute_0_398:[bind(Y,$fot(X_43))]]) ).

cnf(refute_0_400,plain,
    ( join(X_43,join(X_20,X_43)) != join(X_43,X_20)
    | join(join(X_20,X_43),join(X_44,X_43)) != join(X_44,join(X_43,join(X_20,X_43)))
    | join(join(X_20,X_43),join(X_44,X_43)) = join(X_44,join(X_43,X_20)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_44,join(X_43,join(X_20,X_43)))) ),[1,1],$fot(join(X_43,X_20))]]) ).

cnf(refute_0_401,plain,
    ( join(join(X_20,X_43),join(X_44,X_43)) != join(X_44,join(X_43,join(X_20,X_43)))
    | join(join(X_20,X_43),join(X_44,X_43)) = join(X_44,join(X_43,X_20)) ),
    inference(resolve,[$cnf( $equal(join(X_43,join(X_20,X_43)),join(X_43,X_20)) )],[refute_0_399,refute_0_400]) ).

cnf(refute_0_402,plain,
    join(join(X_20,X_43),join(X_44,X_43)) = join(X_44,join(X_43,X_20)),
    inference(resolve,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_44,join(X_43,join(X_20,X_43)))) )],[refute_0_390,refute_0_401]) ).

cnf(refute_0_403,plain,
    join(X_21,join(join(X,Y),X_21)) = join(X_21,join(X,Y)),
    inference(subst,[],[refute_0_398:[bind(Y,$fot(X_21)),bind(X_20,$fot(join(X,Y)))]]) ).

cnf(refute_0_404,plain,
    join(join(X,Y),X_21) = join(X,join(Y,X_21)),
    inference(subst,[],[associativity_of_join:[bind(Z,$fot(X_21))]]) ).

cnf(refute_0_405,plain,
    ( join(X_21,join(join(X,Y),X_21)) != join(X_21,join(X,Y))
    | join(join(X,Y),X_21) != join(X,join(Y,X_21))
    | join(X_21,join(X,join(Y,X_21))) = join(X_21,join(X,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_21,join(join(X,Y),X_21)),join(X_21,join(X,Y))) ),[0,1],$fot(join(X,join(Y,X_21)))]]) ).

cnf(refute_0_406,plain,
    ( join(X_21,join(join(X,Y),X_21)) != join(X_21,join(X,Y))
    | join(X_21,join(X,join(Y,X_21))) = join(X_21,join(X,Y)) ),
    inference(resolve,[$cnf( $equal(join(join(X,Y),X_21),join(X,join(Y,X_21))) )],[refute_0_404,refute_0_405]) ).

cnf(refute_0_407,plain,
    join(X_21,join(X,join(Y,X_21))) = join(X_21,join(X,Y)),
    inference(resolve,[$cnf( $equal(join(X_21,join(join(X,Y),X_21)),join(X_21,join(X,Y))) )],[refute_0_403,refute_0_406]) ).

cnf(refute_0_408,plain,
    join(X_43,join(X_44,join(X_20,X_43))) = join(X_43,join(X_44,X_20)),
    inference(subst,[],[refute_0_407:[bind(X,$fot(X_44)),bind(Y,$fot(X_20)),bind(X_21,$fot(X_43))]]) ).

cnf(refute_0_409,plain,
    join(X_42,join(X_44,join(X_20,X_44))) = join(X_44,join(join(X_20,X_44),X_42)),
    inference(subst,[],[refute_0_389:[bind(X,$fot(X_42)),bind(X_10,$fot(join(X_20,X_44))),bind(X_9,$fot(X_44))]]) ).

cnf(refute_0_410,plain,
    join(X_44,join(X_20,X_44)) = join(X_44,X_20),
    inference(subst,[],[refute_0_398:[bind(Y,$fot(X_44))]]) ).

cnf(refute_0_411,plain,
    ( join(X_42,join(X_44,join(X_20,X_44))) != join(X_44,join(join(X_20,X_44),X_42))
    | join(X_44,join(X_20,X_44)) != join(X_44,X_20)
    | join(X_42,join(X_44,X_20)) = join(X_44,join(join(X_20,X_44),X_42)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_42,join(X_44,join(X_20,X_44))),join(X_44,join(join(X_20,X_44),X_42))) ),[0,1],$fot(join(X_44,X_20))]]) ).

cnf(refute_0_412,plain,
    ( join(X_42,join(X_44,join(X_20,X_44))) != join(X_44,join(join(X_20,X_44),X_42))
    | join(X_42,join(X_44,X_20)) = join(X_44,join(join(X_20,X_44),X_42)) ),
    inference(resolve,[$cnf( $equal(join(X_44,join(X_20,X_44)),join(X_44,X_20)) )],[refute_0_410,refute_0_411]) ).

cnf(refute_0_413,plain,
    join(X_42,join(X_44,X_20)) = join(X_44,join(join(X_20,X_44),X_42)),
    inference(resolve,[$cnf( $equal(join(X_42,join(X_44,join(X_20,X_44))),join(X_44,join(join(X_20,X_44),X_42))) )],[refute_0_409,refute_0_412]) ).

cnf(refute_0_414,plain,
    join(X_44,join(X_20,join(X_44,X_42))) = join(X_20,join(X_44,X_42)),
    inference(subst,[],[refute_0_268:[bind(X,$fot(X_20)),bind(Y,$fot(X_44)),bind(X_20,$fot(X_42))]]) ).

cnf(refute_0_415,plain,
    join(join(X_20,X_44),X_42) = join(X_20,join(X_44,X_42)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_20)),bind(Y,$fot(X_44)),bind(Z,$fot(X_42))]]) ).

cnf(refute_0_416,plain,
    join(X_44,join(join(X_20,X_44),X_42)) = join(X_44,join(join(X_20,X_44),X_42)),
    introduced(tautology,[refl,[$fot(join(X_44,join(join(X_20,X_44),X_42)))]]) ).

cnf(refute_0_417,plain,
    ( join(X_44,join(join(X_20,X_44),X_42)) != join(X_44,join(join(X_20,X_44),X_42))
    | join(join(X_20,X_44),X_42) != join(X_20,join(X_44,X_42))
    | join(X_44,join(join(X_20,X_44),X_42)) = join(X_44,join(X_20,join(X_44,X_42))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_44,join(join(X_20,X_44),X_42)),join(X_44,join(join(X_20,X_44),X_42))) ),[1,1],$fot(join(X_20,join(X_44,X_42)))]]) ).

cnf(refute_0_418,plain,
    ( join(join(X_20,X_44),X_42) != join(X_20,join(X_44,X_42))
    | join(X_44,join(join(X_20,X_44),X_42)) = join(X_44,join(X_20,join(X_44,X_42))) ),
    inference(resolve,[$cnf( $equal(join(X_44,join(join(X_20,X_44),X_42)),join(X_44,join(join(X_20,X_44),X_42))) )],[refute_0_416,refute_0_417]) ).

cnf(refute_0_419,plain,
    join(X_44,join(join(X_20,X_44),X_42)) = join(X_44,join(X_20,join(X_44,X_42))),
    inference(resolve,[$cnf( $equal(join(join(X_20,X_44),X_42),join(X_20,join(X_44,X_42))) )],[refute_0_415,refute_0_418]) ).

cnf(refute_0_420,plain,
    ( join(X_44,join(X_20,join(X_44,X_42))) != join(X_20,join(X_44,X_42))
    | join(X_44,join(join(X_20,X_44),X_42)) != join(X_44,join(X_20,join(X_44,X_42)))
    | join(X_44,join(join(X_20,X_44),X_42)) = join(X_20,join(X_44,X_42)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(X_44,join(join(X_20,X_44),X_42)))),bind(Y0,$fot(join(X_44,join(X_20,join(X_44,X_42))))),bind(Z0,$fot(join(X_20,join(X_44,X_42))))]]) ).

cnf(refute_0_421,plain,
    ( join(X_44,join(X_20,join(X_44,X_42))) != join(X_20,join(X_44,X_42))
    | join(X_44,join(join(X_20,X_44),X_42)) = join(X_20,join(X_44,X_42)) ),
    inference(resolve,[$cnf( $equal(join(X_44,join(join(X_20,X_44),X_42)),join(X_44,join(X_20,join(X_44,X_42)))) )],[refute_0_419,refute_0_420]) ).

cnf(refute_0_422,plain,
    join(X_44,join(join(X_20,X_44),X_42)) = join(X_20,join(X_44,X_42)),
    inference(resolve,[$cnf( $equal(join(X_44,join(X_20,join(X_44,X_42))),join(X_20,join(X_44,X_42))) )],[refute_0_414,refute_0_421]) ).

cnf(refute_0_423,plain,
    ( join(X_42,join(X_44,X_20)) != join(X_44,join(join(X_20,X_44),X_42))
    | join(X_44,join(join(X_20,X_44),X_42)) != join(X_20,join(X_44,X_42))
    | join(X_42,join(X_44,X_20)) = join(X_20,join(X_44,X_42)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_42,join(X_44,X_20)),join(X_20,join(X_44,X_42))) ),[0],$fot(join(X_44,join(join(X_20,X_44),X_42)))]]) ).

cnf(refute_0_424,plain,
    ( join(X_42,join(X_44,X_20)) != join(X_44,join(join(X_20,X_44),X_42))
    | join(X_42,join(X_44,X_20)) = join(X_20,join(X_44,X_42)) ),
    inference(resolve,[$cnf( $equal(join(X_44,join(join(X_20,X_44),X_42)),join(X_20,join(X_44,X_42))) )],[refute_0_422,refute_0_423]) ).

cnf(refute_0_425,plain,
    join(X_42,join(X_44,X_20)) = join(X_20,join(X_44,X_42)),
    inference(resolve,[$cnf( $equal(join(X_42,join(X_44,X_20)),join(X_44,join(join(X_20,X_44),X_42))) )],[refute_0_413,refute_0_424]) ).

cnf(refute_0_426,plain,
    ( join(X_42,join(X_44,X_20)) != join(X_20,join(X_44,X_42))
    | join(X_20,join(X_44,X_42)) = join(X_42,join(X_44,X_20)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_42,join(X_44,X_20)))),bind(Y0,$fot(join(X_20,join(X_44,X_42))))]]) ).

cnf(refute_0_427,plain,
    join(X_20,join(X_44,X_42)) = join(X_42,join(X_44,X_20)),
    inference(resolve,[$cnf( $equal(join(X_42,join(X_44,X_20)),join(X_20,join(X_44,X_42))) )],[refute_0_425,refute_0_426]) ).

cnf(refute_0_428,plain,
    join(join(X_20,X_43),join(X_44,X_43)) = join(X_43,join(X_44,join(X_20,X_43))),
    inference(subst,[],[refute_0_427:[bind(X_20,$fot(join(X_20,X_43))),bind(X_42,$fot(X_43))]]) ).

cnf(refute_0_429,plain,
    ( join(X_43,join(X_44,join(X_20,X_43))) != join(X_43,join(X_44,X_20))
    | join(join(X_20,X_43),join(X_44,X_43)) != join(X_43,join(X_44,join(X_20,X_43)))
    | join(join(X_20,X_43),join(X_44,X_43)) = join(X_43,join(X_44,X_20)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_20,X_43),join(X_44,X_43)))),bind(Y0,$fot(join(X_43,join(X_44,join(X_20,X_43))))),bind(Z0,$fot(join(X_43,join(X_44,X_20))))]]) ).

cnf(refute_0_430,plain,
    ( join(X_43,join(X_44,join(X_20,X_43))) != join(X_43,join(X_44,X_20))
    | join(join(X_20,X_43),join(X_44,X_43)) = join(X_43,join(X_44,X_20)) ),
    inference(resolve,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_43,join(X_44,join(X_20,X_43)))) )],[refute_0_428,refute_0_429]) ).

cnf(refute_0_431,plain,
    join(join(X_20,X_43),join(X_44,X_43)) = join(X_43,join(X_44,X_20)),
    inference(resolve,[$cnf( $equal(join(X_43,join(X_44,join(X_20,X_43))),join(X_43,join(X_44,X_20))) )],[refute_0_408,refute_0_430]) ).

cnf(refute_0_432,plain,
    ( join(join(X_20,X_43),join(X_44,X_43)) != join(X_43,join(X_44,X_20))
    | join(join(X_20,X_43),join(X_44,X_43)) != join(X_44,join(X_43,X_20))
    | join(X_43,join(X_44,X_20)) = join(X_44,join(X_43,X_20)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_44,join(X_43,X_20))) ),[0],$fot(join(X_43,join(X_44,X_20)))]]) ).

cnf(refute_0_433,plain,
    ( join(join(X_20,X_43),join(X_44,X_43)) != join(X_44,join(X_43,X_20))
    | join(X_43,join(X_44,X_20)) = join(X_44,join(X_43,X_20)) ),
    inference(resolve,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_43,join(X_44,X_20))) )],[refute_0_431,refute_0_432]) ).

cnf(refute_0_434,plain,
    join(X_43,join(X_44,X_20)) = join(X_44,join(X_43,X_20)),
    inference(resolve,[$cnf( $equal(join(join(X_20,X_43),join(X_44,X_43)),join(X_44,join(X_43,X_20))) )],[refute_0_402,refute_0_433]) ).

cnf(refute_0_435,plain,
    ( join(X_43,join(X_44,X_20)) != join(X_44,join(X_43,X_20))
    | join(X_44,join(X_43,X_20)) = join(X_43,join(X_44,X_20)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_43,join(X_44,X_20)))),bind(Y0,$fot(join(X_44,join(X_43,X_20))))]]) ).

cnf(refute_0_436,plain,
    join(X_44,join(X_43,X_20)) = join(X_43,join(X_44,X_20)),
    inference(resolve,[$cnf( $equal(join(X_43,join(X_44,X_20)),join(X_44,join(X_43,X_20))) )],[refute_0_434,refute_0_435]) ).

cnf(refute_0_437,plain,
    join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))),
    inference(subst,[],[refute_0_436:[bind(X_20,$fot(meet(X_13,join(X_59,meet(X_59,X_13))))),bind(X_43,$fot(X_13)),bind(X_44,$fot(join(X_59,meet(X_59,X_13))))]]) ).

cnf(refute_0_438,plain,
    ( join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_13,join(X_59,meet(X_13,X_59)))
    | join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))))),bind(Y0,$fot(join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))))),bind(Z0,$fot(join(X_13,join(X_59,meet(X_13,X_59)))))]]) ).

cnf(refute_0_439,plain,
    ( join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_13,join(X_59,meet(X_13,X_59)))
    | join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    inference(resolve,[$cnf( $equal(join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_437,refute_0_438]) ).

cnf(refute_0_440,plain,
    join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) = join(X_13,join(X_59,meet(X_13,X_59))),
    inference(resolve,[$cnf( $equal(join(X_13,join(join(X_59,meet(X_59,X_13)),meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_13,join(X_59,meet(X_13,X_59)))) )],[refute_0_384,refute_0_439]) ).

cnf(refute_0_441,plain,
    ( join(X_59,X_13) != join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))) != join(X_13,join(X_59,meet(X_13,X_59)))
    | join(X_59,X_13) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_59,X_13),join(X_13,join(X_59,meet(X_13,X_59)))) ),[0],$fot(join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))))]]) ).

cnf(refute_0_442,plain,
    ( join(X_59,X_13) != join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))
    | join(X_59,X_13) = join(X_13,join(X_59,meet(X_13,X_59))) ),
    inference(resolve,[$cnf( $equal(join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13))))),join(X_13,join(X_59,meet(X_13,X_59)))) )],[refute_0_440,refute_0_441]) ).

cnf(refute_0_443,plain,
    join(X_59,X_13) = join(X_13,join(X_59,meet(X_13,X_59))),
    inference(resolve,[$cnf( $equal(join(X_59,X_13),join(join(X_59,meet(X_59,X_13)),join(X_13,meet(X_13,join(X_59,meet(X_59,X_13)))))) )],[refute_0_279,refute_0_442]) ).

cnf(refute_0_444,plain,
    join(X_59,X_97) = join(X_97,join(X_59,meet(X_97,X_59))),
    inference(subst,[],[refute_0_443:[bind(X_13,$fot(X_97))]]) ).

cnf(refute_0_445,plain,
    ( join(X_59,X_97) != join(X_97,join(X_59,meet(X_97,X_59)))
    | join(X_97,join(X_59,meet(X_97,X_59))) = join(X_59,X_97) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_59,X_97))),bind(Y0,$fot(join(X_97,join(X_59,meet(X_97,X_59)))))]]) ).

cnf(refute_0_446,plain,
    join(X_97,join(X_59,meet(X_97,X_59))) = join(X_59,X_97),
    inference(resolve,[$cnf( $equal(join(X_59,X_97),join(X_97,join(X_59,meet(X_97,X_59)))) )],[refute_0_444,refute_0_445]) ).

cnf(refute_0_447,plain,
    ( join(X_97,join(X_59,meet(X_97,X_59))) != join(X_59,X_97)
    | meet(join(X_97,X_96),join(X_97,join(X_59,meet(X_97,X_59)))) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,join(X_59,meet(X_97,X_59)))),join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))) ),[0,1],$fot(join(X_59,X_97))]]) ).

cnf(refute_0_448,plain,
    ( meet(join(X_97,X_96),join(X_97,join(X_59,meet(X_97,X_59)))) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) ),
    inference(resolve,[$cnf( $equal(join(X_97,join(X_59,meet(X_97,X_59))),join(X_59,X_97)) )],[refute_0_446,refute_0_447]) ).

cnf(refute_0_449,plain,
    meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_97,join(X_59,meet(X_97,X_59)))),join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))) )],[refute_0_179,refute_0_448]) ).

cnf(refute_0_450,plain,
    join(X_97,meet(join(X_97,X_96),X_59)) = join(X_97,meet(X_96,join(X_97,X_59))),
    inference(subst,[],[refute_0_172:[bind(X_98,$fot(X_59))]]) ).

cnf(refute_0_451,plain,
    meet(join(X_34,X_14),join(X_34,X_35)) = join(meet(X_34,join(X_34,X_14)),meet(join(X_34,X_14),X_35)),
    inference(subst,[],[refute_0_113:[bind(X_12,$fot(join(X_34,X_14))),bind(X_13,$fot(X_34)),bind(X_14,$fot(X_35))]]) ).

cnf(refute_0_452,plain,
    meet(X_34,join(X_34,X_14)) = join(X_34,meet(X_34,X_14)),
    inference(subst,[],[refute_0_205:[bind(X_13,$fot(X_34))]]) ).

cnf(refute_0_453,plain,
    ( meet(X_34,join(X_34,X_14)) != join(X_34,meet(X_34,X_14))
    | meet(join(X_34,X_14),join(X_34,X_35)) != join(meet(X_34,join(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | meet(join(X_34,X_14),join(X_34,X_35)) = join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_34,X_14),join(X_34,X_35)),join(meet(X_34,join(X_34,X_14)),meet(join(X_34,X_14),X_35))) ),[1,0],$fot(join(X_34,meet(X_34,X_14)))]]) ).

cnf(refute_0_454,plain,
    ( meet(join(X_34,X_14),join(X_34,X_35)) != join(meet(X_34,join(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | meet(join(X_34,X_14),join(X_34,X_35)) = join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) ),
    inference(resolve,[$cnf( $equal(meet(X_34,join(X_34,X_14)),join(X_34,meet(X_34,X_14))) )],[refute_0_452,refute_0_453]) ).

cnf(refute_0_455,plain,
    meet(join(X_34,X_14),join(X_34,X_35)) = join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)),
    inference(resolve,[$cnf( $equal(meet(join(X_34,X_14),join(X_34,X_35)),join(meet(X_34,join(X_34,X_14)),meet(join(X_34,X_14),X_35))) )],[refute_0_451,refute_0_454]) ).

cnf(refute_0_456,plain,
    meet(join(X_34,X_14),join(X_34,X_35)) = join(X_34,meet(join(X_34,X_14),X_35)),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_14)),bind(X_25,$fot(X_34)),bind(X_27,$fot(X_35))]]) ).

cnf(refute_0_457,plain,
    ( meet(join(X_34,X_14),join(X_34,X_35)) != join(X_34,meet(join(X_34,X_14),X_35))
    | meet(join(X_34,X_14),join(X_34,X_35)) != join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | join(X_34,meet(join(X_34,X_14),X_35)) = join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_34,X_14),join(X_34,X_35)),join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))) ),[0],$fot(join(X_34,meet(join(X_34,X_14),X_35)))]]) ).

cnf(refute_0_458,plain,
    ( meet(join(X_34,X_14),join(X_34,X_35)) != join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | join(X_34,meet(join(X_34,X_14),X_35)) = join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_34,X_14),join(X_34,X_35)),join(X_34,meet(join(X_34,X_14),X_35))) )],[refute_0_456,refute_0_457]) ).

cnf(refute_0_459,plain,
    meet(X_14,X_12) = meet(X_12,X_14),
    inference(subst,[],[commutativity_of_meet:[bind(X,$fot(X_14)),bind(Y,$fot(X_12))]]) ).

cnf(refute_0_460,plain,
    ( meet(X_14,X_12) != meet(X_12,X_14)
    | meet(X_12,X_14) = meet(X_14,X_12) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(X_14,X_12))),bind(Y0,$fot(meet(X_12,X_14)))]]) ).

cnf(refute_0_461,plain,
    meet(X_12,X_14) = meet(X_14,X_12),
    inference(resolve,[$cnf( $equal(meet(X_14,X_12),meet(X_12,X_14)) )],[refute_0_459,refute_0_460]) ).

cnf(refute_0_462,plain,
    ( meet(X_12,X_14) != meet(X_14,X_12)
    | meet(X_12,join(X_13,X_14)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | meet(X_12,join(X_13,X_14)) = join(meet(X_12,X_13),meet(X_14,X_12)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_12,X_13),meet(X_12,X_14))) ),[1,1],$fot(meet(X_14,X_12))]]) ).

cnf(refute_0_463,plain,
    ( meet(X_12,join(X_13,X_14)) != join(meet(X_12,X_13),meet(X_12,X_14))
    | meet(X_12,join(X_13,X_14)) = join(meet(X_12,X_13),meet(X_14,X_12)) ),
    inference(resolve,[$cnf( $equal(meet(X_12,X_14),meet(X_14,X_12)) )],[refute_0_461,refute_0_462]) ).

cnf(refute_0_464,plain,
    meet(X_12,join(X_13,X_14)) = join(meet(X_12,X_13),meet(X_14,X_12)),
    inference(resolve,[$cnf( $equal(meet(X_12,join(X_13,X_14)),join(meet(X_12,X_13),meet(X_12,X_14))) )],[refute_0_68,refute_0_463]) ).

cnf(refute_0_465,plain,
    meet(join(X_32,X_14),join(X_31,X_32)) = join(meet(join(X_32,X_14),X_31),meet(X_32,join(X_32,X_14))),
    inference(subst,[],[refute_0_464:[bind(X_12,$fot(join(X_32,X_14))),bind(X_13,$fot(X_31)),bind(X_14,$fot(X_32))]]) ).

cnf(refute_0_466,plain,
    meet(X_32,join(X_32,X_14)) = join(X_32,meet(X_32,X_14)),
    inference(subst,[],[refute_0_205:[bind(X_13,$fot(X_32))]]) ).

cnf(refute_0_467,plain,
    ( meet(X_32,join(X_32,X_14)) != join(X_32,meet(X_32,X_14))
    | meet(join(X_32,X_14),join(X_31,X_32)) != join(meet(join(X_32,X_14),X_31),meet(X_32,join(X_32,X_14)))
    | meet(join(X_32,X_14),join(X_31,X_32)) = join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_32,X_14),join(X_31,X_32)),join(meet(join(X_32,X_14),X_31),meet(X_32,join(X_32,X_14)))) ),[1,1],$fot(join(X_32,meet(X_32,X_14)))]]) ).

cnf(refute_0_468,plain,
    ( meet(join(X_32,X_14),join(X_31,X_32)) != join(meet(join(X_32,X_14),X_31),meet(X_32,join(X_32,X_14)))
    | meet(join(X_32,X_14),join(X_31,X_32)) = join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) ),
    inference(resolve,[$cnf( $equal(meet(X_32,join(X_32,X_14)),join(X_32,meet(X_32,X_14))) )],[refute_0_466,refute_0_467]) ).

cnf(refute_0_469,plain,
    meet(join(X_32,X_14),join(X_31,X_32)) = join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))),
    inference(resolve,[$cnf( $equal(meet(join(X_32,X_14),join(X_31,X_32)),join(meet(join(X_32,X_14),X_31),meet(X_32,join(X_32,X_14)))) )],[refute_0_465,refute_0_468]) ).

cnf(refute_0_470,plain,
    join(X_11,X_10) = join(X_10,X_11),
    inference(subst,[],[commutativity_of_join:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_471,plain,
    ( join(X_11,X_10) != join(X_10,X_11)
    | join(X_10,X_11) = join(X_11,X_10) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_11,X_10))),bind(Y0,$fot(join(X_10,X_11)))]]) ).

cnf(refute_0_472,plain,
    join(X_10,X_11) = join(X_11,X_10),
    inference(resolve,[$cnf( $equal(join(X_11,X_10),join(X_10,X_11)) )],[refute_0_470,refute_0_471]) ).

cnf(refute_0_473,plain,
    ( join(X_10,X_11) != join(X_11,X_10)
    | join(join(X_9,X_10),X_11) != join(X_9,join(X_10,X_11))
    | join(join(X_9,X_10),X_11) = join(X_9,join(X_11,X_10)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_10,X_11))) ),[1,1],$fot(join(X_11,X_10))]]) ).

cnf(refute_0_474,plain,
    ( join(join(X_9,X_10),X_11) != join(X_9,join(X_10,X_11))
    | join(join(X_9,X_10),X_11) = join(X_9,join(X_11,X_10)) ),
    inference(resolve,[$cnf( $equal(join(X_10,X_11),join(X_11,X_10)) )],[refute_0_472,refute_0_473]) ).

cnf(refute_0_475,plain,
    join(join(X_9,X_10),X_11) = join(X_9,join(X_11,X_10)),
    inference(resolve,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_10,X_11))) )],[refute_0_249,refute_0_474]) ).

cnf(refute_0_476,plain,
    ( join(join(X_9,X_10),X_11) != join(X_9,join(X_10,X_11))
    | join(join(X_9,X_10),X_11) != join(X_9,join(X_11,X_10))
    | join(X_9,join(X_10,X_11)) = join(X_9,join(X_11,X_10)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_11,X_10))) ),[0],$fot(join(X_9,join(X_10,X_11)))]]) ).

cnf(refute_0_477,plain,
    ( join(join(X_9,X_10),X_11) != join(X_9,join(X_11,X_10))
    | join(X_9,join(X_10,X_11)) = join(X_9,join(X_11,X_10)) ),
    inference(resolve,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_10,X_11))) )],[refute_0_249,refute_0_476]) ).

cnf(refute_0_478,plain,
    join(X_9,join(X_10,X_11)) = join(X_9,join(X_11,X_10)),
    inference(resolve,[$cnf( $equal(join(join(X_9,X_10),X_11),join(X_9,join(X_11,X_10))) )],[refute_0_475,refute_0_477]) ).

cnf(refute_0_479,plain,
    ( join(X_9,join(X_10,X_11)) != join(X_9,join(X_11,X_10))
    | join(X_9,join(X_11,X_10)) = join(X_9,join(X_10,X_11)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_9,join(X_10,X_11)))),bind(Y0,$fot(join(X_9,join(X_11,X_10))))]]) ).

cnf(refute_0_480,plain,
    join(X_9,join(X_11,X_10)) = join(X_9,join(X_10,X_11)),
    inference(resolve,[$cnf( $equal(join(X_9,join(X_10,X_11)),join(X_9,join(X_11,X_10))) )],[refute_0_478,refute_0_479]) ).

cnf(refute_0_481,plain,
    join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))),
    inference(subst,[],[refute_0_480:[bind(X_10,$fot(meet(X_32,X_14))),bind(X_11,$fot(meet(join(X_32,X_14),X_31))),bind(X_9,$fot(X_32))]]) ).

cnf(refute_0_482,plain,
    meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),
    inference(subst,[],[refute_0_205:[bind(X_13,$fot(join(X_25,X_26))),bind(X_14,$fot(join(X_25,meet(X_26,X_27))))]]) ).

cnf(refute_0_483,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) ),[1,1],$fot(join(X_25,meet(X_26,X_27)))]]) ).

cnf(refute_0_484,plain,
    ( meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_9,refute_0_483]) ).

cnf(refute_0_485,plain,
    meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(join(X_25,X_26),join(X_25,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) )],[refute_0_482,refute_0_484]) ).

cnf(refute_0_486,plain,
    join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))),
    inference(subst,[],[refute_0_268:[bind(X,$fot(X_26)),bind(Y,$fot(X_25)),bind(X_20,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_487,plain,
    join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),
    introduced(tautology,[refl,[$fot(join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))]]) ).

cnf(refute_0_488,plain,
    ( join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) ),[1,1],$fot(join(X_25,meet(X_26,X_27)))]]) ).

cnf(refute_0_489,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) )],[refute_0_487,refute_0_488]) ).

cnf(refute_0_490,plain,
    join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_9,refute_0_489]) ).

cnf(refute_0_491,plain,
    join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),
    introduced(tautology,[refl,[$fot(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))))]]) ).

cnf(refute_0_492,plain,
    ( join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) != join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))
    | join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))) ),[1,1],$fot(join(X_26,join(X_25,meet(X_26,X_27))))]]) ).

cnf(refute_0_493,plain,
    ( join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))) ),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))) )],[refute_0_491,refute_0_492]) ).

cnf(refute_0_494,plain,
    join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))),
    inference(resolve,[$cnf( $equal(join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_26,join(X_25,meet(X_26,X_27)))) )],[refute_0_490,refute_0_493]) ).

cnf(refute_0_495,plain,
    ( join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) != join(X_25,join(X_26,join(X_25,meet(X_26,X_27))))
    | join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))))),bind(Y0,$fot(join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))))),bind(Z0,$fot(join(X_26,join(X_25,meet(X_26,X_27)))))]]) ).

cnf(refute_0_496,plain,
    ( join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),join(X_25,join(X_26,join(X_25,meet(X_26,X_27))))) )],[refute_0_494,refute_0_495]) ).

cnf(refute_0_497,plain,
    join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) = join(X_26,join(X_25,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_26,join(X_25,meet(X_26,X_27)))),join(X_26,join(X_25,meet(X_26,X_27)))) )],[refute_0_486,refute_0_496]) ).

cnf(refute_0_498,plain,
    join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))]]) ).

cnf(refute_0_499,plain,
    ( join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))),bind(Y0,$fot(join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))),bind(Z0,$fot(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))))]]) ).

cnf(refute_0_500,plain,
    ( join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) )],[refute_0_482,refute_0_499]) ).

cnf(refute_0_501,plain,
    meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_26),meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))) )],[refute_0_498,refute_0_500]) ).

cnf(refute_0_502,plain,
    ( join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))),bind(Y0,$fot(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))))),bind(Z0,$fot(join(X_26,join(X_25,meet(X_26,X_27)))))]]) ).

cnf(refute_0_503,plain,
    ( join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27)))))) )],[refute_0_501,refute_0_502]) ).

cnf(refute_0_504,plain,
    meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) = join(X_26,join(X_25,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_26,meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),join(X_26,join(X_25,meet(X_26,X_27)))) )],[refute_0_497,refute_0_503]) ).

cnf(refute_0_505,plain,
    ( meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(X_26,join(X_25,meet(X_26,X_27)))
    | meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))
    | join(X_26,join(X_25,meet(X_26,X_27))) = join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) ),[0],$fot(join(X_26,join(X_25,meet(X_26,X_27))))]]) ).

cnf(refute_0_506,plain,
    ( meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))
    | join(X_26,join(X_25,meet(X_26,X_27))) = join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(X_26,join(X_25,meet(X_26,X_27)))) )],[refute_0_504,refute_0_505]) ).

cnf(refute_0_507,plain,
    join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))) = join(X_25,join(X_26,meet(X_26,X_27))),
    inference(subst,[],[refute_0_102:[bind(X_10,$fot(X_25)),bind(X_11,$fot(join(X_26,meet(X_26,X_27))))]]) ).

cnf(refute_0_508,plain,
    join(join(X_25,X_26),meet(X_26,X_27)) = join(X_25,join(X_26,meet(X_26,X_27))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_25)),bind(Y,$fot(X_26)),bind(Z,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_509,plain,
    join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),
    introduced(tautology,[refl,[$fot(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))))]]) ).

cnf(refute_0_510,plain,
    ( join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) != join(X_25,join(join(X_25,X_26),meet(X_26,X_27)))
    | join(join(X_25,X_26),meet(X_26,X_27)) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),join(X_25,join(join(X_25,X_26),meet(X_26,X_27)))) ),[1,1],$fot(join(X_25,join(X_26,meet(X_26,X_27))))]]) ).

cnf(refute_0_511,plain,
    ( join(join(X_25,X_26),meet(X_26,X_27)) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))) ),
    inference(resolve,[$cnf( $equal(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),join(X_25,join(join(X_25,X_26),meet(X_26,X_27)))) )],[refute_0_509,refute_0_510]) ).

cnf(refute_0_512,plain,
    join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_26),meet(X_26,X_27)),join(X_25,join(X_26,meet(X_26,X_27)))) )],[refute_0_508,refute_0_511]) ).

cnf(refute_0_513,plain,
    ( join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) != join(X_25,join(X_25,join(X_26,meet(X_26,X_27))))
    | join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))))),bind(Y0,$fot(join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))))),bind(Z0,$fot(join(X_25,join(X_26,meet(X_26,X_27)))))]]) ).

cnf(refute_0_514,plain,
    ( join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),join(X_25,join(X_25,join(X_26,meet(X_26,X_27))))) )],[refute_0_512,refute_0_513]) ).

cnf(refute_0_515,plain,
    join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(join(X_25,join(X_25,join(X_26,meet(X_26,X_27)))),join(X_25,join(X_26,meet(X_26,X_27)))) )],[refute_0_507,refute_0_514]) ).

cnf(refute_0_516,plain,
    join(join(X,join(X_22,X)),Z) = join(X,join(join(X_22,X),Z)),
    inference(subst,[],[associativity_of_join:[bind(Y,$fot(join(X_22,X)))]]) ).

cnf(refute_0_517,plain,
    join(X,join(X_22,X)) = join(X,X_22),
    inference(subst,[],[refute_0_398:[bind(Y,$fot(X)),bind(X_20,$fot(X_22))]]) ).

cnf(refute_0_518,plain,
    ( join(X,join(X_22,X)) != join(X,X_22)
    | join(join(X,join(X_22,X)),Z) != join(X,join(join(X_22,X),Z))
    | join(join(X,X_22),Z) = join(X,join(join(X_22,X),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,join(X_22,X)),Z),join(X,join(join(X_22,X),Z))) ),[0,0],$fot(join(X,X_22))]]) ).

cnf(refute_0_519,plain,
    ( join(join(X,join(X_22,X)),Z) != join(X,join(join(X_22,X),Z))
    | join(join(X,X_22),Z) = join(X,join(join(X_22,X),Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(X_22,X)),join(X,X_22)) )],[refute_0_517,refute_0_518]) ).

cnf(refute_0_520,plain,
    join(join(X,X_22),Z) = join(X,join(join(X_22,X),Z)),
    inference(resolve,[$cnf( $equal(join(join(X,join(X_22,X)),Z),join(X,join(join(X_22,X),Z))) )],[refute_0_516,refute_0_519]) ).

cnf(refute_0_521,plain,
    join(join(X,X_22),Z) = join(X,join(X_22,Z)),
    inference(subst,[],[associativity_of_join:[bind(Y,$fot(X_22))]]) ).

cnf(refute_0_522,plain,
    ( join(join(X,X_22),Z) != join(X,join(X_22,Z))
    | join(join(X,X_22),Z) != join(X,join(join(X_22,X),Z))
    | join(X,join(X_22,Z)) = join(X,join(join(X_22,X),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(join(X,X_22),Z),join(X,join(join(X_22,X),Z))) ),[0],$fot(join(X,join(X_22,Z)))]]) ).

cnf(refute_0_523,plain,
    ( join(join(X,X_22),Z) != join(X,join(join(X_22,X),Z))
    | join(X,join(X_22,Z)) = join(X,join(join(X_22,X),Z)) ),
    inference(resolve,[$cnf( $equal(join(join(X,X_22),Z),join(X,join(X_22,Z))) )],[refute_0_521,refute_0_522]) ).

cnf(refute_0_524,plain,
    join(X,join(X_22,join(X,Z))) = join(X_22,join(X,Z)),
    inference(subst,[],[refute_0_268:[bind(X,$fot(X_22)),bind(Y,$fot(X)),bind(X_20,$fot(Z))]]) ).

cnf(refute_0_525,plain,
    join(join(X_22,X),Z) = join(X_22,join(X,Z)),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_22)),bind(Y,$fot(X))]]) ).

cnf(refute_0_526,plain,
    join(X,join(join(X_22,X),Z)) = join(X,join(join(X_22,X),Z)),
    introduced(tautology,[refl,[$fot(join(X,join(join(X_22,X),Z)))]]) ).

cnf(refute_0_527,plain,
    ( join(X,join(join(X_22,X),Z)) != join(X,join(join(X_22,X),Z))
    | join(join(X_22,X),Z) != join(X_22,join(X,Z))
    | join(X,join(join(X_22,X),Z)) = join(X,join(X_22,join(X,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X,join(join(X_22,X),Z)),join(X,join(join(X_22,X),Z))) ),[1,1],$fot(join(X_22,join(X,Z)))]]) ).

cnf(refute_0_528,plain,
    ( join(join(X_22,X),Z) != join(X_22,join(X,Z))
    | join(X,join(join(X_22,X),Z)) = join(X,join(X_22,join(X,Z))) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_22,X),Z)),join(X,join(join(X_22,X),Z))) )],[refute_0_526,refute_0_527]) ).

cnf(refute_0_529,plain,
    join(X,join(join(X_22,X),Z)) = join(X,join(X_22,join(X,Z))),
    inference(resolve,[$cnf( $equal(join(join(X_22,X),Z),join(X_22,join(X,Z))) )],[refute_0_525,refute_0_528]) ).

cnf(refute_0_530,plain,
    ( join(X,join(X_22,join(X,Z))) != join(X_22,join(X,Z))
    | join(X,join(join(X_22,X),Z)) != join(X,join(X_22,join(X,Z)))
    | join(X,join(join(X_22,X),Z)) = join(X_22,join(X,Z)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(X,join(join(X_22,X),Z)))),bind(Y0,$fot(join(X,join(X_22,join(X,Z))))),bind(Z0,$fot(join(X_22,join(X,Z))))]]) ).

cnf(refute_0_531,plain,
    ( join(X,join(X_22,join(X,Z))) != join(X_22,join(X,Z))
    | join(X,join(join(X_22,X),Z)) = join(X_22,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_22,X),Z)),join(X,join(X_22,join(X,Z)))) )],[refute_0_529,refute_0_530]) ).

cnf(refute_0_532,plain,
    join(X,join(join(X_22,X),Z)) = join(X_22,join(X,Z)),
    inference(resolve,[$cnf( $equal(join(X,join(X_22,join(X,Z))),join(X_22,join(X,Z))) )],[refute_0_524,refute_0_531]) ).

cnf(refute_0_533,plain,
    ( join(X,join(X_22,Z)) != join(X,join(join(X_22,X),Z))
    | join(X,join(join(X_22,X),Z)) != join(X_22,join(X,Z))
    | join(X,join(X_22,Z)) = join(X_22,join(X,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X,join(X_22,Z)),join(X_22,join(X,Z))) ),[0],$fot(join(X,join(join(X_22,X),Z)))]]) ).

cnf(refute_0_534,plain,
    ( join(X,join(X_22,Z)) != join(X,join(join(X_22,X),Z))
    | join(X,join(X_22,Z)) = join(X_22,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(join(X_22,X),Z)),join(X_22,join(X,Z))) )],[refute_0_532,refute_0_533]) ).

cnf(refute_0_535,plain,
    ( join(join(X,X_22),Z) != join(X,join(join(X_22,X),Z))
    | join(X,join(X_22,Z)) = join(X_22,join(X,Z)) ),
    inference(resolve,[$cnf( $equal(join(X,join(X_22,Z)),join(X,join(join(X_22,X),Z))) )],[refute_0_523,refute_0_534]) ).

cnf(refute_0_536,plain,
    join(X,join(X_22,Z)) = join(X_22,join(X,Z)),
    inference(resolve,[$cnf( $equal(join(join(X,X_22),Z),join(X,join(join(X_22,X),Z))) )],[refute_0_520,refute_0_535]) ).

cnf(refute_0_537,plain,
    ( join(X,join(X_22,Z)) != join(X_22,join(X,Z))
    | join(X_22,join(X,Z)) = join(X,join(X_22,Z)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X,join(X_22,Z)))),bind(Y0,$fot(join(X_22,join(X,Z))))]]) ).

cnf(refute_0_538,plain,
    join(X_22,join(X,Z)) = join(X,join(X_22,Z)),
    inference(resolve,[$cnf( $equal(join(X,join(X_22,Z)),join(X_22,join(X,Z))) )],[refute_0_536,refute_0_537]) ).

cnf(refute_0_539,plain,
    join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),
    inference(subst,[],[refute_0_538:[bind(X,$fot(X_25)),bind(Z,$fot(meet(X_26,X_27))),bind(X_22,$fot(join(X_25,X_26)))]]) ).

cnf(refute_0_540,plain,
    ( join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,join(join(X_25,X_26),meet(X_26,X_27)))
    | join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_25,X_26),join(X_25,meet(X_26,X_27))))),bind(Y0,$fot(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))))),bind(Z0,$fot(join(X_25,join(X_26,meet(X_26,X_27)))))]]) ).

cnf(refute_0_541,plain,
    ( join(X_25,join(join(X_25,X_26),meet(X_26,X_27))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,join(join(X_25,X_26),meet(X_26,X_27)))) )],[refute_0_539,refute_0_540]) ).

cnf(refute_0_542,plain,
    join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(join(X_25,join(join(X_25,X_26),meet(X_26,X_27))),join(X_25,join(X_26,meet(X_26,X_27)))) )],[refute_0_515,refute_0_541]) ).

cnf(refute_0_543,plain,
    ( join(X_26,join(X_25,meet(X_26,X_27))) != join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))
    | join(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_26,join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_26,join(X_25,meet(X_26,X_27))),join(X_25,join(X_26,meet(X_26,X_27)))) ),[0],$fot(join(join(X_25,X_26),join(X_25,meet(X_26,X_27))))]]) ).

cnf(refute_0_544,plain,
    ( join(X_26,join(X_25,meet(X_26,X_27))) != join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))
    | join(X_26,join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,join(X_26,meet(X_26,X_27)))) )],[refute_0_542,refute_0_543]) ).

cnf(refute_0_545,plain,
    ( meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) != join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))
    | join(X_26,join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))) ),
    inference(resolve,[$cnf( $equal(join(X_26,join(X_25,meet(X_26,X_27))),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) )],[refute_0_506,refute_0_544]) ).

cnf(refute_0_546,plain,
    join(X_26,join(X_25,meet(X_26,X_27))) = join(X_25,join(X_26,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))),join(join(X_25,X_26),join(X_25,meet(X_26,X_27)))) )],[refute_0_485,refute_0_545]) ).

cnf(refute_0_547,plain,
    ( join(X_26,join(X_25,meet(X_26,X_27))) != join(X_25,join(X_26,meet(X_26,X_27)))
    | join(X_25,join(X_26,meet(X_26,X_27))) = join(X_26,join(X_25,meet(X_26,X_27))) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_26,join(X_25,meet(X_26,X_27))))),bind(Y0,$fot(join(X_25,join(X_26,meet(X_26,X_27)))))]]) ).

cnf(refute_0_548,plain,
    join(X_25,join(X_26,meet(X_26,X_27))) = join(X_26,join(X_25,meet(X_26,X_27))),
    inference(resolve,[$cnf( $equal(join(X_26,join(X_25,meet(X_26,X_27))),join(X_25,join(X_26,meet(X_26,X_27)))) )],[refute_0_546,refute_0_547]) ).

cnf(refute_0_549,plain,
    join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) = join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))),
    inference(subst,[],[refute_0_548:[bind(X_25,$fot(meet(join(X_32,X_14),X_31))),bind(X_26,$fot(X_32)),bind(X_27,$fot(X_14))]]) ).

cnf(refute_0_550,plain,
    ( join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))) != join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))
    | join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) != join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14)))
    | join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))))),bind(Y0,$fot(join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))))),bind(Z0,$fot(join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))))]]) ).

cnf(refute_0_551,plain,
    ( join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))) != join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))
    | join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) ),
    inference(resolve,[$cnf( $equal(join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))),join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14)))) )],[refute_0_549,refute_0_550]) ).

cnf(refute_0_552,plain,
    join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))),
    inference(resolve,[$cnf( $equal(join(X_32,join(meet(join(X_32,X_14),X_31),meet(X_32,X_14))),join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))) )],[refute_0_481,refute_0_551]) ).

cnf(refute_0_553,plain,
    ( join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))) != join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))
    | meet(join(X_32,X_14),join(X_31,X_32)) != join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14)))
    | meet(join(X_32,X_14),join(X_31,X_32)) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_32,X_14),join(X_31,X_32)),join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14)))) ),[1],$fot(join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))))]]) ).

cnf(refute_0_554,plain,
    ( meet(join(X_32,X_14),join(X_31,X_32)) != join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14)))
    | meet(join(X_32,X_14),join(X_31,X_32)) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) ),
    inference(resolve,[$cnf( $equal(join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14))),join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))) )],[refute_0_552,refute_0_553]) ).

cnf(refute_0_555,plain,
    meet(join(X_32,X_14),join(X_31,X_32)) = join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))),
    inference(resolve,[$cnf( $equal(meet(join(X_32,X_14),join(X_31,X_32)),join(meet(join(X_32,X_14),X_31),join(X_32,meet(X_32,X_14)))) )],[refute_0_469,refute_0_554]) ).

cnf(refute_0_556,plain,
    ( meet(join(X_32,X_14),join(X_31,X_32)) != join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))
    | join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) = meet(join(X_32,X_14),join(X_31,X_32)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(meet(join(X_32,X_14),join(X_31,X_32)))),bind(Y0,$fot(join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))))]]) ).

cnf(refute_0_557,plain,
    join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31))) = meet(join(X_32,X_14),join(X_31,X_32)),
    inference(resolve,[$cnf( $equal(meet(join(X_32,X_14),join(X_31,X_32)),join(X_32,join(meet(X_32,X_14),meet(join(X_32,X_14),X_31)))) )],[refute_0_555,refute_0_556]) ).

cnf(refute_0_558,plain,
    join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))) = meet(join(X_34,X_14),join(X_35,X_34)),
    inference(subst,[],[refute_0_557:[bind(X_31,$fot(X_35)),bind(X_32,$fot(X_34))]]) ).

cnf(refute_0_559,plain,
    join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) = join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))),
    inference(subst,[],[associativity_of_join:[bind(X,$fot(X_34)),bind(Y,$fot(meet(X_34,X_14))),bind(Z,$fot(meet(join(X_34,X_14),X_35)))]]) ).

cnf(refute_0_560,plain,
    ( join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))) != meet(join(X_34,X_14),join(X_35,X_34))
    | join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) != join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35)))
    | join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)))),bind(Y0,$fot(join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))))),bind(Z0,$fot(meet(join(X_34,X_14),join(X_35,X_34))))]]) ).

cnf(refute_0_561,plain,
    ( join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))) != meet(join(X_34,X_14),join(X_35,X_34))
    | join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)) ),
    inference(resolve,[$cnf( $equal(join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)),join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35)))) )],[refute_0_559,refute_0_560]) ).

cnf(refute_0_562,plain,
    join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)),
    inference(resolve,[$cnf( $equal(join(X_34,join(meet(X_34,X_14),meet(join(X_34,X_14),X_35))),meet(join(X_34,X_14),join(X_35,X_34))) )],[refute_0_558,refute_0_561]) ).

cnf(refute_0_563,plain,
    ( join(X_34,meet(join(X_34,X_14),X_35)) != join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)) != meet(join(X_34,X_14),join(X_35,X_34))
    | join(X_34,meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_34,meet(join(X_34,X_14),X_35)),meet(join(X_34,X_14),join(X_35,X_34))) ),[0],$fot(join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)))]]) ).

cnf(refute_0_564,plain,
    ( join(X_34,meet(join(X_34,X_14),X_35)) != join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | join(X_34,meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)) ),
    inference(resolve,[$cnf( $equal(join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35)),meet(join(X_34,X_14),join(X_35,X_34))) )],[refute_0_562,refute_0_563]) ).

cnf(refute_0_565,plain,
    ( meet(join(X_34,X_14),join(X_34,X_35)) != join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))
    | join(X_34,meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)) ),
    inference(resolve,[$cnf( $equal(join(X_34,meet(join(X_34,X_14),X_35)),join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))) )],[refute_0_458,refute_0_564]) ).

cnf(refute_0_566,plain,
    join(X_34,meet(join(X_34,X_14),X_35)) = meet(join(X_34,X_14),join(X_35,X_34)),
    inference(resolve,[$cnf( $equal(meet(join(X_34,X_14),join(X_34,X_35)),join(join(X_34,meet(X_34,X_14)),meet(join(X_34,X_14),X_35))) )],[refute_0_455,refute_0_565]) ).

cnf(refute_0_567,plain,
    ( join(X_34,meet(join(X_34,X_14),X_35)) != meet(join(X_34,X_14),join(X_35,X_34))
    | meet(join(X_34,X_14),join(X_35,X_34)) = join(X_34,meet(join(X_34,X_14),X_35)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_34,meet(join(X_34,X_14),X_35)))),bind(Y0,$fot(meet(join(X_34,X_14),join(X_35,X_34))))]]) ).

cnf(refute_0_568,plain,
    meet(join(X_34,X_14),join(X_35,X_34)) = join(X_34,meet(join(X_34,X_14),X_35)),
    inference(resolve,[$cnf( $equal(join(X_34,meet(join(X_34,X_14),X_35)),meet(join(X_34,X_14),join(X_35,X_34))) )],[refute_0_566,refute_0_567]) ).

cnf(refute_0_569,plain,
    meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(join(X_97,X_96),X_59)),
    inference(subst,[],[refute_0_568:[bind(X_14,$fot(X_96)),bind(X_34,$fot(X_97)),bind(X_35,$fot(X_59))]]) ).

cnf(refute_0_570,plain,
    ( join(X_97,meet(join(X_97,X_96),X_59)) != join(X_97,meet(X_96,join(X_97,X_59)))
    | meet(join(X_97,X_96),join(X_59,X_97)) != join(X_97,meet(join(X_97,X_96),X_59))
    | meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(X_96,join(X_97,X_59))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_97,X_96),join(X_59,X_97)))),bind(Y0,$fot(join(X_97,meet(join(X_97,X_96),X_59)))),bind(Z0,$fot(join(X_97,meet(X_96,join(X_97,X_59)))))]]) ).

cnf(refute_0_571,plain,
    ( join(X_97,meet(join(X_97,X_96),X_59)) != join(X_97,meet(X_96,join(X_97,X_59)))
    | meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(X_96,join(X_97,X_59))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_59,X_97)),join(X_97,meet(join(X_97,X_96),X_59))) )],[refute_0_569,refute_0_570]) ).

cnf(refute_0_572,plain,
    meet(join(X_97,X_96),join(X_59,X_97)) = join(X_97,meet(X_96,join(X_97,X_59))),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),X_59)),join(X_97,meet(X_96,join(X_97,X_59)))) )],[refute_0_450,refute_0_571]) ).

cnf(refute_0_573,plain,
    ( meet(join(X_97,X_96),join(X_59,X_97)) != join(X_97,meet(X_96,join(X_97,X_59)))
    | meet(join(X_97,X_96),join(X_59,X_97)) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_97,X_96),join(X_59,X_97)),join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))) ),[0],$fot(join(X_97,meet(X_96,join(X_97,X_59))))]]) ).

cnf(refute_0_574,plain,
    ( meet(join(X_97,X_96),join(X_59,X_97)) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_59,X_97)),join(X_97,meet(X_96,join(X_97,X_59)))) )],[refute_0_572,refute_0_573]) ).

cnf(refute_0_575,plain,
    meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) = meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))),
    introduced(tautology,[refl,[$fot(meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))]]) ).

cnf(refute_0_576,plain,
    ( join(X_97,join(X_59,meet(X_97,X_59))) != join(X_59,X_97)
    | meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) != meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))
    | meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) = meet(X_96,join(X_59,X_97)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))),meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) ),[1,1],$fot(join(X_59,X_97))]]) ).

cnf(refute_0_577,plain,
    ( join(X_97,join(X_59,meet(X_97,X_59))) != join(X_59,X_97)
    | meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) = meet(X_96,join(X_59,X_97)) ),
    inference(resolve,[$cnf( $equal(meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))),meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) )],[refute_0_575,refute_0_576]) ).

cnf(refute_0_578,plain,
    meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) = meet(X_96,join(X_59,X_97)),
    inference(resolve,[$cnf( $equal(join(X_97,join(X_59,meet(X_97,X_59))),join(X_59,X_97)) )],[refute_0_446,refute_0_577]) ).

cnf(refute_0_579,plain,
    join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) = join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))),
    introduced(tautology,[refl,[$fot(join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))))]]) ).

cnf(refute_0_580,plain,
    ( join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) != join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))
    | meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) != meet(X_96,join(X_59,X_97))
    | join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))),join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))) ),[1,1],$fot(meet(X_96,join(X_59,X_97)))]]) ).

cnf(refute_0_581,plain,
    ( meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))) != meet(X_96,join(X_59,X_97))
    | join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))),join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))) )],[refute_0_579,refute_0_580]) ).

cnf(refute_0_582,plain,
    join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) = join(X_97,meet(X_96,join(X_59,X_97))),
    inference(resolve,[$cnf( $equal(meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))),meet(X_96,join(X_59,X_97))) )],[refute_0_578,refute_0_581]) ).

cnf(refute_0_583,plain,
    join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) = join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))),
    inference(subst,[],[refute_0_172:[bind(X_98,$fot(join(X_59,meet(X_97,X_59))))]]) ).

cnf(refute_0_584,plain,
    ( join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) != join(X_97,meet(X_96,join(X_59,X_97)))
    | join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) != join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))
    | join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))))),bind(Y0,$fot(join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))))),bind(Z0,$fot(join(X_97,meet(X_96,join(X_59,X_97)))))]]) ).

cnf(refute_0_585,plain,
    ( join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))) != join(X_97,meet(X_96,join(X_59,X_97)))
    | join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))),join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59)))))) )],[refute_0_583,refute_0_584]) ).

cnf(refute_0_586,plain,
    join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) = join(X_97,meet(X_96,join(X_59,X_97))),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,join(X_59,meet(X_97,X_59))))),join(X_97,meet(X_96,join(X_59,X_97)))) )],[refute_0_582,refute_0_585]) ).

cnf(refute_0_587,plain,
    ( join(X_97,meet(X_96,join(X_97,X_59))) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))) != join(X_97,meet(X_96,join(X_59,X_97)))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_97,meet(X_96,join(X_97,X_59))),join(X_97,meet(X_96,join(X_59,X_97)))) ),[0],$fot(join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))))]]) ).

cnf(refute_0_588,plain,
    ( join(X_97,meet(X_96,join(X_97,X_59))) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59)))),join(X_97,meet(X_96,join(X_59,X_97)))) )],[refute_0_586,refute_0_587]) ).

cnf(refute_0_589,plain,
    ( meet(join(X_97,X_96),join(X_59,X_97)) != join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,join(X_59,X_97))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_59))),join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))) )],[refute_0_574,refute_0_588]) ).

cnf(refute_0_590,plain,
    join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,join(X_59,X_97))),
    inference(resolve,[$cnf( $equal(meet(join(X_97,X_96),join(X_59,X_97)),join(X_97,meet(join(X_97,X_96),join(X_59,meet(X_97,X_59))))) )],[refute_0_449,refute_0_589]) ).

cnf(refute_0_591,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_592,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_2:[bind(X0,$fot(join(X_26,X_25))),bind(Y0,$fot(join(X_25,X_26)))]]) ).

cnf(refute_0_593,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_591,refute_0_592]) ).

cnf(refute_0_594,plain,
    ( join(X_25,X_26) != join(X_26,X_25)
    | meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) ),[0,0],$fot(join(X_26,X_25))]]) ).

cnf(refute_0_595,plain,
    ( meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(join(X_25,X_26),join(X_26,X_25)) )],[refute_0_593,refute_0_594]) ).

cnf(refute_0_596,plain,
    meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,X_27)),
    inference(resolve,[$cnf( $equal(meet(join(X_25,X_26),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_9,refute_0_595]) ).

cnf(refute_0_597,plain,
    meet(X,join(meet(X,X_18),Z)) = join(meet(X,meet(X,X_18)),meet(X,Z)),
    inference(subst,[],[distributivity_law:[bind(Y,$fot(meet(X,X_18)))]]) ).

cnf(refute_0_598,plain,
    ( meet(X,join(meet(X,X_18),Z)) != join(meet(X,meet(X,X_18)),meet(X,Z))
    | meet(X,meet(X,X_18)) != meet(X,X_18)
    | meet(X,join(meet(X,X_18),Z)) = join(meet(X,X_18),meet(X,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(meet(X,X_18),Z)),join(meet(X,meet(X,X_18)),meet(X,Z))) ),[1,0],$fot(meet(X,X_18))]]) ).

cnf(refute_0_599,plain,
    ( meet(X,join(meet(X,X_18),Z)) != join(meet(X,meet(X,X_18)),meet(X,Z))
    | meet(X,join(meet(X,X_18),Z)) = join(meet(X,X_18),meet(X,Z)) ),
    inference(resolve,[$cnf( $equal(meet(X,meet(X,X_18)),meet(X,X_18)) )],[refute_0_42,refute_0_598]) ).

cnf(refute_0_600,plain,
    meet(X,join(meet(X,X_18),Z)) = join(meet(X,X_18),meet(X,Z)),
    inference(resolve,[$cnf( $equal(meet(X,join(meet(X,X_18),Z)),join(meet(X,meet(X,X_18)),meet(X,Z))) )],[refute_0_597,refute_0_599]) ).

cnf(refute_0_601,plain,
    join(meet(X,X_18),meet(X,Z)) = meet(X,join(X_18,Z)),
    inference(subst,[],[refute_0_47:[bind(Y,$fot(X_18))]]) ).

cnf(refute_0_602,plain,
    ( join(meet(X,X_18),meet(X,Z)) != meet(X,join(X_18,Z))
    | meet(X,join(meet(X,X_18),Z)) != join(meet(X,X_18),meet(X,Z))
    | meet(X,join(meet(X,X_18),Z)) = meet(X,join(X_18,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(X,join(meet(X,X_18),Z)),join(meet(X,X_18),meet(X,Z))) ),[1],$fot(meet(X,join(X_18,Z)))]]) ).

cnf(refute_0_603,plain,
    ( meet(X,join(meet(X,X_18),Z)) != join(meet(X,X_18),meet(X,Z))
    | meet(X,join(meet(X,X_18),Z)) = meet(X,join(X_18,Z)) ),
    inference(resolve,[$cnf( $equal(join(meet(X,X_18),meet(X,Z)),meet(X,join(X_18,Z))) )],[refute_0_601,refute_0_602]) ).

cnf(refute_0_604,plain,
    meet(X,join(meet(X,X_18),Z)) = meet(X,join(X_18,Z)),
    inference(resolve,[$cnf( $equal(meet(X,join(meet(X,X_18),Z)),join(meet(X,X_18),meet(X,Z))) )],[refute_0_600,refute_0_603]) ).

cnf(refute_0_605,plain,
    meet(X_26,join(meet(X_26,X_27),X_25)) = meet(X_26,join(X_27,X_25)),
    inference(subst,[],[refute_0_604:[bind(X,$fot(X_26)),bind(Z,$fot(X_25)),bind(X_18,$fot(X_27))]]) ).

cnf(refute_0_606,plain,
    join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) = join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),
    introduced(tautology,[refl,[$fot(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))))]]) ).

cnf(refute_0_607,plain,
    ( join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) != join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))
    | meet(X_26,join(meet(X_26,X_27),X_25)) != meet(X_26,join(X_27,X_25))
    | join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) = join(X_25,meet(X_26,join(X_27,X_25))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))) ),[1,1],$fot(meet(X_26,join(X_27,X_25)))]]) ).

cnf(refute_0_608,plain,
    ( meet(X_26,join(meet(X_26,X_27),X_25)) != meet(X_26,join(X_27,X_25))
    | join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) = join(X_25,meet(X_26,join(X_27,X_25))) ),
    inference(resolve,[$cnf( $equal(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))) )],[refute_0_606,refute_0_607]) ).

cnf(refute_0_609,plain,
    join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) = join(X_25,meet(X_26,join(X_27,X_25))),
    inference(resolve,[$cnf( $equal(meet(X_26,join(meet(X_26,X_27),X_25)),meet(X_26,join(X_27,X_25))) )],[refute_0_605,refute_0_608]) ).

cnf(refute_0_610,plain,
    join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))) = join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),
    inference(subst,[],[refute_0_178:[bind(X_96,$fot(meet(X_26,X_27))),bind(X_97,$fot(X_25)),bind(X_98,$fot(X_26))]]) ).

cnf(refute_0_611,plain,
    meet(join(X_52,X_51),join(X_51,X_96)) = meet(join(X_51,X_96),join(X_51,X_52)),
    inference(subst,[],[refute_0_81:[bind(Y,$fot(join(X_51,X_96)))]]) ).

cnf(refute_0_612,plain,
    meet(join(X_51,X_96),join(X_51,X_52)) = join(X_51,meet(join(X_51,X_96),X_52)),
    inference(subst,[],[refute_0_55:[bind(X_11,$fot(X_96)),bind(X_25,$fot(X_51)),bind(X_27,$fot(X_52))]]) ).

cnf(refute_0_613,plain,
    ( meet(join(X_51,X_96),join(X_51,X_52)) != join(X_51,meet(join(X_51,X_96),X_52))
    | meet(join(X_52,X_51),join(X_51,X_96)) != meet(join(X_51,X_96),join(X_51,X_52))
    | meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(join(X_51,X_96),X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_52,X_51),join(X_51,X_96)),meet(join(X_51,X_96),join(X_51,X_52))) ),[1],$fot(join(X_51,meet(join(X_51,X_96),X_52)))]]) ).

cnf(refute_0_614,plain,
    ( meet(join(X_52,X_51),join(X_51,X_96)) != meet(join(X_51,X_96),join(X_51,X_52))
    | meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(join(X_51,X_96),X_52)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_51,X_96),join(X_51,X_52)),join(X_51,meet(join(X_51,X_96),X_52))) )],[refute_0_612,refute_0_613]) ).

cnf(refute_0_615,plain,
    meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(join(X_51,X_96),X_52)),
    inference(resolve,[$cnf( $equal(meet(join(X_52,X_51),join(X_51,X_96)),meet(join(X_51,X_96),join(X_51,X_52))) )],[refute_0_611,refute_0_614]) ).

cnf(refute_0_616,plain,
    join(X_51,meet(join(X_51,X_96),X_52)) = join(X_51,meet(X_96,join(X_51,X_52))),
    inference(subst,[],[refute_0_172:[bind(X_97,$fot(X_51)),bind(X_98,$fot(X_52))]]) ).

cnf(refute_0_617,plain,
    ( join(X_51,meet(join(X_51,X_96),X_52)) != join(X_51,meet(X_96,join(X_51,X_52)))
    | meet(join(X_52,X_51),join(X_51,X_96)) != join(X_51,meet(join(X_51,X_96),X_52))
    | meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(X_96,join(X_51,X_52))) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_52,X_51),join(X_51,X_96)),join(X_51,meet(join(X_51,X_96),X_52))) ),[1],$fot(join(X_51,meet(X_96,join(X_51,X_52))))]]) ).

cnf(refute_0_618,plain,
    ( meet(join(X_52,X_51),join(X_51,X_96)) != join(X_51,meet(join(X_51,X_96),X_52))
    | meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(X_96,join(X_51,X_52))) ),
    inference(resolve,[$cnf( $equal(join(X_51,meet(join(X_51,X_96),X_52)),join(X_51,meet(X_96,join(X_51,X_52)))) )],[refute_0_616,refute_0_617]) ).

cnf(refute_0_619,plain,
    meet(join(X_52,X_51),join(X_51,X_96)) = join(X_51,meet(X_96,join(X_51,X_52))),
    inference(resolve,[$cnf( $equal(meet(join(X_52,X_51),join(X_51,X_96)),join(X_51,meet(join(X_51,X_96),X_52))) )],[refute_0_615,refute_0_618]) ).

cnf(refute_0_620,plain,
    meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))),
    inference(subst,[],[refute_0_619:[bind(X_51,$fot(X_25)),bind(X_52,$fot(X_26)),bind(X_96,$fot(meet(X_26,X_27)))]]) ).

cnf(refute_0_621,plain,
    ( join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))) != join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) != join(X_25,meet(meet(X_26,X_27),join(X_25,X_26)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))))),bind(Y0,$fot(join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))))),bind(Z0,$fot(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))))]]) ).

cnf(refute_0_622,plain,
    ( join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))) != join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))),join(X_25,meet(meet(X_26,X_27),join(X_25,X_26)))) )],[refute_0_620,refute_0_621]) ).

cnf(refute_0_623,plain,
    meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),
    inference(resolve,[$cnf( $equal(join(X_25,meet(meet(X_26,X_27),join(X_25,X_26))),join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))) )],[refute_0_610,refute_0_622]) ).

cnf(refute_0_624,plain,
    ( join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) != join(X_25,meet(X_26,join(X_27,X_25)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(X_27,X_25))) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))))),bind(Y0,$fot(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))))),bind(Z0,$fot(join(X_25,meet(X_26,join(X_27,X_25)))))]]) ).

cnf(refute_0_625,plain,
    ( join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))) != join(X_25,meet(X_26,join(X_27,X_25)))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(X_27,X_25))) ),
    inference(resolve,[$cnf( $equal(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,join(meet(X_26,X_27),X_25)))) )],[refute_0_623,refute_0_624]) ).

cnf(refute_0_626,plain,
    meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) = join(X_25,meet(X_26,join(X_27,X_25))),
    inference(resolve,[$cnf( $equal(join(X_25,meet(X_26,join(meet(X_26,X_27),X_25))),join(X_25,meet(X_26,join(X_27,X_25)))) )],[refute_0_609,refute_0_625]) ).

cnf(refute_0_627,plain,
    ( meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,join(X_27,X_25)))
    | join(X_25,meet(X_26,join(X_27,X_25))) = join(X_25,meet(X_26,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) ),[0],$fot(join(X_25,meet(X_26,join(X_27,X_25))))]]) ).

cnf(refute_0_628,plain,
    ( meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))) != join(X_25,meet(X_26,X_27))
    | join(X_25,meet(X_26,join(X_27,X_25))) = join(X_25,meet(X_26,X_27)) ),
    inference(resolve,[$cnf( $equal(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,join(X_27,X_25)))) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    join(X_25,meet(X_26,join(X_27,X_25))) = join(X_25,meet(X_26,X_27)),
    inference(resolve,[$cnf( $equal(meet(join(X_26,X_25),join(X_25,meet(X_26,X_27))),join(X_25,meet(X_26,X_27))) )],[refute_0_596,refute_0_628]) ).

cnf(refute_0_630,plain,
    join(X_97,meet(X_96,join(X_59,X_97))) = join(X_97,meet(X_96,X_59)),
    inference(subst,[],[refute_0_629:[bind(X_25,$fot(X_97)),bind(X_26,$fot(X_96)),bind(X_27,$fot(X_59))]]) ).

cnf(refute_0_631,plain,
    ( join(X_97,meet(X_96,join(X_59,X_97))) != join(X_97,meet(X_96,X_59))
    | join(X_97,meet(X_96,join(X_97,X_59))) != join(X_97,meet(X_96,join(X_59,X_97)))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,X_59)) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_59))),join(X_97,meet(X_96,join(X_59,X_97)))) ),[1],$fot(join(X_97,meet(X_96,X_59)))]]) ).

cnf(refute_0_632,plain,
    ( join(X_97,meet(X_96,join(X_97,X_59))) != join(X_97,meet(X_96,join(X_59,X_97)))
    | join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,X_59)) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_59,X_97))),join(X_97,meet(X_96,X_59))) )],[refute_0_630,refute_0_631]) ).

cnf(refute_0_633,plain,
    join(X_97,meet(X_96,join(X_97,X_59))) = join(X_97,meet(X_96,X_59)),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_59))),join(X_97,meet(X_96,join(X_59,X_97)))) )],[refute_0_590,refute_0_632]) ).

cnf(refute_0_634,plain,
    join(X_97,meet(X_96,join(X_97,X_98))) = join(X_97,meet(X_96,X_98)),
    inference(subst,[],[refute_0_633:[bind(X_59,$fot(X_98))]]) ).

cnf(refute_0_635,plain,
    ( join(X_97,meet(X_96,join(X_97,X_98))) != join(X_97,meet(X_96,X_98))
    | join(X_97,meet(X_96,join(X_97,X_98))) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    introduced(tautology,[equality,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_98))),join(X_97,meet(X_98,join(X_96,X_97)))) ),[0],$fot(join(X_97,meet(X_96,X_98)))]]) ).

cnf(refute_0_636,plain,
    ( join(X_97,meet(X_96,join(X_97,X_98))) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,join(X_96,X_97))) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_98))),join(X_97,meet(X_96,X_98))) )],[refute_0_634,refute_0_635]) ).

cnf(refute_0_637,plain,
    join(X_97,meet(X_98,join(X_96,X_97))) = join(X_97,meet(X_98,X_96)),
    inference(subst,[],[refute_0_629:[bind(X_25,$fot(X_97)),bind(X_26,$fot(X_98)),bind(X_27,$fot(X_96))]]) ).

cnf(refute_0_638,plain,
    ( join(X_97,meet(X_96,X_98)) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_98,join(X_96,X_97))) != join(X_97,meet(X_98,X_96))
    | join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,X_96)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(X_97,meet(X_96,X_98)),join(X_97,meet(X_98,X_96))) ),[0],$fot(join(X_97,meet(X_98,join(X_96,X_97))))]]) ).

cnf(refute_0_639,plain,
    ( join(X_97,meet(X_96,X_98)) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,X_96)) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_98,join(X_96,X_97))),join(X_97,meet(X_98,X_96))) )],[refute_0_637,refute_0_638]) ).

cnf(refute_0_640,plain,
    ( join(X_97,meet(X_96,join(X_97,X_98))) != join(X_97,meet(X_98,join(X_96,X_97)))
    | join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,X_96)) ),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,X_98)),join(X_97,meet(X_98,join(X_96,X_97)))) )],[refute_0_636,refute_0_639]) ).

cnf(refute_0_641,plain,
    join(X_97,meet(X_96,X_98)) = join(X_97,meet(X_98,X_96)),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,join(X_97,X_98))),join(X_97,meet(X_98,join(X_96,X_97)))) )],[refute_0_178,refute_0_640]) ).

cnf(refute_0_642,plain,
    ( join(X_97,meet(X_96,X_98)) != join(X_97,meet(X_98,X_96))
    | join(X_97,meet(X_98,X_96)) = join(X_97,meet(X_96,X_98)) ),
    inference(subst,[],[refute_0_2:[bind(X0,$fot(join(X_97,meet(X_96,X_98)))),bind(Y0,$fot(join(X_97,meet(X_98,X_96))))]]) ).

cnf(refute_0_643,plain,
    join(X_97,meet(X_98,X_96)) = join(X_97,meet(X_96,X_98)),
    inference(resolve,[$cnf( $equal(join(X_97,meet(X_96,X_98)),join(X_97,meet(X_98,X_96))) )],[refute_0_641,refute_0_642]) ).

cnf(refute_0_644,plain,
    join(a,meet(c,b)) = join(a,meet(b,c)),
    inference(subst,[],[refute_0_643:[bind(X_96,$fot(b)),bind(X_97,$fot(a)),bind(X_98,$fot(c))]]) ).

cnf(refute_0_645,plain,
    join(a,meet(c,join(a,b))) = join(a,meet(c,b)),
    inference(subst,[],[refute_0_633:[bind(X_59,$fot(b)),bind(X_96,$fot(c)),bind(X_97,$fot(a))]]) ).

cnf(refute_0_646,plain,
    ( join(a,meet(c,b)) != join(a,meet(b,c))
    | join(a,meet(c,join(a,b))) != join(a,meet(c,b))
    | join(a,meet(c,join(a,b))) = join(a,meet(b,c)) ),
    inference(subst,[],[refute_0_58:[bind(X0,$fot(join(a,meet(c,join(a,b))))),bind(Y0,$fot(join(a,meet(c,b)))),bind(Z0,$fot(join(a,meet(b,c))))]]) ).

cnf(refute_0_647,plain,
    ( join(a,meet(c,b)) != join(a,meet(b,c))
    | join(a,meet(c,join(a,b))) = join(a,meet(b,c)) ),
    inference(resolve,[$cnf( $equal(join(a,meet(c,join(a,b))),join(a,meet(c,b))) )],[refute_0_645,refute_0_646]) ).

cnf(refute_0_648,plain,
    join(a,meet(c,join(a,b))) = join(a,meet(b,c)),
    inference(resolve,[$cnf( $equal(join(a,meet(c,b)),join(a,meet(b,c))) )],[refute_0_644,refute_0_647]) ).

cnf(refute_0_649,plain,
    ( join(a,meet(b,c)) != join(a,meet(b,c))
    | join(a,meet(c,join(a,b))) != join(a,meet(b,c))
    | join(a,meet(b,c)) = join(a,meet(c,join(a,b))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(join(a,meet(b,c)),join(a,meet(c,join(a,b)))) ),[1],$fot(join(a,meet(b,c)))]]) ).

cnf(refute_0_650,plain,
    ( join(a,meet(b,c)) != join(a,meet(b,c))
    | join(a,meet(b,c)) = join(a,meet(c,join(a,b))) ),
    inference(resolve,[$cnf( $equal(join(a,meet(c,join(a,b))),join(a,meet(b,c))) )],[refute_0_648,refute_0_649]) ).

cnf(refute_0_651,plain,
    join(a,meet(b,c)) != join(a,meet(b,c)),
    inference(resolve,[$cnf( $equal(join(a,meet(b,c)),join(a,meet(c,join(a,b)))) )],[refute_0_650,refute_0_64]) ).

cnf(refute_0_652,plain,
    join(a,meet(b,c)) = join(a,meet(b,c)),
    introduced(tautology,[refl,[$fot(join(a,meet(b,c)))]]) ).

cnf(refute_0_653,plain,
    $false,
    inference(resolve,[$cnf( $equal(join(a,meet(b,c)),join(a,meet(b,c))) )],[refute_0_652,refute_0_651]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : LAT019-1 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.32  % Computer : n025.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Thu Jun 30 10:35:08 EDT 2022
% 0.12/0.32  % CPUTime  : 
% 0.12/0.32  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.22/4.39  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.22/4.39  
% 4.22/4.39  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.28/4.46  
%------------------------------------------------------------------------------