%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 : Sat Jul 16 10:37:49 EDT 2022

% Result   : Unsatisfiable 2.36s 2.59s
% Output   : CNFRefutation 2.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   55
%            Number of leaves      :  183
% Syntax   : Number of clauses     :  885 ( 456 unt;   0 nHn; 436 RR)
%            Number of literals    : 1496 (1495 equ; 614 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    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   : 1697 (  22 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
    multiply(identity,X) = X ).

cnf(left_inverse,axiom,
    multiply(inverse(X),X) = identity ).

cnf(symmetry_of_glb,axiom,
    greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).

cnf(symmetry_of_lub,axiom,
    least_upper_bound(X,Y) = least_upper_bound(Y,X) ).

cnf(associativity_of_glb,axiom,
    greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z) ).

cnf(associativity_of_lub,axiom,
    least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z) ).

cnf(idempotence_of_lub,axiom,
    least_upper_bound(X,X) = X ).

cnf(lub_absorbtion,axiom,
    least_upper_bound(X,greatest_lower_bound(X,Y)) = X ).

cnf(glb_absorbtion,axiom,
    greatest_lower_bound(X,least_upper_bound(X,Y)) = X ).

cnf(monotony_lub1,axiom,
    multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).

cnf(monotony_glb1,axiom,
    multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)) ).

cnf(monotony_lub2,axiom,
    multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).

cnf(p21x_1,hypothesis,
    inverse(identity) = identity ).

cnf(p21x_2,hypothesis,
    inverse(inverse(X)) = X ).

cnf(p21x_3,hypothesis,
    inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).

cnf(p21x_4,hypothesis,
    inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(X),inverse(Y)) ).

cnf(p21x_5,hypothesis,
    inverse(least_upper_bound(X,Y)) = greatest_lower_bound(inverse(X),inverse(Y)) ).

cnf(prove_p21x,negated_conjecture,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ).

cnf(refute_0_0,plain,
    inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(inverse(X_6),inverse(identity)),
    inference(subst,[],[p21x_4:[bind(X,$fot(X_6)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_1,plain,
    ( inverse(greatest_lower_bound(X_6,identity)) != least_upper_bound(inverse(X_6),inverse(identity))
    | inverse(identity) != identity
    | inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(inverse(X_6),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_6,identity)),least_upper_bound(inverse(X_6),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_2,plain,
    ( inverse(greatest_lower_bound(X_6,identity)) != least_upper_bound(inverse(X_6),inverse(identity))
    | inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(inverse(X_6),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_1]) ).

cnf(refute_0_3,plain,
    inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(inverse(X_6),identity),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_6,identity)),least_upper_bound(inverse(X_6),inverse(identity))) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_5,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_6,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( least_upper_bound(X,Y) != least_upper_bound(Y,X)
    | least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).

cnf(refute_0_8,plain,
    least_upper_bound(Y,X) = least_upper_bound(X,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_7]) ).

cnf(refute_0_9,plain,
    least_upper_bound(inverse(X_6),identity) = least_upper_bound(identity,inverse(X_6)),
    inference(subst,[],[refute_0_8:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_6)))]]) ).

cnf(refute_0_10,plain,
    ( inverse(greatest_lower_bound(X_6,identity)) != least_upper_bound(inverse(X_6),identity)
    | least_upper_bound(inverse(X_6),identity) != least_upper_bound(identity,inverse(X_6))
    | inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(identity,inverse(X_6)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_6,identity)),least_upper_bound(identity,inverse(X_6))) ),[0],$fot(least_upper_bound(inverse(X_6),identity))]]) ).

cnf(refute_0_11,plain,
    ( inverse(greatest_lower_bound(X_6,identity)) != least_upper_bound(inverse(X_6),identity)
    | inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(identity,inverse(X_6)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_6),identity),least_upper_bound(identity,inverse(X_6))) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    inverse(greatest_lower_bound(X_6,identity)) = least_upper_bound(identity,inverse(X_6)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_6,identity)),least_upper_bound(inverse(X_6),identity)) )],[refute_0_3,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( inverse(greatest_lower_bound(X_6,identity)) != least_upper_bound(identity,inverse(X_6))
    | least_upper_bound(identity,inverse(X_6)) = inverse(greatest_lower_bound(X_6,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(greatest_lower_bound(X_6,identity)))),bind(Y0,$fot(least_upper_bound(identity,inverse(X_6))))]]) ).

cnf(refute_0_14,plain,
    least_upper_bound(identity,inverse(X_6)) = inverse(greatest_lower_bound(X_6,identity)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_6,identity)),least_upper_bound(identity,inverse(X_6))) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    least_upper_bound(identity,inverse(a)) = inverse(greatest_lower_bound(a,identity)),
    inference(subst,[],[refute_0_14:[bind(X_6,$fot(a))]]) ).

cnf(refute_0_16,plain,
    least_upper_bound(a,least_upper_bound(identity,inverse(a))) = least_upper_bound(a,least_upper_bound(identity,inverse(a))),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,least_upper_bound(identity,inverse(a))))]]) ).

cnf(refute_0_17,plain,
    ( least_upper_bound(a,least_upper_bound(identity,inverse(a))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(a,least_upper_bound(identity,inverse(a))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,inverse(a))),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) ),[1,1],$fot(inverse(greatest_lower_bound(a,identity)))]]) ).

cnf(refute_0_18,plain,
    ( least_upper_bound(identity,inverse(a)) != inverse(greatest_lower_bound(a,identity))
    | least_upper_bound(a,least_upper_bound(identity,inverse(a))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,inverse(a))),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) )],[refute_0_16,refute_0_17]) ).

cnf(refute_0_19,plain,
    least_upper_bound(a,least_upper_bound(identity,inverse(a))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(a)),inverse(greatest_lower_bound(a,identity))) )],[refute_0_15,refute_0_18]) ).

cnf(refute_0_20,plain,
    inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),inverse(inverse(X))),
    inference(subst,[],[p21x_3:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_24))]]) ).

cnf(refute_0_21,plain,
    ( inverse(multiply(inverse(X),X_24)) != multiply(inverse(X_24),inverse(inverse(X)))
    | inverse(inverse(X)) != X
    | inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),X_24)),multiply(inverse(X_24),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).

cnf(refute_0_22,plain,
    ( inverse(multiply(inverse(X),X_24)) != multiply(inverse(X_24),inverse(inverse(X)))
    | inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_21]) ).

cnf(refute_0_23,plain,
    inverse(multiply(inverse(X),X_24)) = multiply(inverse(X_24),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),X_24)),multiply(inverse(X_24),inverse(inverse(X)))) )],[refute_0_20,refute_0_22]) ).

cnf(refute_0_24,plain,
    inverse(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity)))) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),
    inference(subst,[],[refute_0_23:[bind(X_24,$fot(inverse(least_upper_bound(inverse(X),identity))))]]) ).

cnf(refute_0_25,plain,
    multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(multiply(X_95,X_96),multiply(X_95,inverse(X_95))),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(X_95)),bind(Y,$fot(X_96)),bind(Z,$fot(inverse(X_95)))]]) ).

cnf(refute_0_26,plain,
    multiply(inverse(inverse(X)),inverse(X)) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(inverse(X)))]]) ).

cnf(refute_0_27,plain,
    ( multiply(inverse(inverse(X)),inverse(X)) != identity
    | inverse(inverse(X)) != X
    | multiply(X,inverse(X)) = identity ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(X)),inverse(X)),identity) ),[0,0],$fot(X)]]) ).

cnf(refute_0_28,plain,
    ( multiply(inverse(inverse(X)),inverse(X)) != identity
    | multiply(X,inverse(X)) = identity ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_27]) ).

cnf(refute_0_29,plain,
    multiply(X,inverse(X)) = identity,
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(X)),inverse(X)),identity) )],[refute_0_26,refute_0_28]) ).

cnf(refute_0_30,plain,
    multiply(X_95,inverse(X_95)) = identity,
    inference(subst,[],[refute_0_29:[bind(X,$fot(X_95))]]) ).

cnf(refute_0_31,plain,
    ( multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) != greatest_lower_bound(multiply(X_95,X_96),multiply(X_95,inverse(X_95)))
    | multiply(X_95,inverse(X_95)) != identity
    | multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(multiply(X_95,X_96),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))),greatest_lower_bound(multiply(X_95,X_96),multiply(X_95,inverse(X_95)))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_32,plain,
    ( multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) != greatest_lower_bound(multiply(X_95,X_96),multiply(X_95,inverse(X_95)))
    | multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(multiply(X_95,X_96),identity) ),
    inference(resolve,[$cnf( $equal(multiply(X_95,inverse(X_95)),identity) )],[refute_0_30,refute_0_31]) ).

cnf(refute_0_33,plain,
    multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(multiply(X_95,X_96),identity),
    inference(resolve,[$cnf( $equal(multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))),greatest_lower_bound(multiply(X_95,X_96),multiply(X_95,inverse(X_95)))) )],[refute_0_25,refute_0_32]) ).

cnf(refute_0_34,plain,
    inverse(inverse(greatest_lower_bound(X_14,X_15))) = greatest_lower_bound(X_14,X_15),
    inference(subst,[],[p21x_2:[bind(X,$fot(greatest_lower_bound(X_14,X_15)))]]) ).

cnf(refute_0_35,plain,
    least_upper_bound(inverse(X),inverse(Y)) = least_upper_bound(inverse(Y),inverse(X)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(inverse(X))),bind(Y,$fot(inverse(Y)))]]) ).

cnf(refute_0_36,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(X),inverse(Y))
    | least_upper_bound(inverse(X),inverse(Y)) != least_upper_bound(inverse(Y),inverse(X))
    | inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(Y),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(Y),inverse(X))) ),[0],$fot(least_upper_bound(inverse(X),inverse(Y)))]]) ).

cnf(refute_0_37,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(X),inverse(Y))
    | inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(Y),inverse(X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),least_upper_bound(inverse(Y),inverse(X))) )],[refute_0_35,refute_0_36]) ).

cnf(refute_0_38,plain,
    inverse(greatest_lower_bound(X,Y)) = least_upper_bound(inverse(Y),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(X),inverse(Y))) )],[p21x_4,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(X),inverse(Y))
    | least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Y0,$fot(least_upper_bound(inverse(X),inverse(Y))))]]) ).

cnf(refute_0_40,plain,
    least_upper_bound(inverse(X),inverse(Y)) = inverse(greatest_lower_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(X),inverse(Y))) )],[p21x_4,refute_0_39]) ).

cnf(refute_0_41,plain,
    least_upper_bound(inverse(Y),inverse(X)) = inverse(greatest_lower_bound(Y,X)),
    inference(subst,[],[refute_0_40:[bind(X,$fot(Y)),bind(Y,$fot(X))]]) ).

cnf(refute_0_42,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(Y),inverse(X))
    | least_upper_bound(inverse(Y),inverse(X)) != inverse(greatest_lower_bound(Y,X))
    | inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X,Y)),inverse(greatest_lower_bound(Y,X))) ),[0],$fot(least_upper_bound(inverse(Y),inverse(X)))]]) ).

cnf(refute_0_43,plain,
    ( inverse(greatest_lower_bound(X,Y)) != least_upper_bound(inverse(Y),inverse(X))
    | inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(Y),inverse(X)),inverse(greatest_lower_bound(Y,X))) )],[refute_0_41,refute_0_42]) ).

cnf(refute_0_44,plain,
    inverse(greatest_lower_bound(X,Y)) = inverse(greatest_lower_bound(Y,X)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),least_upper_bound(inverse(Y),inverse(X))) )],[refute_0_38,refute_0_43]) ).

cnf(refute_0_45,plain,
    inverse(greatest_lower_bound(X_14,X_15)) = inverse(greatest_lower_bound(X_15,X_14)),
    inference(subst,[],[refute_0_44:[bind(X,$fot(X_14)),bind(Y,$fot(X_15))]]) ).

cnf(refute_0_46,plain,
    ( inverse(greatest_lower_bound(X_14,X_15)) != inverse(greatest_lower_bound(X_15,X_14))
    | inverse(inverse(greatest_lower_bound(X_14,X_15))) != greatest_lower_bound(X_14,X_15)
    | inverse(inverse(greatest_lower_bound(X_15,X_14))) = greatest_lower_bound(X_14,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_14,X_15))),greatest_lower_bound(X_14,X_15)) ),[0,0],$fot(inverse(greatest_lower_bound(X_15,X_14)))]]) ).

cnf(refute_0_47,plain,
    ( inverse(inverse(greatest_lower_bound(X_14,X_15))) != greatest_lower_bound(X_14,X_15)
    | inverse(inverse(greatest_lower_bound(X_15,X_14))) = greatest_lower_bound(X_14,X_15) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_14,X_15)),inverse(greatest_lower_bound(X_15,X_14))) )],[refute_0_45,refute_0_46]) ).

cnf(refute_0_48,plain,
    inverse(inverse(greatest_lower_bound(X_15,X_14))) = greatest_lower_bound(X_14,X_15),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_14,X_15))),greatest_lower_bound(X_14,X_15)) )],[refute_0_34,refute_0_47]) ).

cnf(refute_0_49,plain,
    inverse(inverse(greatest_lower_bound(X_15,X_14))) = greatest_lower_bound(X_15,X_14),
    inference(subst,[],[p21x_2:[bind(X,$fot(greatest_lower_bound(X_15,X_14)))]]) ).

cnf(refute_0_50,plain,
    ( inverse(inverse(greatest_lower_bound(X_15,X_14))) != greatest_lower_bound(X_14,X_15)
    | inverse(inverse(greatest_lower_bound(X_15,X_14))) != greatest_lower_bound(X_15,X_14)
    | greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_15,X_14))),greatest_lower_bound(X_14,X_15)) ),[0],$fot(greatest_lower_bound(X_15,X_14))]]) ).

cnf(refute_0_51,plain,
    ( inverse(inverse(greatest_lower_bound(X_15,X_14))) != greatest_lower_bound(X_14,X_15)
    | greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_15,X_14))),greatest_lower_bound(X_15,X_14)) )],[refute_0_49,refute_0_50]) ).

cnf(refute_0_52,plain,
    greatest_lower_bound(X_15,X_14) = greatest_lower_bound(X_14,X_15),
    inference(resolve,[$cnf( $equal(inverse(inverse(greatest_lower_bound(X_15,X_14))),greatest_lower_bound(X_14,X_15)) )],[refute_0_48,refute_0_51]) ).

cnf(refute_0_53,plain,
    ( greatest_lower_bound(X_15,X_14) != greatest_lower_bound(X_14,X_15)
    | greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(X_15,X_14))),bind(Y0,$fot(greatest_lower_bound(X_14,X_15)))]]) ).

cnf(refute_0_54,plain,
    greatest_lower_bound(X_14,X_15) = greatest_lower_bound(X_15,X_14),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_15,X_14),greatest_lower_bound(X_14,X_15)) )],[refute_0_52,refute_0_53]) ).

cnf(refute_0_55,plain,
    greatest_lower_bound(multiply(X_95,X_96),identity) = greatest_lower_bound(identity,multiply(X_95,X_96)),
    inference(subst,[],[refute_0_54:[bind(X_14,$fot(multiply(X_95,X_96))),bind(X_15,$fot(identity))]]) ).

cnf(refute_0_56,plain,
    ( multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) != greatest_lower_bound(multiply(X_95,X_96),identity)
    | greatest_lower_bound(multiply(X_95,X_96),identity) != greatest_lower_bound(identity,multiply(X_95,X_96))
    | multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(identity,multiply(X_95,X_96)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))),greatest_lower_bound(identity,multiply(X_95,X_96))) ),[0],$fot(greatest_lower_bound(multiply(X_95,X_96),identity))]]) ).

cnf(refute_0_57,plain,
    ( multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) != greatest_lower_bound(multiply(X_95,X_96),identity)
    | multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(identity,multiply(X_95,X_96)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(multiply(X_95,X_96),identity),greatest_lower_bound(identity,multiply(X_95,X_96))) )],[refute_0_55,refute_0_56]) ).

cnf(refute_0_58,plain,
    multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))) = greatest_lower_bound(identity,multiply(X_95,X_96)),
    inference(resolve,[$cnf( $equal(multiply(X_95,greatest_lower_bound(X_96,inverse(X_95))),greatest_lower_bound(multiply(X_95,X_96),identity)) )],[refute_0_33,refute_0_57]) ).

cnf(refute_0_59,plain,
    multiply(X_98,greatest_lower_bound(identity,inverse(X_98))) = greatest_lower_bound(identity,multiply(X_98,identity)),
    inference(subst,[],[refute_0_58:[bind(X_95,$fot(X_98)),bind(X_96,$fot(identity))]]) ).

cnf(refute_0_60,plain,
    inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),inverse(identity)),
    inference(subst,[],[p21x_5:[bind(X,$fot(X_27)),bind(Y,$fot(identity))]]) ).

cnf(refute_0_61,plain,
    ( inverse(identity) != identity
    | inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),inverse(identity))
    | inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_62,plain,
    ( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),inverse(identity))
    | inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_61]) ).

cnf(refute_0_63,plain,
    inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(inverse(X_27),identity),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),inverse(identity))) )],[refute_0_60,refute_0_62]) ).

cnf(refute_0_64,plain,
    greatest_lower_bound(inverse(X_27),identity) = greatest_lower_bound(identity,inverse(X_27)),
    inference(subst,[],[refute_0_54:[bind(X_14,$fot(inverse(X_27))),bind(X_15,$fot(identity))]]) ).

cnf(refute_0_65,plain,
    ( greatest_lower_bound(inverse(X_27),identity) != greatest_lower_bound(identity,inverse(X_27))
    | inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),identity)
    | inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),identity)) ),[1],$fot(greatest_lower_bound(identity,inverse(X_27)))]]) ).

cnf(refute_0_66,plain,
    ( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(inverse(X_27),identity)
    | inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(X_27),identity),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_64,refute_0_65]) ).

cnf(refute_0_67,plain,
    inverse(least_upper_bound(X_27,identity)) = greatest_lower_bound(identity,inverse(X_27)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(inverse(X_27),identity)) )],[refute_0_63,refute_0_66]) ).

cnf(refute_0_68,plain,
    inverse(least_upper_bound(X_98,identity)) = greatest_lower_bound(identity,inverse(X_98)),
    inference(subst,[],[refute_0_67:[bind(X_27,$fot(X_98))]]) ).

cnf(refute_0_69,plain,
    ( inverse(least_upper_bound(X_98,identity)) != greatest_lower_bound(identity,inverse(X_98))
    | greatest_lower_bound(identity,inverse(X_98)) = inverse(least_upper_bound(X_98,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(least_upper_bound(X_98,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_98))))]]) ).

cnf(refute_0_70,plain,
    greatest_lower_bound(identity,inverse(X_98)) = inverse(least_upper_bound(X_98,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_98,identity)),greatest_lower_bound(identity,inverse(X_98))) )],[refute_0_68,refute_0_69]) ).

cnf(refute_0_71,plain,
    ( multiply(X_98,greatest_lower_bound(identity,inverse(X_98))) != greatest_lower_bound(identity,multiply(X_98,identity))
    | greatest_lower_bound(identity,inverse(X_98)) != inverse(least_upper_bound(X_98,identity))
    | multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,multiply(X_98,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_98,greatest_lower_bound(identity,inverse(X_98))),greatest_lower_bound(identity,multiply(X_98,identity))) ),[0,1],$fot(inverse(least_upper_bound(X_98,identity)))]]) ).

cnf(refute_0_72,plain,
    ( multiply(X_98,greatest_lower_bound(identity,inverse(X_98))) != greatest_lower_bound(identity,multiply(X_98,identity))
    | multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,multiply(X_98,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_98)),inverse(least_upper_bound(X_98,identity))) )],[refute_0_70,refute_0_71]) ).

cnf(refute_0_73,plain,
    multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,multiply(X_98,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_98,greatest_lower_bound(identity,inverse(X_98))),greatest_lower_bound(identity,multiply(X_98,identity))) )],[refute_0_59,refute_0_72]) ).

cnf(refute_0_74,plain,
    inverse(multiply(identity,X_24)) = multiply(inverse(X_24),inverse(identity)),
    inference(subst,[],[p21x_3:[bind(X,$fot(identity)),bind(Y,$fot(X_24))]]) ).

cnf(refute_0_75,plain,
    ( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),inverse(identity))
    | inverse(identity) != identity
    | inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_76,plain,
    ( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),inverse(identity))
    | inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity) ),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_75]) ).

cnf(refute_0_77,plain,
    inverse(multiply(identity,X_24)) = multiply(inverse(X_24),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),inverse(identity))) )],[refute_0_74,refute_0_76]) ).

cnf(refute_0_78,plain,
    multiply(identity,X_24) = X_24,
    inference(subst,[],[left_identity:[bind(X,$fot(X_24))]]) ).

cnf(refute_0_79,plain,
    inverse(multiply(identity,X_24)) = inverse(multiply(identity,X_24)),
    introduced(tautology,[refl,[$fot(inverse(multiply(identity,X_24)))]]) ).

cnf(refute_0_80,plain,
    ( multiply(identity,X_24) != X_24
    | inverse(multiply(identity,X_24)) != inverse(multiply(identity,X_24))
    | inverse(multiply(identity,X_24)) = inverse(X_24) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(multiply(identity,X_24))) ),[1,0],$fot(X_24)]]) ).

cnf(refute_0_81,plain,
    ( multiply(identity,X_24) != X_24
    | inverse(multiply(identity,X_24)) = inverse(X_24) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(multiply(identity,X_24))) )],[refute_0_79,refute_0_80]) ).

cnf(refute_0_82,plain,
    inverse(multiply(identity,X_24)) = inverse(X_24),
    inference(resolve,[$cnf( $equal(multiply(identity,X_24),X_24) )],[refute_0_78,refute_0_81]) ).

cnf(refute_0_83,plain,
    ( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),identity)
    | inverse(multiply(identity,X_24)) != inverse(X_24)
    | inverse(X_24) = multiply(inverse(X_24),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),identity)) ),[0],$fot(inverse(X_24))]]) ).

cnf(refute_0_84,plain,
    ( inverse(multiply(identity,X_24)) != multiply(inverse(X_24),identity)
    | inverse(X_24) = multiply(inverse(X_24),identity) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),inverse(X_24)) )],[refute_0_82,refute_0_83]) ).

cnf(refute_0_85,plain,
    inverse(X_24) = multiply(inverse(X_24),identity),
    inference(resolve,[$cnf( $equal(inverse(multiply(identity,X_24)),multiply(inverse(X_24),identity)) )],[refute_0_77,refute_0_84]) ).

cnf(refute_0_86,plain,
    inverse(inverse(X)) = multiply(inverse(inverse(X)),identity),
    inference(subst,[],[refute_0_85:[bind(X_24,$fot(inverse(X)))]]) ).

cnf(refute_0_87,plain,
    ( inverse(inverse(X)) != X
    | inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
    | inverse(inverse(X)) = multiply(X,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) ),[1,0],$fot(X)]]) ).

cnf(refute_0_88,plain,
    ( inverse(inverse(X)) != multiply(inverse(inverse(X)),identity)
    | inverse(inverse(X)) = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_87]) ).

cnf(refute_0_89,plain,
    inverse(inverse(X)) = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(inverse(inverse(X)),identity)) )],[refute_0_86,refute_0_88]) ).

cnf(refute_0_90,plain,
    ( inverse(inverse(X)) != X
    | inverse(inverse(X)) != multiply(X,identity)
    | X = multiply(X,identity) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) ),[0],$fot(X)]]) ).

cnf(refute_0_91,plain,
    ( inverse(inverse(X)) != multiply(X,identity)
    | X = multiply(X,identity) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_90]) ).

cnf(refute_0_92,plain,
    X = multiply(X,identity),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),multiply(X,identity)) )],[refute_0_89,refute_0_91]) ).

cnf(refute_0_93,plain,
    ( X != multiply(X,identity)
    | multiply(X,identity) = X ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X)),bind(Y0,$fot(multiply(X,identity)))]]) ).

cnf(refute_0_94,plain,
    multiply(X,identity) = X,
    inference(resolve,[$cnf( $equal(X,multiply(X,identity)) )],[refute_0_92,refute_0_93]) ).

cnf(refute_0_95,plain,
    multiply(X_98,identity) = X_98,
    inference(subst,[],[refute_0_94:[bind(X,$fot(X_98))]]) ).

cnf(refute_0_96,plain,
    greatest_lower_bound(identity,multiply(X_98,identity)) = greatest_lower_bound(identity,multiply(X_98,identity)),
    introduced(tautology,[refl,[$fot(greatest_lower_bound(identity,multiply(X_98,identity)))]]) ).

cnf(refute_0_97,plain,
    ( multiply(X_98,identity) != X_98
    | greatest_lower_bound(identity,multiply(X_98,identity)) != greatest_lower_bound(identity,multiply(X_98,identity))
    | greatest_lower_bound(identity,multiply(X_98,identity)) = greatest_lower_bound(identity,X_98) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_98,identity)),greatest_lower_bound(identity,multiply(X_98,identity))) ),[1,1],$fot(X_98)]]) ).

cnf(refute_0_98,plain,
    ( multiply(X_98,identity) != X_98
    | greatest_lower_bound(identity,multiply(X_98,identity)) = greatest_lower_bound(identity,X_98) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_98,identity)),greatest_lower_bound(identity,multiply(X_98,identity))) )],[refute_0_96,refute_0_97]) ).

cnf(refute_0_99,plain,
    greatest_lower_bound(identity,multiply(X_98,identity)) = greatest_lower_bound(identity,X_98),
    inference(resolve,[$cnf( $equal(multiply(X_98,identity),X_98) )],[refute_0_95,refute_0_98]) ).

cnf(refute_0_100,plain,
    ( multiply(X_98,inverse(least_upper_bound(X_98,identity))) != greatest_lower_bound(identity,multiply(X_98,identity))
    | greatest_lower_bound(identity,multiply(X_98,identity)) != greatest_lower_bound(identity,X_98)
    | multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,X_98) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_98,inverse(least_upper_bound(X_98,identity))),greatest_lower_bound(identity,X_98)) ),[0],$fot(greatest_lower_bound(identity,multiply(X_98,identity)))]]) ).

cnf(refute_0_101,plain,
    ( multiply(X_98,inverse(least_upper_bound(X_98,identity))) != greatest_lower_bound(identity,multiply(X_98,identity))
    | multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,X_98) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,multiply(X_98,identity)),greatest_lower_bound(identity,X_98)) )],[refute_0_99,refute_0_100]) ).

cnf(refute_0_102,plain,
    multiply(X_98,inverse(least_upper_bound(X_98,identity))) = greatest_lower_bound(identity,X_98),
    inference(resolve,[$cnf( $equal(multiply(X_98,inverse(least_upper_bound(X_98,identity))),greatest_lower_bound(identity,multiply(X_98,identity))) )],[refute_0_73,refute_0_101]) ).

cnf(refute_0_103,plain,
    multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity))) = greatest_lower_bound(identity,inverse(X)),
    inference(subst,[],[refute_0_102:[bind(X_98,$fot(inverse(X)))]]) ).

cnf(refute_0_104,plain,
    ( multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity))) != greatest_lower_bound(identity,inverse(X))
    | inverse(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity)))) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | inverse(greatest_lower_bound(identity,inverse(X))) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity)))),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) ),[0,0],$fot(greatest_lower_bound(identity,inverse(X)))]]) ).

cnf(refute_0_105,plain,
    ( inverse(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity)))) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | inverse(greatest_lower_bound(identity,inverse(X))) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity))),greatest_lower_bound(identity,inverse(X))) )],[refute_0_103,refute_0_104]) ).

cnf(refute_0_106,plain,
    inverse(greatest_lower_bound(identity,inverse(X))) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X),inverse(least_upper_bound(inverse(X),identity)))),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) )],[refute_0_24,refute_0_105]) ).

cnf(refute_0_107,plain,
    least_upper_bound(inverse(identity),X) = least_upper_bound(inverse(identity),X),
    introduced(tautology,[refl,[$fot(least_upper_bound(inverse(identity),X))]]) ).

cnf(refute_0_108,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X) != least_upper_bound(inverse(identity),X)
    | least_upper_bound(inverse(identity),X) = least_upper_bound(identity,X) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(identity),X),least_upper_bound(inverse(identity),X)) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_109,plain,
    ( inverse(identity) != identity
    | least_upper_bound(inverse(identity),X) = least_upper_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X),least_upper_bound(inverse(identity),X)) )],[refute_0_107,refute_0_108]) ).

cnf(refute_0_110,plain,
    least_upper_bound(inverse(identity),X) = least_upper_bound(identity,X),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_109]) ).

cnf(refute_0_111,plain,
    inverse(greatest_lower_bound(X_6,inverse(X))) = least_upper_bound(inverse(X_6),inverse(inverse(X))),
    inference(subst,[],[p21x_4:[bind(X,$fot(X_6)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_112,plain,
    ( inverse(greatest_lower_bound(X_6,inverse(X))) != least_upper_bound(inverse(X_6),inverse(inverse(X)))
    | inverse(inverse(X)) != X
    | inverse(greatest_lower_bound(X_6,inverse(X))) = least_upper_bound(inverse(X_6),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_6,inverse(X))),least_upper_bound(inverse(X_6),inverse(inverse(X)))) ),[1,1],$fot(X)]]) ).

cnf(refute_0_113,plain,
    ( inverse(greatest_lower_bound(X_6,inverse(X))) != least_upper_bound(inverse(X_6),inverse(inverse(X)))
    | inverse(greatest_lower_bound(X_6,inverse(X))) = least_upper_bound(inverse(X_6),X) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_112]) ).

cnf(refute_0_114,plain,
    inverse(greatest_lower_bound(X_6,inverse(X))) = least_upper_bound(inverse(X_6),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_6,inverse(X))),least_upper_bound(inverse(X_6),inverse(inverse(X)))) )],[refute_0_111,refute_0_113]) ).

cnf(refute_0_115,plain,
    inverse(greatest_lower_bound(identity,inverse(X))) = least_upper_bound(inverse(identity),X),
    inference(subst,[],[refute_0_114:[bind(X_6,$fot(identity))]]) ).

cnf(refute_0_116,plain,
    ( Y0 != X0
    | Y0 != Z0
    | X0 = Z0 ),
    introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).

cnf(refute_0_117,plain,
    ( X0 != Y0
    | Y0 != Z0
    | X0 = Z0 ),
    inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_6,refute_0_116]) ).

cnf(refute_0_118,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X))) != least_upper_bound(inverse(identity),X)
    | least_upper_bound(inverse(identity),X) != least_upper_bound(identity,X)
    | inverse(greatest_lower_bound(identity,inverse(X))) = least_upper_bound(identity,X) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(inverse(greatest_lower_bound(identity,inverse(X))))),bind(Y0,$fot(least_upper_bound(inverse(identity),X))),bind(Z0,$fot(least_upper_bound(identity,X)))]]) ).

cnf(refute_0_119,plain,
    ( least_upper_bound(inverse(identity),X) != least_upper_bound(identity,X)
    | inverse(greatest_lower_bound(identity,inverse(X))) = least_upper_bound(identity,X) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(inverse(identity),X)) )],[refute_0_115,refute_0_118]) ).

cnf(refute_0_120,plain,
    inverse(greatest_lower_bound(identity,inverse(X))) = least_upper_bound(identity,X),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(identity),X),least_upper_bound(identity,X)) )],[refute_0_110,refute_0_119]) ).

cnf(refute_0_121,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X))) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | inverse(greatest_lower_bound(identity,inverse(X))) != least_upper_bound(identity,X)
    | least_upper_bound(identity,X) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) ),[0],$fot(least_upper_bound(identity,X))]]) ).

cnf(refute_0_122,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X))) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | least_upper_bound(identity,X) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),least_upper_bound(identity,X)) )],[refute_0_120,refute_0_121]) ).

cnf(refute_0_123,plain,
    least_upper_bound(identity,inverse(X)) = inverse(greatest_lower_bound(X,identity)),
    inference(subst,[],[refute_0_14:[bind(X_6,$fot(X))]]) ).

cnf(refute_0_124,plain,
    least_upper_bound(X_51,X_50) = least_upper_bound(X_50,X_51),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_51)),bind(Y,$fot(X_50))]]) ).

cnf(refute_0_125,plain,
    least_upper_bound(inverse(X),identity) = least_upper_bound(identity,inverse(X)),
    inference(subst,[],[refute_0_124:[bind(X_50,$fot(identity)),bind(X_51,$fot(inverse(X)))]]) ).

cnf(refute_0_126,plain,
    ( least_upper_bound(identity,inverse(X)) != inverse(greatest_lower_bound(X,identity))
    | least_upper_bound(inverse(X),identity) != least_upper_bound(identity,inverse(X))
    | least_upper_bound(inverse(X),identity) = inverse(greatest_lower_bound(X,identity)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(inverse(X),identity))),bind(Y0,$fot(least_upper_bound(identity,inverse(X)))),bind(Z0,$fot(inverse(greatest_lower_bound(X,identity))))]]) ).

cnf(refute_0_127,plain,
    ( least_upper_bound(identity,inverse(X)) != inverse(greatest_lower_bound(X,identity))
    | least_upper_bound(inverse(X),identity) = inverse(greatest_lower_bound(X,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),identity),least_upper_bound(identity,inverse(X))) )],[refute_0_125,refute_0_126]) ).

cnf(refute_0_128,plain,
    least_upper_bound(inverse(X),identity) = inverse(greatest_lower_bound(X,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X)),inverse(greatest_lower_bound(X,identity))) )],[refute_0_123,refute_0_127]) ).

cnf(refute_0_129,plain,
    inverse(inverse(least_upper_bound(inverse(X),identity))) = least_upper_bound(inverse(X),identity),
    inference(subst,[],[p21x_2:[bind(X,$fot(least_upper_bound(inverse(X),identity)))]]) ).

cnf(refute_0_130,plain,
    ( inverse(inverse(least_upper_bound(inverse(X),identity))) != least_upper_bound(inverse(X),identity)
    | least_upper_bound(inverse(X),identity) != inverse(greatest_lower_bound(X,identity))
    | inverse(inverse(least_upper_bound(inverse(X),identity))) = inverse(greatest_lower_bound(X,identity)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(inverse(inverse(least_upper_bound(inverse(X),identity))))),bind(Y0,$fot(least_upper_bound(inverse(X),identity))),bind(Z0,$fot(inverse(greatest_lower_bound(X,identity))))]]) ).

cnf(refute_0_131,plain,
    ( least_upper_bound(inverse(X),identity) != inverse(greatest_lower_bound(X,identity))
    | inverse(inverse(least_upper_bound(inverse(X),identity))) = inverse(greatest_lower_bound(X,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X),identity))),least_upper_bound(inverse(X),identity)) )],[refute_0_129,refute_0_130]) ).

cnf(refute_0_132,plain,
    inverse(inverse(least_upper_bound(inverse(X),identity))) = inverse(greatest_lower_bound(X,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),identity),inverse(greatest_lower_bound(X,identity))) )],[refute_0_128,refute_0_131]) ).

cnf(refute_0_133,plain,
    multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) = multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),
    introduced(tautology,[refl,[$fot(multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X))]]) ).

cnf(refute_0_134,plain,
    ( multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | inverse(inverse(least_upper_bound(inverse(X),identity))) != inverse(greatest_lower_bound(X,identity))
    | multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) = multiply(inverse(greatest_lower_bound(X,identity)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) ),[1,0],$fot(inverse(greatest_lower_bound(X,identity)))]]) ).

cnf(refute_0_135,plain,
    ( inverse(inverse(least_upper_bound(inverse(X),identity))) != inverse(greatest_lower_bound(X,identity))
    | multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) = multiply(inverse(greatest_lower_bound(X,identity)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) )],[refute_0_133,refute_0_134]) ).

cnf(refute_0_136,plain,
    multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) = multiply(inverse(greatest_lower_bound(X,identity)),X),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(inverse(X),identity))),inverse(greatest_lower_bound(X,identity))) )],[refute_0_132,refute_0_135]) ).

cnf(refute_0_137,plain,
    ( multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X) != multiply(inverse(greatest_lower_bound(X,identity)),X)
    | least_upper_bound(identity,X) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | least_upper_bound(identity,X) = multiply(inverse(greatest_lower_bound(X,identity)),X) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) ),[1],$fot(multiply(inverse(greatest_lower_bound(X,identity)),X))]]) ).

cnf(refute_0_138,plain,
    ( least_upper_bound(identity,X) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | least_upper_bound(identity,X) = multiply(inverse(greatest_lower_bound(X,identity)),X) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X),multiply(inverse(greatest_lower_bound(X,identity)),X)) )],[refute_0_136,refute_0_137]) ).

cnf(refute_0_139,plain,
    ( inverse(greatest_lower_bound(identity,inverse(X))) != multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)
    | least_upper_bound(identity,X) = multiply(inverse(greatest_lower_bound(X,identity)),X) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) )],[refute_0_122,refute_0_138]) ).

cnf(refute_0_140,plain,
    least_upper_bound(identity,X) = multiply(inverse(greatest_lower_bound(X,identity)),X),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,inverse(X))),multiply(inverse(inverse(least_upper_bound(inverse(X),identity))),X)) )],[refute_0_106,refute_0_139]) ).

cnf(refute_0_141,plain,
    least_upper_bound(identity,X_107) = multiply(inverse(greatest_lower_bound(X_107,identity)),X_107),
    inference(subst,[],[refute_0_140:[bind(X,$fot(X_107))]]) ).

cnf(refute_0_142,plain,
    greatest_lower_bound(identity,X_107) = greatest_lower_bound(X_107,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_107))]]) ).

cnf(refute_0_143,plain,
    ( greatest_lower_bound(identity,X_107) != greatest_lower_bound(X_107,identity)
    | greatest_lower_bound(X_107,identity) = greatest_lower_bound(identity,X_107) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(identity,X_107))),bind(Y0,$fot(greatest_lower_bound(X_107,identity)))]]) ).

cnf(refute_0_144,plain,
    greatest_lower_bound(X_107,identity) = greatest_lower_bound(identity,X_107),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_107),greatest_lower_bound(X_107,identity)) )],[refute_0_142,refute_0_143]) ).

cnf(refute_0_145,plain,
    ( greatest_lower_bound(X_107,identity) != greatest_lower_bound(identity,X_107)
    | least_upper_bound(identity,X_107) != multiply(inverse(greatest_lower_bound(X_107,identity)),X_107)
    | least_upper_bound(identity,X_107) = multiply(inverse(greatest_lower_bound(identity,X_107)),X_107) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,X_107),multiply(inverse(greatest_lower_bound(X_107,identity)),X_107)) ),[1,0,0],$fot(greatest_lower_bound(identity,X_107))]]) ).

cnf(refute_0_146,plain,
    ( least_upper_bound(identity,X_107) != multiply(inverse(greatest_lower_bound(X_107,identity)),X_107)
    | least_upper_bound(identity,X_107) = multiply(inverse(greatest_lower_bound(identity,X_107)),X_107) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_107,identity),greatest_lower_bound(identity,X_107)) )],[refute_0_144,refute_0_145]) ).

cnf(refute_0_147,plain,
    least_upper_bound(identity,X_107) = multiply(inverse(greatest_lower_bound(identity,X_107)),X_107),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_107),multiply(inverse(greatest_lower_bound(X_107,identity)),X_107)) )],[refute_0_141,refute_0_146]) ).

cnf(refute_0_148,plain,
    least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))),least_upper_bound(X_159,least_upper_bound(X_160,identity))),
    inference(subst,[],[refute_0_147:[bind(X_107,$fot(least_upper_bound(X_159,least_upper_bound(X_160,identity))))]]) ).

cnf(refute_0_149,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) = X_10,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_10)),bind(Y,$fot(X_11))]]) ).

cnf(refute_0_150,plain,
    least_upper_bound(X_11,X_10) = least_upper_bound(X_10,X_11),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_11)),bind(Y,$fot(X_10))]]) ).

cnf(refute_0_151,plain,
    ( least_upper_bound(X_11,X_10) != least_upper_bound(X_10,X_11)
    | least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_11,X_10))),bind(Y0,$fot(least_upper_bound(X_10,X_11)))]]) ).

cnf(refute_0_152,plain,
    least_upper_bound(X_10,X_11) = least_upper_bound(X_11,X_10),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,X_10),least_upper_bound(X_10,X_11)) )],[refute_0_150,refute_0_151]) ).

cnf(refute_0_153,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
    | least_upper_bound(X_10,X_11) != least_upper_bound(X_11,X_10)
    | greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) ),[0,1],$fot(least_upper_bound(X_11,X_10))]]) ).

cnf(refute_0_154,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)) != X_10
    | greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_10,X_11),least_upper_bound(X_11,X_10)) )],[refute_0_152,refute_0_153]) ).

cnf(refute_0_155,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_11,X_10)) = X_10,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(X_10,X_11)),X_10) )],[refute_0_149,refute_0_154]) ).

cnf(refute_0_156,plain,
    greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_49,X_50),X_10)) = X_10,
    inference(subst,[],[refute_0_155:[bind(X_11,$fot(least_upper_bound(X_49,X_50)))]]) ).

cnf(refute_0_157,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X_10)) = least_upper_bound(least_upper_bound(X_49,X_50),X_10),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(X_10))]]) ).

cnf(refute_0_158,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X_10)) != least_upper_bound(least_upper_bound(X_49,X_50),X_10)
    | least_upper_bound(least_upper_bound(X_49,X_50),X_10) = least_upper_bound(X_49,least_upper_bound(X_50,X_10)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_49,least_upper_bound(X_50,X_10)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_49,X_50),X_10)))]]) ).

cnf(refute_0_159,plain,
    least_upper_bound(least_upper_bound(X_49,X_50),X_10) = least_upper_bound(X_49,least_upper_bound(X_50,X_10)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_10)),least_upper_bound(least_upper_bound(X_49,X_50),X_10)) )],[refute_0_157,refute_0_158]) ).

cnf(refute_0_160,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_49,X_50),X_10)) != X_10
    | least_upper_bound(least_upper_bound(X_49,X_50),X_10) != least_upper_bound(X_49,least_upper_bound(X_50,X_10))
    | greatest_lower_bound(X_10,least_upper_bound(X_49,least_upper_bound(X_50,X_10))) = X_10 ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_49,X_50),X_10)),X_10) ),[0,1],$fot(least_upper_bound(X_49,least_upper_bound(X_50,X_10)))]]) ).

cnf(refute_0_161,plain,
    ( greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_49,X_50),X_10)) != X_10
    | greatest_lower_bound(X_10,least_upper_bound(X_49,least_upper_bound(X_50,X_10))) = X_10 ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_49,X_50),X_10),least_upper_bound(X_49,least_upper_bound(X_50,X_10))) )],[refute_0_159,refute_0_160]) ).

cnf(refute_0_162,plain,
    greatest_lower_bound(X_10,least_upper_bound(X_49,least_upper_bound(X_50,X_10))) = X_10,
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_10,least_upper_bound(least_upper_bound(X_49,X_50),X_10)),X_10) )],[refute_0_156,refute_0_161]) ).

cnf(refute_0_163,plain,
    greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = identity,
    inference(subst,[],[refute_0_162:[bind(X_10,$fot(identity)),bind(X_49,$fot(X_159)),bind(X_50,$fot(X_160))]]) ).

cnf(refute_0_164,plain,
    ( greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != identity
    | least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) ),[1,0,0],$fot(identity)]]) ).

cnf(refute_0_165,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),identity) )],[refute_0_163,refute_0_164]) ).

cnf(refute_0_166,plain,
    least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(greatest_lower_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) )],[refute_0_148,refute_0_165]) ).

cnf(refute_0_167,plain,
    inverse(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)))) = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)),
    inference(subst,[],[p21x_2:[bind(X,$fot(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))))]]) ).

cnf(refute_0_168,plain,
    greatest_lower_bound(inverse(Y),least_upper_bound(inverse(X),inverse(Y))) = inverse(Y),
    inference(subst,[],[refute_0_155:[bind(X_10,$fot(inverse(Y))),bind(X_11,$fot(inverse(X)))]]) ).

cnf(refute_0_169,plain,
    ( greatest_lower_bound(inverse(Y),least_upper_bound(inverse(X),inverse(Y))) != inverse(Y)
    | least_upper_bound(inverse(X),inverse(Y)) != inverse(greatest_lower_bound(X,Y))
    | greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) = inverse(Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(Y),least_upper_bound(inverse(X),inverse(Y))),inverse(Y)) ),[0,1],$fot(inverse(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_170,plain,
    ( greatest_lower_bound(inverse(Y),least_upper_bound(inverse(X),inverse(Y))) != inverse(Y)
    | greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) = inverse(Y) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X),inverse(Y)),inverse(greatest_lower_bound(X,Y))) )],[refute_0_40,refute_0_169]) ).

cnf(refute_0_171,plain,
    greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) = inverse(Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),least_upper_bound(inverse(X),inverse(Y))),inverse(Y)) )],[refute_0_168,refute_0_170]) ).

cnf(refute_0_172,plain,
    ( inverse(least_upper_bound(X,Y)) != greatest_lower_bound(inverse(X),inverse(Y))
    | greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(least_upper_bound(X,Y)))),bind(Y0,$fot(greatest_lower_bound(inverse(X),inverse(Y))))]]) ).

cnf(refute_0_173,plain,
    greatest_lower_bound(inverse(X),inverse(Y)) = inverse(least_upper_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X,Y)),greatest_lower_bound(inverse(X),inverse(Y))) )],[p21x_5,refute_0_172]) ).

cnf(refute_0_174,plain,
    greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) = inverse(least_upper_bound(Y,greatest_lower_bound(X,Y))),
    inference(subst,[],[refute_0_173:[bind(X,$fot(Y)),bind(Y,$fot(greatest_lower_bound(X,Y)))]]) ).

cnf(refute_0_175,plain,
    ( greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) != inverse(Y)
    | greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) != inverse(least_upper_bound(Y,greatest_lower_bound(X,Y)))
    | inverse(least_upper_bound(Y,greatest_lower_bound(X,Y))) = inverse(Y) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))),inverse(Y)) ),[0],$fot(inverse(least_upper_bound(Y,greatest_lower_bound(X,Y))))]]) ).

cnf(refute_0_176,plain,
    ( greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))) != inverse(Y)
    | inverse(least_upper_bound(Y,greatest_lower_bound(X,Y))) = inverse(Y) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))),inverse(least_upper_bound(Y,greatest_lower_bound(X,Y)))) )],[refute_0_174,refute_0_175]) ).

cnf(refute_0_177,plain,
    inverse(least_upper_bound(Y,greatest_lower_bound(X,Y))) = inverse(Y),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(inverse(Y),inverse(greatest_lower_bound(X,Y))),inverse(Y)) )],[refute_0_171,refute_0_176]) ).

cnf(refute_0_178,plain,
    inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) = inverse(X_17),
    inference(subst,[],[refute_0_177:[bind(X,$fot(X_16)),bind(Y,$fot(X_17))]]) ).

cnf(refute_0_179,plain,
    ( inverse(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)))) != least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))
    | inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) != inverse(X_17)
    | inverse(inverse(X_17)) = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)))),least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) ),[0,0],$fot(inverse(X_17))]]) ).

cnf(refute_0_180,plain,
    ( inverse(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)))) != least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))
    | inverse(inverse(X_17)) = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))),inverse(X_17)) )],[refute_0_178,refute_0_179]) ).

cnf(refute_0_181,plain,
    inverse(inverse(X_17)) = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)),
    inference(resolve,[$cnf( $equal(inverse(inverse(least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)))),least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) )],[refute_0_167,refute_0_180]) ).

cnf(refute_0_182,plain,
    inverse(inverse(X_17)) = X_17,
    inference(subst,[],[p21x_2:[bind(X,$fot(X_17))]]) ).

cnf(refute_0_183,plain,
    ( inverse(inverse(X_17)) != X_17
    | inverse(inverse(X_17)) != least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))
    | X_17 = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(inverse(X_17)),least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) ),[0],$fot(X_17)]]) ).

cnf(refute_0_184,plain,
    ( inverse(inverse(X_17)) != least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))
    | X_17 = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_17)),X_17) )],[refute_0_182,refute_0_183]) ).

cnf(refute_0_185,plain,
    X_17 = least_upper_bound(X_17,greatest_lower_bound(X_16,X_17)),
    inference(resolve,[$cnf( $equal(inverse(inverse(X_17)),least_upper_bound(X_17,greatest_lower_bound(X_16,X_17))) )],[refute_0_181,refute_0_184]) ).

cnf(refute_0_186,plain,
    least_upper_bound(X_39,Y) = least_upper_bound(least_upper_bound(X_39,Y),greatest_lower_bound(X_39,least_upper_bound(X_39,Y))),
    inference(subst,[],[refute_0_185:[bind(X_16,$fot(X_39)),bind(X_17,$fot(least_upper_bound(X_39,Y)))]]) ).

cnf(refute_0_187,plain,
    greatest_lower_bound(X_39,least_upper_bound(X_39,Y)) = X_39,
    inference(subst,[],[glb_absorbtion:[bind(X,$fot(X_39))]]) ).

cnf(refute_0_188,plain,
    ( greatest_lower_bound(X_39,least_upper_bound(X_39,Y)) != X_39
    | least_upper_bound(X_39,Y) != least_upper_bound(least_upper_bound(X_39,Y),greatest_lower_bound(X_39,least_upper_bound(X_39,Y)))
    | least_upper_bound(X_39,Y) = least_upper_bound(least_upper_bound(X_39,Y),X_39) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_39,Y),least_upper_bound(least_upper_bound(X_39,Y),greatest_lower_bound(X_39,least_upper_bound(X_39,Y)))) ),[1,1],$fot(X_39)]]) ).

cnf(refute_0_189,plain,
    ( least_upper_bound(X_39,Y) != least_upper_bound(least_upper_bound(X_39,Y),greatest_lower_bound(X_39,least_upper_bound(X_39,Y)))
    | least_upper_bound(X_39,Y) = least_upper_bound(least_upper_bound(X_39,Y),X_39) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_39,least_upper_bound(X_39,Y)),X_39) )],[refute_0_187,refute_0_188]) ).

cnf(refute_0_190,plain,
    least_upper_bound(X_39,Y) = least_upper_bound(least_upper_bound(X_39,Y),X_39),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_39,Y),least_upper_bound(least_upper_bound(X_39,Y),greatest_lower_bound(X_39,least_upper_bound(X_39,Y)))) )],[refute_0_186,refute_0_189]) ).

cnf(refute_0_191,plain,
    ( least_upper_bound(X,least_upper_bound(Y,Z)) != least_upper_bound(least_upper_bound(X,Y),Z)
    | least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),Z)))]]) ).

cnf(refute_0_192,plain,
    least_upper_bound(least_upper_bound(X,Y),Z) = least_upper_bound(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,Z)),least_upper_bound(least_upper_bound(X,Y),Z)) )],[associativity_of_lub,refute_0_191]) ).

cnf(refute_0_193,plain,
    least_upper_bound(least_upper_bound(X_39,Y),X_39) = least_upper_bound(X_39,least_upper_bound(Y,X_39)),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_39)),bind(Z,$fot(X_39))]]) ).

cnf(refute_0_194,plain,
    ( least_upper_bound(X_39,Y) != least_upper_bound(least_upper_bound(X_39,Y),X_39)
    | least_upper_bound(least_upper_bound(X_39,Y),X_39) != least_upper_bound(X_39,least_upper_bound(Y,X_39))
    | least_upper_bound(X_39,Y) = least_upper_bound(X_39,least_upper_bound(Y,X_39)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_39,Y),least_upper_bound(X_39,least_upper_bound(Y,X_39))) ),[0],$fot(least_upper_bound(least_upper_bound(X_39,Y),X_39))]]) ).

cnf(refute_0_195,plain,
    ( least_upper_bound(X_39,Y) != least_upper_bound(least_upper_bound(X_39,Y),X_39)
    | least_upper_bound(X_39,Y) = least_upper_bound(X_39,least_upper_bound(Y,X_39)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_39,Y),X_39),least_upper_bound(X_39,least_upper_bound(Y,X_39))) )],[refute_0_193,refute_0_194]) ).

cnf(refute_0_196,plain,
    least_upper_bound(X_39,Y) = least_upper_bound(X_39,least_upper_bound(Y,X_39)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_39,Y),least_upper_bound(least_upper_bound(X_39,Y),X_39)) )],[refute_0_190,refute_0_195]) ).

cnf(refute_0_197,plain,
    least_upper_bound(X_138,least_upper_bound(X,Y)) = least_upper_bound(X_138,least_upper_bound(least_upper_bound(X,Y),X_138)),
    inference(subst,[],[refute_0_196:[bind(Y,$fot(least_upper_bound(X,Y))),bind(X_39,$fot(X_138))]]) ).

cnf(refute_0_198,plain,
    least_upper_bound(X,least_upper_bound(Y,X_138)) = least_upper_bound(least_upper_bound(X,Y),X_138),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(X_138))]]) ).

cnf(refute_0_199,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_138)) != least_upper_bound(least_upper_bound(X,Y),X_138)
    | least_upper_bound(least_upper_bound(X,Y),X_138) = least_upper_bound(X,least_upper_bound(Y,X_138)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_138)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X,Y),X_138)))]]) ).

cnf(refute_0_200,plain,
    least_upper_bound(least_upper_bound(X,Y),X_138) = least_upper_bound(X,least_upper_bound(Y,X_138)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_138)),least_upper_bound(least_upper_bound(X,Y),X_138)) )],[refute_0_198,refute_0_199]) ).

cnf(refute_0_201,plain,
    ( least_upper_bound(X_138,least_upper_bound(X,Y)) != least_upper_bound(X_138,least_upper_bound(least_upper_bound(X,Y),X_138))
    | least_upper_bound(least_upper_bound(X,Y),X_138) != least_upper_bound(X,least_upper_bound(Y,X_138))
    | least_upper_bound(X_138,least_upper_bound(X,Y)) = least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_138,least_upper_bound(X,Y)),least_upper_bound(X_138,least_upper_bound(least_upper_bound(X,Y),X_138))) ),[1,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_138)))]]) ).

cnf(refute_0_202,plain,
    ( least_upper_bound(X_138,least_upper_bound(X,Y)) != least_upper_bound(X_138,least_upper_bound(least_upper_bound(X,Y),X_138))
    | least_upper_bound(X_138,least_upper_bound(X,Y)) = least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_138),least_upper_bound(X,least_upper_bound(Y,X_138))) )],[refute_0_200,refute_0_201]) ).

cnf(refute_0_203,plain,
    least_upper_bound(X_138,least_upper_bound(X,Y)) = least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_138,least_upper_bound(X,Y)),least_upper_bound(X_138,least_upper_bound(least_upper_bound(X,Y),X_138))) )],[refute_0_197,refute_0_202]) ).

cnf(refute_0_204,plain,
    ( least_upper_bound(X_138,least_upper_bound(X,Y)) != least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138)))
    | least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138))) = least_upper_bound(X_138,least_upper_bound(X,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_138,least_upper_bound(X,Y)))),bind(Y0,$fot(least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138)))))]]) ).

cnf(refute_0_205,plain,
    least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138))) = least_upper_bound(X_138,least_upper_bound(X,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_138,least_upper_bound(X,Y)),least_upper_bound(X_138,least_upper_bound(X,least_upper_bound(Y,X_138)))) )],[refute_0_203,refute_0_204]) ).

cnf(refute_0_206,plain,
    least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = least_upper_bound(identity,least_upper_bound(X_159,X_160)),
    inference(subst,[],[refute_0_205:[bind(X,$fot(X_159)),bind(Y,$fot(X_160)),bind(X_138,$fot(identity))]]) ).

cnf(refute_0_207,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != least_upper_bound(identity,least_upper_bound(X_159,X_160))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_159,X_160)))]]) ).

cnf(refute_0_208,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),least_upper_bound(identity,least_upper_bound(X_159,X_160))) )],[refute_0_206,refute_0_207]) ).

cnf(refute_0_209,plain,
    multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) = least_upper_bound(X_159,least_upper_bound(X_160,identity)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(X_159,least_upper_bound(X_160,identity))))]]) ).

cnf(refute_0_210,plain,
    multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))))]]) ).

cnf(refute_0_211,plain,
    ( multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_212,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) )],[refute_0_210,refute_0_211]) ).

cnf(refute_0_213,plain,
    multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_212]) ).

cnf(refute_0_214,plain,
    ( multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != least_upper_bound(X_159,least_upper_bound(X_160,identity))
    | multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = least_upper_bound(X_159,least_upper_bound(X_160,identity)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))))),bind(Y0,$fot(multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))))),bind(Z0,$fot(least_upper_bound(X_159,least_upper_bound(X_160,identity))))]]) ).

cnf(refute_0_215,plain,
    ( multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != least_upper_bound(X_159,least_upper_bound(X_160,identity))
    | multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = least_upper_bound(X_159,least_upper_bound(X_160,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity)))) )],[refute_0_213,refute_0_214]) ).

cnf(refute_0_216,plain,
    multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) = least_upper_bound(X_159,least_upper_bound(X_160,identity)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),least_upper_bound(X_159,least_upper_bound(X_160,identity))) )],[refute_0_209,refute_0_215]) ).

cnf(refute_0_217,plain,
    ( multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))) != least_upper_bound(X_159,least_upper_bound(X_160,identity))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,X_160)),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) ),[1],$fot(least_upper_bound(X_159,least_upper_bound(X_160,identity)))]]) ).

cnf(refute_0_218,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,X_160)) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity))),least_upper_bound(X_159,least_upper_bound(X_160,identity))) )],[refute_0_216,refute_0_217]) ).

cnf(refute_0_219,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))) != multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))
    | least_upper_bound(identity,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,X_160)),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) )],[refute_0_208,refute_0_218]) ).

cnf(refute_0_220,plain,
    least_upper_bound(identity,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_160,identity))),multiply(inverse(identity),least_upper_bound(X_159,least_upper_bound(X_160,identity)))) )],[refute_0_166,refute_0_219]) ).

cnf(refute_0_221,plain,
    least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_162,identity))) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)),
    inference(subst,[],[refute_0_220:[bind(X_160,$fot(least_upper_bound(X_162,identity)))]]) ).

cnf(refute_0_222,plain,
    least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(X_162,identity)),
    inference(subst,[],[refute_0_220:[bind(X_160,$fot(X_162))]]) ).

cnf(refute_0_223,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,X_162)) != least_upper_bound(X_159,least_upper_bound(X_162,identity))
    | least_upper_bound(X_159,least_upper_bound(X_162,identity)) = least_upper_bound(identity,least_upper_bound(X_159,X_162)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(X_159,X_162)))),bind(Y0,$fot(least_upper_bound(X_159,least_upper_bound(X_162,identity))))]]) ).

cnf(refute_0_224,plain,
    least_upper_bound(X_159,least_upper_bound(X_162,identity)) = least_upper_bound(identity,least_upper_bound(X_159,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,X_162)),least_upper_bound(X_159,least_upper_bound(X_162,identity))) )],[refute_0_222,refute_0_223]) ).

cnf(refute_0_225,plain,
    ( least_upper_bound(X_159,least_upper_bound(X_162,identity)) != least_upper_bound(identity,least_upper_bound(X_159,X_162))
    | least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_162,identity))) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_162,identity))),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) ),[0,1],$fot(least_upper_bound(identity,least_upper_bound(X_159,X_162)))]]) ).

cnf(refute_0_226,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_162,identity))) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(X_162,identity)),least_upper_bound(identity,least_upper_bound(X_159,X_162))) )],[refute_0_224,refute_0_225]) ).

cnf(refute_0_227,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,least_upper_bound(X_162,identity))),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) )],[refute_0_221,refute_0_226]) ).

cnf(refute_0_228,plain,
    least_upper_bound(X_50,least_upper_bound(X_50,X_51)) = least_upper_bound(least_upper_bound(X_50,X_50),X_51),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_50)),bind(Y,$fot(X_50)),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_229,plain,
    least_upper_bound(X_50,X_50) = X_50,
    inference(subst,[],[idempotence_of_lub:[bind(X,$fot(X_50))]]) ).

cnf(refute_0_230,plain,
    ( least_upper_bound(X_50,X_50) != X_50
    | least_upper_bound(X_50,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_50,X_50),X_51)
    | least_upper_bound(X_50,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,X_51) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_50,X_51)),least_upper_bound(least_upper_bound(X_50,X_50),X_51)) ),[1,0],$fot(X_50)]]) ).

cnf(refute_0_231,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_50,X_50),X_51)
    | least_upper_bound(X_50,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,X_51) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,X_50),X_50) )],[refute_0_229,refute_0_230]) ).

cnf(refute_0_232,plain,
    least_upper_bound(X_50,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,X_51),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_50,X_51)),least_upper_bound(least_upper_bound(X_50,X_50),X_51)) )],[refute_0_228,refute_0_231]) ).

cnf(refute_0_233,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) = least_upper_bound(identity,least_upper_bound(X_159,X_162)),
    inference(subst,[],[refute_0_232:[bind(X_50,$fot(identity)),bind(X_51,$fot(least_upper_bound(X_159,X_162)))]]) ).

cnf(refute_0_234,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) != least_upper_bound(identity,least_upper_bound(X_159,X_162))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_159,X_162)))]]) ).

cnf(refute_0_235,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))),least_upper_bound(identity,least_upper_bound(X_159,X_162))) )],[refute_0_233,refute_0_234]) ).

cnf(refute_0_236,plain,
    ( least_upper_bound(X_39,Y) != least_upper_bound(X_39,least_upper_bound(Y,X_39))
    | least_upper_bound(X_39,least_upper_bound(Y,X_39)) = least_upper_bound(X_39,Y) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_39,Y))),bind(Y0,$fot(least_upper_bound(X_39,least_upper_bound(Y,X_39))))]]) ).

cnf(refute_0_237,plain,
    least_upper_bound(X_39,least_upper_bound(Y,X_39)) = least_upper_bound(X_39,Y),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_39,Y),least_upper_bound(X_39,least_upper_bound(Y,X_39))) )],[refute_0_196,refute_0_236]) ).

cnf(refute_0_238,plain,
    least_upper_bound(identity,least_upper_bound(X_162,identity)) = least_upper_bound(identity,X_162),
    inference(subst,[],[refute_0_237:[bind(Y,$fot(X_162)),bind(X_39,$fot(identity))]]) ).

cnf(refute_0_239,plain,
    least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) = least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))))]]) ).

cnf(refute_0_240,plain,
    ( least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) != least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity)))
    | least_upper_bound(identity,least_upper_bound(X_162,identity)) != least_upper_bound(identity,X_162)
    | least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))),least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_162))]]) ).

cnf(refute_0_241,plain,
    ( least_upper_bound(identity,least_upper_bound(X_162,identity)) != least_upper_bound(identity,X_162)
    | least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))),least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity)))) )],[refute_0_239,refute_0_240]) ).

cnf(refute_0_242,plain,
    least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) = least_upper_bound(X_159,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_162,identity)),least_upper_bound(identity,X_162)) )],[refute_0_238,refute_0_241]) ).

cnf(refute_0_243,plain,
    multiply(least_upper_bound(X_110,X_111),inverse(X_110)) = least_upper_bound(multiply(X_110,inverse(X_110)),multiply(X_111,inverse(X_110))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_110))),bind(Y,$fot(X_110)),bind(Z,$fot(X_111))]]) ).

cnf(refute_0_244,plain,
    multiply(X_110,inverse(X_110)) = identity,
    inference(subst,[],[refute_0_29:[bind(X,$fot(X_110))]]) ).

cnf(refute_0_245,plain,
    ( multiply(X_110,inverse(X_110)) != identity
    | multiply(least_upper_bound(X_110,X_111),inverse(X_110)) != least_upper_bound(multiply(X_110,inverse(X_110)),multiply(X_111,inverse(X_110)))
    | multiply(least_upper_bound(X_110,X_111),inverse(X_110)) = least_upper_bound(identity,multiply(X_111,inverse(X_110))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_110,X_111),inverse(X_110)),least_upper_bound(multiply(X_110,inverse(X_110)),multiply(X_111,inverse(X_110)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_246,plain,
    ( multiply(least_upper_bound(X_110,X_111),inverse(X_110)) != least_upper_bound(multiply(X_110,inverse(X_110)),multiply(X_111,inverse(X_110)))
    | multiply(least_upper_bound(X_110,X_111),inverse(X_110)) = least_upper_bound(identity,multiply(X_111,inverse(X_110))) ),
    inference(resolve,[$cnf( $equal(multiply(X_110,inverse(X_110)),identity) )],[refute_0_244,refute_0_245]) ).

cnf(refute_0_247,plain,
    multiply(least_upper_bound(X_110,X_111),inverse(X_110)) = least_upper_bound(identity,multiply(X_111,inverse(X_110))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_110,X_111),inverse(X_110)),least_upper_bound(multiply(X_110,inverse(X_110)),multiply(X_111,inverse(X_110)))) )],[refute_0_243,refute_0_246]) ).

cnf(refute_0_248,plain,
    multiply(least_upper_bound(identity,least_upper_bound(X_161,X_162)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))),
    inference(subst,[],[refute_0_247:[bind(X_110,$fot(identity)),bind(X_111,$fot(least_upper_bound(X_161,X_162)))]]) ).

cnf(refute_0_249,plain,
    least_upper_bound(identity,least_upper_bound(X_161,X_162)) = least_upper_bound(X_161,least_upper_bound(X_162,identity)),
    inference(subst,[],[refute_0_220:[bind(X_159,$fot(X_161)),bind(X_160,$fot(X_162))]]) ).

cnf(refute_0_250,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_161,X_162)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(identity,least_upper_bound(X_161,X_162)) != least_upper_bound(X_161,least_upper_bound(X_162,identity))
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_161,X_162)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))) ),[0,0],$fot(least_upper_bound(X_161,least_upper_bound(X_162,identity)))]]) ).

cnf(refute_0_251,plain,
    ( multiply(least_upper_bound(identity,least_upper_bound(X_161,X_162)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_161,X_162)),least_upper_bound(X_161,least_upper_bound(X_162,identity))) )],[refute_0_249,refute_0_250]) ).

cnf(refute_0_252,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(identity,least_upper_bound(X_161,X_162)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))) )],[refute_0_248,refute_0_251]) ).

cnf(refute_0_253,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity) = least_upper_bound(X_161,least_upper_bound(X_162,identity)),
    inference(subst,[],[refute_0_94:[bind(X,$fot(least_upper_bound(X_161,least_upper_bound(X_162,identity))))]]) ).

cnf(refute_0_254,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)))]]) ).

cnf(refute_0_255,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity))
    | inverse(identity) != identity
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_256,plain,
    ( inverse(identity) != identity
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity))) )],[refute_0_254,refute_0_255]) ).

cnf(refute_0_257,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_256]) ).

cnf(refute_0_258,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity) != least_upper_bound(X_161,least_upper_bound(X_162,identity))
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity)
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(X_162,identity)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity))),bind(Z0,$fot(least_upper_bound(X_161,least_upper_bound(X_162,identity))))]]) ).

cnf(refute_0_259,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity) != least_upper_bound(X_161,least_upper_bound(X_162,identity))
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(X_162,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity)) )],[refute_0_257,refute_0_258]) ).

cnf(refute_0_260,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(X_162,identity)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),identity),least_upper_bound(X_161,least_upper_bound(X_162,identity))) )],[refute_0_253,refute_0_259]) ).

cnf(refute_0_261,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != least_upper_bound(X_161,least_upper_bound(X_162,identity))
    | multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))) ),[0],$fot(least_upper_bound(X_161,least_upper_bound(X_162,identity)))]]) ).

cnf(refute_0_262,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),least_upper_bound(X_161,least_upper_bound(X_162,identity))) )],[refute_0_260,refute_0_261]) ).

cnf(refute_0_263,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity) = least_upper_bound(X_161,least_upper_bound(identity,X_162)),
    inference(subst,[],[refute_0_94:[bind(X,$fot(least_upper_bound(X_161,least_upper_bound(identity,X_162))))]]) ).

cnf(refute_0_264,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)))]]) ).

cnf(refute_0_265,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) != multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity))
    | inverse(identity) != identity
    | multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity))) ),[1,1],$fot(identity)]]) ).

cnf(refute_0_266,plain,
    ( inverse(identity) != identity
    | multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity))) )],[refute_0_264,refute_0_265]) ).

cnf(refute_0_267,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_266]) ).

cnf(refute_0_268,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity) != least_upper_bound(X_161,least_upper_bound(identity,X_162))
    | multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) != multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity)
    | multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity))),bind(Z0,$fot(least_upper_bound(X_161,least_upper_bound(identity,X_162))))]]) ).

cnf(refute_0_269,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity) != least_upper_bound(X_161,least_upper_bound(identity,X_162))
    | multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity)) )],[refute_0_267,refute_0_268]) ).

cnf(refute_0_270,plain,
    multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),identity),least_upper_bound(X_161,least_upper_bound(identity,X_162))) )],[refute_0_263,refute_0_269]) ).

cnf(refute_0_271,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(multiply(Y,inverse(X_118)),multiply(least_upper_bound(X_118,X_119),inverse(X_118))),
    inference(subst,[],[monotony_lub2:[bind(X,$fot(inverse(X_118))),bind(Z,$fot(least_upper_bound(X_118,X_119)))]]) ).

cnf(refute_0_272,plain,
    multiply(least_upper_bound(X_118,X_119),inverse(X_118)) = least_upper_bound(identity,multiply(X_119,inverse(X_118))),
    inference(subst,[],[refute_0_247:[bind(X_110,$fot(X_118)),bind(X_111,$fot(X_119))]]) ).

cnf(refute_0_273,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) != least_upper_bound(multiply(Y,inverse(X_118)),multiply(least_upper_bound(X_118,X_119),inverse(X_118)))
    | multiply(least_upper_bound(X_118,X_119),inverse(X_118)) != least_upper_bound(identity,multiply(X_119,inverse(X_118)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),least_upper_bound(multiply(Y,inverse(X_118)),multiply(least_upper_bound(X_118,X_119),inverse(X_118)))) ),[1,1],$fot(least_upper_bound(identity,multiply(X_119,inverse(X_118))))]]) ).

cnf(refute_0_274,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) != least_upper_bound(multiply(Y,inverse(X_118)),multiply(least_upper_bound(X_118,X_119),inverse(X_118)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_118,X_119),inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) )],[refute_0_272,refute_0_273]) ).

cnf(refute_0_275,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),least_upper_bound(multiply(Y,inverse(X_118)),multiply(least_upper_bound(X_118,X_119),inverse(X_118)))) )],[refute_0_271,refute_0_274]) ).

cnf(refute_0_276,plain,
    ( multiply(least_upper_bound(Y,Z),X) != least_upper_bound(multiply(Y,X),multiply(Z,X))
    | least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(least_upper_bound(Y,Z),X))),bind(Y0,$fot(least_upper_bound(multiply(Y,X),multiply(Z,X))))]]) ).

cnf(refute_0_277,plain,
    least_upper_bound(multiply(Y,X),multiply(Z,X)) = multiply(least_upper_bound(Y,Z),X),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,Z),X),least_upper_bound(multiply(Y,X),multiply(Z,X))) )],[monotony_lub2,refute_0_276]) ).

cnf(refute_0_278,plain,
    least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))) = multiply(least_upper_bound(Y,X_119),inverse(X_118)),
    inference(subst,[],[refute_0_277:[bind(X,$fot(inverse(X_118))),bind(Z,$fot(X_119))]]) ).

cnf(refute_0_279,plain,
    least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))))]]) ).

cnf(refute_0_280,plain,
    ( least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))) != multiply(least_upper_bound(Y,X_119),inverse(X_118))
    | least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) != least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))))
    | least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))))) ),[1,1],$fot(multiply(least_upper_bound(Y,X_119),inverse(X_118)))]]) ).

cnf(refute_0_281,plain,
    ( least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))) != multiply(least_upper_bound(Y,X_119),inverse(X_118))
    | least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))))) )],[refute_0_279,refute_0_280]) ).

cnf(refute_0_282,plain,
    least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))),multiply(least_upper_bound(Y,X_119),inverse(X_118))) )],[refute_0_278,refute_0_281]) ).

cnf(refute_0_283,plain,
    multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity))))]]) ).

cnf(refute_0_284,plain,
    least_upper_bound(identity,least_upper_bound(Y,Z)) = multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),
    inference(subst,[],[refute_0_140:[bind(X,$fot(least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_285,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,Z)) != multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z))
    | multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = least_upper_bound(identity,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(Y,Z)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z))))]]) ).

cnf(refute_0_286,plain,
    multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = least_upper_bound(identity,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,Z)),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z))) )],[refute_0_284,refute_0_285]) ).

cnf(refute_0_287,plain,
    ( multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))
    | multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != least_upper_bound(identity,least_upper_bound(Y,Z))
    | least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(Y,Z)))]]) ).

cnf(refute_0_288,plain,
    ( multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))
    | least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),least_upper_bound(identity,least_upper_bound(Y,Z))) )],[refute_0_286,refute_0_287]) ).

cnf(refute_0_289,plain,
    least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))) )],[refute_0_283,refute_0_288]) ).

cnf(refute_0_290,plain,
    multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))) = least_upper_bound(Y,least_upper_bound(identity,Z)),
    inference(subst,[],[left_identity:[bind(X,$fot(least_upper_bound(Y,least_upper_bound(identity,Z))))]]) ).

cnf(refute_0_291,plain,
    multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),
    introduced(tautology,[refl,[$fot(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))))]]) ).

cnf(refute_0_292,plain,
    ( multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_293,plain,
    ( inverse(identity) != identity
    | multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))) )],[refute_0_291,refute_0_292]) ).

cnf(refute_0_294,plain,
    multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))),
    inference(resolve,[$cnf( $equal(inverse(identity),identity) )],[p21x_1,refute_0_293]) ).

cnf(refute_0_295,plain,
    ( multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) != multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z)))
    | multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))))),bind(Y0,$fot(multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(identity,Z))))]]) ).

cnf(refute_0_296,plain,
    ( multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z)))) )],[refute_0_294,refute_0_295]) ).

cnf(refute_0_297,plain,
    multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) = least_upper_bound(Y,least_upper_bound(identity,Z)),
    inference(resolve,[$cnf( $equal(multiply(identity,least_upper_bound(Y,least_upper_bound(identity,Z))),least_upper_bound(Y,least_upper_bound(identity,Z))) )],[refute_0_290,refute_0_296]) ).

cnf(refute_0_298,plain,
    multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),least_upper_bound(X_92,X_93))),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_92))),bind(Z,$fot(least_upper_bound(X_92,X_93)))]]) ).

cnf(refute_0_299,plain,
    multiply(inverse(X_83),least_upper_bound(X_83,X_84)) = least_upper_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_83))),bind(Y,$fot(X_83)),bind(Z,$fot(X_84))]]) ).

cnf(refute_0_300,plain,
    multiply(inverse(X_83),X_83) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_83))]]) ).

cnf(refute_0_301,plain,
    ( multiply(inverse(X_83),X_83) != identity
    | multiply(inverse(X_83),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))
    | multiply(inverse(X_83),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_83),X_84)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_83),least_upper_bound(X_83,X_84)),least_upper_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_302,plain,
    ( multiply(inverse(X_83),least_upper_bound(X_83,X_84)) != least_upper_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))
    | multiply(inverse(X_83),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_83),X_84)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_83),X_83),identity) )],[refute_0_300,refute_0_301]) ).

cnf(refute_0_303,plain,
    multiply(inverse(X_83),least_upper_bound(X_83,X_84)) = least_upper_bound(identity,multiply(inverse(X_83),X_84)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_83),least_upper_bound(X_83,X_84)),least_upper_bound(multiply(inverse(X_83),X_83),multiply(inverse(X_83),X_84))) )],[refute_0_299,refute_0_302]) ).

cnf(refute_0_304,plain,
    multiply(inverse(X_92),least_upper_bound(X_92,X_93)) = least_upper_bound(identity,multiply(inverse(X_92),X_93)),
    inference(subst,[],[refute_0_303:[bind(X_83,$fot(X_92)),bind(X_84,$fot(X_93))]]) ).

cnf(refute_0_305,plain,
    ( multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) != least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),least_upper_bound(X_92,X_93)))
    | multiply(inverse(X_92),least_upper_bound(X_92,X_93)) != least_upper_bound(identity,multiply(inverse(X_92),X_93))
    | multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),least_upper_bound(X_92,X_93)))) ),[1,1],$fot(least_upper_bound(identity,multiply(inverse(X_92),X_93)))]]) ).

cnf(refute_0_306,plain,
    ( multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) != least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),least_upper_bound(X_92,X_93)))
    | multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_92),least_upper_bound(X_92,X_93)),least_upper_bound(identity,multiply(inverse(X_92),X_93))) )],[refute_0_304,refute_0_305]) ).

cnf(refute_0_307,plain,
    multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),least_upper_bound(X_92,X_93)))) )],[refute_0_298,refute_0_306]) ).

cnf(refute_0_308,plain,
    ( multiply(X,least_upper_bound(Y,Z)) != least_upper_bound(multiply(X,Y),multiply(X,Z))
    | least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(multiply(X,Y),multiply(X,Z))))]]) ).

cnf(refute_0_309,plain,
    least_upper_bound(multiply(X,Y),multiply(X,Z)) = multiply(X,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(multiply(X,least_upper_bound(Y,Z)),least_upper_bound(multiply(X,Y),multiply(X,Z))) )],[monotony_lub1,refute_0_308]) ).

cnf(refute_0_310,plain,
    least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)) = multiply(inverse(X_92),least_upper_bound(Y,X_93)),
    inference(subst,[],[refute_0_309:[bind(X,$fot(inverse(X_92))),bind(Z,$fot(X_93))]]) ).

cnf(refute_0_311,plain,
    least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))))]]) ).

cnf(refute_0_312,plain,
    ( least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)) != multiply(inverse(X_92),least_upper_bound(Y,X_93))
    | least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)))
    | least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)))) ),[1,1],$fot(multiply(inverse(X_92),least_upper_bound(Y,X_93)))]]) ).

cnf(refute_0_313,plain,
    ( least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)) != multiply(inverse(X_92),least_upper_bound(Y,X_93))
    | least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)))) )],[refute_0_311,refute_0_312]) ).

cnf(refute_0_314,plain,
    least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)),multiply(inverse(X_92),least_upper_bound(Y,X_93))) )],[refute_0_310,refute_0_313]) ).

cnf(refute_0_315,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(least_upper_bound(X_49,X_50),X_51),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_316,plain,
    least_upper_bound(X_50,X_49) = least_upper_bound(X_49,X_50),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_50)),bind(Y,$fot(X_49))]]) ).

cnf(refute_0_317,plain,
    ( least_upper_bound(X_50,X_49) != least_upper_bound(X_49,X_50)
    | least_upper_bound(X_49,X_50) = least_upper_bound(X_50,X_49) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_50,X_49))),bind(Y0,$fot(least_upper_bound(X_49,X_50)))]]) ).

cnf(refute_0_318,plain,
    least_upper_bound(X_49,X_50) = least_upper_bound(X_50,X_49),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,X_49),least_upper_bound(X_49,X_50)) )],[refute_0_316,refute_0_317]) ).

cnf(refute_0_319,plain,
    ( least_upper_bound(X_49,X_50) != least_upper_bound(X_50,X_49)
    | least_upper_bound(X_49,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_49,X_50),X_51)
    | least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(least_upper_bound(X_50,X_49),X_51) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_51)),least_upper_bound(least_upper_bound(X_49,X_50),X_51)) ),[1,0],$fot(least_upper_bound(X_50,X_49))]]) ).

cnf(refute_0_320,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_49,X_50),X_51)
    | least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(least_upper_bound(X_50,X_49),X_51) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,X_50),least_upper_bound(X_50,X_49)) )],[refute_0_318,refute_0_319]) ).

cnf(refute_0_321,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(least_upper_bound(X_50,X_49),X_51),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_51)),least_upper_bound(least_upper_bound(X_49,X_50),X_51)) )],[refute_0_315,refute_0_320]) ).

cnf(refute_0_322,plain,
    least_upper_bound(least_upper_bound(X_50,X_49),X_51) = least_upper_bound(X_50,least_upper_bound(X_49,X_51)),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_50)),bind(Y,$fot(X_49)),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_323,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_50,X_49),X_51)
    | least_upper_bound(least_upper_bound(X_50,X_49),X_51) != least_upper_bound(X_50,least_upper_bound(X_49,X_51))
    | least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,least_upper_bound(X_49,X_51)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_51)),least_upper_bound(X_50,least_upper_bound(X_49,X_51))) ),[0],$fot(least_upper_bound(least_upper_bound(X_50,X_49),X_51))]]) ).

cnf(refute_0_324,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X_51)) != least_upper_bound(least_upper_bound(X_50,X_49),X_51)
    | least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,least_upper_bound(X_49,X_51)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_50,X_49),X_51),least_upper_bound(X_50,least_upper_bound(X_49,X_51))) )],[refute_0_322,refute_0_323]) ).

cnf(refute_0_325,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X_51)) = least_upper_bound(X_50,least_upper_bound(X_49,X_51)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_51)),least_upper_bound(least_upper_bound(X_50,X_49),X_51)) )],[refute_0_321,refute_0_324]) ).

cnf(refute_0_326,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X_51)) != least_upper_bound(X_50,least_upper_bound(X_49,X_51))
    | least_upper_bound(X_50,least_upper_bound(X_49,X_51)) = least_upper_bound(X_49,least_upper_bound(X_50,X_51)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_49,least_upper_bound(X_50,X_51)))),bind(Y0,$fot(least_upper_bound(X_50,least_upper_bound(X_49,X_51))))]]) ).

cnf(refute_0_327,plain,
    least_upper_bound(X_50,least_upper_bound(X_49,X_51)) = least_upper_bound(X_49,least_upper_bound(X_50,X_51)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X_51)),least_upper_bound(X_50,least_upper_bound(X_49,X_51))) )],[refute_0_325,refute_0_326]) ).

cnf(refute_0_328,plain,
    least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) = least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))),
    inference(subst,[],[refute_0_327:[bind(X_49,$fot(identity)),bind(X_50,$fot(multiply(inverse(X_92),Y))),bind(X_51,$fot(multiply(inverse(X_92),X_93)))]]) ).

cnf(refute_0_329,plain,
    ( least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) != least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)))
    | least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) != least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))
    | least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))))),bind(Z0,$fot(least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))))]]) ).

cnf(refute_0_330,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))) != least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))
    | least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))),least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93)))) )],[refute_0_328,refute_0_329]) ).

cnf(refute_0_331,plain,
    least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(inverse(X_92),Y),multiply(inverse(X_92),X_93))),least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))) )],[refute_0_314,refute_0_330]) ).

cnf(refute_0_332,plain,
    ( multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) != least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93)))
    | least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))) != least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))
    | multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))) ),[0],$fot(least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))))]]) ).

cnf(refute_0_333,plain,
    ( multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) != least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93)))
    | multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93))),least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))) )],[refute_0_331,refute_0_332]) ).

cnf(refute_0_334,plain,
    multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) = least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),least_upper_bound(multiply(inverse(X_92),Y),least_upper_bound(identity,multiply(inverse(X_92),X_93)))) )],[refute_0_307,refute_0_333]) ).

cnf(refute_0_335,plain,
    ( multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) != least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))
    | least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) = multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))))]]) ).

cnf(refute_0_336,plain,
    least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93))) = multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_92),least_upper_bound(Y,least_upper_bound(X_92,X_93))),least_upper_bound(identity,multiply(inverse(X_92),least_upper_bound(Y,X_93)))) )],[refute_0_334,refute_0_335]) ).

cnf(refute_0_337,plain,
    least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),
    inference(subst,[],[refute_0_336:[bind(X_92,$fot(identity)),bind(X_93,$fot(Z))]]) ).

cnf(refute_0_338,plain,
    inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))),
    inference(subst,[],[p21x_3:[bind(X,$fot(inverse(X_105))),bind(Y,$fot(greatest_lower_bound(X_105,X_106)))]]) ).

cnf(refute_0_339,plain,
    multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) = greatest_lower_bound(multiply(inverse(X_96),X_96),multiply(inverse(X_96),X_97)),
    inference(subst,[],[monotony_glb1:[bind(X,$fot(inverse(X_96))),bind(Y,$fot(X_96)),bind(Z,$fot(X_97))]]) ).

cnf(refute_0_340,plain,
    multiply(inverse(X_96),X_96) = identity,
    inference(subst,[],[left_inverse:[bind(X,$fot(X_96))]]) ).

cnf(refute_0_341,plain,
    ( multiply(inverse(X_96),X_96) != identity
    | multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) != greatest_lower_bound(multiply(inverse(X_96),X_96),multiply(inverse(X_96),X_97))
    | multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) = greatest_lower_bound(identity,multiply(inverse(X_96),X_97)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)),greatest_lower_bound(multiply(inverse(X_96),X_96),multiply(inverse(X_96),X_97))) ),[1,0],$fot(identity)]]) ).

cnf(refute_0_342,plain,
    ( multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) != greatest_lower_bound(multiply(inverse(X_96),X_96),multiply(inverse(X_96),X_97))
    | multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) = greatest_lower_bound(identity,multiply(inverse(X_96),X_97)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),X_96),identity) )],[refute_0_340,refute_0_341]) ).

cnf(refute_0_343,plain,
    multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)) = greatest_lower_bound(identity,multiply(inverse(X_96),X_97)),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_96),greatest_lower_bound(X_96,X_97)),greatest_lower_bound(multiply(inverse(X_96),X_96),multiply(inverse(X_96),X_97))) )],[refute_0_339,refute_0_342]) ).

cnf(refute_0_344,plain,
    multiply(inverse(X_105),greatest_lower_bound(X_105,X_106)) = greatest_lower_bound(identity,multiply(inverse(X_105),X_106)),
    inference(subst,[],[refute_0_343:[bind(X_96,$fot(X_105)),bind(X_97,$fot(X_106))]]) ).

cnf(refute_0_345,plain,
    ( multiply(inverse(X_105),greatest_lower_bound(X_105,X_106)) != greatest_lower_bound(identity,multiply(inverse(X_105),X_106))
    | inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) ),[0,0],$fot(greatest_lower_bound(identity,multiply(inverse(X_105),X_106)))]]) ).

cnf(refute_0_346,plain,
    ( inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106)),greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) )],[refute_0_344,refute_0_345]) ).

cnf(refute_0_347,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) )],[refute_0_338,refute_0_346]) ).

cnf(refute_0_348,plain,
    inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) = least_upper_bound(identity,inverse(multiply(inverse(X_52),X_53))),
    inference(subst,[],[refute_0_12:[bind(X_6,$fot(multiply(inverse(X_52),X_53)))]]) ).

cnf(refute_0_349,plain,
    inverse(multiply(inverse(X_52),X_53)) = multiply(inverse(X_53),X_52),
    inference(subst,[],[refute_0_23:[bind(X,$fot(X_52)),bind(X_24,$fot(X_53))]]) ).

cnf(refute_0_350,plain,
    ( inverse(multiply(inverse(X_52),X_53)) != multiply(inverse(X_53),X_52)
    | inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) != least_upper_bound(identity,inverse(multiply(inverse(X_52),X_53)))
    | inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)),least_upper_bound(identity,inverse(multiply(inverse(X_52),X_53)))) ),[1,1],$fot(multiply(inverse(X_53),X_52))]]) ).

cnf(refute_0_351,plain,
    ( inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) != least_upper_bound(identity,inverse(multiply(inverse(X_52),X_53)))
    | inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_52),X_53)),multiply(inverse(X_53),X_52)) )],[refute_0_349,refute_0_350]) ).

cnf(refute_0_352,plain,
    inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) = least_upper_bound(identity,multiply(inverse(X_53),X_52)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)),least_upper_bound(identity,inverse(multiply(inverse(X_52),X_53)))) )],[refute_0_348,refute_0_351]) ).

cnf(refute_0_353,plain,
    ( inverse(greatest_lower_bound(X,Y)) != inverse(greatest_lower_bound(Y,X))
    | inverse(greatest_lower_bound(Y,X)) = inverse(greatest_lower_bound(X,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(greatest_lower_bound(X,Y)))),bind(Y0,$fot(inverse(greatest_lower_bound(Y,X))))]]) ).

cnf(refute_0_354,plain,
    inverse(greatest_lower_bound(Y,X)) = inverse(greatest_lower_bound(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X,Y)),inverse(greatest_lower_bound(Y,X))) )],[refute_0_44,refute_0_353]) ).

cnf(refute_0_355,plain,
    inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) = inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53))),
    inference(subst,[],[refute_0_354:[bind(X,$fot(identity)),bind(Y,$fot(multiply(inverse(X_52),X_53)))]]) ).

cnf(refute_0_356,plain,
    ( inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) != inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53)))
    | inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) != least_upper_bound(identity,multiply(inverse(X_53),X_52))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53))) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)),least_upper_bound(identity,multiply(inverse(X_53),X_52))) ),[0],$fot(inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53))))]]) ).

cnf(refute_0_357,plain,
    ( inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)) != least_upper_bound(identity,multiply(inverse(X_53),X_52))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53))) = least_upper_bound(identity,multiply(inverse(X_53),X_52)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)),inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53)))) )],[refute_0_355,refute_0_356]) ).

cnf(refute_0_358,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_52),X_53))) = least_upper_bound(identity,multiply(inverse(X_53),X_52)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(multiply(inverse(X_52),X_53),identity)),least_upper_bound(identity,multiply(inverse(X_53),X_52))) )],[refute_0_352,refute_0_357]) ).

cnf(refute_0_359,plain,
    inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) = least_upper_bound(identity,multiply(inverse(X_106),X_105)),
    inference(subst,[],[refute_0_358:[bind(X_52,$fot(X_105)),bind(X_53,$fot(X_106))]]) ).

cnf(refute_0_360,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) != least_upper_bound(identity,multiply(inverse(X_106),X_105))
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) ),[0],$fot(least_upper_bound(identity,multiply(inverse(X_106),X_105)))]]) ).

cnf(refute_0_361,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))),least_upper_bound(identity,multiply(inverse(X_106),X_105))) )],[refute_0_359,refute_0_360]) ).

cnf(refute_0_362,plain,
    inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105),
    inference(subst,[],[refute_0_23:[bind(X,$fot(X_105)),bind(X_24,$fot(greatest_lower_bound(X_105,X_106)))]]) ).

cnf(refute_0_363,plain,
    ( inverse(multiply(X,Y)) != multiply(inverse(Y),inverse(X))
    | multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(multiply(X,Y)))),bind(Y0,$fot(multiply(inverse(Y),inverse(X))))]]) ).

cnf(refute_0_364,plain,
    multiply(inverse(Y),inverse(X)) = inverse(multiply(X,Y)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,Y)),multiply(inverse(Y),inverse(X))) )],[p21x_3,refute_0_363]) ).

cnf(refute_0_365,plain,
    multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) = inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))),
    inference(subst,[],[refute_0_364:[bind(X,$fot(inverse(X_105))),bind(Y,$fot(greatest_lower_bound(X_105,X_106)))]]) ).

cnf(refute_0_366,plain,
    ( multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) != inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106)))
    | inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)
    | multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))))),bind(Y0,$fot(inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))))),bind(Z0,$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)))]]) ).

cnf(refute_0_367,plain,
    ( inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)
    | multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))),inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106)))) )],[refute_0_365,refute_0_366]) ).

cnf(refute_0_368,plain,
    multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105),
    inference(resolve,[$cnf( $equal(inverse(multiply(inverse(X_105),greatest_lower_bound(X_105,X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)) )],[refute_0_362,refute_0_367]) ).

cnf(refute_0_369,plain,
    ( multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_106),X_105)),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) ),[1],$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105))]]) ).

cnf(refute_0_370,plain,
    ( least_upper_bound(identity,multiply(inverse(X_106),X_105)) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105))),multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)) )],[refute_0_368,refute_0_369]) ).

cnf(refute_0_371,plain,
    ( inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))) != multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))
    | least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_106),X_105)),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) )],[refute_0_361,refute_0_370]) ).

cnf(refute_0_372,plain,
    least_upper_bound(identity,multiply(inverse(X_106),X_105)) = multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,multiply(inverse(X_105),X_106))),multiply(inverse(greatest_lower_bound(X_105,X_106)),inverse(inverse(X_105)))) )],[refute_0_347,refute_0_371]) ).

cnf(refute_0_373,plain,
    ( least_upper_bound(identity,multiply(inverse(X_106),X_105)) != multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)
    | multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) = least_upper_bound(identity,multiply(inverse(X_106),X_105)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,multiply(inverse(X_106),X_105)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)))]]) ).

cnf(refute_0_374,plain,
    multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105) = least_upper_bound(identity,multiply(inverse(X_106),X_105)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(X_106),X_105)),multiply(inverse(greatest_lower_bound(X_105,X_106)),X_105)) )],[refute_0_372,refute_0_373]) ).

cnf(refute_0_375,plain,
    multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))),
    inference(subst,[],[refute_0_374:[bind(X_105,$fot(least_upper_bound(Y,Z))),bind(X_106,$fot(identity))]]) ).

cnf(refute_0_376,plain,
    ( multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z)))
    | least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))))),bind(Z0,$fot(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))))]]) ).

cnf(refute_0_377,plain,
    ( least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z)))) )],[refute_0_375,refute_0_376]) ).

cnf(refute_0_378,plain,
    multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(identity),least_upper_bound(Y,Z))),multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))) )],[refute_0_337,refute_0_377]) ).

cnf(refute_0_379,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),
    inference(subst,[],[refute_0_309:[bind(X,$fot(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity))))]]) ).

cnf(refute_0_380,plain,
    ( multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) != multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)))),bind(Z0,$fot(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))))]]) ).

cnf(refute_0_381,plain,
    ( multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z))) )],[refute_0_379,refute_0_380]) ).

cnf(refute_0_382,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),least_upper_bound(Y,Z)),multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))) )],[refute_0_378,refute_0_381]) ).

cnf(refute_0_383,plain,
    ( multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) != multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)))),bind(Y0,$fot(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(identity,Z))))]]) ).

cnf(refute_0_384,plain,
    ( multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)),multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z)))) )],[refute_0_382,refute_0_383]) ).

cnf(refute_0_385,plain,
    least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)),
    inference(resolve,[$cnf( $equal(multiply(inverse(identity),least_upper_bound(Y,least_upper_bound(identity,Z))),least_upper_bound(Y,least_upper_bound(identity,Z))) )],[refute_0_297,refute_0_384]) ).

cnf(refute_0_386,plain,
    ( least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | least_upper_bound(identity,least_upper_bound(Y,Z)) != least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))
    | least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,Z)),least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))) ),[1],$fot(least_upper_bound(Y,least_upper_bound(identity,Z)))]]) ).

cnf(refute_0_387,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,Z)) != least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))
    | least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z)),least_upper_bound(Y,least_upper_bound(identity,Z))) )],[refute_0_385,refute_0_386]) ).

cnf(refute_0_388,plain,
    least_upper_bound(identity,least_upper_bound(Y,Z)) = least_upper_bound(Y,least_upper_bound(identity,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,Z)),least_upper_bound(multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Y),multiply(inverse(greatest_lower_bound(least_upper_bound(Y,Z),identity)),Z))) )],[refute_0_289,refute_0_387]) ).

cnf(refute_0_389,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,Z)) != least_upper_bound(Y,least_upper_bound(identity,Z))
    | least_upper_bound(Y,least_upper_bound(identity,Z)) = least_upper_bound(identity,least_upper_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(Y,Z)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(identity,Z))))]]) ).

cnf(refute_0_390,plain,
    least_upper_bound(Y,least_upper_bound(identity,Z)) = least_upper_bound(identity,least_upper_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,Z)),least_upper_bound(Y,least_upper_bound(identity,Z))) )],[refute_0_388,refute_0_389]) ).

cnf(refute_0_391,plain,
    least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))),
    inference(subst,[],[refute_0_390:[bind(Y,$fot(multiply(Y,inverse(X_118)))),bind(Z,$fot(multiply(X_119,inverse(X_118))))]]) ).

cnf(refute_0_392,plain,
    ( least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) != least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))))
    | least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))
    | least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))))),bind(Z0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))))]]) ).

cnf(refute_0_393,plain,
    ( least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))
    | least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))),least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118))))) )],[refute_0_391,refute_0_392]) ).

cnf(refute_0_394,plain,
    least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(multiply(Y,inverse(X_118)),multiply(X_119,inverse(X_118)))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))) )],[refute_0_282,refute_0_393]) ).

cnf(refute_0_395,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) != least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118))))
    | least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))
    | multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))) ),[0],$fot(least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))))]]) ).

cnf(refute_0_396,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) != least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118))))
    | multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118)))),least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))) )],[refute_0_394,refute_0_395]) ).

cnf(refute_0_397,plain,
    multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) = least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),least_upper_bound(multiply(Y,inverse(X_118)),least_upper_bound(identity,multiply(X_119,inverse(X_118))))) )],[refute_0_275,refute_0_396]) ).

cnf(refute_0_398,plain,
    ( multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) != least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))
    | least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) = multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)))),bind(Y0,$fot(least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))))]]) ).

cnf(refute_0_399,plain,
    least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118))) = multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(Y,least_upper_bound(X_118,X_119)),inverse(X_118)),least_upper_bound(identity,multiply(least_upper_bound(Y,X_119),inverse(X_118)))) )],[refute_0_397,refute_0_398]) ).

cnf(refute_0_400,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) = multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),
    inference(subst,[],[refute_0_399:[bind(Y,$fot(X_161)),bind(X_118,$fot(identity)),bind(X_119,$fot(X_162))]]) ).

cnf(refute_0_401,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) != least_upper_bound(X_161,least_upper_bound(identity,X_162))
    | least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) != multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity))
    | least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))))),bind(Y0,$fot(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)))),bind(Z0,$fot(least_upper_bound(X_161,least_upper_bound(identity,X_162))))]]) ).

cnf(refute_0_402,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)) != least_upper_bound(X_161,least_upper_bound(identity,X_162))
    | least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))),multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity))) )],[refute_0_400,refute_0_401]) ).

cnf(refute_0_403,plain,
    least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) = least_upper_bound(X_161,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(identity,X_162)),inverse(identity)),least_upper_bound(X_161,least_upper_bound(identity,X_162))) )],[refute_0_270,refute_0_402]) ).

cnf(refute_0_404,plain,
    ( least_upper_bound(X_161,least_upper_bound(X_162,identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))) != least_upper_bound(X_161,least_upper_bound(identity,X_162))
    | least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_161,least_upper_bound(X_162,identity)),least_upper_bound(X_161,least_upper_bound(identity,X_162))) ),[0],$fot(least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))))]]) ).

cnf(refute_0_405,plain,
    ( least_upper_bound(X_161,least_upper_bound(X_162,identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity))),least_upper_bound(X_161,least_upper_bound(identity,X_162))) )],[refute_0_403,refute_0_404]) ).

cnf(refute_0_406,plain,
    ( multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)) != least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))
    | least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_161,least_upper_bound(X_162,identity)),least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))) )],[refute_0_262,refute_0_405]) ).

cnf(refute_0_407,plain,
    least_upper_bound(X_161,least_upper_bound(X_162,identity)) = least_upper_bound(X_161,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_161,least_upper_bound(X_162,identity)),inverse(identity)),least_upper_bound(identity,multiply(least_upper_bound(X_161,X_162),inverse(identity)))) )],[refute_0_252,refute_0_406]) ).

cnf(refute_0_408,plain,
    least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) = least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))),
    inference(subst,[],[refute_0_407:[bind(X_161,$fot(X_159)),bind(X_162,$fot(least_upper_bound(X_162,identity)))]]) ).

cnf(refute_0_409,plain,
    ( least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) != least_upper_bound(X_159,least_upper_bound(identity,X_162))
    | least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) != least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity)))
    | least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)))),bind(Y0,$fot(least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))))),bind(Z0,$fot(least_upper_bound(X_159,least_upper_bound(identity,X_162))))]]) ).

cnf(refute_0_410,plain,
    ( least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))) != least_upper_bound(X_159,least_upper_bound(identity,X_162))
    | least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)),least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity)))) )],[refute_0_408,refute_0_409]) ).

cnf(refute_0_411,plain,
    least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(identity,least_upper_bound(X_162,identity))),least_upper_bound(X_159,least_upper_bound(identity,X_162))) )],[refute_0_242,refute_0_410]) ).

cnf(refute_0_412,plain,
    ( least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)) != least_upper_bound(X_159,least_upper_bound(identity,X_162))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,X_162)),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) ),[1],$fot(least_upper_bound(X_159,least_upper_bound(identity,X_162)))]]) ).

cnf(refute_0_413,plain,
    ( least_upper_bound(identity,least_upper_bound(X_159,X_162)) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity)),least_upper_bound(X_159,least_upper_bound(identity,X_162))) )],[refute_0_411,refute_0_412]) ).

cnf(refute_0_414,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))) != least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))
    | least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_159,X_162)),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) )],[refute_0_235,refute_0_413]) ).

cnf(refute_0_415,plain,
    least_upper_bound(identity,least_upper_bound(X_159,X_162)) = least_upper_bound(X_159,least_upper_bound(identity,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_159,X_162))),least_upper_bound(X_159,least_upper_bound(least_upper_bound(X_162,identity),identity))) )],[refute_0_227,refute_0_414]) ).

cnf(refute_0_416,plain,
    least_upper_bound(identity,least_upper_bound(a,inverse(a))) = least_upper_bound(a,least_upper_bound(identity,inverse(a))),
    inference(subst,[],[refute_0_415:[bind(X_159,$fot(a)),bind(X_162,$fot(inverse(a)))]]) ).

cnf(refute_0_417,plain,
    multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity)),
    inference(subst,[],[monotony_lub1:[bind(X,$fot(X_82)),bind(Y,$fot(X_83)),bind(Z,$fot(identity))]]) ).

cnf(refute_0_418,plain,
    X_82 = multiply(X_82,identity),
    inference(subst,[],[refute_0_92:[bind(X,$fot(X_82))]]) ).

cnf(refute_0_419,plain,
    ( X_82 != multiply(X_82,identity)
    | multiply(X_82,identity) = X_82 ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X_82)),bind(Y0,$fot(multiply(X_82,identity)))]]) ).

cnf(refute_0_420,plain,
    multiply(X_82,identity) = X_82,
    inference(resolve,[$cnf( $equal(X_82,multiply(X_82,identity)) )],[refute_0_418,refute_0_419]) ).

cnf(refute_0_421,plain,
    ( multiply(X_82,identity) != X_82
    | multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))
    | multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))) ),[1,1],$fot(X_82)]]) ).

cnf(refute_0_422,plain,
    ( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))
    | multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82) ),
    inference(resolve,[$cnf( $equal(multiply(X_82,identity),X_82) )],[refute_0_420,refute_0_421]) ).

cnf(refute_0_423,plain,
    multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(multiply(X_82,X_83),X_82),
    inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),multiply(X_82,identity))) )],[refute_0_417,refute_0_422]) ).

cnf(refute_0_424,plain,
    least_upper_bound(multiply(X_82,X_83),X_82) = least_upper_bound(X_82,multiply(X_82,X_83)),
    inference(subst,[],[refute_0_124:[bind(X_50,$fot(X_82)),bind(X_51,$fot(multiply(X_82,X_83)))]]) ).

cnf(refute_0_425,plain,
    ( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),X_82)
    | least_upper_bound(multiply(X_82,X_83),X_82) != least_upper_bound(X_82,multiply(X_82,X_83))
    | multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(X_82,multiply(X_82,X_83))) ),[0],$fot(least_upper_bound(multiply(X_82,X_83),X_82))]]) ).

cnf(refute_0_426,plain,
    ( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(multiply(X_82,X_83),X_82)
    | multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_82,X_83),X_82),least_upper_bound(X_82,multiply(X_82,X_83))) )],[refute_0_424,refute_0_425]) ).

cnf(refute_0_427,plain,
    multiply(X_82,least_upper_bound(X_83,identity)) = least_upper_bound(X_82,multiply(X_82,X_83)),
    inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(multiply(X_82,X_83),X_82)) )],[refute_0_423,refute_0_426]) ).

cnf(refute_0_428,plain,
    multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152)),
    inference(subst,[],[refute_0_427:[bind(X_82,$fot(inverse(greatest_lower_bound(X_152,identity)))),bind(X_83,$fot(X_152))]]) ).

cnf(refute_0_429,plain,
    least_upper_bound(identity,X_152) = multiply(inverse(greatest_lower_bound(X_152,identity)),X_152),
    inference(subst,[],[refute_0_140:[bind(X,$fot(X_152))]]) ).

cnf(refute_0_430,plain,
    ( least_upper_bound(identity,X_152) != multiply(inverse(greatest_lower_bound(X_152,identity)),X_152)
    | multiply(inverse(greatest_lower_bound(X_152,identity)),X_152) = least_upper_bound(identity,X_152) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,X_152))),bind(Y0,$fot(multiply(inverse(greatest_lower_bound(X_152,identity)),X_152)))]]) ).

cnf(refute_0_431,plain,
    multiply(inverse(greatest_lower_bound(X_152,identity)),X_152) = least_upper_bound(identity,X_152),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_152),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152)) )],[refute_0_429,refute_0_430]) ).

cnf(refute_0_432,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),X_152) != least_upper_bound(identity,X_152)
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152))) ),[1,1],$fot(least_upper_bound(identity,X_152))]]) ).

cnf(refute_0_433,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),X_152),least_upper_bound(identity,X_152)) )],[refute_0_431,refute_0_432]) ).

cnf(refute_0_434,plain,
    multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),multiply(inverse(greatest_lower_bound(X_152,identity)),X_152))) )],[refute_0_428,refute_0_433]) ).

cnf(refute_0_435,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity)))),
    inference(subst,[],[refute_0_196:[bind(Y,$fot(X_137)),bind(X_39,$fot(inverse(greatest_lower_bound(X_48,identity))))]]) ).

cnf(refute_0_436,plain,
    inverse(greatest_lower_bound(inverse(X),X_7)) = least_upper_bound(inverse(inverse(X)),inverse(X_7)),
    inference(subst,[],[p21x_4:[bind(X,$fot(inverse(X))),bind(Y,$fot(X_7))]]) ).

cnf(refute_0_437,plain,
    ( inverse(greatest_lower_bound(inverse(X),X_7)) != least_upper_bound(inverse(inverse(X)),inverse(X_7))
    | inverse(inverse(X)) != X
    | inverse(greatest_lower_bound(inverse(X),X_7)) = least_upper_bound(X,inverse(X_7)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),X_7)),least_upper_bound(inverse(inverse(X)),inverse(X_7))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_438,plain,
    ( inverse(greatest_lower_bound(inverse(X),X_7)) != least_upper_bound(inverse(inverse(X)),inverse(X_7))
    | inverse(greatest_lower_bound(inverse(X),X_7)) = least_upper_bound(X,inverse(X_7)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_437]) ).

cnf(refute_0_439,plain,
    inverse(greatest_lower_bound(inverse(X),X_7)) = least_upper_bound(X,inverse(X_7)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X),X_7)),least_upper_bound(inverse(inverse(X)),inverse(X_7))) )],[refute_0_436,refute_0_438]) ).

cnf(refute_0_440,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(identity,X_27)),X_48)) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)),
    inference(subst,[],[refute_0_439:[bind(X,$fot(least_upper_bound(identity,X_27))),bind(X_7,$fot(X_48))]]) ).

cnf(refute_0_441,plain,
    greatest_lower_bound(greatest_lower_bound(X_11,X_21),least_upper_bound(X_11,greatest_lower_bound(X_11,X_21))) = greatest_lower_bound(X_11,X_21),
    inference(subst,[],[refute_0_155:[bind(X_10,$fot(greatest_lower_bound(X_11,X_21)))]]) ).

cnf(refute_0_442,plain,
    least_upper_bound(X_11,greatest_lower_bound(X_11,X_21)) = X_11,
    inference(subst,[],[lub_absorbtion:[bind(X,$fot(X_11)),bind(Y,$fot(X_21))]]) ).

cnf(refute_0_443,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_11,X_21),least_upper_bound(X_11,greatest_lower_bound(X_11,X_21))) != greatest_lower_bound(X_11,X_21)
    | least_upper_bound(X_11,greatest_lower_bound(X_11,X_21)) != X_11
    | greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) = greatest_lower_bound(X_11,X_21) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_21),least_upper_bound(X_11,greatest_lower_bound(X_11,X_21))),greatest_lower_bound(X_11,X_21)) ),[0,1],$fot(X_11)]]) ).

cnf(refute_0_444,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_11,X_21),least_upper_bound(X_11,greatest_lower_bound(X_11,X_21))) != greatest_lower_bound(X_11,X_21)
    | greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) = greatest_lower_bound(X_11,X_21) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,greatest_lower_bound(X_11,X_21)),X_11) )],[refute_0_442,refute_0_443]) ).

cnf(refute_0_445,plain,
    greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) = greatest_lower_bound(X_11,X_21),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_21),least_upper_bound(X_11,greatest_lower_bound(X_11,X_21))),greatest_lower_bound(X_11,X_21)) )],[refute_0_441,refute_0_444]) ).

cnf(refute_0_446,plain,
    greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) = greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21)),
    inference(subst,[],[refute_0_54:[bind(X_14,$fot(greatest_lower_bound(X_11,X_21))),bind(X_15,$fot(X_11))]]) ).

cnf(refute_0_447,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) != greatest_lower_bound(X_11,X_21)
    | greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) != greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21))
    | greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21)) = greatest_lower_bound(X_11,X_21) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11),greatest_lower_bound(X_11,X_21)) ),[0],$fot(greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21)))]]) ).

cnf(refute_0_448,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11) != greatest_lower_bound(X_11,X_21)
    | greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21)) = greatest_lower_bound(X_11,X_21) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21))) )],[refute_0_446,refute_0_447]) ).

cnf(refute_0_449,plain,
    greatest_lower_bound(X_11,greatest_lower_bound(X_11,X_21)) = greatest_lower_bound(X_11,X_21),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_11,X_21),X_11),greatest_lower_bound(X_11,X_21)) )],[refute_0_445,refute_0_448]) ).

cnf(refute_0_450,plain,
    greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_27))) = greatest_lower_bound(identity,inverse(X_27)),
    inference(subst,[],[refute_0_449:[bind(X_11,$fot(identity)),bind(X_21,$fot(inverse(X_27)))]]) ).

cnf(refute_0_451,plain,
    ( inverse(least_upper_bound(X_27,identity)) != greatest_lower_bound(identity,inverse(X_27))
    | greatest_lower_bound(identity,inverse(X_27)) = inverse(least_upper_bound(X_27,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(least_upper_bound(X_27,identity)))),bind(Y0,$fot(greatest_lower_bound(identity,inverse(X_27))))]]) ).

cnf(refute_0_452,plain,
    greatest_lower_bound(identity,inverse(X_27)) = inverse(least_upper_bound(X_27,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_27,identity)),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_67,refute_0_451]) ).

cnf(refute_0_453,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_27))) != greatest_lower_bound(identity,inverse(X_27))
    | greatest_lower_bound(identity,inverse(X_27)) != inverse(least_upper_bound(X_27,identity))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = greatest_lower_bound(identity,inverse(X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_27))),greatest_lower_bound(identity,inverse(X_27))) ),[0,1],$fot(inverse(least_upper_bound(X_27,identity)))]]) ).

cnf(refute_0_454,plain,
    ( greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_27))) != greatest_lower_bound(identity,inverse(X_27))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = greatest_lower_bound(identity,inverse(X_27)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_27)),inverse(least_upper_bound(X_27,identity))) )],[refute_0_452,refute_0_453]) ).

cnf(refute_0_455,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = greatest_lower_bound(identity,inverse(X_27)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,greatest_lower_bound(identity,inverse(X_27))),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_450,refute_0_454]) ).

cnf(refute_0_456,plain,
    least_upper_bound(identity,least_upper_bound(X_27,identity)) = least_upper_bound(identity,X_27),
    inference(subst,[],[refute_0_237:[bind(Y,$fot(X_27)),bind(X_39,$fot(identity))]]) ).

cnf(refute_0_457,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),
    introduced(tautology,[refl,[$fot(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))))]]) ).

cnf(refute_0_458,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) != inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))
    | least_upper_bound(identity,least_upper_bound(X_27,identity)) != least_upper_bound(identity,X_27)
    | inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))) ),[1,0],$fot(least_upper_bound(identity,X_27))]]) ).

cnf(refute_0_459,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,identity)) != least_upper_bound(identity,X_27)
    | inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))) )],[refute_0_457,refute_0_458]) ).

cnf(refute_0_460,plain,
    inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,identity)),least_upper_bound(identity,X_27)) )],[refute_0_456,refute_0_459]) ).

cnf(refute_0_461,plain,
    inverse(least_upper_bound(X_41,identity)) = greatest_lower_bound(identity,inverse(X_41)),
    inference(subst,[],[refute_0_67:[bind(X_27,$fot(X_41))]]) ).

cnf(refute_0_462,plain,
    least_upper_bound(identity,X_41) = least_upper_bound(X_41,identity),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_41))]]) ).

cnf(refute_0_463,plain,
    ( least_upper_bound(identity,X_41) != least_upper_bound(X_41,identity)
    | least_upper_bound(X_41,identity) = least_upper_bound(identity,X_41) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,X_41))),bind(Y0,$fot(least_upper_bound(X_41,identity)))]]) ).

cnf(refute_0_464,plain,
    least_upper_bound(X_41,identity) = least_upper_bound(identity,X_41),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_41),least_upper_bound(X_41,identity)) )],[refute_0_462,refute_0_463]) ).

cnf(refute_0_465,plain,
    ( inverse(least_upper_bound(X_41,identity)) != greatest_lower_bound(identity,inverse(X_41))
    | least_upper_bound(X_41,identity) != least_upper_bound(identity,X_41)
    | inverse(least_upper_bound(identity,X_41)) = greatest_lower_bound(identity,inverse(X_41)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(X_41,identity)),greatest_lower_bound(identity,inverse(X_41))) ),[0,0],$fot(least_upper_bound(identity,X_41))]]) ).

cnf(refute_0_466,plain,
    ( inverse(least_upper_bound(X_41,identity)) != greatest_lower_bound(identity,inverse(X_41))
    | inverse(least_upper_bound(identity,X_41)) = greatest_lower_bound(identity,inverse(X_41)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_41,identity),least_upper_bound(identity,X_41)) )],[refute_0_464,refute_0_465]) ).

cnf(refute_0_467,plain,
    inverse(least_upper_bound(identity,X_41)) = greatest_lower_bound(identity,inverse(X_41)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(X_41,identity)),greatest_lower_bound(identity,inverse(X_41))) )],[refute_0_461,refute_0_466]) ).

cnf(refute_0_468,plain,
    greatest_lower_bound(identity,inverse(X_41)) = inverse(least_upper_bound(X_41,identity)),
    inference(subst,[],[refute_0_452:[bind(X_27,$fot(X_41))]]) ).

cnf(refute_0_469,plain,
    ( greatest_lower_bound(identity,inverse(X_41)) != inverse(least_upper_bound(X_41,identity))
    | inverse(least_upper_bound(identity,X_41)) != greatest_lower_bound(identity,inverse(X_41))
    | inverse(least_upper_bound(identity,X_41)) = inverse(least_upper_bound(X_41,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_41)),greatest_lower_bound(identity,inverse(X_41))) ),[1],$fot(inverse(least_upper_bound(X_41,identity)))]]) ).

cnf(refute_0_470,plain,
    ( inverse(least_upper_bound(identity,X_41)) != greatest_lower_bound(identity,inverse(X_41))
    | inverse(least_upper_bound(identity,X_41)) = inverse(least_upper_bound(X_41,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_41)),inverse(least_upper_bound(X_41,identity))) )],[refute_0_468,refute_0_469]) ).

cnf(refute_0_471,plain,
    inverse(least_upper_bound(identity,X_41)) = inverse(least_upper_bound(X_41,identity)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_41)),greatest_lower_bound(identity,inverse(X_41))) )],[refute_0_467,refute_0_470]) ).

cnf(refute_0_472,plain,
    ( inverse(least_upper_bound(identity,X_41)) != inverse(least_upper_bound(X_41,identity))
    | inverse(least_upper_bound(X_41,identity)) = inverse(least_upper_bound(identity,X_41)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(least_upper_bound(identity,X_41)))),bind(Y0,$fot(inverse(least_upper_bound(X_41,identity))))]]) ).

cnf(refute_0_473,plain,
    inverse(least_upper_bound(X_41,identity)) = inverse(least_upper_bound(identity,X_41)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_41)),inverse(least_upper_bound(X_41,identity))) )],[refute_0_471,refute_0_472]) ).

cnf(refute_0_474,plain,
    inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)) = inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),
    inference(subst,[],[refute_0_473:[bind(X_41,$fot(least_upper_bound(X_27,identity)))]]) ).

cnf(refute_0_475,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)),
    inference(subst,[],[refute_0_452:[bind(X_27,$fot(least_upper_bound(X_27,identity)))]]) ).

cnf(refute_0_476,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != inverse(least_upper_bound(least_upper_bound(X_27,identity),identity))
    | inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)) != inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))))),bind(Y0,$fot(inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)))),bind(Z0,$fot(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))))]]) ).

cnf(refute_0_477,plain,
    ( inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)) != inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))),inverse(least_upper_bound(least_upper_bound(X_27,identity),identity))) )],[refute_0_475,refute_0_476]) ).

cnf(refute_0_478,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(least_upper_bound(X_27,identity),identity)),inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))) )],[refute_0_474,refute_0_477]) ).

cnf(refute_0_479,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))
    | inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) != inverse(least_upper_bound(identity,X_27))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))))),bind(Y0,$fot(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))))),bind(Z0,$fot(inverse(least_upper_bound(identity,X_27))))]]) ).

cnf(refute_0_480,plain,
    ( inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))) != inverse(least_upper_bound(identity,X_27))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))),inverse(least_upper_bound(identity,least_upper_bound(X_27,identity)))) )],[refute_0_478,refute_0_479]) ).

cnf(refute_0_481,plain,
    greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) = inverse(least_upper_bound(identity,X_27)),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,least_upper_bound(X_27,identity))),inverse(least_upper_bound(identity,X_27))) )],[refute_0_460,refute_0_480]) ).

cnf(refute_0_482,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != greatest_lower_bound(identity,inverse(X_27))
    | greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != inverse(least_upper_bound(identity,X_27))
    | inverse(least_upper_bound(identity,X_27)) = greatest_lower_bound(identity,inverse(X_27)) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))),greatest_lower_bound(identity,inverse(X_27))) ),[0],$fot(inverse(least_upper_bound(identity,X_27)))]]) ).

cnf(refute_0_483,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != greatest_lower_bound(identity,inverse(X_27))
    | inverse(least_upper_bound(identity,X_27)) = greatest_lower_bound(identity,inverse(X_27)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))),inverse(least_upper_bound(identity,X_27))) )],[refute_0_481,refute_0_482]) ).

cnf(refute_0_484,plain,
    ( greatest_lower_bound(identity,inverse(X_27)) != inverse(least_upper_bound(X_27,identity))
    | inverse(least_upper_bound(identity,X_27)) != greatest_lower_bound(identity,inverse(X_27))
    | inverse(least_upper_bound(identity,X_27)) = inverse(least_upper_bound(X_27,identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(least_upper_bound(identity,X_27)),greatest_lower_bound(identity,inverse(X_27))) ),[1],$fot(inverse(least_upper_bound(X_27,identity)))]]) ).

cnf(refute_0_485,plain,
    ( inverse(least_upper_bound(identity,X_27)) != greatest_lower_bound(identity,inverse(X_27))
    | inverse(least_upper_bound(identity,X_27)) = inverse(least_upper_bound(X_27,identity)) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(X_27)),inverse(least_upper_bound(X_27,identity))) )],[refute_0_452,refute_0_484]) ).

cnf(refute_0_486,plain,
    ( greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))) != greatest_lower_bound(identity,inverse(X_27))
    | inverse(least_upper_bound(identity,X_27)) = inverse(least_upper_bound(X_27,identity)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_27)),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_483,refute_0_485]) ).

cnf(refute_0_487,plain,
    inverse(least_upper_bound(identity,X_27)) = inverse(least_upper_bound(X_27,identity)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,inverse(least_upper_bound(X_27,identity))),greatest_lower_bound(identity,inverse(X_27))) )],[refute_0_455,refute_0_486]) ).

cnf(refute_0_488,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(identity,X_27)),X_48)) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | inverse(least_upper_bound(identity,X_27)) != inverse(least_upper_bound(X_27,identity))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,X_27)),X_48)),least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))) ),[0,0,0],$fot(inverse(least_upper_bound(X_27,identity)))]]) ).

cnf(refute_0_489,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(identity,X_27)),X_48)) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) ),
    inference(resolve,[$cnf( $equal(inverse(least_upper_bound(identity,X_27)),inverse(least_upper_bound(X_27,identity))) )],[refute_0_487,refute_0_488]) ).

cnf(refute_0_490,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(identity,X_27)),X_48)),least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))) )],[refute_0_440,refute_0_489]) ).

cnf(refute_0_491,plain,
    least_upper_bound(identity,inverse(X_48)) = inverse(greatest_lower_bound(X_48,identity)),
    inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_48))]]) ).

cnf(refute_0_492,plain,
    least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) = least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),
    introduced(tautology,[refl,[$fot(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))))]]) ).

cnf(refute_0_493,plain,
    ( least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) != least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))
    | least_upper_bound(identity,inverse(X_48)) != inverse(greatest_lower_bound(X_48,identity))
    | least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))) ),[1,1],$fot(inverse(greatest_lower_bound(X_48,identity)))]]) ).

cnf(refute_0_494,plain,
    ( least_upper_bound(identity,inverse(X_48)) != inverse(greatest_lower_bound(X_48,identity))
    | least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))) )],[refute_0_492,refute_0_493]) ).

cnf(refute_0_495,plain,
    least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_48)),inverse(greatest_lower_bound(X_48,identity))) )],[refute_0_491,refute_0_494]) ).

cnf(refute_0_496,plain,
    least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)) = least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_27)),bind(Y,$fot(identity)),bind(Z,$fot(inverse(X_48)))]]) ).

cnf(refute_0_497,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)),
    inference(subst,[],[refute_0_439:[bind(X,$fot(least_upper_bound(X_27,identity))),bind(X_7,$fot(X_48))]]) ).

cnf(refute_0_498,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48))
    | least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)) != least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)))),bind(Z0,$fot(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))))]]) ).

cnf(refute_0_499,plain,
    ( least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)) != least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)),least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48))) )],[refute_0_497,refute_0_498]) ).

cnf(refute_0_500,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_27,identity),inverse(X_48)),least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))) )],[refute_0_496,refute_0_499]) ).

cnf(refute_0_501,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))
    | least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) != least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)))),bind(Y0,$fot(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))))),bind(Z0,$fot(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))))]]) ).

cnf(refute_0_502,plain,
    ( least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))) != least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)),least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48)))) )],[refute_0_500,refute_0_501]) ).

cnf(refute_0_503,plain,
    inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,least_upper_bound(identity,inverse(X_48))),least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) )],[refute_0_495,refute_0_502]) ).

cnf(refute_0_504,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))
    | inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)),least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))) ),[0],$fot(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))))]]) ).

cnf(refute_0_505,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)),least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) )],[refute_0_503,refute_0_504]) ).

cnf(refute_0_506,plain,
    least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),
    inference(subst,[],[refute_0_192:[bind(X,$fot(identity)),bind(Y,$fot(X_27)),bind(Z,$fot(inverse(X_48)))]]) ).

cnf(refute_0_507,plain,
    ( least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)) != least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))
    | least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) ),[0],$fot(least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)))]]) ).

cnf(refute_0_508,plain,
    ( least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48)),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) )],[refute_0_506,refute_0_507]) ).

cnf(refute_0_509,plain,
    ( inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)) != least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))
    | least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))) )],[refute_0_505,refute_0_508]) ).

cnf(refute_0_510,plain,
    least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(least_upper_bound(X_27,identity)),X_48)),least_upper_bound(least_upper_bound(identity,X_27),inverse(X_48))) )],[refute_0_490,refute_0_509]) ).

cnf(refute_0_511,plain,
    least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(subst,[],[refute_0_510:[bind(X_27,$fot(X_137))]]) ).

cnf(refute_0_512,plain,
    ( least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137),least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_513,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_511,refute_0_512]) ).

cnf(refute_0_514,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137),least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(greatest_lower_bound(X_48,identity))))) )],[refute_0_435,refute_0_513]) ).

cnf(refute_0_515,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) = least_upper_bound(least_upper_bound(identity,inverse(X_6)),X_51),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(inverse(X_6))),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_516,plain,
    ( least_upper_bound(identity,inverse(X_6)) != inverse(greatest_lower_bound(X_6,identity))
    | least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) != least_upper_bound(least_upper_bound(identity,inverse(X_6)),X_51)
    | least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) = least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)),least_upper_bound(least_upper_bound(identity,inverse(X_6)),X_51)) ),[1,0],$fot(inverse(greatest_lower_bound(X_6,identity)))]]) ).

cnf(refute_0_517,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) != least_upper_bound(least_upper_bound(identity,inverse(X_6)),X_51)
    | least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) = least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_6)),inverse(greatest_lower_bound(X_6,identity))) )],[refute_0_14,refute_0_516]) ).

cnf(refute_0_518,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) = least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)),least_upper_bound(least_upper_bound(identity,inverse(X_6)),X_51)) )],[refute_0_515,refute_0_517]) ).

cnf(refute_0_519,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) != least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51)
    | least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51) = least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)))),bind(Y0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51)))]]) ).

cnf(refute_0_520,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51) = least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_6),X_51)),least_upper_bound(inverse(greatest_lower_bound(X_6,identity)),X_51)) )],[refute_0_518,refute_0_519]) ).

cnf(refute_0_521,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) = least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)),
    inference(subst,[],[refute_0_520:[bind(X_51,$fot(X_137)),bind(X_6,$fot(X_48))]]) ).

cnf(refute_0_522,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137),least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)))]]) ).

cnf(refute_0_523,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137),least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137))) )],[refute_0_521,refute_0_522]) ).

cnf(refute_0_524,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(subst,[],[refute_0_232:[bind(X_50,$fot(identity)),bind(X_51,$fot(least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_525,plain,
    inverse(greatest_lower_bound(inverse(X_137),X_48)) = least_upper_bound(X_137,inverse(X_48)),
    inference(subst,[],[refute_0_439:[bind(X,$fot(X_137)),bind(X_7,$fot(X_48))]]) ).

cnf(refute_0_526,plain,
    greatest_lower_bound(greatest_lower_bound(X_39,X_11),least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))) = greatest_lower_bound(X_39,X_11),
    inference(subst,[],[refute_0_155:[bind(X_10,$fot(greatest_lower_bound(X_39,X_11)))]]) ).

cnf(refute_0_527,plain,
    X_11 = least_upper_bound(X_11,greatest_lower_bound(X_39,X_11)),
    inference(subst,[],[refute_0_185:[bind(X_16,$fot(X_39)),bind(X_17,$fot(X_11))]]) ).

cnf(refute_0_528,plain,
    ( X_11 != least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))
    | least_upper_bound(X_11,greatest_lower_bound(X_39,X_11)) = X_11 ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(X_11)),bind(Y0,$fot(least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))))]]) ).

cnf(refute_0_529,plain,
    least_upper_bound(X_11,greatest_lower_bound(X_39,X_11)) = X_11,
    inference(resolve,[$cnf( $equal(X_11,least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))) )],[refute_0_527,refute_0_528]) ).

cnf(refute_0_530,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_39,X_11),least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))) != greatest_lower_bound(X_39,X_11)
    | least_upper_bound(X_11,greatest_lower_bound(X_39,X_11)) != X_11
    | greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) = greatest_lower_bound(X_39,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_11),least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))),greatest_lower_bound(X_39,X_11)) ),[0,1],$fot(X_11)]]) ).

cnf(refute_0_531,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_39,X_11),least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))) != greatest_lower_bound(X_39,X_11)
    | greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) = greatest_lower_bound(X_39,X_11) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_11,greatest_lower_bound(X_39,X_11)),X_11) )],[refute_0_529,refute_0_530]) ).

cnf(refute_0_532,plain,
    greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) = greatest_lower_bound(X_39,X_11),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_11),least_upper_bound(X_11,greatest_lower_bound(X_39,X_11))),greatest_lower_bound(X_39,X_11)) )],[refute_0_526,refute_0_531]) ).

cnf(refute_0_533,plain,
    greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) = greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11)),
    inference(subst,[],[refute_0_54:[bind(X_14,$fot(greatest_lower_bound(X_39,X_11))),bind(X_15,$fot(X_11))]]) ).

cnf(refute_0_534,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) != greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11))
    | greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) != greatest_lower_bound(X_39,X_11)
    | greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11)) = greatest_lower_bound(X_39,X_11) ),
    introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11),greatest_lower_bound(X_39,X_11)) ),[0],$fot(greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11)))]]) ).

cnf(refute_0_535,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11) != greatest_lower_bound(X_39,X_11)
    | greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11)) = greatest_lower_bound(X_39,X_11) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11),greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11))) )],[refute_0_533,refute_0_534]) ).

cnf(refute_0_536,plain,
    greatest_lower_bound(X_11,greatest_lower_bound(X_39,X_11)) = greatest_lower_bound(X_39,X_11),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_39,X_11),X_11),greatest_lower_bound(X_39,X_11)) )],[refute_0_532,refute_0_535]) ).

cnf(refute_0_537,plain,
    greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)) = greatest_lower_bound(inverse(X_137),X_48),
    inference(subst,[],[refute_0_536:[bind(X_11,$fot(X_48)),bind(X_39,$fot(inverse(X_137)))]]) ).

cnf(refute_0_538,plain,
    inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))))]]) ).

cnf(refute_0_539,plain,
    ( greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)) != greatest_lower_bound(inverse(X_137),X_48)
    | inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) != inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)))
    | inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = inverse(greatest_lower_bound(inverse(X_137),X_48)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)))) ),[1,0],$fot(greatest_lower_bound(inverse(X_137),X_48))]]) ).

cnf(refute_0_540,plain,
    ( greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)) != greatest_lower_bound(inverse(X_137),X_48)
    | inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = inverse(greatest_lower_bound(inverse(X_137),X_48)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)))) )],[refute_0_538,refute_0_539]) ).

cnf(refute_0_541,plain,
    inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = inverse(greatest_lower_bound(inverse(X_137),X_48)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)),greatest_lower_bound(inverse(X_137),X_48)) )],[refute_0_537,refute_0_540]) ).

cnf(refute_0_542,plain,
    ( inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) != inverse(greatest_lower_bound(inverse(X_137),X_48))
    | inverse(greatest_lower_bound(inverse(X_137),X_48)) != least_upper_bound(X_137,inverse(X_48))
    | inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = least_upper_bound(X_137,inverse(X_48)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))))),bind(Y0,$fot(inverse(greatest_lower_bound(inverse(X_137),X_48)))),bind(Z0,$fot(least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_543,plain,
    ( inverse(greatest_lower_bound(inverse(X_137),X_48)) != least_upper_bound(X_137,inverse(X_48))
    | inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = least_upper_bound(X_137,inverse(X_48)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),inverse(greatest_lower_bound(inverse(X_137),X_48))) )],[refute_0_541,refute_0_542]) ).

cnf(refute_0_544,plain,
    inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) = least_upper_bound(X_137,inverse(X_48)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(inverse(X_137),X_48)),least_upper_bound(X_137,inverse(X_48))) )],[refute_0_525,refute_0_543]) ).

cnf(refute_0_545,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = least_upper_bound(inverse(greatest_lower_bound(X_46,inverse(X_45))),inverse(Y)),
    inference(subst,[],[p21x_4:[bind(X,$fot(greatest_lower_bound(X_46,inverse(X_45))))]]) ).

cnf(refute_0_546,plain,
    inverse(greatest_lower_bound(X_46,inverse(X_45))) = least_upper_bound(inverse(X_46),X_45),
    inference(subst,[],[refute_0_114:[bind(X,$fot(X_45)),bind(X_6,$fot(X_46))]]) ).

cnf(refute_0_547,plain,
    ( inverse(greatest_lower_bound(X_46,inverse(X_45))) != least_upper_bound(inverse(X_46),X_45)
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_46,inverse(X_45))),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),least_upper_bound(inverse(greatest_lower_bound(X_46,inverse(X_45))),inverse(Y))) ),[1,0],$fot(least_upper_bound(inverse(X_46),X_45))]]) ).

cnf(refute_0_548,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != least_upper_bound(inverse(greatest_lower_bound(X_46,inverse(X_45))),inverse(Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,inverse(X_45))),least_upper_bound(inverse(X_46),X_45)) )],[refute_0_546,refute_0_547]) ).

cnf(refute_0_549,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),least_upper_bound(inverse(greatest_lower_bound(X_46,inverse(X_45))),inverse(Y))) )],[refute_0_545,refute_0_548]) ).

cnf(refute_0_550,plain,
    ( greatest_lower_bound(X,greatest_lower_bound(Y,Z)) != greatest_lower_bound(greatest_lower_bound(X,Y),Z)
    | greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(X,greatest_lower_bound(Y,Z)))),bind(Y0,$fot(greatest_lower_bound(greatest_lower_bound(X,Y),Z)))]]) ).

cnf(refute_0_551,plain,
    greatest_lower_bound(greatest_lower_bound(X,Y),Z) = greatest_lower_bound(X,greatest_lower_bound(Y,Z)),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X,greatest_lower_bound(Y,Z)),greatest_lower_bound(greatest_lower_bound(X,Y),Z)) )],[associativity_of_glb,refute_0_550]) ).

cnf(refute_0_552,plain,
    greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y) = greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y)),
    inference(subst,[],[refute_0_551:[bind(X,$fot(X_46)),bind(Y,$fot(inverse(X_45))),bind(Z,$fot(Y))]]) ).

cnf(refute_0_553,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),
    introduced(tautology,[refl,[$fot(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)))]]) ).

cnf(refute_0_554,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y) != greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y))) ),[1,0],$fot(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y)))]]) ).

cnf(refute_0_555,plain,
    ( greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y) != greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y))) )],[refute_0_553,refute_0_554]) ).

cnf(refute_0_556,plain,
    inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) = inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y),greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) )],[refute_0_552,refute_0_555]) ).

cnf(refute_0_557,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y)))
    | inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))
    | inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))) ),[0],$fot(inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))))]]) ).

cnf(refute_0_558,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))
    | inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y)))) )],[refute_0_556,refute_0_557]) ).

cnf(refute_0_559,plain,
    least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) = least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))),
    inference(subst,[],[refute_0_192:[bind(X,$fot(inverse(X_46))),bind(Y,$fot(X_45)),bind(Z,$fot(inverse(Y)))]]) ).

cnf(refute_0_560,plain,
    ( inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) != least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))
    | least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)) != least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))
    | inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))),least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))) ),[0],$fot(least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)))]]) ).

cnf(refute_0_561,plain,
    ( inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) != least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))
    | inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y)),least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))) )],[refute_0_559,refute_0_560]) ).

cnf(refute_0_562,plain,
    ( inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)) != least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))
    | inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))) ),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))),least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))) )],[refute_0_558,refute_0_561]) ).

cnf(refute_0_563,plain,
    inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) = least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(greatest_lower_bound(X_46,inverse(X_45)),Y)),least_upper_bound(least_upper_bound(inverse(X_46),X_45),inverse(Y))) )],[refute_0_549,refute_0_562]) ).

cnf(refute_0_564,plain,
    ( inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) != least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))
    | least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))) = inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))))),bind(Y0,$fot(least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))))]]) ).

cnf(refute_0_565,plain,
    least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y))) = inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_46,greatest_lower_bound(inverse(X_45),Y))),least_upper_bound(inverse(X_46),least_upper_bound(X_45,inverse(Y)))) )],[refute_0_563,refute_0_564]) ).

cnf(refute_0_566,plain,
    least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) = inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),
    inference(subst,[],[refute_0_565:[bind(Y,$fot(X_48)),bind(X_45,$fot(X_137)),bind(X_46,$fot(X_48))]]) ).

cnf(refute_0_567,plain,
    ( inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) != least_upper_bound(X_137,inverse(X_48))
    | least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) != inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)))
    | least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(X_137,inverse(X_48)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))),bind(Y0,$fot(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))))),bind(Z0,$fot(least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_568,plain,
    ( inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))) != least_upper_bound(X_137,inverse(X_48))
    | least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(X_137,inverse(X_48)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))),inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48)))) )],[refute_0_566,refute_0_567]) ).

cnf(refute_0_569,plain,
    least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(X_137,inverse(X_48)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(X_48,greatest_lower_bound(inverse(X_137),X_48))),least_upper_bound(X_137,inverse(X_48))) )],[refute_0_544,refute_0_568]) ).

cnf(refute_0_570,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_571,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) != least_upper_bound(X_137,inverse(X_48))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))) ),[1,1],$fot(least_upper_bound(X_137,inverse(X_48)))]]) ).

cnf(refute_0_572,plain,
    ( least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))) != least_upper_bound(X_137,inverse(X_48))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_570,refute_0_571]) ).

cnf(refute_0_573,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))),least_upper_bound(X_137,inverse(X_48))) )],[refute_0_569,refute_0_572]) ).

cnf(refute_0_574,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))),
    inference(subst,[],[refute_0_520:[bind(X_51,$fot(least_upper_bound(X_137,inverse(X_48)))),bind(X_6,$fot(X_48))]]) ).

cnf(refute_0_575,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) != least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_576,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))),least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_574,refute_0_575]) ).

cnf(refute_0_577,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_48),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_573,refute_0_576]) ).

cnf(refute_0_578,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),
    introduced(tautology,[refl,[$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_579,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))) ),[1,1],$fot(least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_580,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_578,refute_0_579]) ).

cnf(refute_0_581,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_577,refute_0_580]) ).

cnf(refute_0_582,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_583,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_581,refute_0_582]) ).

cnf(refute_0_584,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_524,refute_0_583]) ).

cnf(refute_0_585,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_137,Y))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(X_137,Y)))]]) ).

cnf(refute_0_586,plain,
    least_upper_bound(Y,X_137) = least_upper_bound(Y,least_upper_bound(X_137,Y)),
    inference(subst,[],[refute_0_196:[bind(Y,$fot(X_137)),bind(X_39,$fot(Y))]]) ).

cnf(refute_0_587,plain,
    ( least_upper_bound(Y,X_137) != least_upper_bound(Y,least_upper_bound(X_137,Y))
    | least_upper_bound(Y,least_upper_bound(X_137,Y)) = least_upper_bound(Y,X_137) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(Y,X_137))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_137,Y))))]]) ).

cnf(refute_0_588,plain,
    least_upper_bound(Y,least_upper_bound(X_137,Y)) = least_upper_bound(Y,X_137),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,X_137),least_upper_bound(Y,least_upper_bound(X_137,Y))) )],[refute_0_586,refute_0_587]) ).

cnf(refute_0_589,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_137,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))
    | least_upper_bound(Y,least_upper_bound(X_137,Y)) != least_upper_bound(Y,X_137)
    | least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_137,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))) ),[0,1],$fot(least_upper_bound(Y,X_137))]]) ).

cnf(refute_0_590,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_137,Y))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))
    | least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_137,Y)),least_upper_bound(Y,X_137)) )],[refute_0_588,refute_0_589]) ).

cnf(refute_0_591,plain,
    least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_137,Y))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))) )],[refute_0_585,refute_0_590]) ).

cnf(refute_0_592,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(least_upper_bound(X,least_upper_bound(X_137,X)),Z),
    inference(subst,[],[associativity_of_lub:[bind(Y,$fot(least_upper_bound(X_137,X)))]]) ).

cnf(refute_0_593,plain,
    least_upper_bound(X,X_137) = least_upper_bound(X,least_upper_bound(X_137,X)),
    inference(subst,[],[refute_0_196:[bind(Y,$fot(X_137)),bind(X_39,$fot(X))]]) ).

cnf(refute_0_594,plain,
    ( least_upper_bound(X,X_137) != least_upper_bound(X,least_upper_bound(X_137,X))
    | least_upper_bound(X,least_upper_bound(X_137,X)) = least_upper_bound(X,X_137) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,X_137))),bind(Y0,$fot(least_upper_bound(X,least_upper_bound(X_137,X))))]]) ).

cnf(refute_0_595,plain,
    least_upper_bound(X,least_upper_bound(X_137,X)) = least_upper_bound(X,X_137),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,X_137),least_upper_bound(X,least_upper_bound(X_137,X))) )],[refute_0_593,refute_0_594]) ).

cnf(refute_0_596,plain,
    ( least_upper_bound(X,least_upper_bound(X_137,X)) != least_upper_bound(X,X_137)
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_137,X)),Z)
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(least_upper_bound(X,X_137),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_137,X)),Z)) ),[1,0],$fot(least_upper_bound(X,X_137))]]) ).

cnf(refute_0_597,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(least_upper_bound(X,least_upper_bound(X_137,X)),Z)
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(least_upper_bound(X,X_137),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_137,X)),least_upper_bound(X,X_137)) )],[refute_0_595,refute_0_596]) ).

cnf(refute_0_598,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(least_upper_bound(X,X_137),Z),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(least_upper_bound(X,least_upper_bound(X_137,X)),Z)) )],[refute_0_592,refute_0_597]) ).

cnf(refute_0_599,plain,
    least_upper_bound(least_upper_bound(X_137,X),Z) = least_upper_bound(X_137,least_upper_bound(X,Z)),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_137)),bind(Y,$fot(X))]]) ).

cnf(refute_0_600,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),
    introduced(tautology,[refl,[$fot(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)))]]) ).

cnf(refute_0_601,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z))
    | least_upper_bound(least_upper_bound(X_137,X),Z) != least_upper_bound(X_137,least_upper_bound(X,Z))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z))) ),[1,1],$fot(least_upper_bound(X_137,least_upper_bound(X,Z)))]]) ).

cnf(refute_0_602,plain,
    ( least_upper_bound(least_upper_bound(X_137,X),Z) != least_upper_bound(X_137,least_upper_bound(X,Z))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z))) )],[refute_0_600,refute_0_601]) ).

cnf(refute_0_603,plain,
    least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) = least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_137,X),Z),least_upper_bound(X_137,least_upper_bound(X,Z))) )],[refute_0_599,refute_0_602]) ).

cnf(refute_0_604,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z)))
    | least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(least_upper_bound(X,X_137),Z)
    | least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(least_upper_bound(X,X_137),Z) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(least_upper_bound(X,X_137),Z)) ),[0],$fot(least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))))]]) ).

cnf(refute_0_605,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(least_upper_bound(X,X_137),Z)
    | least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(least_upper_bound(X,X_137),Z) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z)))) )],[refute_0_603,refute_0_604]) ).

cnf(refute_0_606,plain,
    least_upper_bound(least_upper_bound(X,X_137),Z) = least_upper_bound(X,least_upper_bound(X_137,Z)),
    inference(subst,[],[refute_0_192:[bind(Y,$fot(X_137))]]) ).

cnf(refute_0_607,plain,
    ( least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) != least_upper_bound(least_upper_bound(X,X_137),Z)
    | least_upper_bound(least_upper_bound(X,X_137),Z) != least_upper_bound(X,least_upper_bound(X_137,Z))
    | least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_137,Z)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))),least_upper_bound(X,least_upper_bound(X_137,Z))) ),[0],$fot(least_upper_bound(least_upper_bound(X,X_137),Z))]]) ).

cnf(refute_0_608,plain,
    ( least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) != least_upper_bound(least_upper_bound(X,X_137),Z)
    | least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_137,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,X_137),Z),least_upper_bound(X,least_upper_bound(X_137,Z))) )],[refute_0_606,refute_0_607]) ).

cnf(refute_0_609,plain,
    ( least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)) != least_upper_bound(least_upper_bound(X,X_137),Z)
    | least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_137,Z)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))),least_upper_bound(least_upper_bound(X,X_137),Z)) )],[refute_0_605,refute_0_608]) ).

cnf(refute_0_610,plain,
    least_upper_bound(X,least_upper_bound(X_137,least_upper_bound(X,Z))) = least_upper_bound(X,least_upper_bound(X_137,Z)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(least_upper_bound(X_137,X),Z)),least_upper_bound(least_upper_bound(X,X_137),Z)) )],[refute_0_598,refute_0_609]) ).

cnf(refute_0_611,plain,
    least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))) = least_upper_bound(Y,least_upper_bound(X,X_137)),
    inference(subst,[],[refute_0_610:[bind(X,$fot(Y)),bind(Z,$fot(X_137)),bind(X_137,$fot(X))]]) ).

cnf(refute_0_612,plain,
    least_upper_bound(least_upper_bound(X,Y),X_137) = least_upper_bound(X,least_upper_bound(Y,X_137)),
    inference(subst,[],[refute_0_192:[bind(Z,$fot(X_137))]]) ).

cnf(refute_0_613,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),
    introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)))]]) ).

cnf(refute_0_614,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137))
    | least_upper_bound(least_upper_bound(X,Y),X_137) != least_upper_bound(X,least_upper_bound(Y,X_137))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137))) ),[1,1],$fot(least_upper_bound(X,least_upper_bound(Y,X_137)))]]) ).

cnf(refute_0_615,plain,
    ( least_upper_bound(least_upper_bound(X,Y),X_137) != least_upper_bound(X,least_upper_bound(Y,X_137))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137))) )],[refute_0_613,refute_0_614]) ).

cnf(refute_0_616,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),X_137),least_upper_bound(X,least_upper_bound(Y,X_137))) )],[refute_0_612,refute_0_615]) ).

cnf(refute_0_617,plain,
    ( least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) != least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137)))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X,X_137))))]]) ).

cnf(refute_0_618,plain,
    ( least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137)))) )],[refute_0_616,refute_0_617]) ).

cnf(refute_0_619,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X,least_upper_bound(Y,X_137))),least_upper_bound(Y,least_upper_bound(X,X_137))) )],[refute_0_611,refute_0_618]) ).

cnf(refute_0_620,plain,
    least_upper_bound(X,least_upper_bound(X_49,X_50)) = least_upper_bound(least_upper_bound(X_49,X_50),X),
    inference(subst,[],[symmetry_of_lub:[bind(Y,$fot(least_upper_bound(X_49,X_50)))]]) ).

cnf(refute_0_621,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X)) = least_upper_bound(least_upper_bound(X_49,X_50),X),
    inference(subst,[],[associativity_of_lub:[bind(X,$fot(X_49)),bind(Y,$fot(X_50)),bind(Z,$fot(X))]]) ).

cnf(refute_0_622,plain,
    ( least_upper_bound(X_49,least_upper_bound(X_50,X)) != least_upper_bound(least_upper_bound(X_49,X_50),X)
    | least_upper_bound(least_upper_bound(X_49,X_50),X) = least_upper_bound(X_49,least_upper_bound(X_50,X)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_49,least_upper_bound(X_50,X)))),bind(Y0,$fot(least_upper_bound(least_upper_bound(X_49,X_50),X)))]]) ).

cnf(refute_0_623,plain,
    least_upper_bound(least_upper_bound(X_49,X_50),X) = least_upper_bound(X_49,least_upper_bound(X_50,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_49,least_upper_bound(X_50,X)),least_upper_bound(least_upper_bound(X_49,X_50),X)) )],[refute_0_621,refute_0_622]) ).

cnf(refute_0_624,plain,
    ( least_upper_bound(X,least_upper_bound(X_49,X_50)) != least_upper_bound(least_upper_bound(X_49,X_50),X)
    | least_upper_bound(least_upper_bound(X_49,X_50),X) != least_upper_bound(X_49,least_upper_bound(X_50,X))
    | least_upper_bound(X,least_upper_bound(X_49,X_50)) = least_upper_bound(X_49,least_upper_bound(X_50,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_49,X_50)),least_upper_bound(X_49,least_upper_bound(X_50,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X_49,X_50),X))]]) ).

cnf(refute_0_625,plain,
    ( least_upper_bound(X,least_upper_bound(X_49,X_50)) != least_upper_bound(least_upper_bound(X_49,X_50),X)
    | least_upper_bound(X,least_upper_bound(X_49,X_50)) = least_upper_bound(X_49,least_upper_bound(X_50,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_49,X_50),X),least_upper_bound(X_49,least_upper_bound(X_50,X))) )],[refute_0_623,refute_0_624]) ).

cnf(refute_0_626,plain,
    least_upper_bound(X,least_upper_bound(X_49,X_50)) = least_upper_bound(X_49,least_upper_bound(X_50,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_49,X_50)),least_upper_bound(least_upper_bound(X_49,X_50),X)) )],[refute_0_620,refute_0_625]) ).

cnf(refute_0_627,plain,
    ( least_upper_bound(X,least_upper_bound(X_49,X_50)) != least_upper_bound(X_49,least_upper_bound(X_50,X))
    | least_upper_bound(X_49,least_upper_bound(X_50,X)) = least_upper_bound(X,least_upper_bound(X_49,X_50)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_49,X_50)))),bind(Y0,$fot(least_upper_bound(X_49,least_upper_bound(X_50,X))))]]) ).

cnf(refute_0_628,plain,
    least_upper_bound(X_49,least_upper_bound(X_50,X)) = least_upper_bound(X,least_upper_bound(X_49,X_50)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_49,X_50)),least_upper_bound(X_49,least_upper_bound(X_50,X))) )],[refute_0_626,refute_0_627]) ).

cnf(refute_0_629,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),
    inference(subst,[],[refute_0_628:[bind(X,$fot(Y)),bind(X_49,$fot(least_upper_bound(X,Y))),bind(X_50,$fot(X_137))]]) ).

cnf(refute_0_630,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X,X_137))))]]) ).

cnf(refute_0_631,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137))) )],[refute_0_629,refute_0_630]) ).

cnf(refute_0_632,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) = least_upper_bound(Y,least_upper_bound(X,X_137)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X,Y),X_137)),least_upper_bound(Y,least_upper_bound(X,X_137))) )],[refute_0_619,refute_0_631]) ).

cnf(refute_0_633,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_137)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(Y,X_137)),least_upper_bound(Y,least_upper_bound(X,X_137))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)))]]) ).

cnf(refute_0_634,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_137)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))
    | least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y)),least_upper_bound(Y,least_upper_bound(X,X_137))) )],[refute_0_632,refute_0_633]) ).

cnf(refute_0_635,plain,
    least_upper_bound(X,least_upper_bound(Y,X_137)) = least_upper_bound(Y,least_upper_bound(X,X_137)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_137)),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(X_137,Y))) )],[refute_0_591,refute_0_634]) ).

cnf(refute_0_636,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_137)) != least_upper_bound(Y,least_upper_bound(X,X_137))
    | least_upper_bound(Y,least_upper_bound(X,X_137)) = least_upper_bound(X,least_upper_bound(Y,X_137)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(Y,X_137)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X,X_137))))]]) ).

cnf(refute_0_637,plain,
    least_upper_bound(Y,least_upper_bound(X,X_137)) = least_upper_bound(X,least_upper_bound(Y,X_137)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_137)),least_upper_bound(Y,least_upper_bound(X,X_137))) )],[refute_0_635,refute_0_636]) ).

cnf(refute_0_638,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),
    inference(subst,[],[refute_0_637:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(X_48,identity)))),bind(X_137,$fot(least_upper_bound(X_137,inverse(X_48))))]]) ).

cnf(refute_0_639,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_640,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_638,refute_0_639]) ).

cnf(refute_0_641,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_584,refute_0_640]) ).

cnf(refute_0_642,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))))]]) ).

cnf(refute_0_643,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48)))) )],[refute_0_641,refute_0_642]) ).

cnf(refute_0_644,plain,
    ( least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137) != least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)),least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_523,refute_0_643]) ).

cnf(refute_0_645,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_48),X_137)) = least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),X_137),least_upper_bound(inverse(greatest_lower_bound(X_48,identity)),least_upper_bound(identity,least_upper_bound(X_137,inverse(X_48))))) )],[refute_0_514,refute_0_644]) ).

cnf(refute_0_646,plain,
    least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))),
    inference(subst,[],[refute_0_645:[bind(X_137,$fot(X_152)),bind(X_48,$fot(greatest_lower_bound(X_152,identity)))]]) ).

cnf(refute_0_647,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) = least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)),
    inference(subst,[],[refute_0_637:[bind(X,$fot(identity)),bind(Y,$fot(inverse(greatest_lower_bound(X_152,identity)))),bind(X_137,$fot(X_152))]]) ).

cnf(refute_0_648,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)) != least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) != least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152))
    | least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))))]]) ).

cnf(refute_0_649,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)) != least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))
    | least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)),least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152))) )],[refute_0_647,refute_0_648]) ).

cnf(refute_0_650,plain,
    least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),X_152)),least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))) )],[refute_0_646,refute_0_649]) ).

cnf(refute_0_651,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152))
    | least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)) != least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))) ),[0],$fot(least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)))]]) ).

cnf(refute_0_652,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152)),least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))) )],[refute_0_650,refute_0_651]) ).

cnf(refute_0_653,plain,
    multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(identity,X_152))) )],[refute_0_434,refute_0_652]) ).

cnf(refute_0_654,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)),
    inference(subst,[],[refute_0_220:[bind(X_159,$fot(identity)),bind(X_160,$fot(least_upper_bound(X_27,inverse(X_48))))]]) ).

cnf(refute_0_655,plain,
    ( least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) != least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))))]]) ).

cnf(refute_0_656,plain,
    least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) = least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) )],[refute_0_510,refute_0_655]) ).

cnf(refute_0_657,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) != least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))
    | least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))) ),[0,1],$fot(least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity))))]]) ).

cnf(refute_0_658,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) )],[refute_0_656,refute_0_657]) ).

cnf(refute_0_659,plain,
    least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))) )],[refute_0_654,refute_0_658]) ).

cnf(refute_0_660,plain,
    least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),
    inference(subst,[],[refute_0_232:[bind(X_50,$fot(identity)),bind(X_51,$fot(least_upper_bound(X_27,inverse(X_48))))]]) ).

cnf(refute_0_661,plain,
    least_upper_bound(least_upper_bound(X_162,identity),Y) = least_upper_bound(Y,least_upper_bound(X_162,identity)),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(least_upper_bound(X_162,identity)))]]) ).

cnf(refute_0_662,plain,
    least_upper_bound(identity,least_upper_bound(Y,X_162)) = least_upper_bound(Y,least_upper_bound(X_162,identity)),
    inference(subst,[],[refute_0_220:[bind(X_159,$fot(Y)),bind(X_160,$fot(X_162))]]) ).

cnf(refute_0_663,plain,
    ( least_upper_bound(identity,least_upper_bound(Y,X_162)) != least_upper_bound(Y,least_upper_bound(X_162,identity))
    | least_upper_bound(Y,least_upper_bound(X_162,identity)) = least_upper_bound(identity,least_upper_bound(Y,X_162)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(Y,X_162)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_162,identity))))]]) ).

cnf(refute_0_664,plain,
    least_upper_bound(Y,least_upper_bound(X_162,identity)) = least_upper_bound(identity,least_upper_bound(Y,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(Y,X_162)),least_upper_bound(Y,least_upper_bound(X_162,identity))) )],[refute_0_662,refute_0_663]) ).

cnf(refute_0_665,plain,
    ( least_upper_bound(Y,least_upper_bound(X_162,identity)) != least_upper_bound(identity,least_upper_bound(Y,X_162))
    | least_upper_bound(least_upper_bound(X_162,identity),Y) != least_upper_bound(Y,least_upper_bound(X_162,identity))
    | least_upper_bound(least_upper_bound(X_162,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_162,identity),Y),least_upper_bound(Y,least_upper_bound(X_162,identity))) ),[1],$fot(least_upper_bound(identity,least_upper_bound(Y,X_162)))]]) ).

cnf(refute_0_666,plain,
    ( least_upper_bound(least_upper_bound(X_162,identity),Y) != least_upper_bound(Y,least_upper_bound(X_162,identity))
    | least_upper_bound(least_upper_bound(X_162,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_162,identity)),least_upper_bound(identity,least_upper_bound(Y,X_162))) )],[refute_0_664,refute_0_665]) ).

cnf(refute_0_667,plain,
    least_upper_bound(least_upper_bound(X_162,identity),Y) = least_upper_bound(identity,least_upper_bound(Y,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_162,identity),Y),least_upper_bound(Y,least_upper_bound(X_162,identity))) )],[refute_0_661,refute_0_666]) ).

cnf(refute_0_668,plain,
    least_upper_bound(least_upper_bound(X_162,identity),Y) = least_upper_bound(X_162,least_upper_bound(identity,Y)),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_162)),bind(Y,$fot(identity)),bind(Z,$fot(Y))]]) ).

cnf(refute_0_669,plain,
    ( least_upper_bound(least_upper_bound(X_162,identity),Y) != least_upper_bound(X_162,least_upper_bound(identity,Y))
    | least_upper_bound(least_upper_bound(X_162,identity),Y) != least_upper_bound(identity,least_upper_bound(Y,X_162))
    | least_upper_bound(X_162,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_162)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(least_upper_bound(X_162,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_162))) ),[0],$fot(least_upper_bound(X_162,least_upper_bound(identity,Y)))]]) ).

cnf(refute_0_670,plain,
    ( least_upper_bound(least_upper_bound(X_162,identity),Y) != least_upper_bound(identity,least_upper_bound(Y,X_162))
    | least_upper_bound(X_162,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_162)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_162,identity),Y),least_upper_bound(X_162,least_upper_bound(identity,Y))) )],[refute_0_668,refute_0_669]) ).

cnf(refute_0_671,plain,
    least_upper_bound(X_162,least_upper_bound(identity,Y)) = least_upper_bound(identity,least_upper_bound(Y,X_162)),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_162,identity),Y),least_upper_bound(identity,least_upper_bound(Y,X_162))) )],[refute_0_667,refute_0_670]) ).

cnf(refute_0_672,plain,
    ( least_upper_bound(X_162,least_upper_bound(identity,Y)) != least_upper_bound(identity,least_upper_bound(Y,X_162))
    | least_upper_bound(identity,least_upper_bound(Y,X_162)) = least_upper_bound(X_162,least_upper_bound(identity,Y)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_162,least_upper_bound(identity,Y)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(Y,X_162))))]]) ).

cnf(refute_0_673,plain,
    least_upper_bound(identity,least_upper_bound(Y,X_162)) = least_upper_bound(X_162,least_upper_bound(identity,Y)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_162,least_upper_bound(identity,Y)),least_upper_bound(identity,least_upper_bound(Y,X_162))) )],[refute_0_671,refute_0_672]) ).

cnf(refute_0_674,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) = least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))),
    inference(subst,[],[refute_0_673:[bind(Y,$fot(least_upper_bound(X_27,inverse(X_48)))),bind(X_162,$fot(identity))]]) ).

cnf(refute_0_675,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) != least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))))]]) ).

cnf(refute_0_676,plain,
    ( least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) != least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)),least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))))) )],[refute_0_674,refute_0_675]) ).

cnf(refute_0_677,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) )],[refute_0_660,refute_0_676]) ).

cnf(refute_0_678,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)) != least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)))]]) ).

cnf(refute_0_679,plain,
    ( least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))
    | least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity)),least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48)))) )],[refute_0_677,refute_0_678]) ).

cnf(refute_0_680,plain,
    least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))) = least_upper_bound(identity,least_upper_bound(X_27,inverse(X_48))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_27,inverse(greatest_lower_bound(X_48,identity)))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_27,inverse(X_48)),identity))) )],[refute_0_659,refute_0_679]) ).

cnf(refute_0_681,plain,
    least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) = least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152))),
    inference(subst,[],[refute_0_680:[bind(X_27,$fot(X_152)),bind(X_48,$fot(X_152))]]) ).

cnf(refute_0_682,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))
    | least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))) != least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152)))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152)))) ),[0],$fot(least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))))]]) ).

cnf(refute_0_683,plain,
    ( multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) != least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))
    | multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity)))),least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152)))) )],[refute_0_681,refute_0_682]) ).

cnf(refute_0_684,plain,
    multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)) = least_upper_bound(identity,least_upper_bound(X_152,inverse(X_152))),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(X_152,identity)),least_upper_bound(X_152,identity)),least_upper_bound(identity,least_upper_bound(X_152,inverse(greatest_lower_bound(X_152,identity))))) )],[refute_0_653,refute_0_683]) ).

cnf(refute_0_685,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(identity,least_upper_bound(a,inverse(a))),
    inference(subst,[],[refute_0_684:[bind(X_152,$fot(a))]]) ).

cnf(refute_0_686,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != least_upper_bound(identity,least_upper_bound(a,inverse(a)))
    | least_upper_bound(identity,least_upper_bound(a,inverse(a))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,least_upper_bound(identity,inverse(a))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(a,inverse(a))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(identity,inverse(a)))))]]) ).

cnf(refute_0_687,plain,
    ( least_upper_bound(identity,least_upper_bound(a,inverse(a))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,least_upper_bound(identity,inverse(a))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),least_upper_bound(identity,least_upper_bound(a,inverse(a)))) )],[refute_0_685,refute_0_686]) ).

cnf(refute_0_688,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,least_upper_bound(identity,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(a,inverse(a))),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) )],[refute_0_416,refute_0_687]) ).

cnf(refute_0_689,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | least_upper_bound(a,least_upper_bound(identity,inverse(a))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,inverse(a))))),bind(Z0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_690,plain,
    ( least_upper_bound(a,least_upper_bound(identity,inverse(a))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) )],[refute_0_688,refute_0_689]) ).

cnf(refute_0_691,plain,
    multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,inverse(a))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_19,refute_0_690]) ).

cnf(refute_0_692,plain,
    ( multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))) ),[1],$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_693,plain,
    ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity)),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_691,refute_0_692]) ).

cnf(refute_0_694,plain,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),multiply(inverse(greatest_lower_bound(a,identity)),least_upper_bound(a,identity))) )],[refute_0_693,prove_p21x]) ).

cnf(refute_0_695,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = least_upper_bound(least_upper_bound(X_180,identity),multiply(least_upper_bound(X_180,identity),inverse(X_180))),
    inference(subst,[],[refute_0_427:[bind(X_82,$fot(least_upper_bound(X_180,identity))),bind(X_83,$fot(inverse(X_180)))]]) ).

cnf(refute_0_696,plain,
    inverse(multiply(X,inverse(least_upper_bound(X,identity)))) = multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)),
    inference(subst,[],[p21x_3:[bind(Y,$fot(inverse(least_upper_bound(X,identity))))]]) ).

cnf(refute_0_697,plain,
    multiply(X,inverse(least_upper_bound(X,identity))) = greatest_lower_bound(identity,X),
    inference(subst,[],[refute_0_102:[bind(X_98,$fot(X))]]) ).

cnf(refute_0_698,plain,
    ( multiply(X,inverse(least_upper_bound(X,identity))) != greatest_lower_bound(identity,X)
    | inverse(multiply(X,inverse(least_upper_bound(X,identity)))) != multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))
    | inverse(greatest_lower_bound(identity,X)) = multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X,identity)))),multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))) ),[0,0],$fot(greatest_lower_bound(identity,X))]]) ).

cnf(refute_0_699,plain,
    ( inverse(multiply(X,inverse(least_upper_bound(X,identity)))) != multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))
    | inverse(greatest_lower_bound(identity,X)) = multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) ),
    inference(resolve,[$cnf( $equal(multiply(X,inverse(least_upper_bound(X,identity))),greatest_lower_bound(identity,X)) )],[refute_0_697,refute_0_698]) ).

cnf(refute_0_700,plain,
    inverse(greatest_lower_bound(identity,X)) = multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X,identity)))),multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))) )],[refute_0_696,refute_0_699]) ).

cnf(refute_0_701,plain,
    inverse(multiply(X_23,inverse(X))) = multiply(inverse(inverse(X)),inverse(X_23)),
    inference(subst,[],[p21x_3:[bind(X,$fot(X_23)),bind(Y,$fot(inverse(X)))]]) ).

cnf(refute_0_702,plain,
    ( inverse(multiply(X_23,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_23))
    | inverse(inverse(X)) != X
    | inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(multiply(X_23,inverse(X))),multiply(inverse(inverse(X)),inverse(X_23))) ),[1,0],$fot(X)]]) ).

cnf(refute_0_703,plain,
    ( inverse(multiply(X_23,inverse(X))) != multiply(inverse(inverse(X)),inverse(X_23))
    | inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)) ),
    inference(resolve,[$cnf( $equal(inverse(inverse(X)),X) )],[p21x_2,refute_0_702]) ).

cnf(refute_0_704,plain,
    inverse(multiply(X_23,inverse(X))) = multiply(X,inverse(X_23)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X_23,inverse(X))),multiply(inverse(inverse(X)),inverse(X_23))) )],[refute_0_701,refute_0_703]) ).

cnf(refute_0_705,plain,
    inverse(multiply(X,inverse(least_upper_bound(X,identity)))) = multiply(least_upper_bound(X,identity),inverse(X)),
    inference(subst,[],[refute_0_704:[bind(X,$fot(least_upper_bound(X,identity))),bind(X_23,$fot(X))]]) ).

cnf(refute_0_706,plain,
    multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) = inverse(multiply(X,inverse(least_upper_bound(X,identity)))),
    inference(subst,[],[refute_0_364:[bind(Y,$fot(inverse(least_upper_bound(X,identity))))]]) ).

cnf(refute_0_707,plain,
    ( multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) != inverse(multiply(X,inverse(least_upper_bound(X,identity))))
    | inverse(multiply(X,inverse(least_upper_bound(X,identity)))) != multiply(least_upper_bound(X,identity),inverse(X))
    | multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) = multiply(least_upper_bound(X,identity),inverse(X)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)))),bind(Y0,$fot(inverse(multiply(X,inverse(least_upper_bound(X,identity)))))),bind(Z0,$fot(multiply(least_upper_bound(X,identity),inverse(X))))]]) ).

cnf(refute_0_708,plain,
    ( inverse(multiply(X,inverse(least_upper_bound(X,identity)))) != multiply(least_upper_bound(X,identity),inverse(X))
    | multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) = multiply(least_upper_bound(X,identity),inverse(X)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)),inverse(multiply(X,inverse(least_upper_bound(X,identity))))) )],[refute_0_706,refute_0_707]) ).

cnf(refute_0_709,plain,
    multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) = multiply(least_upper_bound(X,identity),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(multiply(X,inverse(least_upper_bound(X,identity)))),multiply(least_upper_bound(X,identity),inverse(X))) )],[refute_0_705,refute_0_708]) ).

cnf(refute_0_710,plain,
    ( multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)) != multiply(least_upper_bound(X,identity),inverse(X))
    | inverse(greatest_lower_bound(identity,X)) != multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))
    | inverse(greatest_lower_bound(identity,X)) = multiply(least_upper_bound(X,identity),inverse(X)) ),
    introduced(tautology,[equality,[$cnf( $equal(inverse(greatest_lower_bound(identity,X)),multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))) ),[1],$fot(multiply(least_upper_bound(X,identity),inverse(X)))]]) ).

cnf(refute_0_711,plain,
    ( inverse(greatest_lower_bound(identity,X)) != multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))
    | inverse(greatest_lower_bound(identity,X)) = multiply(least_upper_bound(X,identity),inverse(X)) ),
    inference(resolve,[$cnf( $equal(multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X)),multiply(least_upper_bound(X,identity),inverse(X))) )],[refute_0_709,refute_0_710]) ).

cnf(refute_0_712,plain,
    inverse(greatest_lower_bound(identity,X)) = multiply(least_upper_bound(X,identity),inverse(X)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X)),multiply(inverse(inverse(least_upper_bound(X,identity))),inverse(X))) )],[refute_0_700,refute_0_711]) ).

cnf(refute_0_713,plain,
    inverse(greatest_lower_bound(identity,X_180)) = multiply(least_upper_bound(X_180,identity),inverse(X_180)),
    inference(subst,[],[refute_0_712:[bind(X,$fot(X_180))]]) ).

cnf(refute_0_714,plain,
    ( inverse(greatest_lower_bound(identity,X_180)) != multiply(least_upper_bound(X_180,identity),inverse(X_180))
    | multiply(least_upper_bound(X_180,identity),inverse(X_180)) = inverse(greatest_lower_bound(identity,X_180)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(inverse(greatest_lower_bound(identity,X_180)))),bind(Y0,$fot(multiply(least_upper_bound(X_180,identity),inverse(X_180))))]]) ).

cnf(refute_0_715,plain,
    multiply(least_upper_bound(X_180,identity),inverse(X_180)) = inverse(greatest_lower_bound(identity,X_180)),
    inference(resolve,[$cnf( $equal(inverse(greatest_lower_bound(identity,X_180)),multiply(least_upper_bound(X_180,identity),inverse(X_180))) )],[refute_0_713,refute_0_714]) ).

cnf(refute_0_716,plain,
    ( multiply(least_upper_bound(X_180,identity),inverse(X_180)) != inverse(greatest_lower_bound(identity,X_180))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != least_upper_bound(least_upper_bound(X_180,identity),multiply(least_upper_bound(X_180,identity),inverse(X_180)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),least_upper_bound(least_upper_bound(X_180,identity),multiply(least_upper_bound(X_180,identity),inverse(X_180)))) ),[1,1],$fot(inverse(greatest_lower_bound(identity,X_180)))]]) ).

cnf(refute_0_717,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != least_upper_bound(least_upper_bound(X_180,identity),multiply(least_upper_bound(X_180,identity),inverse(X_180)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),inverse(X_180)),inverse(greatest_lower_bound(identity,X_180))) )],[refute_0_715,refute_0_716]) ).

cnf(refute_0_718,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),least_upper_bound(least_upper_bound(X_180,identity),multiply(least_upper_bound(X_180,identity),inverse(X_180)))) )],[refute_0_695,refute_0_717]) ).

cnf(refute_0_719,plain,
    least_upper_bound(identity,inverse(X_180)) = inverse(greatest_lower_bound(X_180,identity)),
    inference(subst,[],[refute_0_14:[bind(X_6,$fot(X_180))]]) ).

cnf(refute_0_720,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) = multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))),
    introduced(tautology,[refl,[$fot(multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))))]]) ).

cnf(refute_0_721,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) != multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180)))
    | least_upper_bound(identity,inverse(X_180)) != inverse(greatest_lower_bound(X_180,identity))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))),multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180)))) ),[1,1],$fot(inverse(greatest_lower_bound(X_180,identity)))]]) ).

cnf(refute_0_722,plain,
    ( least_upper_bound(identity,inverse(X_180)) != inverse(greatest_lower_bound(X_180,identity))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))),multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180)))) )],[refute_0_720,refute_0_721]) ).

cnf(refute_0_723,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,inverse(X_180)),inverse(greatest_lower_bound(X_180,identity))) )],[refute_0_719,refute_0_722]) ).

cnf(refute_0_724,plain,
    least_upper_bound(X_163,least_upper_bound(X_163,multiply(X_163,X_83))) = least_upper_bound(X_163,multiply(X_163,X_83)),
    inference(subst,[],[refute_0_232:[bind(X_50,$fot(X_163)),bind(X_51,$fot(multiply(X_163,X_83)))]]) ).

cnf(refute_0_725,plain,
    multiply(X_163,least_upper_bound(X_83,identity)) = least_upper_bound(X_163,multiply(X_163,X_83)),
    inference(subst,[],[refute_0_427:[bind(X_82,$fot(X_163))]]) ).

cnf(refute_0_726,plain,
    ( multiply(X_163,least_upper_bound(X_83,identity)) != least_upper_bound(X_163,multiply(X_163,X_83))
    | least_upper_bound(X_163,multiply(X_163,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_163,least_upper_bound(X_83,identity)))),bind(Y0,$fot(least_upper_bound(X_163,multiply(X_163,X_83))))]]) ).

cnf(refute_0_727,plain,
    least_upper_bound(X_163,multiply(X_163,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(X_83,identity)),least_upper_bound(X_163,multiply(X_163,X_83))) )],[refute_0_725,refute_0_726]) ).

cnf(refute_0_728,plain,
    ( least_upper_bound(X_163,multiply(X_163,X_83)) != multiply(X_163,least_upper_bound(X_83,identity))
    | least_upper_bound(X_163,least_upper_bound(X_163,multiply(X_163,X_83))) != least_upper_bound(X_163,multiply(X_163,X_83))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = least_upper_bound(X_163,multiply(X_163,X_83)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_163,least_upper_bound(X_163,multiply(X_163,X_83))),least_upper_bound(X_163,multiply(X_163,X_83))) ),[0,1],$fot(multiply(X_163,least_upper_bound(X_83,identity)))]]) ).

cnf(refute_0_729,plain,
    ( least_upper_bound(X_163,least_upper_bound(X_163,multiply(X_163,X_83))) != least_upper_bound(X_163,multiply(X_163,X_83))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = least_upper_bound(X_163,multiply(X_163,X_83)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,X_83)),multiply(X_163,least_upper_bound(X_83,identity))) )],[refute_0_727,refute_0_728]) ).

cnf(refute_0_730,plain,
    least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = least_upper_bound(X_163,multiply(X_163,X_83)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,least_upper_bound(X_163,multiply(X_163,X_83))),least_upper_bound(X_163,multiply(X_163,X_83))) )],[refute_0_724,refute_0_729]) ).

cnf(refute_0_731,plain,
    least_upper_bound(identity,least_upper_bound(X_83,identity)) = least_upper_bound(identity,X_83),
    inference(subst,[],[refute_0_237:[bind(Y,$fot(X_83)),bind(X_39,$fot(identity))]]) ).

cnf(refute_0_732,plain,
    multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),
    introduced(tautology,[refl,[$fot(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))))]]) ).

cnf(refute_0_733,plain,
    ( multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))
    | least_upper_bound(identity,least_upper_bound(X_83,identity)) != least_upper_bound(identity,X_83)
    | multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))) ),[1,1],$fot(least_upper_bound(identity,X_83))]]) ).

cnf(refute_0_734,plain,
    ( least_upper_bound(identity,least_upper_bound(X_83,identity)) != least_upper_bound(identity,X_83)
    | multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)) ),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))) )],[refute_0_732,refute_0_733]) ).

cnf(refute_0_735,plain,
    multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_83,identity)),least_upper_bound(identity,X_83)) )],[refute_0_731,refute_0_734]) ).

cnf(refute_0_736,plain,
    multiply(X_151,least_upper_bound(X_152,identity)) = least_upper_bound(X_151,multiply(X_151,X_152)),
    inference(subst,[],[refute_0_427:[bind(X_82,$fot(X_151)),bind(X_83,$fot(X_152))]]) ).

cnf(refute_0_737,plain,
    least_upper_bound(identity,X_152) = least_upper_bound(X_152,identity),
    inference(subst,[],[symmetry_of_lub:[bind(X,$fot(identity)),bind(Y,$fot(X_152))]]) ).

cnf(refute_0_738,plain,
    ( least_upper_bound(identity,X_152) != least_upper_bound(X_152,identity)
    | least_upper_bound(X_152,identity) = least_upper_bound(identity,X_152) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(identity,X_152))),bind(Y0,$fot(least_upper_bound(X_152,identity)))]]) ).

cnf(refute_0_739,plain,
    least_upper_bound(X_152,identity) = least_upper_bound(identity,X_152),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,X_152),least_upper_bound(X_152,identity)) )],[refute_0_737,refute_0_738]) ).

cnf(refute_0_740,plain,
    ( multiply(X_151,least_upper_bound(X_152,identity)) != least_upper_bound(X_151,multiply(X_151,X_152))
    | least_upper_bound(X_152,identity) != least_upper_bound(identity,X_152)
    | multiply(X_151,least_upper_bound(identity,X_152)) = least_upper_bound(X_151,multiply(X_151,X_152)) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(X_151,least_upper_bound(X_152,identity)),least_upper_bound(X_151,multiply(X_151,X_152))) ),[0,1],$fot(least_upper_bound(identity,X_152))]]) ).

cnf(refute_0_741,plain,
    ( multiply(X_151,least_upper_bound(X_152,identity)) != least_upper_bound(X_151,multiply(X_151,X_152))
    | multiply(X_151,least_upper_bound(identity,X_152)) = least_upper_bound(X_151,multiply(X_151,X_152)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_152,identity),least_upper_bound(identity,X_152)) )],[refute_0_739,refute_0_740]) ).

cnf(refute_0_742,plain,
    multiply(X_151,least_upper_bound(identity,X_152)) = least_upper_bound(X_151,multiply(X_151,X_152)),
    inference(resolve,[$cnf( $equal(multiply(X_151,least_upper_bound(X_152,identity)),least_upper_bound(X_151,multiply(X_151,X_152))) )],[refute_0_736,refute_0_741]) ).

cnf(refute_0_743,plain,
    ( multiply(X_82,least_upper_bound(X_83,identity)) != least_upper_bound(X_82,multiply(X_82,X_83))
    | least_upper_bound(X_82,multiply(X_82,X_83)) = multiply(X_82,least_upper_bound(X_83,identity)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_82,least_upper_bound(X_83,identity)))),bind(Y0,$fot(least_upper_bound(X_82,multiply(X_82,X_83))))]]) ).

cnf(refute_0_744,plain,
    least_upper_bound(X_82,multiply(X_82,X_83)) = multiply(X_82,least_upper_bound(X_83,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_82,least_upper_bound(X_83,identity)),least_upper_bound(X_82,multiply(X_82,X_83))) )],[refute_0_427,refute_0_743]) ).

cnf(refute_0_745,plain,
    least_upper_bound(X_151,multiply(X_151,X_152)) = multiply(X_151,least_upper_bound(X_152,identity)),
    inference(subst,[],[refute_0_744:[bind(X_82,$fot(X_151)),bind(X_83,$fot(X_152))]]) ).

cnf(refute_0_746,plain,
    ( multiply(X_151,least_upper_bound(identity,X_152)) != least_upper_bound(X_151,multiply(X_151,X_152))
    | least_upper_bound(X_151,multiply(X_151,X_152)) != multiply(X_151,least_upper_bound(X_152,identity))
    | multiply(X_151,least_upper_bound(identity,X_152)) = multiply(X_151,least_upper_bound(X_152,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_151,least_upper_bound(identity,X_152)),multiply(X_151,least_upper_bound(X_152,identity))) ),[0],$fot(least_upper_bound(X_151,multiply(X_151,X_152)))]]) ).

cnf(refute_0_747,plain,
    ( multiply(X_151,least_upper_bound(identity,X_152)) != least_upper_bound(X_151,multiply(X_151,X_152))
    | multiply(X_151,least_upper_bound(identity,X_152)) = multiply(X_151,least_upper_bound(X_152,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_151,multiply(X_151,X_152)),multiply(X_151,least_upper_bound(X_152,identity))) )],[refute_0_745,refute_0_746]) ).

cnf(refute_0_748,plain,
    multiply(X_151,least_upper_bound(identity,X_152)) = multiply(X_151,least_upper_bound(X_152,identity)),
    inference(resolve,[$cnf( $equal(multiply(X_151,least_upper_bound(identity,X_152)),least_upper_bound(X_151,multiply(X_151,X_152))) )],[refute_0_742,refute_0_747]) ).

cnf(refute_0_749,plain,
    ( multiply(X_151,least_upper_bound(identity,X_152)) != multiply(X_151,least_upper_bound(X_152,identity))
    | multiply(X_151,least_upper_bound(X_152,identity)) = multiply(X_151,least_upper_bound(identity,X_152)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_151,least_upper_bound(identity,X_152)))),bind(Y0,$fot(multiply(X_151,least_upper_bound(X_152,identity))))]]) ).

cnf(refute_0_750,plain,
    multiply(X_151,least_upper_bound(X_152,identity)) = multiply(X_151,least_upper_bound(identity,X_152)),
    inference(resolve,[$cnf( $equal(multiply(X_151,least_upper_bound(identity,X_152)),multiply(X_151,least_upper_bound(X_152,identity))) )],[refute_0_748,refute_0_749]) ).

cnf(refute_0_751,plain,
    multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)) = multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),
    inference(subst,[],[refute_0_750:[bind(X_151,$fot(X_163)),bind(X_152,$fot(least_upper_bound(X_83,identity)))]]) ).

cnf(refute_0_752,plain,
    least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)),
    inference(subst,[],[refute_0_744:[bind(X_82,$fot(X_163)),bind(X_83,$fot(least_upper_bound(X_83,identity)))]]) ).

cnf(refute_0_753,plain,
    ( multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)) != multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))))),bind(Y0,$fot(multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)))),bind(Z0,$fot(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))))]]) ).

cnf(refute_0_754,plain,
    ( multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)) != multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity))) )],[refute_0_752,refute_0_753]) ).

cnf(refute_0_755,plain,
    least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(least_upper_bound(X_83,identity),identity)),multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))) )],[refute_0_751,refute_0_754]) ).

cnf(refute_0_756,plain,
    ( multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(identity,X_83))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))))),bind(Y0,$fot(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))))),bind(Z0,$fot(multiply(X_163,least_upper_bound(identity,X_83))))]]) ).

cnf(refute_0_757,plain,
    ( multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(identity,X_83))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity)))) )],[refute_0_755,refute_0_756]) ).

cnf(refute_0_758,plain,
    least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) = multiply(X_163,least_upper_bound(identity,X_83)),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(identity,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(identity,X_83))) )],[refute_0_735,refute_0_757]) ).

cnf(refute_0_759,plain,
    ( least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != multiply(X_163,least_upper_bound(identity,X_83))
    | least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != least_upper_bound(X_163,multiply(X_163,X_83))
    | multiply(X_163,least_upper_bound(identity,X_83)) = least_upper_bound(X_163,multiply(X_163,X_83)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))),least_upper_bound(X_163,multiply(X_163,X_83))) ),[0],$fot(multiply(X_163,least_upper_bound(identity,X_83)))]]) ).

cnf(refute_0_760,plain,
    ( least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != least_upper_bound(X_163,multiply(X_163,X_83))
    | multiply(X_163,least_upper_bound(identity,X_83)) = least_upper_bound(X_163,multiply(X_163,X_83)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))),multiply(X_163,least_upper_bound(identity,X_83))) )],[refute_0_758,refute_0_759]) ).

cnf(refute_0_761,plain,
    ( multiply(X_163,least_upper_bound(identity,X_83)) != least_upper_bound(X_163,multiply(X_163,X_83))
    | least_upper_bound(X_163,multiply(X_163,X_83)) != multiply(X_163,least_upper_bound(X_83,identity))
    | multiply(X_163,least_upper_bound(identity,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(X_163,least_upper_bound(identity,X_83)),multiply(X_163,least_upper_bound(X_83,identity))) ),[0],$fot(least_upper_bound(X_163,multiply(X_163,X_83)))]]) ).

cnf(refute_0_762,plain,
    ( multiply(X_163,least_upper_bound(identity,X_83)) != least_upper_bound(X_163,multiply(X_163,X_83))
    | multiply(X_163,least_upper_bound(identity,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,X_83)),multiply(X_163,least_upper_bound(X_83,identity))) )],[refute_0_727,refute_0_761]) ).

cnf(refute_0_763,plain,
    ( least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))) != least_upper_bound(X_163,multiply(X_163,X_83))
    | multiply(X_163,least_upper_bound(identity,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)) ),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(identity,X_83)),least_upper_bound(X_163,multiply(X_163,X_83))) )],[refute_0_760,refute_0_762]) ).

cnf(refute_0_764,plain,
    multiply(X_163,least_upper_bound(identity,X_83)) = multiply(X_163,least_upper_bound(X_83,identity)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_163,multiply(X_163,least_upper_bound(X_83,identity))),least_upper_bound(X_163,multiply(X_163,X_83))) )],[refute_0_730,refute_0_763]) ).

cnf(refute_0_765,plain,
    ( multiply(X_163,least_upper_bound(identity,X_83)) != multiply(X_163,least_upper_bound(X_83,identity))
    | multiply(X_163,least_upper_bound(X_83,identity)) = multiply(X_163,least_upper_bound(identity,X_83)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(multiply(X_163,least_upper_bound(identity,X_83)))),bind(Y0,$fot(multiply(X_163,least_upper_bound(X_83,identity))))]]) ).

cnf(refute_0_766,plain,
    multiply(X_163,least_upper_bound(X_83,identity)) = multiply(X_163,least_upper_bound(identity,X_83)),
    inference(resolve,[$cnf( $equal(multiply(X_163,least_upper_bound(identity,X_83)),multiply(X_163,least_upper_bound(X_83,identity))) )],[refute_0_764,refute_0_765]) ).

cnf(refute_0_767,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))),
    inference(subst,[],[refute_0_766:[bind(X_163,$fot(least_upper_bound(X_180,identity))),bind(X_83,$fot(inverse(X_180)))]]) ).

cnf(refute_0_768,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) != multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)))),bind(Y0,$fot(multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))))),bind(Z0,$fot(multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))))]]) ).

cnf(refute_0_769,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))) != multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180)))) )],[refute_0_767,refute_0_768]) ).

cnf(refute_0_770,plain,
    multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) = multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(identity,inverse(X_180))),multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))) )],[refute_0_723,refute_0_769]) ).

cnf(refute_0_771,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))
    | multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))
    | multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) ),
    introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))) ),[0],$fot(multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))))]]) ).

cnf(refute_0_772,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))
    | multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity)))) )],[refute_0_770,refute_0_771]) ).

cnf(refute_0_773,plain,
    least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))),
    inference(subst,[],[refute_0_610:[bind(X,$fot(identity)),bind(Z,$fot(inverse(X_180))),bind(X_137,$fot(X_180))]]) ).

cnf(refute_0_774,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_164))) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)),
    inference(subst,[],[associativity_of_lub:[bind(Z,$fot(least_upper_bound(Y,X_164)))]]) ).

cnf(refute_0_775,plain,
    least_upper_bound(Y,least_upper_bound(Y,X_164)) = least_upper_bound(Y,X_164),
    inference(subst,[],[refute_0_232:[bind(X_50,$fot(Y)),bind(X_51,$fot(X_164))]]) ).

cnf(refute_0_776,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_164))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))
    | least_upper_bound(Y,least_upper_bound(Y,X_164)) != least_upper_bound(Y,X_164)
    | least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_164))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))) ),[0,1],$fot(least_upper_bound(Y,X_164))]]) ).

cnf(refute_0_777,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_164))) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))
    | least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(Y,X_164)),least_upper_bound(Y,X_164)) )],[refute_0_775,refute_0_776]) ).

cnf(refute_0_778,plain,
    least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(Y,X_164))),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))) )],[refute_0_774,refute_0_777]) ).

cnf(refute_0_779,plain,
    least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))) = least_upper_bound(Y,least_upper_bound(X_164,X)),
    inference(subst,[],[refute_0_205:[bind(X,$fot(X_164)),bind(Y,$fot(X)),bind(X_138,$fot(Y))]]) ).

cnf(refute_0_780,plain,
    least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16)))),
    inference(subst,[],[refute_0_185:[bind(X_17,$fot(least_upper_bound(X_159,least_upper_bound(X_160,X_16))))]]) ).

cnf(refute_0_781,plain,
    greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))) = X_16,
    inference(subst,[],[refute_0_162:[bind(X_10,$fot(X_16)),bind(X_49,$fot(X_159)),bind(X_50,$fot(X_160))]]) ).

cnf(refute_0_782,plain,
    ( greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))) != X_16
    | least_upper_bound(X_159,least_upper_bound(X_160,X_16)) != least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))))
    | least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))))) ),[1,1],$fot(X_16)]]) ).

cnf(refute_0_783,plain,
    ( least_upper_bound(X_159,least_upper_bound(X_160,X_16)) != least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))))
    | least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))),X_16) )],[refute_0_781,refute_0_782]) ).

cnf(refute_0_784,plain,
    least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),greatest_lower_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))))) )],[refute_0_780,refute_0_783]) ).

cnf(refute_0_785,plain,
    least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)),
    inference(subst,[],[refute_0_205:[bind(X,$fot(X_159)),bind(Y,$fot(X_160)),bind(X_138,$fot(X_16))]]) ).

cnf(refute_0_786,plain,
    least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) = least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))),
    inference(subst,[],[refute_0_124:[bind(X_50,$fot(X_16)),bind(X_51,$fot(least_upper_bound(X_159,least_upper_bound(X_160,X_16))))]]) ).

cnf(refute_0_787,plain,
    ( least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))) != least_upper_bound(X_16,least_upper_bound(X_159,X_160))
    | least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) != least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16)))
    | least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16))),bind(Y0,$fot(least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))))),bind(Z0,$fot(least_upper_bound(X_16,least_upper_bound(X_159,X_160))))]]) ).

cnf(refute_0_788,plain,
    ( least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))) != least_upper_bound(X_16,least_upper_bound(X_159,X_160))
    | least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16),least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16)))) )],[refute_0_786,refute_0_787]) ).

cnf(refute_0_789,plain,
    least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_16,least_upper_bound(X_159,least_upper_bound(X_160,X_16))),least_upper_bound(X_16,least_upper_bound(X_159,X_160))) )],[refute_0_785,refute_0_788]) ).

cnf(refute_0_790,plain,
    ( least_upper_bound(X_159,least_upper_bound(X_160,X_16)) != least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16)
    | least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16) != least_upper_bound(X_16,least_upper_bound(X_159,X_160))
    | least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),least_upper_bound(X_16,least_upper_bound(X_159,X_160))) ),[0],$fot(least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16))]]) ).

cnf(refute_0_791,plain,
    ( least_upper_bound(X_159,least_upper_bound(X_160,X_16)) != least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16)
    | least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16),least_upper_bound(X_16,least_upper_bound(X_159,X_160))) )],[refute_0_789,refute_0_790]) ).

cnf(refute_0_792,plain,
    least_upper_bound(X_159,least_upper_bound(X_160,X_16)) = least_upper_bound(X_16,least_upper_bound(X_159,X_160)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),least_upper_bound(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),X_16)) )],[refute_0_784,refute_0_791]) ).

cnf(refute_0_793,plain,
    ( least_upper_bound(X_159,least_upper_bound(X_160,X_16)) != least_upper_bound(X_16,least_upper_bound(X_159,X_160))
    | least_upper_bound(X_16,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,X_16)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_159,least_upper_bound(X_160,X_16)))),bind(Y0,$fot(least_upper_bound(X_16,least_upper_bound(X_159,X_160))))]]) ).

cnf(refute_0_794,plain,
    least_upper_bound(X_16,least_upper_bound(X_159,X_160)) = least_upper_bound(X_159,least_upper_bound(X_160,X_16)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_159,least_upper_bound(X_160,X_16)),least_upper_bound(X_16,least_upper_bound(X_159,X_160))) )],[refute_0_792,refute_0_793]) ).

cnf(refute_0_795,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))),
    inference(subst,[],[refute_0_794:[bind(X_159,$fot(Y)),bind(X_16,$fot(least_upper_bound(X,Y))),bind(X_160,$fot(X_164))]]) ).

cnf(refute_0_796,plain,
    ( least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_164,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) != least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y)))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))))),bind(Z0,$fot(least_upper_bound(Y,least_upper_bound(X_164,X))))]]) ).

cnf(refute_0_797,plain,
    ( least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))) != least_upper_bound(Y,least_upper_bound(X_164,X))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)),least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y)))) )],[refute_0_795,refute_0_796]) ).

cnf(refute_0_798,plain,
    least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_164,least_upper_bound(X,Y))),least_upper_bound(Y,least_upper_bound(X_164,X))) )],[refute_0_779,refute_0_797]) ).

cnf(refute_0_799,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_164)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))
    | least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)) != least_upper_bound(Y,least_upper_bound(X_164,X))
    | least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(Y,X_164)),least_upper_bound(Y,least_upper_bound(X_164,X))) ),[0],$fot(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)))]]) ).

cnf(refute_0_800,plain,
    ( least_upper_bound(X,least_upper_bound(Y,X_164)) != least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))
    | least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164)),least_upper_bound(Y,least_upper_bound(X_164,X))) )],[refute_0_798,refute_0_799]) ).

cnf(refute_0_801,plain,
    least_upper_bound(X,least_upper_bound(Y,X_164)) = least_upper_bound(Y,least_upper_bound(X_164,X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,X_164)),least_upper_bound(least_upper_bound(X,Y),least_upper_bound(Y,X_164))) )],[refute_0_778,refute_0_800]) ).

cnf(refute_0_802,plain,
    least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_172,X_170))) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),
    inference(subst,[],[refute_0_801:[bind(X_164,$fot(least_upper_bound(X_172,X_170)))]]) ).

cnf(refute_0_803,plain,
    least_upper_bound(X_170,least_upper_bound(Y,X_172)) = least_upper_bound(Y,least_upper_bound(X_172,X_170)),
    inference(subst,[],[refute_0_801:[bind(X,$fot(X_170)),bind(X_164,$fot(X_172))]]) ).

cnf(refute_0_804,plain,
    ( least_upper_bound(X_170,least_upper_bound(Y,X_172)) != least_upper_bound(Y,least_upper_bound(X_172,X_170))
    | least_upper_bound(Y,least_upper_bound(X_172,X_170)) = least_upper_bound(X_170,least_upper_bound(Y,X_172)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_170,least_upper_bound(Y,X_172)))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_172,X_170))))]]) ).

cnf(refute_0_805,plain,
    least_upper_bound(Y,least_upper_bound(X_172,X_170)) = least_upper_bound(X_170,least_upper_bound(Y,X_172)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_170,least_upper_bound(Y,X_172)),least_upper_bound(Y,least_upper_bound(X_172,X_170))) )],[refute_0_803,refute_0_804]) ).

cnf(refute_0_806,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_172,X_170))) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))
    | least_upper_bound(Y,least_upper_bound(X_172,X_170)) != least_upper_bound(X_170,least_upper_bound(Y,X_172))
    | least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_172,X_170))),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))) ),[0,1],$fot(least_upper_bound(X_170,least_upper_bound(Y,X_172)))]]) ).

cnf(refute_0_807,plain,
    ( least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_172,X_170))) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))
    | least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(X_172,X_170)),least_upper_bound(X_170,least_upper_bound(Y,X_172))) )],[refute_0_805,refute_0_806]) ).

cnf(refute_0_808,plain,
    least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(Y,least_upper_bound(X_172,X_170))),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))) )],[refute_0_802,refute_0_807]) ).

cnf(refute_0_809,plain,
    least_upper_bound(least_upper_bound(X_172,X_170),X) = least_upper_bound(X_172,least_upper_bound(X_170,X)),
    inference(subst,[],[refute_0_192:[bind(X,$fot(X_172)),bind(Y,$fot(X_170)),bind(Z,$fot(X))]]) ).

cnf(refute_0_810,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) = least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),
    introduced(tautology,[refl,[$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)))]]) ).

cnf(refute_0_811,plain,
    ( least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))
    | least_upper_bound(least_upper_bound(X_172,X_170),X) != least_upper_bound(X_172,least_upper_bound(X_170,X))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))) ),[1,1],$fot(least_upper_bound(X_172,least_upper_bound(X_170,X)))]]) ).

cnf(refute_0_812,plain,
    ( least_upper_bound(least_upper_bound(X_172,X_170),X) != least_upper_bound(X_172,least_upper_bound(X_170,X))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))) )],[refute_0_810,refute_0_811]) ).

cnf(refute_0_813,plain,
    least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_172,X_170),X),least_upper_bound(X_172,least_upper_bound(X_170,X))) )],[refute_0_809,refute_0_812]) ).

cnf(refute_0_814,plain,
    ( least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))
    | least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)) != least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))
    | least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))),least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))) ),[0],$fot(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)))]]) ).

cnf(refute_0_815,plain,
    ( least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) != least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))
    | least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X)),least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))) )],[refute_0_813,refute_0_814]) ).

cnf(refute_0_816,plain,
    least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) = least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))),least_upper_bound(Y,least_upper_bound(least_upper_bound(X_172,X_170),X))) )],[refute_0_808,refute_0_815]) ).

cnf(refute_0_817,plain,
    ( least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) != least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))
    | least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) = least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))))),bind(Y0,$fot(least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))))]]) ).

cnf(refute_0_818,plain,
    least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X))) = least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X,least_upper_bound(X_170,least_upper_bound(Y,X_172))),least_upper_bound(Y,least_upper_bound(X_172,least_upper_bound(X_170,X)))) )],[refute_0_816,refute_0_817]) ).

cnf(refute_0_819,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))),
    inference(subst,[],[refute_0_818:[bind(X,$fot(identity)),bind(Y,$fot(identity)),bind(X_170,$fot(X_180)),bind(X_172,$fot(inverse(X_180)))]]) ).

cnf(refute_0_820,plain,
    ( least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) != least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180))))
    | least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))))]]) ).

cnf(refute_0_821,plain,
    ( least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))),least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180))))) )],[refute_0_819,refute_0_820]) ).

cnf(refute_0_822,plain,
    least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(X_180,least_upper_bound(identity,inverse(X_180)))),least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))) )],[refute_0_773,refute_0_821]) ).

cnf(refute_0_823,plain,
    least_upper_bound(X_50,least_upper_bound(X_50,least_upper_bound(X_172,X_170))) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)),
    inference(subst,[],[refute_0_232:[bind(X_51,$fot(least_upper_bound(X_172,X_170)))]]) ).

cnf(refute_0_824,plain,
    least_upper_bound(X_170,least_upper_bound(X_50,X_172)) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)),
    inference(subst,[],[refute_0_801:[bind(X,$fot(X_170)),bind(Y,$fot(X_50)),bind(X_164,$fot(X_172))]]) ).

cnf(refute_0_825,plain,
    ( least_upper_bound(X_170,least_upper_bound(X_50,X_172)) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_172,X_170)) = least_upper_bound(X_170,least_upper_bound(X_50,X_172)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_170,least_upper_bound(X_50,X_172)))),bind(Y0,$fot(least_upper_bound(X_50,least_upper_bound(X_172,X_170))))]]) ).

cnf(refute_0_826,plain,
    least_upper_bound(X_50,least_upper_bound(X_172,X_170)) = least_upper_bound(X_170,least_upper_bound(X_50,X_172)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_170,least_upper_bound(X_50,X_172)),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) )],[refute_0_824,refute_0_825]) ).

cnf(refute_0_827,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_172,X_170)) != least_upper_bound(X_170,least_upper_bound(X_50,X_172))
    | least_upper_bound(X_50,least_upper_bound(X_50,least_upper_bound(X_172,X_170))) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_50,least_upper_bound(X_172,X_170))),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) ),[0,1],$fot(least_upper_bound(X_170,least_upper_bound(X_50,X_172)))]]) ).

cnf(refute_0_828,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_50,least_upper_bound(X_172,X_170))) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_172,X_170)),least_upper_bound(X_170,least_upper_bound(X_50,X_172))) )],[refute_0_826,refute_0_827]) ).

cnf(refute_0_829,plain,
    least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_50,least_upper_bound(X_172,X_170))),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) )],[refute_0_823,refute_0_828]) ).

cnf(refute_0_830,plain,
    least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) = least_upper_bound(X_50,least_upper_bound(X_170,X_172)),
    inference(subst,[],[refute_0_610:[bind(X,$fot(X_50)),bind(Z,$fot(X_172)),bind(X_137,$fot(X_170))]]) ).

cnf(refute_0_831,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) != least_upper_bound(X_50,least_upper_bound(X_170,X_172))
    | least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_170,X_172)) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) ),[0],$fot(least_upper_bound(X_50,least_upper_bound(X_170,X_172)))]]) ).

cnf(refute_0_832,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_170,X_172)) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))),least_upper_bound(X_50,least_upper_bound(X_170,X_172))) )],[refute_0_830,refute_0_831]) ).

cnf(refute_0_833,plain,
    least_upper_bound(X_50,least_upper_bound(X_170,X_172)) = least_upper_bound(X_50,least_upper_bound(X_172,X_170)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_170,least_upper_bound(X_50,X_172))),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) )],[refute_0_829,refute_0_832]) ).

cnf(refute_0_834,plain,
    ( least_upper_bound(X_50,least_upper_bound(X_170,X_172)) != least_upper_bound(X_50,least_upper_bound(X_172,X_170))
    | least_upper_bound(X_50,least_upper_bound(X_172,X_170)) = least_upper_bound(X_50,least_upper_bound(X_170,X_172)) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(least_upper_bound(X_50,least_upper_bound(X_170,X_172)))),bind(Y0,$fot(least_upper_bound(X_50,least_upper_bound(X_172,X_170))))]]) ).

cnf(refute_0_835,plain,
    least_upper_bound(X_50,least_upper_bound(X_172,X_170)) = least_upper_bound(X_50,least_upper_bound(X_170,X_172)),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_50,least_upper_bound(X_170,X_172)),least_upper_bound(X_50,least_upper_bound(X_172,X_170))) )],[refute_0_833,refute_0_834]) ).

cnf(refute_0_836,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) = least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))),
    inference(subst,[],[refute_0_835:[bind(X_170,$fot(inverse(X_180))),bind(X_172,$fot(least_upper_bound(X_180,identity))),bind(X_50,$fot(identity))]]) ).

cnf(refute_0_837,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) != least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity)))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))))]]) ).

cnf(refute_0_838,plain,
    ( least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))),least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity)))) )],[refute_0_836,refute_0_837]) ).

cnf(refute_0_839,plain,
    least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(inverse(X_180),least_upper_bound(X_180,identity))),least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))) )],[refute_0_822,refute_0_838]) ).

cnf(refute_0_840,plain,
    least_upper_bound(X_128,inverse(greatest_lower_bound(X_129,identity))) = least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129))),
    inference(subst,[],[refute_0_510:[bind(X_27,$fot(X_128)),bind(X_48,$fot(X_129))]]) ).

cnf(refute_0_841,plain,
    greatest_lower_bound(identity,X_129) = greatest_lower_bound(X_129,identity),
    inference(subst,[],[symmetry_of_glb:[bind(X,$fot(identity)),bind(Y,$fot(X_129))]]) ).

cnf(refute_0_842,plain,
    ( greatest_lower_bound(identity,X_129) != greatest_lower_bound(X_129,identity)
    | greatest_lower_bound(X_129,identity) = greatest_lower_bound(identity,X_129) ),
    inference(subst,[],[refute_0_6:[bind(X0,$fot(greatest_lower_bound(identity,X_129))),bind(Y0,$fot(greatest_lower_bound(X_129,identity)))]]) ).

cnf(refute_0_843,plain,
    greatest_lower_bound(X_129,identity) = greatest_lower_bound(identity,X_129),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,X_129),greatest_lower_bound(X_129,identity)) )],[refute_0_841,refute_0_842]) ).

cnf(refute_0_844,plain,
    ( greatest_lower_bound(X_129,identity) != greatest_lower_bound(identity,X_129)
    | least_upper_bound(X_128,inverse(greatest_lower_bound(X_129,identity))) != least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129)))
    | least_upper_bound(X_128,inverse(greatest_lower_bound(identity,X_129))) = least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129))) ),
    introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(X_128,inverse(greatest_lower_bound(X_129,identity))),least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129)))) ),[0,1,0],$fot(greatest_lower_bound(identity,X_129))]]) ).

cnf(refute_0_845,plain,
    ( least_upper_bound(X_128,inverse(greatest_lower_bound(X_129,identity))) != least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129)))
    | least_upper_bound(X_128,inverse(greatest_lower_bound(identity,X_129))) = least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129))) ),
    inference(resolve,[$cnf( $equal(greatest_lower_bound(X_129,identity),greatest_lower_bound(identity,X_129)) )],[refute_0_843,refute_0_844]) ).

cnf(refute_0_846,plain,
    least_upper_bound(X_128,inverse(greatest_lower_bound(identity,X_129))) = least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129))),
    inference(resolve,[$cnf( $equal(least_upper_bound(X_128,inverse(greatest_lower_bound(X_129,identity))),least_upper_bound(identity,least_upper_bound(X_128,inverse(X_129)))) )],[refute_0_840,refute_0_845]) ).

cnf(refute_0_847,plain,
    least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) = least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))),
    inference(subst,[],[refute_0_846:[bind(X_128,$fot(least_upper_bound(X_180,identity))),bind(X_129,$fot(X_180))]]) ).

cnf(refute_0_848,plain,
    ( least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) != least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180)))
    | least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))))),bind(Z0,$fot(least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))))]]) ).

cnf(refute_0_849,plain,
    ( least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))),least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180)))) )],[refute_0_847,refute_0_848]) ).

cnf(refute_0_850,plain,
    least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(least_upper_bound(X_180,identity),inverse(X_180))),least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))) )],[refute_0_839,refute_0_849]) ).

cnf(refute_0_851,plain,
    ( multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) != least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))
    | least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))) != least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))
    | multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))),least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))) ),[0],$fot(least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))))]]) ).

cnf(refute_0_852,plain,
    ( multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) != least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))
    | multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180))),least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180)))) )],[refute_0_850,refute_0_851]) ).

cnf(refute_0_853,plain,
    ( multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)) != least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))
    | multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))),least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))) )],[refute_0_772,refute_0_852]) ).

cnf(refute_0_854,plain,
    multiply(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(X_180,identity))) = least_upper_bound(identity,least_upper_bound(X_180,inverse(X_180))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_180,identity),least_upper_bound(inverse(X_180),identity)),least_upper_bound(least_upper_bound(X_180,identity),inverse(greatest_lower_bound(identity,X_180)))) )],[refute_0_718,refute_0_853]) ).

cnf(refute_0_855,plain,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(identity,least_upper_bound(a,inverse(a))),
    inference(subst,[],[refute_0_854:[bind(X_180,$fot(a))]]) ).

cnf(refute_0_856,plain,
    ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(identity,least_upper_bound(a,inverse(a)))
    | least_upper_bound(identity,least_upper_bound(a,inverse(a))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,least_upper_bound(identity,inverse(a))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(least_upper_bound(identity,least_upper_bound(a,inverse(a))))),bind(Z0,$fot(least_upper_bound(a,least_upper_bound(identity,inverse(a)))))]]) ).

cnf(refute_0_857,plain,
    ( least_upper_bound(identity,least_upper_bound(a,inverse(a))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,least_upper_bound(identity,inverse(a))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(identity,least_upper_bound(a,inverse(a)))) )],[refute_0_855,refute_0_856]) ).

cnf(refute_0_858,plain,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,least_upper_bound(identity,inverse(a))),
    inference(resolve,[$cnf( $equal(least_upper_bound(identity,least_upper_bound(a,inverse(a))),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) )],[refute_0_416,refute_0_857]) ).

cnf(refute_0_859,plain,
    ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,least_upper_bound(identity,inverse(a)))
    | least_upper_bound(a,least_upper_bound(identity,inverse(a))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(subst,[],[refute_0_117:[bind(X0,$fot(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))))),bind(Y0,$fot(least_upper_bound(a,least_upper_bound(identity,inverse(a))))),bind(Z0,$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))))]]) ).

cnf(refute_0_860,plain,
    ( least_upper_bound(a,least_upper_bound(identity,inverse(a))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,least_upper_bound(identity,inverse(a)))) )],[refute_0_858,refute_0_859]) ).

cnf(refute_0_861,plain,
    multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(least_upper_bound(a,least_upper_bound(identity,inverse(a))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_19,refute_0_860]) ).

cnf(refute_0_862,plain,
    ( multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) ),[0],$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_863,plain,
    ( least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))
    | multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) ),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_861,refute_0_862]) ).

cnf(refute_0_864,plain,
    least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) != least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    inference(resolve,[$cnf( $equal(multiply(least_upper_bound(a,identity),inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_863,refute_0_694]) ).

cnf(refute_0_865,plain,
    least_upper_bound(a,inverse(greatest_lower_bound(a,identity))) = least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),
    introduced(tautology,[refl,[$fot(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))))]]) ).

cnf(refute_0_866,plain,
    $false,
    inference(resolve,[$cnf( $equal(least_upper_bound(a,inverse(greatest_lower_bound(a,identity))),least_upper_bound(a,inverse(greatest_lower_bound(a,identity)))) )],[refute_0_865,refute_0_864]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GRP184-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 13 10:46:18 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.36/2.59  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.36/2.59  
% 2.36/2.59  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.50/2.68  
%------------------------------------------------------------------------------